University of Szeged

Biopharmacy practice

Editor:

Árpád Márki, Ph.D.

Authors:

Árpád Márki, Ph.D.

Adrienn Seres, Ph.D.

Anita Sztojkov-Ivanov, Ph.D.

Reviewed by:

Szilárd Pál, Ph.D.

Szeged, 2015.

This work is supported by the European Union, co-financed by the European Social Fund, within the framework of "Coordinated, practice-oriented, student-friendly modernization of

biomedical education in three Hungarian universities (Pécs, Debrecen, Szeged), with focus on the strengthening of international competitiveness" TÁMOP-4.1.1.C-13/1/KONV-2014-0001

project.

The curriculum cannot be sold in any form!

Contents

Contents ...................................................................................................................................... 2

1. Definitions, routes of drug administration ............................................................................. 6

1.1. Definitions ....................................................................................................................... 6

1.2. Routes of drug administration ......................................................................................... 7

1.3. Questions ....................................................................................................................... 10

2. Receptors .............................................................................................................................. 11

2.1. Definitions ..................................................................................................................... 11

2.2. Characterization of receptors......................................................................................... 11

2.3. Classification of receptors ............................................................................................. 12

2.4. Questions ....................................................................................................................... 13

3. Dose vs. response curves ...................................................................................................... 14

3.1. Definitions ..................................................................................................................... 14

3.2. Standard dose vs. response curve .................................................................................. 15

3.2.1. Exercise 1 ............................................................................................................... 16

3.3. Semilogarithmic dose vs. response curve ..................................................................... 17

3.3.1. Exercise 2 ............................................................................................................... 18

3.4. Double reciprocal dose vs. response curve ................................................................... 18

3.4.1. Exercise 3 ............................................................................................................... 20

3.5. Specific activity ............................................................................................................. 21

3.6. Questions ....................................................................................................................... 22

4. Drug absorption .................................................................................................................... 23

4.1. Definitions ..................................................................................................................... 23

4.2. Factors affecting drug absorption .................................................................................. 23

4.3. Transport mechanisms during absorption ..................................................................... 23

4.4. Drug absorption from different sites ............................................................................. 24

4.4.1. Drug absorption from the oral cavity ..................................................................... 24

4.4.2. Drug absorption from the stomach ......................................................................... 24

4.4.3. Drug absorption from the intestines ....................................................................... 24

4.4.4. Pulmonary absorption ............................................................................................ 25

4.4.5. Transdermal absorption .......................................................................................... 25

4.4.6. Intramuscular and subcutaneous absorption .......................................................... 25

4.5. Questions ....................................................................................................................... 26

5. Distribution of drugs ............................................................................................................ 27

5.1. Volume of distribution .................................................................................................. 27

5.2. Factors influencing distribution .................................................................................... 27

5.2.1 The physicochemical properties of the drugs .......................................................... 27

5.2.2. The permeability of the membranes ....................................................................... 28

5.2.3. The effects of pH .................................................................................................... 29

5.2.4. The binding of the drugs to the tissues ................................................................... 29

5.2.5. The binding of the drugs to the plasma proteins .................................................... 30

5.3. Specialized distribution of drugs ................................................................................... 32

5.3.1. Distribution of drugs into the central nervous system (CNS) ................................ 32

5.3.2. The placental barrier ............................................................................................... 32

5.4. Exercises ........................................................................................................................ 33

5.5. Questions ....................................................................................................................... 37

6. Drug metabolism .................................................................................................................. 38

6.1. Definitions ..................................................................................................................... 38

6.2. Phases of drug metabolism ............................................................................................ 38

6.2.1. Phase 1 reactions .................................................................................................... 38

6.2.2. Phase 2 reactions .................................................................................................... 40

6.2.3. Phase 3 reactions .................................................................................................... 41

6.3. Exercise ......................................................................................................................... 41

6.4. Questions ....................................................................................................................... 43

7. Drug elimination .................................................................................................................. 44

7.1. Excretion of drugs ......................................................................................................... 44

7.1.1. Renal excretion ....................................................................................................... 44

7.1.2. Biliary excretion of drugs ....................................................................................... 46

7.1.3. Excretion in the saliva ............................................................................................ 46

7.1.4. Excretion in the breast milk ................................................................................... 47

7.1.5. Pulmonary excretion of drugs ................................................................................ 47

7.1.6. Excretion in the sweat ............................................................................................ 47

7.2. Multiple dosing - Exercise ............................................................................................ 47

7.2.1. Determination of the kinetic parameters of a drug ................................................. 48

7.2.2. Calculation of the maintenance dose of a drug ...................................................... 48

7.2.3. Administration of the loading dose ........................................................................ 48

7.3. Questions ....................................................................................................................... 49

8. Continuous infusion and multiple drug administration ........................................................ 50

8.1. Infusion .......................................................................................................................... 50

8.2. Multiple dosing ............................................................................................................. 53

8.3. Planning a continuous intravenous infusion .................................................................. 55

8.3.1. Calculation of the kinetic parameters of drug X .................................................... 55

8.3.2. Calculation of the dose for continuous infusion ..................................................... 55

8.3.3. Calculation of loading dose for continuous infusion ............................................. 56

8.4. Questions ....................................................................................................................... 56

9. Pharmacokinetic compartment models ................................................................................ 58

9.1. One-compartment models ............................................................................................. 58

9.1.1. One-compartment intravascular model .................................................................. 58

9.1.2. One-compartment extravascular model ................................................................. 60

9.2. Two-compartment models ............................................................................................. 63

9.2.1. Two-compartment intravascular model.................................................................. 63

9.2.2. Two-compartment extravascular model ................................................................. 65

9.3. Two-compartment iv administration - Exercise ............................................................ 68

9.4. Questions ....................................................................................................................... 71

10. AUC, physiological and bioavailability, equivalences ....................................................... 72

10.1. Determination of AUC value ....................................................................................... 72

10.1.1. Exercise 1 ............................................................................................................. 73

10.1.2. Exercise 2 ............................................................................................................. 76

10.2. Calculation of physiological availability and bioavailability ...................................... 77

10.2.1. Physiological availability ..................................................................................... 77

10.2.2. Bioavailability ...................................................................................................... 77

10.2.3. Exercise 3 ............................................................................................................. 78

10.3. Equivalences ................................................................................................................ 79

10.4. Questions ..................................................................................................................... 80

11. Drug – drug interactions ..................................................................................................... 81

11.1. Competitive antagonism .............................................................................................. 81

11.1.1. Exercise 1 ............................................................................................................. 85

11.2. Non-competitive antagonism ...................................................................................... 86

11.2.1. Exercise 2 ............................................................................................................. 88

11.3. Questions ..................................................................................................................... 89

12. Factors affecting drug actions ............................................................................................ 90

12.1. Body weight and height ............................................................................................... 90

12.2. Obesity ........................................................................................................................ 90

12.3. Age .............................................................................................................................. 91

12.4. Gender ......................................................................................................................... 92

12.5. Pregnancy .................................................................................................................... 93

12.6. Illnesses ....................................................................................................................... 93

12.7. Genetic factors ............................................................................................................. 94

12.8. Other factors ................................................................................................................ 94

12.9. Exercises - Dosage schedule in renal failure ............................................................... 94

12.9.1. Determination of pharmacokinetic parameters .................................................... 94

12.9.2. Determination of the maintenance dose ............................................................... 96

12.9.3. Blood plasma curve for different renal functions ................................................. 97

12.10. Dosage schedule in hepatic dysfunction ................................................................. 100

12.10.1. Determination of pharmacokinetic parameters ................................................ 100

12.10.2. Calculation of the maintenance dose ................................................................ 102

12.10.3. Determination of the maintenance dose for a patient with a hepatic dysfunction ........................................................................................................ 103

12.11. Dosage schedule in children and the elderly ........................................................... 106

12.11.1. Determination of pharmacokinetic parameters ................................................ 106

12.11.2. Calculation of the maintenance dose ................................................................ 108

12.11.3. Application of the loading dose ....................................................................... 110

12.11.4. A repeated dosing regimen for the elderly ....................................................... 112

12.11.5. A repeated dosing regimen for children ........................................................... 114

12.12. Questions ................................................................................................................. 116

13. Nonlinear pharmacokinetics ............................................................................................. 117

13.1. Michaelis–Menten kinetics ....................................................................................... 118

13.2. Computer simulation ................................................................................................. 122

13.2.1. Calculation of pharmacokinetic parameters ....................................................... 122

13.2.2. Planning of the dosage for a multiple regimen on the assumption of first order kinetics ..................................................................................................... 123

13.2.3. Calculation of a repeated dose by Michaelis–Menten kinetics .......................... 123

13.2.4. Administration of the loading dose .................................................................... 124

14. A brief review of Phoenix WinNonlin software – The basic user manual....................... 125

14.1. Start a new project ..................................................................................................... 125

14.2. Create data tables ...................................................................................................... 126

14.3. Complete the data tables – adding the columns ........................................................ 127

14.4. Complete the data tables – adding the missing data .................................................. 128

14.5. Choose and set up your PK model ............................................................................ 129

14.6. Run the analysis ........................................................................................................ 131

1. Definitions, routes of drug administration

1.1. Definitions

Pharmacology: Pharmacology is the study of medicines and drugs, including their actions, their uses and their effects on the body (general or particular).

Pharmacodynamics: Pharmacodynamics describes what the drug does to the body (the effects of the drug on the body), e.g. a reduction of fever.

Pharmacokinetics: Pharmacokinetics refers to what the body does to a drug (the effects of the body on the drug), e.g. the drug metabolism.

Pharmacon (active substance): A pharmacon is a substance, which influences the living system in a well‒defined dose; for example, a decrease/increase in blood pressure, a decrease in gut motility or a reduction of fever, e.g. with nifedipine or atropine, paracetamol.

Medicine: Medicine is a substance used in a certain dose for the diagnosis, prevention and healing of illnesses and/or for the maintanance/restitution of the physiological condition of the living organism. Medicines are produced by adequate technology with the addition of excipients. Examples are Cordaflex retard tablets, Atropinum sulfuricum injection or Rubophen tablets.

Poison: Poisons are substances which in very low doses are able to cause a deterioration of health or death, e.g. tetrodotoxin (the toxin of pufferfish), amanitin (the poison in Amanita

phalloides mushrooms) or arsenic.

Site of action: This is the part of the living organism where the receptor of the pharmacon can be found. The site of action may be an organ, a tissue, a group of cells, a cell or a subcellular particle. Examples include the myocardium where cardiac glycosides act, the kidney where diuretics act, and the DNA where platinum derivatives act.

Mechanism of action: This is the specific biochemical reaction through which an active substance exerts its pharmacological effect, e.g. nifedipine acting as a calcium channel blocking antihypertensive agent, or penicillin acting as an antibiotic agent inhibiting cell wall biosynthesis in bacteria.

Drug effects: The main effect, a side‒effect or a toxic effect of a drug.

Main effect: This is the desired effect of a drug, for which it is used, e.g. the analgesia induced by morphine, or the anticycloplegic action + the inhibition of secretion + the antidote effect against organophosphate poisoning when atropine is administered.

Side‒effect: All the other effects of a drug besides the main effect when it is administered in a therapeutic dose are side‒effects. Examples are the breathing problems caused by morphine, or the urinary retention caused by atropine.

Toxic effect: This is a harmful effect of an overdosed drug, e.g. vomiting or blurred vision caused by cardiac glycosides or irregular heartbeat and cramping caused by theophylline.

Systemic effect: This is an effect produced when the drug is released from the medicine, enters the blood/lymphatic stream and is distributed within the body, e.g. the analgesic effect, breathing problems or constricted pupils caused by morphine.

Local effect: This is the effect observed at the site where the medicine is administered, which is also the site where the pharmacological response is desired (without entering the blood circulation). Examples include the local anaesthetic action of lidocain cream, or the antibiotic action of Tobrex (tobramycin) eyedrops.

1.2. Routes of drug administration

Depending on the site of application, therapeutic agents can be administered enterally

(through the gastrointestinal tract) or parenterally (all the other routes bypassing the gastrointestinal tract). The route of drug administration can also be classified on the basis of the pharmacokinetic attributes of the drug. In this case, the presence or the lack of absorption is examined. The route of administration may be intravascular (there is no absorption) or extravascular (there is absorption and the drug moves from the site of administration into the blood circulation). The routes of drug administration are compared in Table 1.1 and Table 1.2.

Table 1.1. Routes of drug administration.

A. Extravascular administration

A.1. Enteral administration

Route of

administration

Advantages Disdvantages Most popular

pharmaceutical

dosage forms

Limitations,

examples

sublingual

• no first‒pass effect → fast • painless

• limited to drugs

• tablet • spray

• nifedipine • nitroglycerine

buccal

• mainly a local effect • painless

• limited to drugs

• tablet • solution

• antiseptics • nicotine (systemic effect)

perlingual • a local effect • painless

• undesired systemic effect (due to swallowing)

• tablet • solution • spray

• antiseptics • antibiotics

oral • most popular • convenient • safe • painless • economical

• affected by many factors • poor patient compliance (children) • first‒pass effect • acidic pH in stomach

• tablet • capsule • powder • solution, emulsion, suspension

• oesophagus • stomach • duodenum • jejunum • ileum • colon

rectal • lower third: no first‒pass effect • bypasses the acidic pH in the stomach • vomiting patient • comatose patient

• poor patient compliance (unpleasant) • mucosal irritation

• suppository • enema

• dimenhydrinate • glycerol • aminophenazone

A.2. Parenteral administration

A.2.1. Administration through the skin

percutaneous • local or systemic effect • painless

• allergy

• cream • transdermal patch

• lidocaine • nicotine • fentanyl

intracutaneous

(intradermal)

• diagnostics (allergy test)

• allergy

• suspension • 50-100 µl

subcutaneous • injection/implant • absorption affected by many factors

• painful • unsuitable for large volumes

• solution, emulsion, suspension

• up to 1-2 ml • insulin • heparin

intramuscular • absorption affected by many factors • suitable for oily substances

• painful • administration requires skill

• solution, emulsion, suspension

• 1-10 ml • ketamine • metamizole

A.2.2. Administration through the mucosa

nasal • local or systemic effect • painless

• poor patient compliance

• spray, drops • powder

• decongestant • calcitonin

pulmonary • local or systemic effect • fast effect • painless

• poor patient compliance

• spray, drops • powder

• 2-5 µl • terbutaline • isoflurane

conjunctival • local effect • painless

• poor patient compliance

• drops • cream

• atropine • antibiotics

vaginal • local effect • painless

• poor patient compliance

• suppository • tablet

• antibiotics • lactobacillus

B. Intravascular administration

intravenous • fast effect • gastrointestinal disease • unconscious patient • large volume • for irritating substances

• painful • administration requires skill • irreversible

• solution • bolus: 1-10 ml • infusion: ~500 ml • CaCl2

intra‒arterial • drugs for diagnostic imaging analysis

• painful • administration requires skill • irreversible

• solution • contrast agent • chemotherapeutic agents

Table 1.2. Special administrations.

C. Other special administrations

Examples

intracardial • epinephrine

intrathecal • local anaesthetics

peridural • local anaesthetics

• opioid analgesics

intracisternal • antibiotics

intraperitoneal • mainly in animal experiments

intra‒articular • steroid anti‒inflammatory agents

• hyaluronic acid

intraosseal • when intravenous access is not

available (life-threatening conditions)

intraocular • antibiotics

intracavernous • alprostadil

intrauterine • hormonal contraceptives

1.3. Questions

1. What is the definition of pharmacodynamics?

2. Give two examples each of an active substance and a medicine.

3. What is the definition of a poison?

4. What types of effects may a drug have?

5. What is the definition of a local effect? Give an example of local effect.

6. How can drugs be classified on the basis of the site of action?

7. Which of the following routes of administraion are possible when there is no first pass‒effect? (multiple choice)

A. sublingual; B. oral; C. rectal (lower third); D. rectal (upper third); E. intravenous

8. List the advantages, disadvantages and pharmaceutical dosage forms of the pulmonary route of administration, and give some examples.

9. What volume can be used for an intramuscular injection?

10. Give two examples of drugs that can be administered peridurally.

2. Receptors

2.1. Definitions

Receptor: Receptors are macromolecules (usually proteins) which take part in the chemical communication between cells. Receptors are able to recognize special chemical structures and to bind a ligand (signalling molecule) with great selectivity. Receptor‒ligand binding causes a change in the conformation of the receptor (e.g. conformational change or dimerization), which leads to activation of the signal transduction mechanisms (signalling cascade) creating the biological response. Examples are the α1 adrenergic receptor, the oestrogenic receptor and the nicotinic acetylcholine receptor.

Ligand: Ligands are small molecules which can be recognized and bound by receptors, creating a biological response in the living organism. Examples include epinephrine, acetylcholine and acetylsalicylic acid.

Agonist ligand: Drugs that bind to receptors and produce biological responses are called agonists, e.g. endogenous mediators (neurotransmitters and hormones) and pharmacologic agonists (such as the effect of terbutaline on the β2 adrenergic receptor).

Antagonist ligand: Drugs that block/reduce the action of an agonist are called antagonists, e.g. pharmacologic antagonists (atropine inhibits the action of acetylcholine on the muscarinic receptor).

Ligand‒receptor binding (key‒lock theory): A receptor structure (the lock) has a region containing a pocket in which its special molecule (the key) can interact. This interaction (covalent, ionic, hydrogen or van der Waals bonding or a hydrophobic interaction) is energetically beneficial for both the receptor and the ligand.

Orthosteric (primary) site: If the drug binds to the same recognition site as the endogenous agonist, this site is called the primary binding site.

Allosteric site: All of the other specific binding sites to which the ligands can bind (separately from the agonist binding site) without producing a biological response are allosteric sites. If the drug binds together with the non-allosteric ligand, it is able to increase/decrease the effect of the non-allosteric ligand.

Silent site: This is a site which binds the drug, but does not activate the generation of a signal, e.g. plasma proteins or fat tissue.

2.2. Characterization of receptors

Specificity: Specificity is the ability of the receptor to distinguish between closely-related signals.

Affinity: The receptor affinity reflects the power of the ligand to bind to the receptor. An effective receptor is able to detect very low concentrations.

Saturability: Cells have only finite number of receptors, which means that the effect (biological response) of the drug has a limit.

Reversibility: If reversibility exists decrease of the ligand concentration can cause dissociation of the ligand‒receptor complex (reversible binding). Otherwise, the binding is irreversible.

Coupling: Coupling means that the receptor is able to transfer signals (e.g. through second messenger mechanisms) from the ligand to the effector molecules of the cells.

2.3. Classification of receptors

Depending on the localization, receptors can be intracellular (e.g. the ryanodine receptor in the cytosol, or the androgen receptor in the nucleus) or located in the cytoplasmic

membrane.

From the aspects of their common signal transduction and/or localization, receptors can be classified in main families. At present, four main receptor families are known:

1. Ligand-gated ion channels (ionotropic) 2. G protein-coupled receptors 3. Enzyme-linked receptors 4. Intracellular receptors

Table 2.1. The most important attributes of the main receptor families.

Ligand-gated

ion channels

G protein-coupled

receptors

Enzyme-linked

receptors

Intracellular

receptors

Structure 4 TM domains 7 TM domains 1 TM domain different structures

Location cell membrane cell membrane cell membrane cytosol or nucleus

Velocity of

signal

transduction

milliseconds milliseconds, seconds

seconds hours

Type of

coupling

direct G protein + second messegers

direct + MAP kinase

JAK/STAT

nuclear receptor: DNA-mediated

Examples n ACh R

GABAA R

GABAC R

5-HT3 R

glycine R

• Gs: β1, β2 adrenergic R

• Gi: β2 adrenergic R, GABAB R

• Gq: α1 adrenergic R, M1, M3 ACh R

• serine/threonine

kinase: TGF-α R, activin

• tyrosine kinase: insulin R, EGFR

• guanylate cyclase:

ANP R

• tyrosine

phosphatase: CD45R

• tyrosine kinase-

associated receptors: cytokine R

• nuclear receptors: androgenic R oestrogenic R thyroid hormone R VDR RXR PPAR • cytoplasmic R: ryanodine R IP3 R

R: receptor; TM: transmembrane

On the basis of the endogenous ligands, there are multiple receptor families within the main receptor families, e.g. adrenergic receptors and opioid receptors.

Receptors within a family occur in several types and subtypes, with significant differences in signal transduction mechanism, ligand binding, structure or location, e.g. the α1 adrenergic receptor and the M3 muscarinic acetylcholine receptor.

It is possible that two receptors from the same receptor family belong to different main receptor families, e.g. the muscarinic acetylcholine receptor is a G protein-coupled receptor, but the nicotinic acetylcholine receptor is a ligand-gated ion channel.

2.4. Questions

1. What is the definition of a receptor?

2. What are the definitions of an agonist and an antagonist ligand?

3. How can receptors be characterized?

4. How can receptors be classified in the main receptor families?

5. What are the main receptor families?

6. Describe the ligand-gated ion channel (ionotropic) receptors from the aspects of structure, location, velocity of signal transduction and type of coupling.

7. Give two examples of G protein-coupled Gi receptors.

8. Give two examples of nuclear receptors.

9. What is the basis of classifying receptors in families?

10. What is the basis of classifying receptors in types or subtypes?

3. Dose vs. response curves

When a living organism or a tissue is treated with increasing dose of agonist, a pharmacological response is produced. A plot of the responses against increasing doses or concentrations of the drug gives the standard dose vs. response curve (the logarithm to the base 10 of the dose or concentration gives semi-logarithmic dose – response curve).

The features of these dose vs. response curves are discussed in this chapter. 3.1. Definitions

An agonist is a ligand that binds to a receptor and alters the receptor state, resulting in a biological response. Conventional agonists increase the receptor activity, whereas inverse agonists reduce it.

Full agonist: When the receptor stimulus induced by an agonist reaches the maximum response possible in the system (tissue), it will produce the maximum response of the system and be a full agonist in that system.

Inverse agonist: This is a ligand that, by binding to receptors, reduces their fraction in an active conformation, thereby producing the opposite effect.

Partial agonist: This is an agonist that, in a given tissue, under specified conditions, cannot elicit such a large effect (even when applied at high concentration, so that all of the receptors should be occupied) as another agonist can acts through the same receptors in the same tissue.

An antagonist is a drug that reduces the action of another drug, generally an agonist. Many antagonists act at the same receptor macromolecule as the agonist.

Potency: This is the expression of the activity of a drug, in terms of the concentration or amount needed to produce a defined effect.

Efficacy is a concept and numerical term introduced by Stephenson (1956) to express the degree to which different agonists produce varying responses, even when they occupy the same proportion of the receptors.

The dose vs. response curve depicts the relationship between the dose of an administered agonist and its pharmacological effect. There are three different types: a classical dose vs. response curve, a semilogarithmic dose vs. response curve and a double reciprocal dose vs. response curve.

Ligand is a compound, which binds to a specific receptor. An agonist ligand activates the receptor, while an antagonist inhibits the effects of the agonist ligand. Examples of agonist: norepinephrine, oxytocin, testosterone, morphine, etc. Examples of antagonist: prazosin, atosiban, flutamide, naloxone, etc.

A receptor is a cellular macromolecule, or an assembly of macromolecules, that participates directly and specifically in chemical signalling between and within cells. The combination of a hormone, neurotransmitter, drug, or intracellular messenger with its receptor(s) initiates a change in the cell function. Examples include the oxytocin receptor (superfamily: GPCR), the glucocorticoid receptor (superfamily: intracellular receptors), the nicotinic acetylcholine receptor (superfamily: ionotrop receptor), the insulin receptor (superfamily: enzyme-linked receptor).

The effective dose (ED50) is either the dose of a drug that produces, on average, a specified all-or-none response in 50% of a test population or, if the response is graded, the dose that produces 50% of the maximum response to that drug.

The effective concentration (EC50) is the molar concentration of an agonist that produces 50% of the maximum possible effect of that agonist. Other percentage values (EC20, EC40, etc.) can be specified. The action of an agonist may be stimulatory or inhibitory.

pD2 is the negative logarithm of EC50 or ED50.

3.2. Standard dose vs. response curve

When an agonist binds to its own receptor, a specific effect results. The intensity of this effect depends on the dose or concentration of the agonist. The relationship between the dose (or concentration) of a drug and the elicited response is described by a hyperbolic curve (Fig. 3.1).

1.0××××10-8 1.0××××10-6 2.0××××10-6 3.0××××10-6 4.0××××10-60

20

40

60

80

100

120

140

160

E max

E50

ED50

Eff

ect

Dose, mg

Figure 3.1. Schematic representation of the standard dose vs. response curve of an agonist. An increasing amount of the drug causes an increasing response until the maximum effect is reached. The response then remains constant regardless of further increase of the dose. Emax is the maximum effect; E50 is half the maximum effect; and ED50 is the effective dose of the administered drug.

Characteristics of the dose vs. response curve:

� it is a saturation curve, because the number of receptors in the investigated system is finite;

� it has a plateau (further increase of the dose does not increase the observed effect), called the maximum effect (Emax); and

� the effective dose (ED50) or effective concentration (EC50) is defined as the dose or concentration of agonist that provokes half the maximum effect.

3.2.1. Exercise 1

Determine the EC50 and Emax values of a drug by using Pharsight Phoenix software. The required data are shown in the table below. Reproduce this table in the Data group of the software and then choose the PD model as a new workflow to build the model from the WNL5 Classic Modeling option. Choose model number 101 to complete the simulation.

c, mg/l

0.02 0.04 0.1 0.2 0.3 0.5 0.75 1 1.5 2 3

Effect 2 8 16 29 40 52 665 75 81 87 92

Find the values of the following parameters in the Results tab! Do not forget to check the units of the parameters.

Emax =

EC50 =

Answer the following questions.

What is the definition of efficacy? ............................................................................................

....................................................................................................................................................

....................................................................................................................................................

....................................................................................................................................................

What is the definition of potency? ............................................................................................

....................................................................................................................................................

....................................................................................................................................................

....................................................................................................................................................

....................................................................................................................................................

3.3. Semilogarithmic dose vs. response curve

In a semilogarithmic plot (the effect as a function of the logarithm of the dose or the concentration), the shape of the curve is sigmoid (Fig. 3.2).

-8 -7 -6 -50

20

40

60

80

100

120

140

160

Emax

E50

log ED50 log (dose)

Eff

ect

Figure 3.2. Schematic representation of the semilogarithmic dose vs. response curve of an agonist. Emax is the maximum effect; E50 is half the maximum effect; log ED50 is the logarithm to the base 10 of the effective dose.

Advantages of semilogarithmic dose vs.response curves:

• the middle range (between ~20% and ~80%) is almost a straight line,

• the inflection point in the curve, which determines log ED50 and half the maximum effect (E50), can easily be calculated by a computer.

Sometimes, instead of ED50 its negative logarithm is used, i. e. pD2:

pD2 = -logED50

In the Phoenix software, change the scale of X-axis of the previously plotted dose – response curve from linear to logarithmic. What has changed? Check also the calculated parameters.

....................................................................................................................................................

....................................................................................................................................................

....................................................................................................................................................

3.3.1. Exercise 2

Draw the semilogarithmic dose vs. response curve of drugs A and B if you know that drug A is more potent than drug B, and the two drugs have the same efficacy. Indicate the log ED50 values of both drugs in the graph.

-8 -7 -6 -50

20

40

60

80

100

120

140

160

log D

Eff

ect

Which parameter is appropriate for comparing the affinities of the drugs to the same receptor?

Why? .........................................................................................................................................

....................................................................................................................................................

....................................................................................................................................................

3.4. Double reciprocal dose vs. response curve

The third type of dose vs. response curves is the double reciprocal or Lineweaver – Burk plot (Fig. 3.3). In this representation, the reciprocal of the observed effect is plotted as a function of the reciprocal of the dose or concentration of the administered drug. The shape of this plot is a straight line. The determination of Emax and ED50 is quite simple, but for several compounds the comparison of the curves requires experience. The reciprocal of the maximum effect is the intercept of the straight line on the y-axis (1/Emax), while the reciprocal of half the maximum effect (1/E50) is equal with 2/Emax and the reciprocal dose or concentration causing this effect is therefore 1/ED50. The intercept on the x-axis is equal to -1/ED50 (not depicted in Fig. 3.3.).

0 5.0××××106 1.0××××107 1.5××××107 2.0××××107 2.5××××1070.00

0.01

0.02

0.03

0.04

0.05

0.06

1/E50

1/Emax

1/ED501/c

1/E

Figure 3.3. Schematic representation of the double reciprocal dose vs. response curve of an agonist. 1/Emax is the reciprocal of the maximum effect; 1/E50 is half the maximum effect; 1/ED50 is the reciprocal of the effective dose of the investigated drug.

Answer the following questions.

1. Drug A has a higher maximum effect than that of drug B, while they have the same ED50 values. Where do the two lines (the double reciprocal representation of the dose vs. response curves) intersect?

........................................................................................................................................

2. Are these straight lines parallel?

........................................................................................................................................

3. Drug A and drug B have equal maximum effects, while drug B has a lower ED50 value. Where do the two lines (the double reciprocal representation of dose vs. response curves) intersect?

........................................................................................................................................

4. Does the straight line of drug A lie under the curve of drug B?

........................................................................................................................................

3.4.1. Exercise 3

We can compare drugs in terms of their potencies and efficacies or by dose vs. response curves.

Study the data in Table 3.1 and Fig. 3.4 and then answer the questions below.

1. Is drug A or drug B more potent? ............................

2. Does drug A or drug B have higher efficacy? ............................

3. Is drug F or drug G more potent? ............................

4. Does drug F or G have higher efficacy? ............................

Table 3.1.

ED50, mg Emax

A 3×10-7 99

B 3×10-8 74

-9 -8 -7 -6 -50

20

40

60

80

100

120

140

160F

G

log c

Eff

ect

Figure 3.4. Semilogarithmic dose vs.response curves of drugs F and G.

3.5. Specific activity

As long as an agonist binds to the active receptor and demonstrates less efficacy than that of the endogenous agonist (full agonist), this agonist is called a partial agonist. Agonist compounds may be compared through their specific activities, α calculated via the following equation:

� =����

������

where Emax is the maximum effect of the investigated drug, and ������ is the maximum effect

of the full agonist.

The value of α is generally between 0 and 1 (inverse agonists are not mentioned here). On the basis of the α values, the following classes of drugs are distinguished:

- α = 1: full agonists

- 0 < α < 1: partial agonists

- α = 0: antagonists, or the compounds do not bind to the investigated receptor protein.

Calculate the specific activity of drug B, assuming that drug A is a full agonist.

αB = .................

3.6. Questions

1. What is the shape of a standard dose vs. response curve?

2. How can the EC50 value be determined graphically?

3. What is the definition of ED50?

4. Explain the characteristics of semilogarithmic dose vs.response curves.

5. What parameters are defined by the inflection point of a semilogarithmic dose vs. response curve?

6. Study the figure below, and specify which drug is the more potent (A or B).

0 5.0××××106 1.0××××107 1.5××××107 2.0××××107 2.5××××1070.00

0.02

0.04

0.06A

B

1/D

1/E

7. The pD2 value of drug C is 8.3. Calculate the ED50 value.

8. The pD2 value of drug A is 7.5, while that of drug B is 8.2. Which drug is more potent?

9. How can you calculate specific activity?

10. Give the α value of a full agonist.

4. Drug absorption

4.1. Definitions

Absorption: Most drugs have no effect at the site of their administration (local effect), but they move to their site of action via the blood circulation to develop systemic action. The movement of drugs from the site of administration to the bloodstream is called absorption. Absorption is not the same as distribution. Distribution is the movement of the drug from the bloodstream to the site of action, the tissues.

First‒pass effect (FPE): Absorbed drugs first reach the liver via the portal vein. The liver may metabolize the major fraction of a drug before it can reach the site of action.

Enterohepatic circulation: Some metabolized (conjugated) products are excreted into the duodenum via the bile. They become lipophilic again (e.g. via hydrolysis) in the intestine and then can be reabsorbed. Examples are benzodiazepines and sex hormones.

4.2. Factors affecting drug absorption

During absorption (and distribution), drugs must cross biological membranes.

1. The passage of drugs is determined by their lipid solubility because of the lipoid structure of the membranes. This can be characterized by the partition coefficient. The partition coefficient is the ratio of the distribution of a drug between the two phases. The transmembrane movement of lipophilic drugs is unlimited.

2. The partition coefficient of drugs, and hence their absorption, can be affected by the rate

of ionization. Non-ionized, lipid-soluble molecules can diffuse readily through biological membranes.

3. The pH of the surrounding tissues influences the rate of ionization of drug molecules and their passage through membranes.

4. The absorption of a drug can be influenced by its chemical structure (e.g. salt form) or the size of the particles.

5. Some physiological parameters (e.g. perfusion) can also affect drug absorption.

4.3. Transport mechanisms during absorption

1. passive diffusion

2. active transport

3. facilitated diffusion

4. filtration

5. ion-pair transport

6. bulk flow: the transport of drug molecules via the blood stream

7. endocytosis

8. exocytosis

4.4. Drug absorption from different sites

4.4.1. Drug absorption from the oral cavity

Despite its small surface area, the oral cavity and especially the sublingual area is suitable for drug absorption because of its profuse blood flow and thin epithelial layer. The pH of the oral cavity is approximately neutral (pH = 6), and accordingly the absorption of weak bases (mainly in non-ionic form) is efficient. Absorption directly from the oral cavity is prompt, and the drug reaches the blood circulation rapidly bypassing the portal circulation (no first‒pass effect). Examples include the sublingual administration of nicotine, nitroglycerine or nifedipine.

4.4.2. Drug absorption from the stomach

The large surface area and the profuse blood flow of the stomach are favourable conditions for drug absorption. The gastric juice is acidic (pH = 1‒2), and bases are therefore ionized and cannot absorb from the stomach. In contrast with weak bases, weak acids can absorb, because they are non-ionized. The absorption from the stomach can be influenced by other factors, such as gastric emptying (how long the drug is in the stomach). The motility of the stomach can be increased during starvation or by the action of cholinergic drugs, but it can be decreased by repletion, a recumbent position or the administration of anticholinergic agents.

4.4.3. Drug absorption from the intestines

The surface area of the small intestines (the duodenum, jejunum and ileum) is large, and is further increased by the intestinal villi. The blood flow of the intestines is excellent, and their pH (pH = 5‒7) is favourable for the absorption of weak bases. Nearly all of the transport mechanisms are involved in the drug absorption from the intestines, but most of them occur by passive diffusion. The duodenum is too short for absorption, whereas the jejunum is long enough; this is the main absorption surface of the intestines. The lower part of the intestines (e.g. the ileum) would also be suitable for drug absorption, but the drug absorption is usually finished in the upper part of the jejunum. The large intestine (colon) has a smaller absorption surface than that of the small intestines. Since drugs do not usually reach the colon (because they are absorbed earlier, from the small intestines), the large intestines are of importance in absorption only if the absorption was incomplete in the small intestines (e.g. diarrhoea). The bacterial flora of the large intestines (e.g. bacteria with glucuronidase activity) plays an essential role in the enterohepatic circulation.

Although the surface of the rectum is very small, the absorption from this area is very important. From the upper third of the rectum, the absorbed drugs reach the liver via the portal circulation, and are metabolized by liver enzymes (first‒pass effect). The drugs absorbed from the lower third bypass the liver and rapidly reach the circulation. The absorption from the middle third is irregular, and the first‒pass metabolism is unreliable. This route of administration can be very useful in patients who are unable to take medication orally, e.g. in the cases of an unconscious or vomiting patient, young children or gastrointestinal diseases.

The absorption from the intestines can be affected by other factors, such as the intestinal transit time (e.g. diarrhoea or obstipation), the presence of nutrition (e.g. complexing agents) or the dosage form (e.g. liquid or solid forms).

4.4.4. Pulmonary absorption

The large surface area, the thin membranes and the excellent blood flow of the lungs allow them to absorb drug molecules (gaseous drugs, aerosols or inhalation anaesthetics). Particles measuring 2‒5 µm size are required for pulmonary absorption. Passive and facilitated diffusion, endo- and exocytosis play important roles during pulmonary absorption. The partition coefficient between the blood and the air (i.e. the rate of dissolution of the drug in the blood) influences the absorption from the lungs. If an anaesthetic agent dissolves well in the blood (a high blood‒air partition coefficient), the development of equilibrium requires more time and leads to longer sleeping and awakening times.

4.4.5. Transdermal absorption

The large surface and the rich blood circulation of the skin make it suitable for drug absorption, but the cornified layer behaves as a lipid barrier and decreases the rate of drug absorption. Lipid-soluble agents are able to pass through the skin, but water-soluble drugs can also be absorbed from the area of the hair follicles, sweat glands and sebaceous glands. Absorption from the skin can be useful in case of transdermal patches (e.g. a backing layer which blocks evaporation) or liposomes that develop a systemic effect.

4.4.6. Intramuscular and subcutaneous absorption

Both of these routes of administration result in very fast absorption (intramuscular is faster), but there are many other factors that can affect the process of absorption:

• the viscosity and concentration of the pharmacon,

• the volume of the administered drug,

• the use of vasoconstrictors, vasodilatators or hyaluronidase,

• the dosage form (e.g. an oily solution or a suspension), etc.

In the case of intravenous administration, there is no absorption, because the pharmacon is administered directly into the blood circulation.

4.5. Questions

1. What is the definition of absorption?

2. How can the enterohepatic circulation be defined?

3. How can absorption be influenced? Give three examples!

4. List three transport mechanisms, which play a role in drug absorption.

5. Name two pharmacons, which are suitable for sublingual administration because of their appropriate absorption.

6. Give two examples of how the motility of the stomach can be decreased.

7. Which of the following statements are correct? (multiple choices)

A. Considerable absorption takes place from the duodenum. B. Orally administered drugs are mainly absorbed from the jejunum.

C. The only transport mechanism of intestinal absorption is passive diffusion. D. The absorption from the intestines can be influenced by the transit time. E. There is no absorption from the rectum; only a local effect can develop.

8. Describe pulmonary absorption.

9. Give two transport mechanisms which can be involved in pulmonary absorption.

10. Give two examples of how the absorption of subcutaneously administered drugs can be decreased.

5. Distribution of drugs

Distribution is the transfer of a drug from the systemic circulation to the various body tissues and the site of action, i.e. the receptors.

5.1. Volume of distribution

The volume of distribution (Vd) is that part of the body water in which the drug appears and reaches an equilibrium state (i.e. forms a steady-state concentration, css).

The volume of distribution can be real, e.g. the Vd of penicillin is 0.43 l/kg, or it can be apparent, e.g. the Vd of digoxin is 6 l/kg.

The total body water gives approximately 60% of the body weight (in a state of obesity ~55%, and in emaciation ~65%) i.e. there is 0.57 l water per kg body weight, or about 40 l of body water in a 70 kg individual.

An example of the volumes of the body fluids into which a drug may distribute:

Total body water 41 l

Intracellular fluid 29 l

intracellular intravascular fluid 2.5 l (red blood cell volume)

Extracellular fluid 12 l

extracellular intravascular 3 l (plasma fluid)

extracellular extravascular 9 l (interstitial fluid)

Transcellular fluid ~1–2 l (cerebrospinal, ocular, joint, synovial and pleural fluid)

Calculation of volume of distribution: � =�

��

where D is the dose administered [mg], and Cp0 is the hypothetical drug concentration at t = 0

[mg/l]. The units of Vd are [l] or [l/kg].

5.2. Factors influencing distribution

- the physicochemical properties of the drugs, - the effects of pH, - the permeability of the membranes, - the binding of the drug to the tissues, - the binding of the drug to the plasma proteins.

5.2.1 The physicochemical properties of the drugs

Lipophilicity

As a measure of lipophilicity, the logarithm of the partition coefficient (log P) of a compound is defined as the ratio of the concentrations of the non-ionized compound in organic (1-octanol) and in aqueous solvent (water) at equilibrium. The higher the log P value of a drug, the higher its affinity for the lipophilic biological membranes, and the faster the transport of the drug across the membrane by passive diffusion. Compounds with very high log P values (> 6) tend to concentrate in a lipid environment, e.g. adipose or liphophilic membranes. Drugs

with very low log P values are too hydrophilic to cross the biological membranes and reach the site of potential action.

Effects of pH and ionization of drugs

Many drugs and other pharmaceutically important compounds are weak acids or weak bases. A drug passes through membranes more readily if it is in uncharged form. The ratio between the ionized and non-ionized forms is determined by the pH of the environment and by the strength of the weak acid or base, which is represented by the ionization constant, pKa. The pKa is a measure of the ratio of the ionized and non-ionized forms of a drug at a given pH. The lower the pKa of a drug, the more acidic it is. The relationship between the pKa value of a drug and the pH of the environment can be described by the Henderson–Hasselbalch equation. A simplified way of representing the dissociation of any weak acid, denoted as HA for convenience, is as follows:

�� ⇌�� +��

The dissociation constant of the process is

�� =��������

����

The Henderson–Hasselbalch equation for weak acids is

��� = �� + �������

����

The dissociation of weak bases:

��� ⇌ � +��

The dissociation constant in the case of weak bases is

�� =�������

�����

The Henderson–Hasselbalch equation for weak bases is

��� = �� + ��������

���

5.2.2. The permeability of the membranes

Compounds with molecular weights up to about 10,000 to 30,000 can diffuse paracellularly through the 10–30 nm junctions of the capillary endothelium. Drug molecules bound to large plasma proteins (MW > 60,000) will remain in the blood. Evans blue and Geigi blue are dyes that bound to albumin with high affinity and they cannot distribute out of the plasma. They can therefore be used to determine the plasma fluid volume.

Liphophilic, non-ionized solutes can move through the capillaries by paracellular transport or passive transcellular diffusion, while hydrophilic compounds can be transported paracellularly by carrier molecules.

If a free drug can leave the vascular space, it enters treached. Inulin, sucrose, raffinose, Clmembranes, and can therefore be used to determine the interstitial volume.

The free drug may continue to be distributed from the intracellular fluid into the cells of the tissues, i.e. the total body volume. For example, heavy water, azophen, amidazophen and ethanol are distributed in the total body water.

Distribution can occur in both directions between the various body fluids until equilibrium is reached.

The overall distribution of a proteinintracellular fluid is illustrated in Figure 5.1.

Figure 5.1. The distribution of

5.2.3. The effects of pH

The pH of the various body fluids ranges between 1 and approximately 8. Although there is a great variation in pH between the different fluids in the body, there is little variation each system. The lipid solubility and ionization of a drug depend on the pH of the physiological environment. The acidification or alkalization of the body fluids can influence the distribution of drugs.

5.2.4. The binding of the drugs to the tissue

Many drugs with a basic and lipophilic character bind to tissue proteins with high affinity, resulting in a higher than expected amiodarone is 60 l/kg). Examples of the distribution of drugs to spTable 5.1.

ionized solutes can move through the capillaries by paracellular transport or passive transcellular diffusion, while hydrophilic compounds can be transported paracellularly

If a free drug can leave the vascular space, it enters the extracellular fluid until equilibrium is , raffinose, Cl-, Br- and SCN- cannot diffuse through the capillary

membranes, and can therefore be used to determine the interstitial volume.

The free drug may continue to be distributed from the intracellular fluid into the cells of the tissues, i.e. the total body volume. For example, heavy water, azophen, amidazophen and ethanol are distributed in the total body water.

in both directions between the various body fluids until equilibrium is

The overall distribution of a protein-bound drug into the plasma, interstitial fluid and intracellular fluid is illustrated in Figure 5.1.

of a free and protein-bound drug into body fluids.

The pH of the various body fluids ranges between 1 and approximately 8. Although there is a great variation in pH between the different fluids in the body, there is little variation each system. The lipid solubility and ionization of a drug depend on the pH of the physiological environment. The acidification or alkalization of the body fluids can influence

5.2.4. The binding of the drugs to the tissues

Many drugs with a basic and lipophilic character bind to tissue proteins with high affinity, resulting in a higher than expected Vd (e.g. the Vd of amphetamine is ~ 3 l/kg, while that of amiodarone is 60 l/kg). Examples of the distribution of drugs to specific tissues can be seen in

ionized solutes can move through the capillaries by paracellular transport or passive transcellular diffusion, while hydrophilic compounds can be transported paracellularly

he extracellular fluid until equilibrium is cannot diffuse through the capillary

The free drug may continue to be distributed from the intracellular fluid into the cells of the tissues, i.e. the total body volume. For example, heavy water, azophen, amidazophen and

in both directions between the various body fluids until equilibrium is

bound drug into the plasma, interstitial fluid and

bound drug into body fluids.

The pH of the various body fluids ranges between 1 and approximately 8. Although there is a great variation in pH between the different fluids in the body, there is little variation within each system. The lipid solubility and ionization of a drug depend on the pH of the physiological environment. The acidification or alkalization of the body fluids can influence

Many drugs with a basic and lipophilic character bind to tissue proteins with high affinity, of amphetamine is ~ 3 l/kg, while that of

ecific tissues can be seen in

Table 5.1. Examples of specific drug distribution.

Distribution of drugs to specific tissues

Organ, tissue Drug

Liver Cationic amphiphilic drugs (chloroquine, tricyclic antidepressants)

Lysosomal accumulation (acidic pH)

Methotrexate Entrapped in cells as polyglutamate

Lipid-soluble vitamins Entrapped in fat-storing perisinusoidal cells

Lung Cationic amphiphilic drugs: local anaesthetics (tetracaine, bupivacaine), tricyclic antidepressants, propranolol, heroin, amiodarone, amphetamine

Retained by

• binding to negative charges of surfactant

• entrapment in negative interior of mitochondria

• entrapment in acidic interior of lysosomes

Adipose tissue Lipid-soluble drugs: amiodarone, vitamin D2, general anaesthetics, antihistamines

Accumulation, depot formation

Bone Tetracyclines Binding with high affinity to Ca2+

Cd2+, Pb2+, Sr2+ Incorporation in place of Ca2+

Bisphosphonates Incorporation in place of phosphate ions

Fluoride ion Incorporation in place of hydroxide ions

Skin Antimycotic drugs (ketoconazole, terbinafine), As

Binding with high affinity to keratin

5.2.5. The binding of the drugs to the plasma proteins

Many drugs bind reversibly to plasma proteins to form drug–protein complexes. Plasma proteins are relatively non-specific in their binding behaviour. In general, the more lipophilic a drug, the greater its affinity for plasma proteins. Drug binding with high affinity to plasma proteins (> 95%) may cause drug–drug interactions. Table 5.2. lists the extent of protein binding of selected drugs.

The consequences of the plasma protein binding of drugs:

- protein binding influences the distribution of drugs: only the free, unbound fraction is able to cross the capillary endothelium

- as the free drug leaves the capillaries, some of the complex dissociates to release free drug and maintain the equilibrium in the blood

- only the free drug fraction is able to pass through the glomerulus

- drugs with extensive binding can reach the site of action after saturation of the binding sites

- plasma proteins act as a depot and extensive binding may prolong the duration of action

- displacement of one drug from plasma protein binding by another increases the free drug concentration in the plasma, resulting in an increase in the volume of distribution and a therapeutic effect. Toxic effects may occur.

Plasma proteins that bind drugs: albumin

lipoproteins, globulins

glycoproteins (α1-acid glycoprotein)

Albumin is the most important plasma protein involved in drug binding. It has multiple hydrophobic binding sites:

- it binds acidic drugs with high affinity, e.g. salicylic acid, warfarin, penicillins, sulfonamides, barbiturates, tetracyclines and phenylbutazone;

- it binds basic drugs with lower affinity, but higher capacity, e.g. digitoxin, chloramphenicol, propranolol, quinine and steptomycin.

Table 5.2. Extent of plasma protein binding of selected drugs.

Drug Plasma protein binding (%)

Gentamycin 3

Digoxin 25

Lidocaine 51

Phenytoin 89

Propranolol 93

Phenylbutazone, furosemide, tolbutamide 98

Warfarin, diazepam 95-99

Starvation, underfeeding, pregnancy, elderly age and gastrointestinal, liver or kidney diseases are associated with lower serum albumin levels. Neurological disorders, hypothyroidism and high-intensity physical training may increase the amount of albumin in the plasma.

α1-Acidic glycoprotein is the most important glycoprotein. It has one hydrophobic binding site and primarily binds basic drugs with higher affinity than that of albumin.

5.3. Specialized distribution of drugs

5.3.1. Distribution of drugs into the central nervous system (CNS)

The blood–brain barrier

The blood–brain barrier strictly limits the transport of drugs into the brain, due to the tight junctions of the endothelial cells. The structure surrounding the capillaries (pericytes, astrocytes and the basal membrane), the efflux proteins and enzymes further protect the brain from harmful substances.

Paracellular transport through the blood–brain barrier is impossible, even for small solutes. This means that transcellular transport (either by passive diffusion or by a carrier-mediated process) and transcytosis are the only mechanisms for the distribution of solutes into the brain. Even transcellular diffusion is slowed down considerably by the astrocyte sheath. The higher the lipophilicity of a substance, the greater its transcellular passive diffusion into the brain. Even if a drug molecule is lipophilic enough to diffuse transcellularly through the capillary endothelium, carrier-mediated efflux transporters (P-glycoprotein, ATP-binding cassette transporters) oppose uptake into the brain. Polar compounds can be transported into the brain by carrier-mediated active transport. For example, benzodiazepines, barbiturates, intravenous anaesthetics, levodopa, propranolol, caffeine, chloroquine, acyclovir, chloramphenicol, streptomycin, 5-fluorouracil and sulfonamides can be distributed into the brain.

Drug delivery into the brain can be enhanced by osmotic opening of the blood–brain barrier with hyperosmotic (1.4 M) mannitol, by the administration of efflux transporter inhibitors (cyclosporin, verapamil or probenecid) or by the binding of the drug to liphophilic carriers. The breakdown of the blood–brain barrier may be involved in infections or certain brain diseases, such as multiple sclerosis, meningitis, epilepsy and Alzheimer’s disease, and this allows the penetration of drugs into the brain.

The blood–cerebrospinal fluid barrier

The blood–cerebrospinal fluid barrier restricts the passage of substances from the blood into the cerebrospinal fluid by means of tight junctions of choroidal epithelial cells and the basal membranes. This barrier is more permeable than the blood–brain barrier and many low molecular weight plasma proteins can enter the cerebrospinal fluid. Drugs are able to cross the barrier through a paracellular or active transport mechanism. Although lipid-soluble drugs may enter the choroidal epithelial cell membrane, and efflux transporters may rapidly remove them.

5.3.2. The placental barrier

Drug transfer across the placenta depends on the size of the molecule: molecules with molecular weights of less than 500 cross the placenta readily, whereas those with 500–1000 cross with more difficulty, and drugs with molecular weights greater than 1000 cross very poorly. An important clinical application of this property is the administration of heparin to pregnant women. Heparin is a very large and polar molecule, and is unable to cross the placenta. Unlike warfarin, which is teratogenic and should be avoided during pregnancy, heparin may be safely given to pregnant women. The maternal blood has a pH of 7.4 and that of the foetal blood is 7.3. Weakly basic drugs with pKa > 7.4 will be more ionized in the foetal compartment, leading to ion trapping and hence to higher foetal levels. Ionized or larger molecular size drugs can cross the placenta by facilitated diffusion, active transport or

pinocytosis. The placenta also contains a variety of efflux transporters (P-glycoprotein, breast cancer resistance protein and multidrug resistance protein 2), whose role is to remove potentially toxic substances and thus protect the foetus.

Drugs given during pregnancy may affect the foetus directly, by producing a toxic, teratogenic or lethal effect on the foetus. Drugs applied before the 3rd week after fertilization may have an "all-or-nothing" effect, killing the embryo or not affecting it at all. The period of organogenesis between the 3rd and 8th weeks is critical for teratogenesis: xenobiotics reaching the embryo may result in a true teratogenic effect, or a permanent metabolic-functional defect that may manifest later in life (covert embryopathy). Drugs given after the 12th week are unlikely to be teratogenic, but they may alter the growth and function of the well-formed foetal organs and tissues. Table 5.3 gives some examples of drugs that may result in teratogenic effects.

The beneficial effect of therapy must be balanced against the risks to the mother and foetus of increased seizure activity.

Table 5.3. Examples of teratogenic drugs.

Drug Effects

Sex hormones Masculinization or feminization

Tetracyclines Tooth and bone developmental defects

Corticosteroids Growth retardation

Non-steroidal anti-inflammatory drugs (e.g. aspirin or indomethacin)

Onset of labour is delayed and CNS development is impaired

Sedatives and general analgetics Foetal disress and prolongation of labour

Benzodiazepines Hypotonia

Lithium Cardiac defects

ACE inhibitors Renal damage

Warfarin Hypoplastic nasal bridge, CNS malformation and the risk of bleeding

Ethanol Foetal alcohol syndrome and neurodevelopmental defects

Smoking Intrauterine growth retardation, prematurity, sudden infant death syndrome and perinatal complications

5.4. Exercises

360 mg of penicillin was administered to a patient in an intravenous bolus injection. Following the administration, blood samples were taken and the blood concentration of penicillin was determined. Some data are listed in Table 5.4.

Table 5.4. Penicillin concentration after intravenous administration.

Time (h) Concentration (mg/l) ln (concentration)

0.10 12.20

0.25 10.28

0.50 8.00

0.75 5.50

1.00 4.30

1.50 2.75

2.00 1.47

3.00 0.51

The elimination rate constant (ke) is equal to the negative value of the slope of the ln (c) vs. time curve.

Give the equation with which the elimination rate constant can be calculated, and calculate the ke value of penicillin.

Which time points are appropriate for the calculation of ke?

�� =

Calculate the value of the elimination rate constant.

ke = .................... h-1

The elimination half-life time is the ratio of ln 2 and ke. Calculate the elimination half-life time of penicillin.

t1/2 = .................. h

The concentration of a drug in a solution can be calculated via the following formula:

=!

"

where D is the dose of the drug and V is the volume of the solution.

If the drug is distributed in the body, the corresponding formula is

# =!

"$

where %� is the apparent initial concentration (mg/l), Vd is the volume of distribution (l) and D is the intravenous dose of the drug (mg).

Calculate the volume of distribution of penicillin by using the formula above. The %� value of penicillin (D = 360 mg) is 13.65 mg/l.

Vd = ................... l

The total clearance value is the product of the elimination rate constant and the volume of distribution:

&�' = �� ∙ "$

Use this formula to calculate the clearance of penicillin.

ClT = ................. l/h

Run the Phoenix software platform and create a new project (project name: penicillin iv) with two new tables (A: time and concentrations; use the data in Table 5.4; B: dosing information). Create a new workflow (WNL5 Classic modelling – PK Model), and complete the setup. Finally, execute the model, check the calculated parameters and fill inTable 5.5.

Table 5.5.

Calculated from Table 1

Calculated by Phoenix

ke

t1/2

Vd

ClT

c0

Compare the values calculated through the different procedures.

Figure 5.2. Semilogarithmic curve illustrating the blood concentration of intravenous penicillin (360 mg).

Apply the definition of half-life time and fill in the missing data inTable 5.6.

Table 5.6.

Time interval after injection

Amount of penicillin in the body

0 0 360

1 × t1/2

2 × t1/2

3 × t1/2

4 × t1/2

5 × t1/2

5.5. Questions

1. What is the definition of the volume of distribution?

2. How can the volume of distribution be calculated?

3. What parameters control the rate of distribution of a drug?

4. What are the different types of fluid compartments in the body?

5. What physicochemical properties allow a drug to leave the vascular space easily?

6. How does the pH of the physiological environment affect the distribution of drugs?

7. What physicochemical properties are necessary for a drug to be distributed into the brain?

8. What physicochemical properties are necessary for a drug to cross the placenta?

9. Give some examples of teratogenic drugs.

10. Why does the plasma protein binding of a drug influence its distribution?

6. Drug metabolism

6.1. Definitions

Xenobiotic: Xenobiotics are chemicals that are foreign to the body (they are not utilized by the body either as building materials or as energy resources), and the body therefore attempts to eliminate them.

Metabolism: This is the chemical transformation of exogenous compounds so that lipophilic drugs can be eliminated with the decrease of their activity and the increase of their water solubility (the chemical and physicochemical properties of drugs are changed).

Drug‒metabolizing enzymes: These are enzymes which transform lipophilic xenobiotics to hydrophilic products. They are mostly located in the liver, but they can also be found in the lungs, the kidneys, the intestines, the skin or the placenta.

Active metabolite: An active metabolite can result when a drug is metabolized by the body into a modified form which continues to produce effects in the body (the same effect or a more effective one than that of the drug). An example: diazepam → nordazepam and oxazepam.

Prodrug: Prodrugs are substances which are not biologically active themselves, but they are changed to their active forms through biotransformation in the body, e.g. levodopa → dopamine.

CYP 450 enzyme induction: If drugs are co-administered, the activity of the CYP enzyme system can be enhanced. The inactivation of one or the other drug then becomes faster and the duration of action is shortened. Such enzyme inducers include phenobarbital, rifampicin, carbamazepine (self-inducer), phenytoin, chronic alcohol abuse and smoking.

CYP 450 enzyme inhibition: If drugs are co-administered, the activity of the CYP enzyme system can be decreased. The inactivation of drugs then becomes slower and the duration of action is prolonged. Such enzyme inhibitors include cimetidine, erythromycin, ketoconazole, omeprazole and grapefruit juice.

6.2. Phases of drug metabolism

6.2.1. Phase 1 reactions

Phase 1 (i.e. the non-synthetic or functionalization phase) reactions prepare lipophilic drugs to become hydrophilic during further reactions. The chemical structures of pharmacons are changed, they become more polar and they can be eliminated more easily. While microsomal oxidation reactions are carried out in the endoplasmic reticulum, non-microsomal oxidations occur in the cytosol. The types of phase 1 metabolic reactions are shown in Table 6.1.

Table 6.1. Phase I metabolic reactions.

Phase 1 metabolic reactions Examples

Microsomal oxidation (depending on CYP 450)

aromatic oxidation phenobarbital, phenytoin, warfarin

aliphatic oxidation ibuprofen, digitoxin

epoxide formation carbamazepine, aldrin

N-dealkylation morphine, caffeine, theophyllin, diazepam

O-dealkylation codeine, papaverine, diphenhydramine

S-dealkylation 6-methyl thiopurine (prodrug of mercaptopurine)

oxidative desamination amphetamine, histamine, epinephrine, diazepam

S-oxidation cimetidine, chlorpromazine

N-oxidation acetaminophen, nicotine, imipramine

desulfuration heparin, thiopental

Non-microsomal oxidation

action of alcohol dehydrogenase ethanol

action of aldehyde dehydrogenase ethanol

action of flavine monooxygenase chlorpromazine, amitriptyline

action of amine oxidase phenylethylamine, epinephrine

action of aromatase tetrahydrocannabinol, norgestrel

Reduction

aldehyde reduction methadone, naloxone

azo reduction sulfasalazine

nitro reduction cloramphenicol, metronidazole

S-reduction disulfiram

dehalogenation halothane, carbromal, chloramphenicol

Hydrolysis

ester hydrolysis procaine, acetylsalicylic acid, clofibrate, atropine

amide hydrolysis procainamide, lidocaine, indomethacin

azide hydrolysis isonicotinic acid hydrazide

glycoside hydrolysis digoxin, digitoxin

epoxide hydrolysis carbamazepine

Other reactions

isomerization acitretin

decarboxylation alpha-methyldopa, levodopa

ring-opening reaction warfarin

6.2.2. Phase 2 reactions

During phase 2 (i.e. the synthetic or conjugation phase) reactions, the enzymes catalyse the conjugation of the substrate formed in the phase 1 reaction with a second molecule (e.g. glucuronic acid, glycine or sulfate). Phase 2 reactions produce a metabolite with improved water solubility which can be excreted more easily in the urine or the bile. The conjugation reactions are enzyme‒catalysed reactions that require energy. These conjugations usually result in therapeutically inactive metabolites (a notable exception is morphine-6-glucuronide). In general, the conjugation reactions take place in the cytosol.

The types of phase 2 metabolic reactions are presented in Table 6.2.

Table 6.2. Phase 2 metabolic reactions.

Phase 2 metabolic

reactions Enzyme Examples

glucuronidation UDP-glucuronosyltransferases morphine, diazepam, acetaminophen, digoxin, meprobamate

sulfation sulfotransferases α-methyldopa, acetaminophen

methylation methyltransferases dopamine, epinephrine, histamine, methadone

acetylation N-acetyltransferases sulfonamides, isoniazide, clonazepam

conjugation with amino acids

amino acid-N-acyltransferases with glycine: salicylic acid, nicotinic acid

conjugation with glutathione

glutathione-S-transferases acetaminophen, ethacrynic acid, fosfomycin, busulfan

6.2.3. Phase 3 reactions

The conjugated molecules that are produced may be transformed to other metabolites, e.g. conjugated glutathione can be hydrolysed (two amino acids are removed).

6.3. Exercise

After extravascular administration the first process which has influence on change of drug concentration is the absorption. To study this process 1000 mg of a newly developed drug was given for a patient. The concentration – time data pairs are listed in Table 6.3.

Table 6.3.

time (h) concentration (mg/l) extrapolated cc (mg/l) difference cc (mg/l)

0.4 7.39 16.68 9.29

0.6 11.97 15.41 3.44

0.8 12.81 14.20 1.39

1.0 12.50 13.14 0.64

1.2 11.83

1.4 11.07

1.8 9.58

2.0 8.89

3.0 6.04

4.0 4.06

6.0 1.78

12.0 0.13

The plasma concentration of a drug in case of extravascular administration assuming that the duration of distribution is very short comparing to absorption and elimination (one compartment model) can be calculated by the following formula:

) = � ∙ *�+,- − � ∙ *�+/-

Build a pharmacokinetic model to simulate the change of concentration of the new drug using Phoenix software package, then determine the ka and ke values!

ka = ............... h-1

ke = ............... h-1

Please, suggest a method with which you are able to determine the parameter A and B!

..................................................................................................................................................

..................................................................................................................................................

..................................................................................................................................................

..................................................................................................................................................

..................................................................................................................................................

..................................................................................................................................................

A = ................ mg/l

B = ................ mg/l

Figure 6.1. Semilogarithmic blood concentration – time curve of the investigated compound.

Give the following data!

cmax = ............ mg/l

tmax = ............. h

tlag = .............. h

Vd = .............. l

Calculate the tmax value by the following equation!

0��� =1

�� − ��∙ �2

��

��

tmax = ............. h

Calculate the cmax value (use the equation of the plasma curve)!

cmax = ............ mg/l

Compare the calculated tmax, cmax and those that were determined by Phoenix software!

6.4. Questions

1. What is the definition of drug metabolism?

2. What is the definition of a prodrug?

3. Give two examples of active metabolites!

4. What are phase 1 metabolic reactions?

5. List the main phase 1 metabolic reactions (main groups).

6. What are phase 2 metabolic reactions?

7. Which enzyme is involved in conjugation with glutathione?

8. Which of the following are phase 2 metabolic reactions? (multiple choices)

A. microsomal oxidation B. isomerization C. sulfation D. hydrolysis E. glucuronidation

9. Name two drugs, which are metabolized by methylation.

10. Give an example of a phase 3 metabolic reactions.

7. Drug elimination

Drug elimination includes all the processes, which lead to a decrease in the drug concentration in the body water compartments (plasma) independently of the nature of the actions. A drug may be removed from the plasma by excretion or metabolism and it may be deposited in different tissues.

7.1. Excretion of drugs

Drugs can be excreted by various glands (the sweat, saliva and milk), the lungs, the liver and the kidneys.

7.1.1. Renal excretion

The most important route for the removal of a drug from the body is via the kidney into the urine. The elimination of drugs through the kidney involves the following processes:

- glomerular filtration

- active tubular secretion

- passive tubular reabsorption

- active tubular reabsorption

Glomerular filtration

The fenestrated capillaries in the kidney contain pores with diameters of 20–60 nm, which filter the water containing small dissolved solutes as it passes to the Bowman’s capsule. The filtration is assisted by the high hydrostatic pressure due to the higher blood pressure within the glomerulus as compared with other capillaries in the body. All those substances with molecular weights below 5000 pass through the pores without any hindrance. Substances with molecular weights between 5000 and 50,000 are filtered to some extent, while those with molecular weights larger than 50,000 (albumin, globulins and red blood cells) are retained. Drug–plasma protein complexes therefore remain in the circulation. Only the free, unbound fraction of a drug can leave the bloodstream. The glomerular filtrate is the plasma without the plasma proteins. The concentration of a drug in the ultrafiltrate is equal to the concentration of the unbound, free drug in the plasma. The anionic proteins of the basement membrane inhibit the passage of negatively charged anionic substances. The kidneys receive about 20% of the cardiac output (1100-1200 ml/min). Since the blood contains about 55% plasma, the total renal plasma flow is about 600-660 ml/min. Only 20% of the plasma flowing through the kidneys is converted into urine. The glomerular filtration rate (GFR) is therefore about 120 ml/min if the renal function is normal. The GFR is defined as the volume of plasma filtered by the kidneys in 1 minute. Approximately 172 l of plasma is filtered in a day. Since about 1.5 l of urine is formed daily, over 98% of the water is reabsorbed from the filtrate into the blood in the tubuli.

The tubular transport of drugs is bidirectional:

- passive tubular reabsorption (from the tubular lumen toward the blood)

- active tubular secretion (from the blood toward the tubular lumen)

- active tubular reabsorption

Passive tubular reabsorption

In the tubuli, the filtrate becomes more concentrated in the remaining substances as a consequence of the reabsorption of a large proportion of the water. Because of the concentration gradient between the lumen of the tubuli and the blood, the lipid-soluble, non-ionized substances are reabsorbed into the blood by passive diffusion. The extent of the ionization of a drug, and therefore its reabsorption, depends on the pH of the filtrate. The pH of the primary urine is between 4.5 and 8.5. In alkaline urine, acidic drugs are present in ionized form, and they are therefore reabsorbed to a lower extent and excreted to a greater extent, whereas basic drugs are non-ionized, and therefore reabsorbed to a greater extent and excreted to a lower extent. In acidic urine, the situation is the reverse. Altering the pH of the urine is one way to alter the excretion of drugs. Acidifiers such as NH4Cl and aspirin lower the pH of the urine, whereas alkalinizers such as CaCO3 or NaHCO3 increase the pH of the urine. As an example, phenobarbital is a weak acid. In the case of phenobarbital overdose, making the urine alkaline with NaHCO3 can increase the excretion of phenobarbital.

Active tubular secretion

Tubular secretion is an active, ATP-requiring process, which uses carrier molecules to transport solutes from the blood into the filtrate. The filtrate is more concentrated in the tubuli than in the plasma and an active transport mechanism therefore moves substances against the concentration gradient. The process has a high capacity: more drug molecules and metabolites are secreted in this way than by glomerular filtration. Only the free drug fraction may be secreted by transporter molecules. As a result of the high intensity of the process, most drug–plasma protein complexes in the blood dissociate rapidly to give additional free drug in the plasma. Drugs can be completely stripped off plasma proteins, and the drug concentration in the plasma may therefore be reduced to zero by tubular secretion. The transporters bind and secrete ionized, water-soluble substrates such as conjugates of phase 2 reactions. Organic anion transporters (OATs, OATPs) bind and transport many ionized organic acids, and organic cation transporters (OCTs) are specific for many ionized organic bases. The secretion transporters have broad substrate specificity and many drugs share the same transporters, so that competition can occur, leading to drug interactions. For example, penicillin and probenecid are substrates for OATs and probenecid is used in the theraphy to reduce the renal excretion of penicillin. Cimetidine reduces the secretion of procainamide; both are basic drugs and substrates for OCTs. The active secretion process is saturable and can reach a plateau at higher doses, which leads to higher than expected plasma concentrations.

The tubular secretion of H+ is important for the control and maintenance of the pH of the blood. K+ and carbamide are also excreted by tubular secretion.

Drugs secreted by active transport:

Anions: salicylates, NSAIDs Cations: histamine, dopamine penicillin quinine

probenecid procainamide indomethacin neostigmine cephalosporins metformine

para-aminohippuric acid cimetidine

Active tubular reabsorption

Just as certain solutes can be secreted from the blood into the tubular filtrate, the reverse process can occur by active transport. Transporters of tubular secretion can transport endogenous substances (sugars, amino acids, carbamide and ions, such as Na+, K+, Cl- and HCO3

-) and some drug molecules from the filtrate back into the blood against the concentration gradient. Glucose is completely reabsorbed into the plasma, and the urine in a healthy individual therefore contains no glucose. Active reabsorption is a competitive inhibitory process, and the excretion of endogenous compounds (or drugs) can therefore be increased. For example, carbamide is secreted by glomerular filtration and active secretion and most of it is reabsorbed into the blood by active reabsorption. In antigout therapy, the active reabsorption of carbamide can be inhibited by probenecid.

7.1.2. Biliary excretion of drugs

The metabolites formed by the liver can also be secreted into the bile. The biliary excretion of drugs can occur by passive diffusion or active transport mechanisms. The capacity of anion and cation transporters in the hepatocytes is saturable and there is a competition between solutes with similar physicochemical properties. The bile is an aqueous solution, which can dissolve water-soluble substances, and the biliary excretion of polar compounds is therefore intensive. Sulfate or glucuronide conjugates of phase 2 reactions are strongly polar componds with higher molecular weights than those of the parent drugs, and the bile can therefore also secrete them. Lipophilic molecules can also be secreted into the bile, as a result of solubilization by micelle-forming bile acids. The main criterion for biliary excretion is a molecular weight greater than 500. Lower molecular weight compounds are reabsorbed from the bile into the blood before they are transported into the small intestine. About 1 litre of bile is produced daily, and most drugs have much higher concentrations in the bile than in the plasma.

When the bile and its constituents reach the intestines, many compounds can be reabsorbed into the blood; this process is known as enterohepatic recirculation. The enzymes glucuronidase and sulfatase produced by the bacterial flora in the large intestine split the conjugating agent from the drug, giving a more absorbable lipid-soluble form, and the drug can be partially reabsorbed again. The process is continued until some other process eventually eliminates the drug from the body. Enterohepatic recirculation is characteristic for some drugs, such as benzodiazepines, morphine, warfarin, indomethacin, cardiac glycosides and several antimicrobal agents (rifampicin, erythromycin, ampicillin and doxycycline). Bile acids (deoxycholic acid and dehydrocholic acid) or some drugs (spironolactone and phenobarbital) can elicit biliary excretion and enterohepatic recirculation, while adsorbents and ion-exchange resins can inhibit the process.

7.1.3. Excretion in the saliva

Several drugs can be excreted into the saliva by passive diffusion or active transport. The salivary concentrations of some non-ionic, lipid-soluble drugs can be similar to their plasma concentrations. For drugs with a relatively constant plasma/saliva concentration ratio, measurement of the saliva concentration is used for the routine and non-invasive monitoring of plasma drug levels. A drug excreted in the saliva is usually swallowed and can therefore be reabsorbed from the intestine, resulting in salivary recycling. The salivary excretion of a drug

can cause an unpleasant taste in the mouth. Drugs that appear in the saliva include lithium, acetaminophen, procainamide, phenytoin, diazepam, quinine, theophyllin, tolbutamide, sulphonamides and salicylates.

7.1.4. Excretion in the breast milk

Lipid-soluble, non-ionized substances can pass into the milk of lactating mothers by passive diffusion or active transport. While the breast milk has a lower pH (6.5–6.8) as compared with that of the blood (7.4), weakly basic drugs tend to be more concentrated in the breast milk than in the plasma. As an example, the erythromycin concentration is approximately 8 times higher in the breast milk than in the blood. Drugs that are excreted in the breast milk include acetylsalicylic acid, ethanol, morphine, methadone, nicotine, caffeine, theophyllin, theobromine, antihistamines, anticoagulants, benzodiazepines, barbiturates, tetracyclines and sulfonamides. The prescence of high concentrations of drugs in the breast milk can have serious consequences for the infant, and nursing mothers are cautioned against the use of drugs during breast-feeding.

7.1.5. Pulmonary excretion of drugs

The lungs are the major organ of excretion for gases and volatile substances. The partition coefficient of the drug between the blood and the alveolar air, the partition volume of the drug, the respiratory volume and the rate of pulmonary circulation are the factors that can influence excretion in the expired air. The primary mechanism of transport is passive diffusion. Drugs with a high blood/alveolar air coefficient are excreted to a greater extent than drugs with a low blood/air ratio. Examples of drugs that can appear in the expired air include anaesthetics, ethanol, sulphanilamide, sulfapyridine, dinitrogen oxide, diethyl ether and halothane.

7.1.6. Excretion in the sweat

Since the volume of sweat produced is small, excretion in the sweat is a possible but not significant mode of drug excretion. Excreted substances can cause skin reactions; as an example, bromide ion can cause bromine acne, or prolonged amiodarone therapy can cause dermatopathy. Several compounds, such as carbamide, NaCl, evaporating oils (garlic oil), amphetamine, cocaine, morphine and ethanol, have been found in the sweat. Heating and all those substances that increase sweating (e.g. aspirin, caffeine and theobromine) can elicit excretion in the sweat.

7.2. Multiple dosing - Exercise

A repeated drug administration is being planned, and the pharmacokinetic parameters of drug X are needed to calculate the most appropriate dosing.

7.2.1. Determination of the kinetic parameters of a drug

The patient is given a single oral dose of 200 mg. Calculate the pharmacokinetic parameters of the drug and compare the results with the constants calculated with the WinNonlin software.

ke = 0.197 h-1

t1/2 = ...................................... h

AUCT = ................................ h mg/l

tmax = .................................... h

7.2.2. Calculation of the maintenance dose of a drug

The targeted steady-state concentration of drug X is 7 mg/l. Calculate the maintenance dose for repeated administration of drug X every 24 hours, according to the following equation:

! =!′ ∙ 44 ∙ 5

�6&'

where D is the maintenance dose [mg], D' is the single dose of drug [mg], AUCT is the AUCT value of single dose D' of drug [h·mg/l], css is the desired steady-state concentration [mg/l] and τ is thedosing interval [h].

The calculated maintenance dose:

D = ....................................... mg/24 h

Time to reach the minimum effective concentration: ................................. h

Time to reach the desired steady-state concentration:................................. h

7.2.3. Administration of the loading dose

The therapy with the calculated maintenance dose required a long time to achieve the steady-state plasma concentration. In such cases, a loading dose is given in one or more portions.

A loading dose of 600 mg of drug X is administered in two portions during the first day of therapy, and the treatment is continued with the maintenance dose calculated in the previous section.

At what time is the minimum effective concentration reached with the modified therapy?

At what time is the desired plasma level exceeded in the case of the therapy with the loading dose?

7.3. Questions

1. What physicochemical properties favour a) glomerular filtration, b) active secretion, and c) reabsorption of drugs in the kidney?

2. Why is secretion the only process that can be saturated or competitively inhibited? What are the consequences of inhibition and saturation?

3. How can the urinary pH be altered to increase the excretion of a) weak acids or b) weak bases?

4. How can the urinary pH be altered to decrease the excretion of a) weak acids or b) weak bases?

5. What are the non-renal pathways of drug excretion?

6. What types of drugs are successfully eliminated by biliary secretion?

7. What types of drugs undergo enterohepatic recirculation?

8. What types of drugs are excreted by the pulmonary route?

9. Methotrexate is a weak acid used in the treatment of certain neoplastic diseases, severe psoriasis and adult rheumatoid arthritis. The drug is eliminated by renal excretion, but it has poor solubility and may precipitate in the urine, particularly at high doses. Its precipitation can cause renal failure, and will also delay further methotrexate elimination. To avoid the precipitation of methotrexate in the urine, clinicians often hydrate patients aggressively, and administer NaHCO3. Let us consider a practical case. A patient taking methotrexate suffered acute renal failure. The pH of his urine was quite low, in spite of the administration of large amounts of NaHCO3. He had recently started drinking relatively large quantities of caffeine-free cola beverages in an effort to stay hydrated. How might the cola consumption have affected the drug clearance and caused the renal failure?

10. A 150 mg dose of a drug was administered intravenously. The initial plasma concentration at t = 0 time point was 12.5 mg/l. Calculate the volume of distribution of the drug.

8. Continuous infusion and multiple drug administration

Most clinical situations require a therapeutic effect for time periods extending beyond the effect of one dose. In these situagiven. The goal is to maintain a therapeutic effect by maintaining the amount of drug in the body, and the concentration of the drug in the plasma, within the therapeutic range.

8.1. Infusion

The process of infusion is the continuous, slow administration of drugs, electrolytes, fluids or nutrients into a vein by gravitation or with an infusion pump. It maintains an effective constant blood level and allows the precise control of drug concentratineeds of the patient.

The infusion is administered with zeroadministered is constant in each time interval. The elimination of a drug is a firstprocess, so the rate of eliminationbody.

After the initiation of the infusion, the drug concentration gradually rises from zero and becomes constant at a plateau or steadybody increases, the rate of elimination increases, until it reaches the rate of drug administration. At the steady state, therefore the rate of drug input is equal to the rate of drug output and there is no further change in drug concentration as long as the imaintained. The change in drug concentration during a constant infusion is illustrated in Fig.8.1.

Figure 8.1. Plasma concentrations of drug during a continuous infusion

At the steady state, the rate of drug elimination is equal to the rate of drug administration, so the rate of change in the plasma drug concentration is zero, and the infusion may therefore be continued on the plateau level infinitely without any risk of t

Continuous infusion and multiple drug administration

Most clinical situations require a therapeutic effect for time periods extending beyond the effect of one dose. In these situations, a continuous infusion or multiple doses of the drug are given. The goal is to maintain a therapeutic effect by maintaining the amount of drug in the body, and the concentration of the drug in the plasma, within the therapeutic range.

he process of infusion is the continuous, slow administration of drugs, electrolytes, fluids or nutrients into a vein by gravitation or with an infusion pump. It maintains an effective constant blood level and allows the precise control of drug concentrations to fit the individual

The infusion is administered with zero-order kinetics because the amount of drug administered is constant in each time interval. The elimination of a drug is a firstprocess, so the rate of elimination is directly proportional to the amount of the drug in the

After the initiation of the infusion, the drug concentration gradually rises from zero and becomes constant at a plateau or steady-state concentration (css). As the amount of drug in the

increases, the rate of elimination increases, until it reaches the rate of drug administration. At the steady state, therefore the rate of drug input is equal to the rate of drug output and there is no further change in drug concentration as long as the imaintained. The change in drug concentration during a constant infusion is illustrated in

Plasma concentrations of drug during a continuous infusion.

At the steady state, the rate of drug elimination is equal to the rate of drug administration, so the rate of change in the plasma drug concentration is zero, and the infusion may therefore be continued on the plateau level infinitely without any risk of toxicity.

Most clinical situations require a therapeutic effect for time periods extending beyond the tions, a continuous infusion or multiple doses of the drug are

given. The goal is to maintain a therapeutic effect by maintaining the amount of drug in the body, and the concentration of the drug in the plasma, within the therapeutic range.

he process of infusion is the continuous, slow administration of drugs, electrolytes, fluids or nutrients into a vein by gravitation or with an infusion pump. It maintains an effective

ons to fit the individual

order kinetics because the amount of drug administered is constant in each time interval. The elimination of a drug is a first-order

is directly proportional to the amount of the drug in the

After the initiation of the infusion, the drug concentration gradually rises from zero and ). As the amount of drug in the

increases, the rate of elimination increases, until it reaches the rate of drug administration. At the steady state, therefore the rate of drug input is equal to the rate of drug output and there is no further change in drug concentration as long as the infusion is maintained. The change in drug concentration during a constant infusion is illustrated in

At the steady state, the rate of drug elimination is equal to the rate of drug administration, so the rate of change in the plasma drug concentration is zero, and the infusion may therefore be

The plasma concentration resulting from the infusion is determined by the rate of infusion (Xi). Xi is the amount of drug administered by infusion in unit time.

78 =&�' ∙ 44

where Xi is the rate of infusion [mg/h], ClT is the total body clearance [l/h] and css is the steady-state concentration of the drug [mg/l].

The equation shows that the steady-state concentration is determined by the infusion rate and the total body clearance of the drug. css is related to Xi and inversely related to ClT. Thus, any factor that decreases clearance, such as a liver or kidney disease, increases the steady-state concentration of an infused drug. Increasing the rate of infusion results in an increase in css, but it does not influence the time required to reach the steady-state concentration, as shown in Fig. 8.1.

If the plateau is taken as 100%, the plateau fraction (f) at time t is

9 = 1 − *�+,∙-

where ke is the elimination rate constant [1/h].

ke is constant, and consequently the f depends only on the duration of infusion. At 50% of the plateau, f = 0.5:

0.5 = 1 − *�+,∙-

This equation is arranged to solve for t:

−0.5 = −*�+,∙-

�20.5 = −��0

−0.693 = −��0

0 =0.693

��= 0@

AB

The time necessary to reach 50% of the plateau is equal to the elimination half-life (Fig. 8.2).

How much time is needed to reach 95% of the plateau?

0.95 = 1 − *�+,∙-

i.e.

−0.05 = −*�+,∙-

�20.05 = −��0

−2.9957 = −��0

0 =2.9957

��

Substitution of �� =EFA

-GHB gives

0 =

5·t1/2 would be reached not at 95%, but at 97% of the plateau, and this difference is not significant. We cannot statistically detect any difference between 97% and 100% of the plateau; therefore, approximately 5 halfbe reached.

Figure 8.2. Time course of plateau formation and elimination of drug

When the infusion is stopped, the plasma concentration of the drug decreases through firstorder elimination (Fig. 8.2). During one halfand 5·t1/2 is needed to decrease the plasma concentration virtually to zero. Thus, the shorter the half-life of the drug, the more rapidly the desired the drug will be eliminated from the body. The longer the halfplateau will be reached. Since it is necessary to produce an effective drug concentration rapidly in most cases, larger doses, called loading doses, are given initially (Fig. 8.3). When the desired drug level has been reached, the therapy is continued with the smaller maintenance dose.

The following equation can be used to compute the loading dose of infusion:

where XL is the loading dose [mg].

gives

=2.9957

0.6930@

AB= 4.32 ∙ 0@

AB~5 ∙ 0@

AB

would be reached not at 95%, but at 97% of the plateau, and this difference is not significant. We cannot statistically detect any difference between 97% and 100% of the plateau; therefore, approximately 5 half-lives are required for the steady-state concentration to

Time course of plateau formation and elimination of drug.

When the infusion is stopped, the plasma concentration of the drug decreases through firstorder elimination (Fig. 8.2). During one half-life, the steady-state concentration falls by 50%

is needed to decrease the plasma concentration virtually to zero. Thus, the shorter life of the drug, the more rapidly the desired css will be attained and the more rapidly

ated from the body. The longer the half-life, the more slowly the plateau will be reached. Since it is necessary to produce an effective drug concentration rapidly in most cases, larger doses, called loading doses, are given initially (Fig. 8.3). When

desired drug level has been reached, the therapy is continued with the smaller maintenance

The following equation can be used to compute the loading dose of infusion:

7K =&�'��

∙ LL

is the loading dose [mg].

would be reached not at 95%, but at 97% of the plateau, and this difference is not significant. We cannot statistically detect any difference between 97% and 100% of the

state concentration to

When the infusion is stopped, the plasma concentration of the drug decreases through first-state concentration falls by 50%

is needed to decrease the plasma concentration virtually to zero. Thus, the shorter will be attained and the more rapidly

life, the more slowly the plateau will be reached. Since it is necessary to produce an effective drug concentration rapidly in most cases, larger doses, called loading doses, are given initially (Fig. 8.3). When

desired drug level has been reached, the therapy is continued with the smaller maintenance

The following equation can be used to compute the loading dose of infusion:

Figure 8.3. Plasma concentrations resulting from an intravenous loading dose given by infusion.

8.2. Multiple dosing

Administration of a drug in multiple, fixed doses rather than by continuous infusion is often more convenient. Fixed doses by intravenous injection ointervals result in time-dependent fluctuations in the concentration of the drug, which is in contrast with the constant drug concentration observed with continuous infusion.

When the first dose is given, the plasma concdecreases. If the second dose is given at an interval shorter than 5 halfthe first dose still remains in the body at the time the second dose is administered, resulting in a higher maximum. The concentration then decreases again, and so on. The drug therefore accumulates until the rate of drug elimination exactly balances the rate of drug administration and a steady state is achieved (Fig. 8.4). It takes 5 halfsteady-state concentration.

Plasma concentrations resulting from an intravenous loading dose given by

Administration of a drug in multiple, fixed doses rather than by continuous infusion is often more convenient. Fixed doses by intravenous injection or oral administration at fixed time

dependent fluctuations in the concentration of the drug, which is in contrast with the constant drug concentration observed with continuous infusion.

When the first dose is given, the plasma concentration increases to a maximum level and then decreases. If the second dose is given at an interval shorter than 5 half-lives, some drug from the first dose still remains in the body at the time the second dose is administered, resulting in

mum. The concentration then decreases again, and so on. The drug therefore accumulates until the rate of drug elimination exactly balances the rate of drug administration and a steady state is achieved (Fig. 8.4). It takes 5 half-lives of a drug to reach t

Plasma concentrations resulting from an intravenous loading dose given by

Administration of a drug in multiple, fixed doses rather than by continuous infusion is often r oral administration at fixed time

dependent fluctuations in the concentration of the drug, which is in contrast with the constant drug concentration observed with continuous infusion.

entration increases to a maximum level and then lives, some drug from

the first dose still remains in the body at the time the second dose is administered, resulting in mum. The concentration then decreases again, and so on. The drug therefore

accumulates until the rate of drug elimination exactly balances the rate of drug administration lives of a drug to reach the desired

Figure 8.4. Plasma concentrations after multiple dosing of a drug, showing the approach to the steady state.

The maintenance dose can be calculated via the following equation:

where D is the maintenance dose [mg], steady-state concentration [mg/l], [h·mg/l], τ is the dosing interval [h] and

When τ is longer than 5 halfbetween the maximum and zero (Fig. 8.5).

Figure 8.5. Plasma concentrations when the dosing interval is longer than 5 half

If the rate of administration is higher than the rate of elimination and the multiple dosing therapy is continued, the drug accumulates in the body and the plasma concentration will exceed the maximum tolerated level, causing toxicity.

To produce an adequate plasma curve, it is necessary to monitor the plasma concentrations at the times of the maxima and the minima. For multiple dosing, the first concentration maximum is at the tmax value of the drug, while the first concentration minimutimepoint of the second administered dose (after time tmax+τ , the second minimum is at shown in Fig. 8.4.

Plasma concentrations after multiple dosing of a drug, showing the approach to

The maintenance dose can be calculated via the following equation:

! =!′ ∙ &44 ∙ 5

�6&'= &�' ∙ &44 ∙ 5

is the maintenance dose [mg], D' is the single dose of drug [mg], state concentration [mg/l], AUCT is the area under the curve for dose

is the dosing interval [h] and ClT is the total body clearance [l/h].

is longer than 5 half-lives, the plasma concentration of the drug will fluctuate between the maximum and zero (Fig. 8.5).

Plasma concentrations when the dosing interval is longer than 5 half

administration is higher than the rate of elimination and the multiple dosing therapy is continued, the drug accumulates in the body and the plasma concentration will exceed the maximum tolerated level, causing toxicity.

To produce an adequate plasma curve, it is necessary to monitor the plasma concentrations at the times of the maxima and the minima. For multiple dosing, the first concentration

value of the drug, while the first concentration minimutimepoint of the second administered dose (after time τ). The second maximum is at time

, the second minimum is at 2τ, and so on. The timings are given in Table 8.1 and

Plasma concentrations after multiple dosing of a drug, showing the approach to

is the single dose of drug [mg], css is the desired is the area under the curve for dose D' of drug

ance [l/h].

lives, the plasma concentration of the drug will fluctuate

Plasma concentrations when the dosing interval is longer than 5 half-lives.

administration is higher than the rate of elimination and the multiple dosing therapy is continued, the drug accumulates in the body and the plasma concentration will

To produce an adequate plasma curve, it is necessary to monitor the plasma concentrations at the times of the maxima and the minima. For multiple dosing, the first concentration

value of the drug, while the first concentration minimum is at the ). The second maximum is at time

, and so on. The timings are given in Table 8.1 and

Table 8.1. Timing schedule of multiple dosing.

Number of plasma

sample Time point Number of plasma

sample Time point

1 tmax 6 3τ

2 τ 7 3τ+tmax

3 τ+tmax 8 4τ

4 2τ 9 4τ+tmax

5 2τ+tmax 10 5τ, etc.)

8.3. Planning a continuous intravenous infusion

For drug X, maintenance of a consistent plasma concentration for 12 h is advantageous to achieve a consistent effect. To maintain a constant plasma drug concentration, continuous intravenous infusion is used. Compute the dose of the infusion.

8.3.1. Calculation of the kinetic parameters of drug X

In order to calculate the dose of infusion for 12 h, the kinetic parameters of drug X first have to be estimated.

If 200 mg of drug X is administered as a short, 30-min intravenous infusion, we can calculate the following parameters:

ke = ........................................ h-1

t1/2 = ...................................... h

AUCT = ................................. h mg/l

ClT = ..................................... l/h

Vd = ....................................... l

What is the range of the therapeutic plasma concentration?

How long can the therapeutic plasma level of 200 mg of drug X be maintained?

8.3.2. Calculation of the dose for continuous infusion

Calculate the rate of infusion of drug X for a 12 h infusion, which can produce a steady-state concentration of 4 mg/l.

78 = &�' ∙ 44

Xi = ....................................... mg/h

The total dose of infusion for 12 h: ................................. mg

Observe the plasma curve of the calculated therapy with the WinNonlin software.

At what time is the minimum effective concentration reached?

At what time is the desired plasma level exceeded?

8.3.3. Calculation of loading dose for continuous infusion

It is necessary to produce the desired plasma level of 4 mg/l more rapidly. This will be achieved through the administration of a loading dose as a short infusion, and the therapy will then be continued with a smaller maintenance dose.

Let us begin the therapy with a loading dose for 0.05 h, and then administer the maintenance infusion, as calculated in section 8.3.2. The loading dose can be calculated according to the equation

7K =&�'��

∙ 44

XL = ....................................... mg

Evaluate the effect of the loading dose on the plasma concentration of drug X with the WinNonlin software.

Study the plasma curve again and express your opinion about the therapy.

At what time is the desired plasma level exceeded by administration of the loading dose?

Time to reach the plateau of infusion: ............................. h

8.4. Questions

1. What is the reason for the plateau formation in the case of infusion and multiple drug administration?

2. What are the factors determining the steady-state concentration of an infusion?

3. What does the rate of infusion describe?

4. How long will it take to reach the steady-state concentration in the case of multiple dosing?

5. When is the use of a loading dose necessary for effective therapy?

6. Explain what happens if the dosing interval is larger than 5·t1/2.

7. What is the reason for accumulation, and what is the consequence?

8. It may be necessary to maintain a 4 mg/l plasma concentration of a drug for 12 h. Calculate the loading and maintenance doses of infusion. The elimination half-life of the drug is 1.2 h and the volume of distribution is 85.27 l.

9. Calculate the maintenance dose for repeated oral administration of a drug three times a day. The desired steady-state concentration is 6 mg/l. The AUCT value of a 250 mg single oral dose is 125.35 h·mg/l.

10. Give the timings of repeated oral administration if 350 mg of a drug is given three times a day during the first day, and the therapy is then followed by a 180 mg maintenance dose once daily. The tmax value of the drug is 2 h.

9. Pharmacokinetic compartment models

Model pharmacokinetic systems can be used to predict the time courses of drug concentrations in the body and to calculate pharmacokinetic parameters so as to individualize the most effective dose and dosing regimen for the desired pharmacokinetic effect and to avoid adverse effects.

A pharmacokinetic compartment is that part of the body water volume in which the drug concentration is changing with the same kinetics. The compartment is characterized by its volume (Vd) and the concentration of drug in the compartment (cp). The compartments are not specific tissues or fluids but may be groups of similar tissues or fluids.

Compartmental models are categorized by the number of compartments needed to describe the behaviour of a drug in the body. There are one-compartment, two-compartment and multicompartment models. The compartments are symbolized by rectangles, and the drug transfer is indicated by arrows. The rate constants of different processes are indicated by the letter k, with different indices. These models are open models, because there is communication between the compartments and the environment: the drug is administered from outside and it is eliminated to the environment.

9.1. One-compartment models

A one-compartment model assumes that the body is composed of a single, homogeneous compartment into which a drug distributes rapidly and uniformly, e.g. a compartment consisting of plasma and well-perfused tissues. It is assumed that after a dose of drug is administered, it distributes instantaneously to the compartment, with volume Vd, and forms a concentration cp in it. The drug is then eliminated from the compartment by first-order kinetics. A one-compartment model is characteristic, for example, for ethanol, tetracyclines, penicillin and azophen.

9.1.1. One-compartment intravascular model

If dose D of drug is administered intravascularly, there is no absorption and the whole amount of the dose passes into the circulation. The drug distributes rapidly in the volume Vd of the compartment. The administration and distribution are negligible in time as compared with the elimination, and the elimination therefore is basically the only time-controlled process in the system. The one-compartment intravascular model is outlined in Fig. 9.1.

Figure 9.1. One-compartment intravascular model.

Vd

cp

D ke

With first-order elimination, the amount of drug eliminated in a fixed time is directly proportional to the amount of drug in the body (the plasma drug concentration is decreased by half after every half-lifetime):

where cp is the concentration of the drug in the compartment [mg/l] and rate constant [h-1].

If the equation is integrated between

where cp0 is the hypothetical drug concentration at

If we continuously measure the concentration of a drug in the plasma after an intravenous dose and then plot these plasma drug concentrations against the times at which they are measured, the curve is an exponential curve, as shown in Fig. 9.2.

Figure 9.2. Plasma concentration vs. time profile of a drug behaving as in a oneintravascular model.

The prediction of plasma concentrations is easier if the concentrations feature on a straightline rather than on a curve. The plot of a curve can be converted to a straight line by plotting the natural logarithm (ln) of the plasma drug concentration versus time (Fig. 9.3). The line is defined by the equation:

order elimination, the amount of drug eliminated in a fixed time is directly proportional to the amount of drug in the body (the plasma drug concentration is decreased by

M )M0

= −�� ∙ )

is the concentration of the drug in the compartment [mg/l] and k

If the equation is integrated between t = 0 and t = ∞:

) = )# ∙ *�+,∙-

is the hypothetical drug concentration at t = 0 [mg/l].

If we continuously measure the concentration of a drug in the plasma after an intravenous dose and then plot these plasma drug concentrations against the times at which they are

s an exponential curve, as shown in Fig. 9.2.

Plasma concentration vs. time profile of a drug behaving as in a one

The prediction of plasma concentrations is easier if the concentrations feature on a straightline rather than on a curve. The plot of a curve can be converted to a straight line by plotting the natural logarithm (ln) of the plasma drug concentration versus time (Fig. 9.3). The line is

ln ) = �2 )# − �� ∙ 0

order elimination, the amount of drug eliminated in a fixed time is directly proportional to the amount of drug in the body (the plasma drug concentration is decreased by

ke is the elimination

If we continuously measure the concentration of a drug in the plasma after an intravenous dose and then plot these plasma drug concentrations against the times at which they are

Plasma concentration vs. time profile of a drug behaving as in a one-compartment

The prediction of plasma concentrations is easier if the concentrations feature on a straight line rather than on a curve. The plot of a curve can be converted to a straight line by plotting the natural logarithm (ln) of the plasma drug concentration versus time (Fig. 9.3). The line is

Figure 9.3. Time profile of a one(the term semilogarithmic indicates that only one axis is converted)

The intercept of the line on the ydefinition of tangent, the slope is the change in the natural log of plasma concentrations divided by the change in time between the concentrations:

Drug concentrations can be predicted for any time parameters (cp

0 and ke) are known.

9.1.2. One-compartment extravascular model

After extravascular administration of a drug, only a fraction (absorbed in accordance with the rate of absorcompartment depends on the rates of absorption and elimination, while the distribution is a rapid process. The diagram of a one

The concentration of the drug absorption, and then decreases by firstcurve has an ascending (absorption) and a descending (elimination) part (Fig. 9.5).

Figure 9.4. The diagram of a one

D

ka, f (0<f<1)

Time profile of a one-compartment intravascular model in a semilogarithmic plot(the term semilogarithmic indicates that only one axis is converted).

The intercept of the line on the y-axis is ln cp0 and the slope of the line is k

definition of tangent, the slope is the change in the natural log of plasma concentrations divided by the change in time between the concentrations:

�� = 0P2� =�2 @ − �2 A

0A − 0@

Drug concentrations can be predicted for any time after the dose if the pharmacokinetic ) are known.

compartment extravascular model

After extravascular administration of a drug, only a fraction (f) of the administered dose is absorbed in accordance with the rate of absorption (ka). The plasma concentration in the compartment depends on the rates of absorption and elimination, while the distribution is a rapid process. The diagram of a one-compartment extravascular model is shown in Fig. 9.4.

The concentration of the drug increases up to a maximum (cmax) in accordance with the rate of absorption, and then decreases by first-order elimination. The plasma concentration vs. time curve has an ascending (absorption) and a descending (elimination) part (Fig. 9.5).

The diagram of a one-compartment extravascular model.

Vd

cp

ke

<1)

compartment intravascular model in a semilogarithmic plot

ke. According to the definition of tangent, the slope is the change in the natural log of plasma concentrations

after the dose if the pharmacokinetic

) of the administered dose is ). The plasma concentration in the

compartment depends on the rates of absorption and elimination, while the distribution is a compartment extravascular model is shown in Fig. 9.4.

) in accordance with the rate of order elimination. The plasma concentration vs. time

curve has an ascending (absorption) and a descending (elimination) part (Fig. 9.5).

The starting point of the curve is not identical with zero, because some time (the lag time) is needed for the drug to appear in the blood. In the ascending part of the curve, absorption is the dominating process, but the rate of absorption cannot be measudemonstrates the effects of both absorption and elimination. Elimination begins immediately after the drug is administered. The actually measured concentration before difference between the absorption and eldrug increases, the rate of elimination also increases in accordance with firstAt cmax at time tmax, the rate of elimination and the rate of absorption become equal. After the maximum concentration in the curve, the elimination is the dominating process, and the absorption is completed.

Figure 9.5. Semilogarithmic plot of the plasma drug concentration vs. time for a onecompartment extravascular model

In the case of extravascular admindescribed by the parallel absorption and elimination subprocesses. The method of residuals attempts to separate the two subprocesses of absorption and elimination. In the elimination part of the curve, the plasma concentration is formed, similarly as in the oneintravascular model: if the absorption had been instantaneous (i.e. intravascularly) and the distribution had been negligible in time, this would be the plasma concentration. The bextrapolation of the elimination part of the curve is the elimination line, which represents the effect of elimination alone. The elimination concentration can be described by the equation:

The starting point of the curve is not identical with zero, because some time (the lag time) is needed for the drug to appear in the blood. In the ascending part of the curve, absorption is the dominating process, but the rate of absorption cannot be measured directly because the curve demonstrates the effects of both absorption and elimination. Elimination begins immediately after the drug is administered. The actually measured concentration before difference between the absorption and elimination subprocesses. As the concentration of the drug increases, the rate of elimination also increases in accordance with first

, the rate of elimination and the rate of absorption become equal. After the centration in the curve, the elimination is the dominating process, and the

Semilogarithmic plot of the plasma drug concentration vs. time for a onecompartment extravascular model.

In the case of extravascular administration, the actual plasma concentration of drug can be described by the parallel absorption and elimination subprocesses. The method of residuals attempts to separate the two subprocesses of absorption and elimination. In the elimination

ve, the plasma concentration is formed, similarly as in the oneintravascular model: if the absorption had been instantaneous (i.e. intravascularly) and the distribution had been negligible in time, this would be the plasma concentration. The bextrapolation of the elimination part of the curve is the elimination line, which represents the effect of elimination alone. The elimination concentration can be described by the equation:

)Q�R = � ∙ *�+,∙-

The starting point of the curve is not identical with zero, because some time (the lag time) is needed for the drug to appear in the blood. In the ascending part of the curve, absorption is the

red directly because the curve demonstrates the effects of both absorption and elimination. Elimination begins immediately after the drug is administered. The actually measured concentration before cmax value is the

imination subprocesses. As the concentration of the drug increases, the rate of elimination also increases in accordance with first-order kinetics.

, the rate of elimination and the rate of absorption become equal. After the centration in the curve, the elimination is the dominating process, and the

Semilogarithmic plot of the plasma drug concentration vs. time for a one-

istration, the actual plasma concentration of drug can be described by the parallel absorption and elimination subprocesses. The method of residuals attempts to separate the two subprocesses of absorption and elimination. In the elimination

ve, the plasma concentration is formed, similarly as in the one-compartment intravascular model: if the absorption had been instantaneous (i.e. intravascularly) and the distribution had been negligible in time, this would be the plasma concentration. The back-extrapolation of the elimination part of the curve is the elimination line, which represents the effect of elimination alone. The elimination concentration can be described by the equation:

where cp(E) is the concentration of the elimination subprocess [mg/l] and B is the amount of drug eliminated at time t [mg/l].

First-order absorption has been defined as first-order elimination from a depot at the site of administration to the circulation. The absorption concentration may therefore be described by a similar equation, but containing ka instead of ke:

)Q�R = � ∙ *�+/∙-

where cp(A) is the concentration of the absorption subprocess [mg/l], A is the amount of drug absorbed at time t [mg/l] and ka is the absorption rate constant [h-1].

The actual, measured plasma concentration is the difference between the elimination and absorption subprocesses:

) = )Q�R − )Q�R

) = � ∙ *�+,∙- − � ∙ *�+/∙-

The area under the curve (AUCT) of the elimination line is larger than the AUCT of the actual extravascular curve (Fig. 9.5), and the absorption subprocess must therefore be substracted from the elimination subprocess.

The constants ke and B can be determined by the same method as presented in section 9.1.1. The slope of the back-extrapolated elimination line (Fig. 9.5, red line) is the elimination rate constant:

�� = 0P2� =�2 @ − �2 A

0A − 0@

The intercept of the elimination line on the y-axis is ln B.

For the graphical determination of ka and A, concentrations c3 and c4 are measured at times t3 and t4, respectively. The measured concentrations c3 and c4 are the resultants of the elimination and absorption subprocesses. At t3 and t4, there are also two extrapolated concentrations, c3' and c4' on the elimination line which represent the elimination alone, as if absorption had been instantaneous. For calculation of the absorption parameters (ka and A), only the concentrations relating to the absorption need to be known, which can be achieved through the following equation:

)Q�R = )Q�R − )

Subtraction of the actual points on the ascending part of the curve from the extrapolated points (c3' – c3 and c4' – c4) will yield a new set of plasma drug concentrations (c3'' and c4'', respectively) for each time point:

t3: S′′ = S′ − S

t4: T′′ = T′ − T

These values can be plotted with the appropriate times, and the line is then drawn that best fits the new points. This new line is called the absorption line (Fig. 9.5, blue line), which

represents the effect of absorption only. The slope of the line for these new points gives an estimate of the absorption rate constant:

�� =�2Q S′ − SR − �2Q T

U − TR

0T − 0S

The intercept of the absorption line is ln A.

If the intercepts ke and ka of the elimination and the absorption lines are known, the plasma drug concentration at any time after a single dose can be calculated.

9.2. Two-compartment models

The two-compartment model is applied when the distribution of a drug in the body is a two-step process. A two-compartment model divides the body into a central compartment and a second peripheral compartment of poorly perfused tissues. After absorption, all drugs first distribute rapidly into the circulation and the organs with high blood flow (''soft'' tissues, e.g. the kidneys, liver, heart, lungs and muscles). This compartment is specified as the central compartment, where the distribution takes place rapidly and the concentration change can be followed easily in a series of samplings. After some time, the drug distributes in a slower step into the organs with low perfusion (''deep'' tissues, e.g. the skin, bones and adipose tissues). The peripheral compartment is accessible more slowly for the drug and the distribution needs a longer time. The two-compartment model is characteristic for theophyllin, caffeine, digoxin, digitoxin and lidocaine.

9.2.1. Two-compartment intravascular model

After the intravenous injection of a drug, there is no absorption; the dose D of the drug is administred directly into the central compartment, i.e. the circulation, and then it slowly distributes into the peripheral compartment. Drug moves back and forth between these compartments to maintain equilibrium. The distribution can be characterized by the distribution rate microconstants k12 and k21. The drug is eliminated out of the body from both compartments with rate constants k1 and k2. The two-compartment intravascular model can be represented by Fig. 9.6.

Figure 9.6. Diagram of two-compartment intravascular administration.

D

k2

k1

k12 k21

peripheral compartment

Vd(p), cp(p)

central compartment

Vd(c), cp(c)

α β

A natural log plasma drug concentration vs. time curve consists of two parts; it can be depicted as in Fig. 9.7. The first phase reflects the paralel dthe initial portion is determined primarily by the distribution. The second part of the curve is determined by the elimination. The rate of distribution and the rate of elimination can be calculated by using the method oelimination. The plasma concentrations of the elimination subprocess:

where cp (E) is the concentration of the elimination subprocess [mg/l], eliminated at time t [mg/l] and

The elimination hybrid constant is the resultant of the micro elimination constants

The distribution subprocess can be represented as an absorption process from the compartment to the peripheral compartment, and the concentrations relating to only the distribution can therefore be described with the equation

where cp(D) is the concentration of the distribution subprocess [mg/l], distributed at time t [mg/l] and

Figure 9.7. Semilogarithmic plot of plasma drug concentration vs. time for a twocompartment intravascular model

A natural log plasma drug concentration vs. time curve consists of two parts; it can be depicted as in Fig. 9.7. The first phase reflects the paralel distribution and elimination, though the initial portion is determined primarily by the distribution. The second part of the curve is determined by the elimination. The rate of distribution and the rate of elimination can be calculated by using the method of residuals, which separates the effects of distribution and elimination. The plasma concentrations of the elimination subprocess:

)Q�R = � ∙ *�V∙-

is the concentration of the elimination subprocess [mg/l], B is the amount of drug [mg/l] and β is the elimination hybrid constant [h-1].

The elimination hybrid constant is the resultant of the micro elimination constants

W = �@ + �A

The distribution subprocess can be represented as an absorption process from the compartment to the peripheral compartment, and the concentrations relating to only the distribution can therefore be described with the equation

)Q!R = � ∙ *�X∙-

is the concentration of the distribution subprocess [mg/l], A is the a[mg/l] and α is the distribution hybrid constant [h-1].

Semilogarithmic plot of plasma drug concentration vs. time for a twocompartment intravascular model.

A natural log plasma drug concentration vs. time curve consists of two parts; it can be istribution and elimination, though

the initial portion is determined primarily by the distribution. The second part of the curve is determined by the elimination. The rate of distribution and the rate of elimination can be

f residuals, which separates the effects of distribution and

is the amount of drug

The elimination hybrid constant is the resultant of the micro elimination constants k1 and k2:

The distribution subprocess can be represented as an absorption process from the central compartment to the peripheral compartment, and the concentrations relating to only the

is the amount of drug

Semilogarithmic plot of plasma drug concentration vs. time for a two-

The distribution hybrid constant is the resultant of the microconstants k12 and k21:

� = �@A + �A@

The equation of the actual, measured plasma concentration is the sum of the two subprocesses:

) = )Q�R + )Q!R

) = � ∙ *�V∙- + � ∙ *�X∙-

The intercept of the back-extrapolated elimination line (Fig. 9.7, red line) on the y-axis is ln B. The elimination hybrid constant β can also be estimated from the slope of the elimination line:

W =�2 @ − �2 A

0A − 0@

For the graphical determination of constants A and α, plasma concentrations (c3 and c4) are measured at time points t3 and t4 in the distribution part of the curve. The extrapolated plasma concentrations (c3'' and c4'') are read from the back-extrapolated portion of the elimination line. These values are only from the elimination subprocess. The differences between the measured and extrapolated concentrations for times t3 and t4 give the concentrations of the distribution subprocess (c3'' and c4''):

)Q!R = ) − )Q�R

t3: S′′ = S − S′

t4: T′′ = T − T′

The newly generated concentrations c3'' and c4'' represent the distribution alone. A plot of the points at the corresponding time points gives a new line, the distribution line (Fig. 9.7, blue line). The y-intercept of the line is ln A and the slope of the line is α, the distribution hybrid constant:

� =�2Q S − S′R − lnQ T − T′R

0T − 0S

The drug concentration can therefore be determined at any time, if the pharmacokinetic parameters (A, B, α and β) are known.

9.2.2. Two-compartment extravascular model

In the case of the two-compartment extravascular model, only fraction f of the administered dose D will be absorbed in accordance with the rate of absorption (ka). The distribution into the central compartment takes place rapidly, whereas the drug distributes more slowly into the peripheral compartment. The elimination from both compartments is a first-order process. Fig. 9.8 shows a diagram of the two-compartment model after extravascular administration.

Figure 9.8. Schematic diagram of the twoadministration of a drug.

With the maximum concentration and a breakpoint in the curve, the plasma concentration vs. time profile has three different phases, i.e. an absorption phase, followed by a distribution phase and finally the elimination phase (Fig. 9.9).

Figure 9.9. Semilogarithmic plot of plasma drug concentration vs. time for a twocompartment extravascular model

D

α

ka, f (0<f<1)

Schematic diagram of the two-compartment open model for extravascular

With the maximum concentration and a breakpoint in the curve, the plasma concentration vs. ee different phases, i.e. an absorption phase, followed by a distribution

phase and finally the elimination phase (Fig. 9.9).

Semilogarithmic plot of plasma drug concentration vs. time for a twocompartment extravascular model.

k2

k1

k12 k21

peripheral compartment

Vd(p), cp(p)

central compartment

Vd(c), cp(c)

β

compartment open model for extravascular

With the maximum concentration and a breakpoint in the curve, the plasma concentration vs. ee different phases, i.e. an absorption phase, followed by a distribution

Semilogarithmic plot of plasma drug concentration vs. time for a two-

β

In the absorption phase of the curve, absorption is the dominating process and the distribution begins after the drug is given; the rate of elimination is negligible. In the second, distribution part, the absorption is complete, and distribution is the dominating process, while elimination also takes place. The last portion of the curve reflects the effect of elimination alone.

The equation of the curve therefore also has three terms, as follows:

) = )Q�R + )QYR − )QZR

) = � ∙ *�V∙- + � ∙ *�X∙- − )# ∙ *�+/∙-

The rate constants of the three subprocesses are determined by the method of residuals. The intercept of the back-extrapolated line on the elimination part is ln B and the slope of the line is the elimination hybrid constant:

W =�2 @ − �2 A

0A − 0@

For the calculation of constants A and α, let us suppose that c3 and c4 are actual measured concentrations on the plasma curve and c3' and c4' are extrapolated concentrations on the elimination line at time points t3 and t4, respectively. Concentrations only from the distribution phase (c3'' and c4'') are the differences between the measured and the extrapolated values, if the absorption is negligible:

)QYR = ) − )Q�R

t3: S′′ = S − S′

t4: T′′ = T − T′

The concentrations c3'' and c4'' at time points t3 and t4 specify the distribution line (Fig. 9.9, blue line), which has an intercept of ln A and a slope of the distribution hybrid constant (α):

� =�2Q S − S′R − lnQ T − T′R

0T − 0S

The constants cp0 and ka can be determined from the absorption phase of the curve. At time

points t5 and t6, the measured concentrations are c5 and c6, the extrapolated concentrations on the distribution line are c5' and c6'. Subtraction of the actual points from the extrapolated points yields the concentrations relating to only the absorption:

)QZR = )QYR − )

t5: [′′ = [′ − [

t6: \′′ = \′ − \

The line fitted to these points is the absorption line (Fig. 9.9, red line). The intercept of the line is ln cp

0 and the slope of the line is the absorption rate constant (ka):

�� =�2Q [′ − [R − lnQ \′ − \R

0[ − 0\

Determination of B, ke, A, ka and cp0 can be used to predict the resulting plasma drug

concentrations after an oral drug dose at any time point.

9.3. Two-compartment iv administration - Exercise

A woman (50 kg, 168 cm) was given a single intravenous dose of antiasthmatic drug at a doselevel of 4 mg/kg. Blood samples were taken at various time intervals and the plasma concentrations of the drug were determined. The following data were obtained:

Table 9.1.

Time (h) Concentration (mg/ll)

0.2 19.48

0.4 8.79

0.6 5.85

0.8 5.01

1.0 4.73

1.2 4.60

1.4 4.51

1.6 4.43

1.8 4.36

2.0 4.29

3.0 3.96

6.0 3.12

9.0 2.45

12.0 1.93

Use the data in Table 9.1 to plot the plasma concentration vs. time curve of the drug with the Phoenix software and answer the following questions.

1. How do you calculate the plasma concentration at any time? Give the equation.

) =

2. What are the values of the following parameters?

A = .............................. mg/l

B = .............................. mg/l

α = .............................. h-1

β = .............................. h-1

3. Calculate the plasma concentration at the following times.

cp at 20 min = ............. mg/l

value of distribution term = ......................... mg/l

value of elimination term = ......................... mg/l

cp at 10 h = ................. mg/l

value of distribution term = ......................... mg/l

value of elimination term = ......................... mg/l

Compare the values of the corresponding terms. What conclusion can you draw?

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

4. Calculate the value of )#.

)# = .......................... mg/l

5. How do you calculate the distribution and elimination half-lifetimes? Give the equations and the calculated values.

0@/A∝ =

0@/A∝ = ......... h

0@/AV =

0@/AV = ......... h

6. What percentage of the dose is lost in 26 h?

..................................

7. How long does 200 mg of drug produce the therapeutic effect?

..................................

8. How do you calculate the distribution volume? Give the equation and the calculated value.

"$ =

Vd = .......................... l

9. How do you calculate the total body clearance? Give the equation and the calculated value.

&�' =

ClT = ......................... l/h

What is the meaning of this parameter?

........................................................................................................................................

........................................................................................................................................

10. Check the values of the distribution microconstants (k12, k21) in the table of Secondary Parameters calculated with the Phoenix software and characterize the distribution process.

........................................................................................................................................

........................................................................................................................................

........................................................................................................................................

........................................................................................................................................

........................................................................................................................................

........................................................................................................................................

........................................................................................................................................

9.4. Questions

1. What is the definition of a pharmacokinetic compartment?

2. What is the definition of a central compartment?

3. What is the definition of a peripheral compartment?

4. What are the differences between a one- and a two-compartment model?

5. Characterize the one-compartment open model.

6. Characterize the two-compartment open model.

7. How can the plasma concentration be calculated at any time point in the case of the one-compartment extravascular model?

8. Draw the semilogarithmic plasma concentration vs. time curve of a drug described by the two-compartment intravascular model. Indicate the parameters on the graph and give the equations to calculate the pharmacokinetic parameters.

9. Calculate the plasma concentration of a drug 2 h after oral administration. The drug is characterized bythe one-compartment extravascular model. The pharmacokinetic parameters are:

A = 50.11 mg/l ka = 4.72 1/h

B = 18.62 mg/l ke = 0.40 1/h

10. 200 mg of theophylline is administered intravascularly. Calculate the time needed to reach the minimum effective concentration of the drug. The therapeutic range of the drug is 10 to 20 mg/ml. The pharmacokinetic parameters are:

A = 59.3 mg/ml α= 7.21 1/h

B = 5.1 mg/ml β= 0.09 1/h

10. AUC, physiological and bioavailability, equivalences

10.1. Determination of AUC value

The area under the blood concentration vs. time curve (AUC) is a very important pharmacokinetic parameter, and it is therefore a key challenge to determine its value.

The AUC reflects the actual body exposure to the drug after the administration of a dose. In other words, the AUC corresponds to the integral of the plasma concentration versus a definite interval of time. The precision of the AUC determination increases with the number of measurements of concentration. The unit of the AUC is h mg/l.

The AUC is directly proportional to the dose when the drug follows linear kinetics, and inversely proportional to the clearance of the drug (Fig. 10.1).

0 50 100 1500

10

20

30

40

Dose, mg

AU

C,

h m

g/l

A

0 5 10 15 200

20

40

60

80

Cl, l/h

AU

C,

h m

g/l

B

Figure 10.1. The changes in AUC as functions of dose (A) and clearance (B).

There are various options to determine the AUC value:

- planimetry (an old-fashioned method) - on the basis of weight (an old-fashioned method) - the trapezoid method - calculation of the integral of the plasma concentration versus a definite interval of time - on the basis of clearance

The following equations may be used to calculate the value of AUC in the different model systems:

For the one-compartment intravascular model:

�6&' = )��

For the one-compartment extravascular model:

�6&' =�

��−

�

��

For the two-compartment intravascular model:

�6&' =�

W+

�

�

For the two-compartment extravascular model:

�6&' =�

W+

�

�−

)��

10.1.1. Exercise 1

Calculate the AUC for drug A (dose: 250 mg) administered extravascularly

A. using the trapezoid method, B. on the basis of the calculation of ClT.

Table 10.1.

Time (h) Concentration (mg/l)

0.00 0.00

0.25 4.52

0.5 6.82

0.75 8.03

1.0 8.62

1.2 8.79

1.3 8.80

1.4 8.77

1.6 8.63

2.0 8.12

3.0 6.42

4.0 4.86

6.0 2.71

A. Trapezoid method

0 1 2 3 4 5 6 7 8 9 10 11 120

2

4

6

8

10

Time, h

Concentr

ation,

mg/l

Figure 10.2. AUC determination by the trapezoid method.

The area of a trapezoid is given by the following formula:

�-��)�_`8$ =Qa@ + aAR

2ℎ

where b1 and b2 are the lengths of the parallel sides, and h is the altitude.

Modify the above formula so that it applies to the blood concentration vs. time curve.

�-��)�_`8$ =

What is the shape of the first “trapezoid” if the drug was administered extravascularly!

........................................................

Give the formula with which to calculate the area of that first two-dimensional figure.

A =

With the help of Fig. 10.2, complete Table 10.2 and calculate the areas of the two-dimensional figures (AUCn – m)!

Table 10.2.

Side b1 Side b2 Altitude (h) AUCn – m

1.

2. 4.52 6.82 0.25 1.4175

3.

4.

5.

6.

7.

8.

9.

10.

11.

Ʃ

Figure 10.2 and Table 10.2 show that the blood concentration of kanamycin at the last time point is not zero. The sum of the areas of the trapezoids is therefore not equal with the total AUC value. The remaining area under the curve (AUCt-∞) can be calculated via the quotient of the last measured concentration and the elimination rate constant:

�6&-�c = ),-��

The elimination half-life of kanamycin is 2.50 h.

AUC12-∞ = ..........................

Finally, give the total AUC value.

AUCT = ..............................

B. Calculation of AUCT via the clearance

Using the earlier equation, calculate the AUCT of drug A.

Give the formula for the calculation of ClT.

ClT = ...................................

AUCT = ..............................

Compare the two determined AUCT values.

10.1.2. Exercise 2

How does the AUCT value change with increasing dose? Are there any changes in the values of the parameters listed in Table 10.4? To answer these questions, plot the blood concentration vs. time curve of drug A administered in two different doses, using the Pharsight Phoenix software. The time vs. concentration pairs are presented in Table 10.3.

Table 10.3.

Time, h 200 mg A 600 mg A

Concentration, mg/l

0.10 4.78 14.34

0.20 6.43 19.28

0.30 6.77 20.31

0.40 6.58 19.75

0.50 6.20 18.60

0.75 5.09 15.27

1.00 4.11 12.32

1.50 2.66 7.98

2.00 1.72 5.15

2.50 1.11 3.33

3.00 0.72 2.15

3.50 0.46 1.38

4.00 0.30 0.89

6.00 0.05 0.15

Table 10.4.

200 mg A 600 mg A units

ke

t1/2

tmax

cmax

AUCT

10.2. Calculation of physiological availability and bioavailability

10.2.1. Physiological availability

The physiological availability (PA) provides information (in %) about what proportion of a drug (in solution) given to the patient enters the systemic circulation. In cases of intravascular administration, this value is obviously 100%. In this method, drug solutions and not dosage forms are used, and the extent of absorption therefore depends exclusively on the physicochemical characteristics of the drug and the physiological parameters at the site of administration. The formula to calculate PA is

e� =�6&�f

�6&8f100

10.2.2. Bioavailability

The bioavailability (BA) of a drug is the proportion of the drug which enters the systemic circulation after administration of a given dosage forms. During the determination of BA we compare two or more pharmaceutical products containing the same API to find the optimum dosage form or to determine bioequivalence. If the reference route of administration is the intravascular route, the BA is called the absolute BA; if the administration is extravascular, then it is relative BA.

The formula to calculate absolute BA:

���g4 =�6&�f ∙ !8f

�6&8f ∙ !�f100

where AUCev is the AUC for the extravascularly administered dosage form; AUCiv is the AUC for the intravascularly administered dosage form; Dev is the dose of the investigated drug and Div is the dose of the reference drug.

The formula to calculate relative BA:

����E =�6&�f ∙ !��

�6&�� ∙ !�f100

where AUCev is the AUC of the investigated dosage form, AUCref is the AUC of the extravascularly administered reference dosage form, Dev is the dose of the investigated drug and Dref dose of the reference drug.

10.2.3. Exercise 3

a. Calculate the physiological availability of 200 mg of drug A (see Exercise 2). The 200 mg of intravascularly administered drug A has AUC = 12.91 h mg/l.

PA = .......................

b. Calculate the absolute bioavailability of tablet B (see the data in Table 10.5)!

BAabs = ...................

What conclusions can be drawn from this value?

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

c. Calculate the relative bioavailability of suppository B (see the data in Table 10.5)

BArel = ....................

What conclusion can be drawn from this value?

Table 10.5.

D, mg AUCT, h×mg/l

injection B 80 132.58

tablet B 240 92.34

suppository B 180 87.22

10.3. Equivalences

Chemical equivalence: Drug products are said to be chemically equivalent if they contain an identical active substance in identical dose and and identical dosing form manufactured in accordance with the prescription of a pharmacopoeia.

Pharmaceutical equivalence: Drug products are said to be pharmaceutically equivalent if they contain an identical active substance in an identical chemical form (same salt, ester, or chemical form), in an identical dosage form, but the basic excipients are not necesseraly absolutely identical, though they are identical in some features (purity, disintegration time, etc.), and they are optimized from a technological point of view.

Pharmaceutical alternatives: These are drug products that contain the same therapeutic moiety but as different salts, esters or complexes. For example, tetracycline phosphate and tetracycline hydrochloride each of which is equivalent to 250 mg tetracycline base are considered pharmaceutical alternatives.

Biological equivalence: Bioequivalent drug products are pharmaceutical equivalents that have similar bioavailability when given in the same molar dose and studied under identical experimental conditions.

Therapeutic equivalence: Therapeutic equivalents are drug products that contain the same therapeutically active drug and they give the same therapeutic effect and have equal potentials for adverse effects under the conditions specified in the labels of these drug products. Therapeutic drug products may differ in certain characteristics, such as colour, flavour, configuration, packaging and expiry date. Therapeutic equivalent drug products must be safe and effective, pharmaceutical equivalent, bioequivalent, adequately labelled and manufactured in compliance with current good manufacturing practices.

Therapeutic alternatives: There are drug products containing different active ingredients that are indicated for the same therapeutic or clinical objectives. Active ingredients in therapeutic alternatives are from the same pharmacologic class and are expected to have the same therapeutic effect when administered to patients for the same purpose. For example, ibuprofen may be given instead of aspirin; or cimetidin may be given instead of ranitidine.

10.4. Questions

1. What is the definition of AUC?

2. How can the area under the curve be determined?

3. How can AUCt→∞ be calculated after intravascular drug administration (one-compartment model)?

4. The physiological availability of an intramuscularly given drug is 100%. What does this mean?

5. The physiological availability of an orally administrered drug is 67%. What does this mean?

6. What is the definition of pharmaceutical equivalence?

7. How can absolute bioavailability be calculated?

8. What is the difference between physiological availability and bioavailability?

9. Can the AUC of an intravenously administered drug be calculated by using the following equation?

�6& = )#

��

Explain your answer.

10. How can the AUC be calculated if the total body clearance value is known?

11. Drug – drug interactions

If two or more drugs are coadministered, various situations can be occur:

1. there is no interaction between the different drugs, 2. the drugs interact and there is an increased effect: this phenomenon is known as

synergism, 3. the drugs interact and there is a decreased effect: this phenomenon is known as

antagonism.

Interactions of drugs can lead to stimulatory or inhibitory effects through pharmacokinetic or pharmacological processes. Drug interactions can be classified as follows:

1. Pharmacokinetic processes a. absorption b. distribution c. biotransformation d. excretion

2. Pharmacological processes a. synergism

i. additive ii. potentiating

b. antagonism i. chemical

1. acid–base reactions 2. complex formation 3. precipitation

ii. physiological iii. specific

1. competitive 2. non-competitive

a. irreversible b. allosteric

A detailed review of drug interactions is given in the lecture notes.

In the practical work you will study two specific classes of drug interactions: competitive antagonism and non-competitive antagonism.

11.1. Competitive antagonism

If an agonist drug and an antagonist drugs are able to bind to the same active site of the same receptor, they will compete with each other for the binding site. Since equilibrium develops, the final effect will depend on the Kd values of the agonist and the antagonist, and the ratio of the applied doses of these drugs. If the Kd values of the agonist and the antagonist are similar (the same order of magnitude), the intensity of the final effect will depend practically only on the ratio of the applied doses. If the effect of the agonist is determined in the presence and the absence of the competitive antagonist, it may be found that

a. the agonist induces a lower effect in the presence of the antagonist, b. if a sufficiently high concentration of the agonist is applied, the maximum effect can

be induced.

The semilogarithmic dose vs. response curves of the agonist alone or in the presence of the competitive antagonist are shown in Fig. 11.1. These curves allow the following conclusions:

a. the maximum effect (Emax) values are the same, b. the curve in the presence of the competitive antagonist is shifted to the right, i.e. the

ED50 value of the agonist is increased.

-9 -8 -7 -6 -50

20

40

60

80

100

120

140

160A B

log agonist concentration

Eff

ect

Figure 11.1. Semilogarithmic dose vs. response curves illustrating the phenomenon of competitive antagonism. A: the agonist alone, B: the agonist in the presence of a competitive antagonist drug (constant dose).

If a second competitive antagonist is added to the above agonist (in the same constant dose), the curves shown in Fig. 11.2 are obtained. From these curves, it can be conclude that both competitive antagonists inhibit the effect of agonist, and the new antagonist causes a greater shift to the right. This means that the second antagonist is more active competitive antagonist than the first one.

-9 -8 -7 -6 -5 -40

20

40

60

80

100

120

140

160

A B C

log agonist concentration

Eff

ect

Figure 11.2. The semilogarithmic dose vs. response curves illustrating the competitive antagonism in the cases of different antagonists. A: the agonist alone, B: the agonist in the presence of the first competitive antagonist drug, C: agonist in the presence of the second competitive antagonist.

Let us assume that the agonist always induces the same effect when it occupies the same number of binding sites. For example, to produce half of the maximum effect (E50) 50% of the receptors must be occupied by the agonist drug. The remaining 50% of the receptors can be empty or occupied by a competitive agonist. This can be described by the Schild-equation:

��′�

���− 1 =

���

�h

where [A’] is the concentration of the agonist A in the presence of competitive antagonist B, [A] is the concentration of the agonist in the absence of competitive antagonist B, and the KB is the equilibrium dissociation constant of B.

Since [A’] and [A] produce the same magnitude of response (e.g. E50), the equation can be rewritten:

�![#i′

�![#i − 1 =

���

�h

Rearranging the equation:

�h =���

�![#i′

�![#i − 1

=���

j − 1

where x = klmn

o′

klmno

Taking the log of both sides:

��A = ��� − log(j − 1)

where ��A = -log�h and ��� = -log [B]

pA2 is the negative logarithm to the base 10 of the dose or concentration of a competitive antagonist at which the ED50 value of the agonist is doubled; the pA2 is the affinity constant of the competitive antagonist.

The lower pA2 is, the more effective the competitive antagonist.

Examples of agonist – competitive antagonist – receptor triads:

• norepinephrine – prazosin – α1-adrenergic receptor • histamine – loratadine – histamine 1 receptor • progesterone – mifepristone (RU486) – progesterone receptor

11.1.1. Exercise 1

Determine the ED50 values of an agonist in the presence and absence of competitive antagonist drug at 0.01 µM using the Pharsight Phoenix software with the data in Table 11.1.

Calculate the pA2 value of the competitive antagonist.

Table 11.1.

[A], M E E’

1.0×10-8 5 2

3.0×10-8 30 3

5.0×10-8 45 12

7.0×10-8 60 18

1.0×10-7 75 30

3.0×10-7 110 74

5.0×10-7 120 92

7.0×10-7 130 110

1.0×10-6 135 120

3.0×10-6 140 135

5.0×10-6 145 140

1.0×10-5 145 143

1.5×10-5 - 145

2.0×10-5 - 146

ED50: ......................

ED’50: ....................

pAx: ........................

x: ............................

pD2: ........................

pA2: ........................

11.2. Non-competitive antagonism

In the case of non-competitive antagonism, there is no competition between the agonist and antagonist drugs.

a. The antagonist drug binds the same active site of the receptor as the agonist does, but the binding of the antagonist is irreversible or pseudoirreversible, and

b. the antagonist drug binds to an allosteric binding site.

The number of free receptors (which can bind the agonist) is decreased in both cases, and the maximum effect of the agonist (Emax) is therefore also lowered.

The semilogarithmic dose vs. response curves of the agonist alone or in the presence of the non-competitive antagonist are shown in Fig. 11.3. These curves allow the following conclusions:

a. in the presence of the non-competitive antagonist, Emax decreases, whereas b. the value of ED50 does not change.

-9 -8 -7 -6 -5 -40

20

40

60

80

100

120

140

160

A

B

log ED50

log agonist concentration

Eff

ect

Figure 11.3. Semilogarithmic dose vs. response curves illustrating the phenomenon of non-competitive antagonism. A: The agonist alone. B: The agonist in the presence of a non-competitive antagonist drug (constant dose).

If a second non-competitive antagonist is added to the same agonist (in the same constant) the curves shown in Fig. 11.4 are obtained. From these curves, it can be concluded that both non-competitive antagonists decrease the Emax value of the agonist, and the second antagonist is more potent than the first one.

-9 -8 -7 -6 -5 -40

20

40

60

80

100

120

140

160

A

B

C

log agonist concentration

Eff

ect

log ED50

Figure 11.4. The semilogarithmic dose vs. response curves illustrating the non-competitive antagonism in the case of different antagonists. A: The agonist alone. B: The agonist in the presence of the first non- competitive antagonist drug. C: The agonist in the presence of the second non- competitive antagonist.

Analogously as in the case of competitive antagonism, the affinity constant (�!A′ ) of non-

competitive antagonists is given by the following equation:

�!A′ = �!� − log(j − 1)

where x = Emax/E’max, and pDx is the negative logarithm of the dose of the non-competitive antagonist.

Be careful! Remember that pD’2 is NOT the same as pD2!

�!A′ is the negative logarithm to the base 10 of the dose or concentration of a non-competitive

antagonist at which the Emax value of the agonist is decreased by half; �!A′ is the affinity

constant of the non-competitive antagonist.

The lower �!A′ is, the more effective the non-competitive antagonist.

Examples of agonist – non-competitive antagonist – receptor triads:

• norepinephrine – phenoxybenzamine – α1-adrenergic receptor (irreversible binding) • glycine – strychnine – glycine receptor • nicotine – d-tubocurarine – nicotinic acetylcholine receptor

11.2.1. Exercise 2

Determine the ED50 values of an agonist in the presence and absence of a non-competitive antagonist drug B at 0.05 µM using the Pharsight Phoenix software with the data in Table 11.2.

Calculate the pA2 value of the competitive antagonist.

Table 11.2.

[A], M E E’

1.0×10-8 5 1

3.0×10-8 30 3

5.0×10-8 45 3

7.0×10-8 60 5

1.0×10-7 75 7

3.0×10-7 110 25

5.0×10-7 120 43

7.0×10-7 130 58

1.0×10-6 135 70

3.0×10-6 140 87

5.0×10-6 145 95

1.0×10-5 145 97

1.5×10-5 146 102

2.0×10-5 1146 101

pDx: ............

Emax: ...........

E’max: ..........

x: ................

pD2: ............

pD’2: ..........

11.3. Questions

1. Define pA2.

2. Verify the definition of pA2 by solving the equation to calculate its value.

3. What is competitive antagonism?

4. What types of pharmacokinetic interactions are there?

5. What is additive synergism?

6. Antagonist A has a �!A′ value of 3x10-7 M, while the �!A

′ of drug B is 2x10-8 M. Which drug is the more potent antagonist? What types of antagonists are A and B?

7. What is non-competitive antagonism?

8. The semilogarithmic dose vs. response curve of a drug in the presence of an antagonist (constant dose) is shifted to the right as compared with the dose vs. response curve of drug alone. What type of interaction is this? Are the values of Emax the same in the two cases?

9. How can be the affinity constant of a non-competitive antagonist calculated?

10. What is chemical antagonism?

12. Factors affecting drug actions

During medical treatment, many intraindividual variations may be observed as concerns therapeutic effects, side‒effects or toxic effects. The therapeutic effect of a drug (the absorption, the distribution and the elimination) can be modified by numerous factors:

• body weight and height (e.g. obesity)

• age (e.g. neonates or the elderly)

• gender

• pregnancy

• illnesses (e.g. kidney diseases, liver diseases or other diseases)

• genetic factors

• others (e.g. smoking, drug interactions or the extent of patient compliance)

12.1. Body weight and height

The apparent volume of distribution (Vd), the total body water volume (VTBW) and the volume of extracellular fluid (VECF) are directly proportional to the body weight. A higher Vd results in a lower drug concentration, which means that the body weight is inversely proportional to the pharmacon concentration.

12.2. Obesity

Table 12.1 illustrates the differences caused in the physiological and pharmacokinetic parameters by obesity.

Table 12.1. Differences caused in physiological and pharmacokinetic parameters by obesity.

Differences in physiological and

pharmacokinetic parameters Examples

A higher proportion of adipose tissue The higher Vd as a result of the long t1/2 of lipophilic pharmacons (e.g. phenytoin or diazepam) causes slower elimination

A higher volume of distribution A decreased drug (e.g. caffeine or theophylline) concentration

Increased elimination (increased GFR, RBF, ClT

or ClR) A shorter t1/2, when the elimination of pharmacons (e.g. cimetidine) becomes faster

Increased metabolism (an increased liver size, an enhanced liver circulation and conjugation reactions)

A shorter t1/2with a faster metabolism and faster inactivation

12.3. Age

Differences in pharmacokinetic parameters with changing age are shown in Table 12.2.

Table 12.2. Changes in pharmacokinetic parameters with age.

Pharmacokinetic

parameters Neonates, infants and children The elderly

Absorption • decreased in neonates

• absorption in children is similar to that in adults

• slow and incomplete

• delayed stomach movement

• decreased splanchnic circulation

• decreased production of gastric acid (hypoacidity)

Distribution • increased permeability of the skin, mucosa and blood‒brain barrier

• in neonates: decreased plasma albumin concentration (enhanced free fraction)

• increased rate of VECF and VTBW, decreased rate of intracellular fluid

• diminished adipose tissue

• decreased plasma albumin concentration (enhanced free fraction)

• decreased rate of VTBW

• enhanced rate of adipose tissue

• diminished rate of muscle weight

Metabolism

• decreased oxidation activity reaction after birth

• increased reduction and methylation after birth

• phase 1 enzymes exceed adult levels until the 6 months

• alcohol dehydrogenase exceeds the adult level until the 5 years

• decreased activity of glucuronidation in neonates (e.g. bilirubin-jaundice)

• increased sulfate conjugation in neonates

• diminished activity of liver enzymes

• decreased liver size and liver circulation

• phase 1 oxidation becomes slower

• conjugation reactions usually do not change

elimination • decreased GFR, RBF, tubular transport

• decreased kidney circulation

• decreased GFR

• decreased tubular secretion

• decreased number of functioning nephrons

In neonates, infants and children, dosing requirements are mainly defined by the body surface area (BSA) and the volume of the extracellular fluid (ECF), these two parameters are differing essentially from those in adults.

BSA is calculated as follows:

Mosteller equation:

�r�(sA) =tℎ*u�ℎ0( s) ∙ a�Mvw*u�ℎ0(��)

60

DuBois & DuBois equation:

�r�(sA) = 0.20247 ∙ ℎ*u�ℎ0#.xA[(s) ∙ a�Mvw*u�ℎ0#.TA[(��)

For calculation of doses in children, the BSA has been found to give more accurate correlation for dosing requirements than the body weight, because the correlation between the BSA and the cardiac output, the kidney or liver blood flow and the GFR is more strict and more precise.

The dose for children (ChD) can be calculated as follows:

&ℎ! = ℎu�M′y�r�(sA)PMz�0′y�r�(sA)

∙ PMz�0M�y*(s�MPvB )

The BSA of a 70 kg, 170 cm adult is 1.8 m2.

12.4. Gender

Differences in pharmacokinetic parameters with gender are presented in Table 12.3.

Table 12.3. Differences in pharmacokinetic parameters with gender.

Pharmacokinetic

parameters Females relative to males

Absorption • less

• lower production of gastric acid

• slower stomach movement

Distribution • lipophilic drugs: larger volume of distribution (longer duration)

• hydrophilic drugs: lower volume of distribution (shorter duration)

• lower muscle weight

• no difference in concentration of albumin

Metabolism • less microsomal liver enzymes (e.g. CYP3A), hence phase 2 metabolic reactions are slower

• slower conjugation reactions (e.g. glucuronidation, glycine conjugation)

• less alcohol dehydrogenase

Elimination • less

12.5. Pregnancy

Table 12.4 presents the differences in pharmacokinetic parameters during pregnancy.

Table 12.4. Differences in pharmacokinetic parameters during pregnancy.

Pharmacokinetic

parameters Differences during pregnancy

Absorption • slower stomach movement

• decreased production of gastric acid

• decreased intestinal motility

Distribution

• new volumes of body water

• increased apparent volume of distribution

• increased adipose tissue ratio

• decreased albumin concentration

Metabolism • increased phase 1 reactions

• decreased conjugation reactions

Elimination • enhanced GFR

• increased elimination

12.6. Illnesses

Table 12.5 shows the differences in pharmacokinetic parameters during different illnesses.

Table 12.5. Differences in pharmacokinetic parameters during different illnesses.

Illnesses Pharmacokinetic differences

Renal disease Depending on the degree of renal impairment (based on creatinine clearance): • lower renal clearance • prolonged t1/2

• lower elimination of drugs excreted via the kidney (e.g. aminoglycosides)

Liver disease • lower number and activity of metabolic enzymes (slower metabolism) • lower liver blood flow, less drug reaches the liver • diminished first‒pass effect • lower amount of bile acids, cholestasis can develop (lower elimination of drugs excreted via the bile acid e.g. rifampicin)

Cardiac failure • lower cardiac output • lower liver circulation • lower hepatic clearance (e.g. lidocaine, verapamil, propranolol)

Thyroid disease • hypothyroidism decreases metabolic activity; hyperthyroidism increases it

Burn injury • lower amount of blood plasma • lower amount of albumin • higher GFR

Gastrointestinal disease

• hypoacidity decreases the absorption of acidic pharmacons from the stomach

• the absorption and bacterial flora of the gut can change (e.g. decreased glucuronidase activity) during gastrointestinal diseases

Infections • the CYP 450 system is blocked by infuenza

12.7. Genetic factors

The biological and physiological response of the patient or the occurence of side‒effects during medical treatment can be determined by genetic features (e.g. enzyme polymorphism or receptor differences).

Examples:

• slow (mutant) or fast acetylation: in slow metabolizers, peripheral neuropathy can develop during isoniazide therapy

• extensive or slow metabolizers: in slow metabolizers, high dose of propafenone can cause a higher plasma concentration than expected

12.8. Other factors

Many other factors can influence the actions of a drug, e.g.

• smoking: - induces the isoenzyme CYP 1A2, which increases the metabolism of theophylline and decreases its duration - decreases the absorption of insulin via peripheral endothelial contraction, necessitating an increased dose of insulin

• nutrition: - a high‒fat diet increases the absorption of lipophilic pharmacons (e.g. phenytoin) from the gut - the consumption of grapefruit juice (which inhibits CYP 3A4) significantly increases the bioavailability of drugs metabolized with this enzyme (e.g. lovastatin and simvastatin)

• patient compliance: - during medical treatments, the patient should cooperate with the doctor and the pharmacist and observe the recommendations relating to the taking of medicine

12.9. Exercises - Dosage schedule in renal failure

During renal failure, renal elimination becomes slower, and the pharmacokinetic parameters of the drug are therefore changed. Information about renal impairment is very important in connection with drugs which have nephrotoxic side‒effects and which are excreted through the kidney (e.g. the aminoglycoside antibiotics: gentamycin and amikacin or the platinum derivatives: cisplatin and carboplatin). The doses of these drugs should be determined by the creatinine clearance or the GFR. To prevent accumulation, doses should be reduced and/or dosage intervals should last longer.

12.9.1. Determination of pharmacokinetic parameters

Calculate the pharmacokinetic parameters of pharmacon X and draw the blood plasma curve after administration of a single intramuscular dose (250 mg) by using the Phoenix WinNonlin software. After this dosage schedule, the measured plasma concentrations were as follows:

Time (h)

Plasma concentration (mg/ml) Amount of drug excreted in the urine (mg/h)

normal GFR decreased GFR normal GFR decreased GFR

0.1 9.76 10.12 3.21 0.63

0.3 11.14 12.36 5.82 1.22

0.5 11.98 12.68 10.03 4.85

0.75 12.21 13.02 21.91 12.11

1 11.65 12.54 33.18 20.06

2 9.17 11.12 74.31 49.81

3 6.84 9.68 100.49 87.98

4 5.24 8.36 123.72 109.25

6 3.82 6.87 152.18 131.19

9 2.24 5.23 194.87 156.66

12 0.36 4.23 238.13 197.88

ke = ....................................... 1/h

t1/2 = ...................................... h

AUCT = 41.71 (h mg/ml)

ClT = ..................................... l/h

Figure 12.1. The plasma curve of pharmacon X after administration of a single intramuscular dose.

Calculate the renal clearance value of drug X between 4 and 6 h according to the following equation:

&{| =j} ̅

where j} is the amount of excreted drug in the urine in unit time (mg/h) and ̅is the average plasma concentration of the drug during the given period (mg/ml).

ClR = ..................................... l/h

Finally, it may be concluded that pharmacon X has a short half-lifetime, and repeated doses are therefore required to maintain the therapeutic plasma level (4-13 mg/ml).

12.9.2. Determination of the maintenance dose

Calculate the maintenance dose of pharmacon X, which is able to maintain a steady-state plasma concentration of 6 mg/ml when it is administered four times a day.

! =&{' ∙ 44 ∙ 5

9

where 9 is the absorbed fraction (in this exercise f = 1).

D = ........................................ mg/ hours

12.9.3. Blood plasma curve for different renal functions

Ilustrate the blood plasma concentration of pharmacon X when the GFR is normal (7.5 l/h) or decreased (3 l/h) when X is administered four times a day. The timings are shown in the table below:

GFR = 7.5 l/h

(normal)

GFR = 3.0 l/h

(decreased)

Time (h) Plasma concentration (mg/ml) Plasma concentration (mg/ml)

0.5 8.73 9.03

3 5.47 7.03

6 1.87 4.98

6.5 10.23 13.25

9 6.32 10.89

12 2.76 8.11

12.5 11.96 15.26

15 7.11 12.54

18 2.74 9.23

18.5 12.57 17.65

21 8.45 13.69

24 2.75 9.68

24.5 12.54 19.02

27 8.47 14.21

30 2.75 9.88

30.5 12.56 19.36

33 8.46 14.83

36 2.75 10.11

36.5 12.55 19.43

39 8.43 14.86

42 2.76 10.15

42.5 12.55 19.46

45 8.44 14.87

48 2.75 10.21

Calculate the changed pharmacokinetic parameters due to the renal impairment (decreased GFR).

ke = .............................................1/h

t1/2 = ...........................................h

ClT = .......................................... l/h

ClR = .......................................... l/h

For the calculation, see the values in the table in exercise 1 (between 4 and 6 h).

Figure 12.2. The plasma curve of pharmacon X after its repeated administration in the case of normal GFR.

Figure 12.3. The plasma curve of pharmacon X after its repeated administration in the case of decreased GFR.

Calculate the maintenance dose of pharmacon X that is required in renal failure (GFR=3 l/h).

D = ........................................ mg/ hours

Illustrate the blood plasma curve of pharmacon X in a patient with renal impairment after administration of the modified dosage schedule (every 6 hours), if the required steady-state concentration is 6 mg/l.

The timings are shown in the table below:

Time (h) Plasma concentration (mg/ml)

GFR = 3.0 l/h

0.5 4.11

3 3.74

6 3.01

6.5 6.14

9 4.79

12 3.21

12.5 6.98

15 5.67

18 3.56

18.5 7.87

21 6.01

24 3.95

24.5 7.85

27 6.03

30 4.11

30.5 7.84

33 6.05

36 4.19

36.5 7.88

39 6.05

42 4.23

42.5 7.91

45 6.07

48 4.24

Figure 12.4. The plasma curve of pharmacon X after the administration of modified repeated doses in a patient with a renal impairment.

12.10. Dosage schedule in hepatic dysfunction

During a hepatic dysfunction, the drug metabolism becomes slower, and the pharmacokinetic parameters of the drug therefore change. Information about the hepatic dysfunction is very important in the cases of drugs with a hepatic metabolism and hepatotoxic side‒effects (e.g. paracetamol, methotrexate and isoniazide). To prevent the accumulation of drugs, doses should be reduced and/or dosage intervals should be made longer.

12.10.1. Determination of pharmacokinetic parameters

Calculate the pharmacokinetic parameters of pharmacon X and draw the blood plasma curve after a single orally administered dose (650 mg) by using Phoenix WinNonlin software (therapeutic range: 5-32 mg/ml). The blood plasma concentrations were measured as follows:

Time (h)

Plasma concentration (mg/ml) Amount of drug excreted in the urine (mg/h)

Normal hepatic

function Decreased hepatic

function Normal hepatic

function

Decreased hepatic

function

0.1 2.16 10.12 24.92 14.68

0.2 3.68 12.36 59.97 29.34

0.3 5.46 12.68 124.52 58.98

0.4 6.95 13.02 203.73 102.69

0.5 8.01 12.54 287.49 168.36

1 7.41 11.12 364.96 213.65

2 4.63 9.68 401.78 296.45

3 2.28 8.36 479.14 376.23

6 0.97 6.87 585.28 454.83

12 0.29 5.23 603.15 491.67

ke = ........................................ 1/h

t1/2 = ...................................... h

AUCT = 19.25 h mg/ml

tmax = ..................................... h

Vd = ....................................... l

ClT = ..................................... ml/h

Figure 12.5. The plasma curve of pharmacon X after oral administration of a single dose.

How long does the therapeutic plasma level persist in the patient after an oral dose (650 mg)?

....................................................................................................................................................

Calculate the amount of drug X metabolized in the liver during 6 h.

....................................................................................................................................................

12.10.2. Calculation of the maintenance dose

Calculate the maintenance dose of pharmacon X, which is able to maintain a steady-state plasma concentration of 10 mg/ml after its administration every 6 h for 48 h.

! =&{' ∙ 44 ∙ 5

9

where

9 is the absorbed fraction (in this exercise f = 1).

D = ........................................ mg/ hours

Draw the blood plasma curve of the patient after the calculated dosage schedule (normal elimination rate of the liver = 1)! The timings are shown in the table below:

Time (h) Plasma concentration (mg/ml)

normal hepatic function

Plasma concentration (mg/ml)

decreased hepatic function

0.8 17.69 24.67

3 12.45 19.47

6 4.12 13.65

6.8 22.36 35.68

9 13.87 31.02

12 4.98 24.36

12.8 24.65 45.23

15 15.89 37.24

18 5.68 30.21

18.8 26.31 50.13

21 16.23 43.99

24 5.71 36.89

24.8 26.47 56.38

27 16.26 47.87

30 5.72 41.21

30.8 26.48 60.35

33 16.27 53.11

36 5.73 42.56

36.8 26.47 64.87

39 16.28 55.43

42 5.72 45.32

42.8 26.47 67.11

45 16.28 57.96

48 5.74 46.03

Figure 12.6. The plasma curve of pharmacon X after repeated doses in the case of normal hepatic function.

12.10.3. Determination of the maintenance dose for a patient with a hepatic dysfunction

Draw the blood plasma curve of pharmacon X in the case of a decreased hepatic function (elimination rate of the liver = 0.4) after the dosage schedule given in exercise 2. To draw the plasma curve, use the values in the table in exercise 2.

Figure 12.7. The plasma curve of pharmacon X after repeated doses in the case of decreased hepatic function.

Determine the changed pharmacokinetic parameters due to the hepatic dysfunction (a decreased elimination rate).

ke = ........................................ 1/h

t1/2 = ...................................... h

AUCT = ................................. h mg/ml

ClT = ..................................... ml/h

Vd = ....................................... l

Calculate the maintenance dose of pharmacon X required in the case of a hepatic dysfunction.

D = ........................................ mg/ hours

Draw the blood plasma curve of a patient with hepatic failure after the modified dosage schedule (every 6 h), if the required steady-state concentration is 10 mg/l. The timings are shown in the table below:

Time (h) Plasma concentration (mg/ml)

decreased hepatic function

0.8 8.13

3 6.45

6 4.93

6.8 12.43

9 10.42

12 6.71

12.8 14.56

15 12.43

18 7.65

18.8 15.36

21 12.46

24 8.11

24.8 15.42

27 12.49

30 8.13

30.8 15.46

33 12.54

36 8.16

36.8 15.45

39 12.53

42 8.21

42.8 15.42

45 12.55

48 8.22

Figure 12.8. The blood plasma curve of pharmacon X after modified repeated doses in a patient with a hepatic dysfunction.

12.11. Dosage schedule in children and the elderly

In children and elderly patients, an inaccurate dosage may cause accumulation because of the different pharmacokinetic parameters. This is very important in the case of drugs with narrow therapeutic range (e.g. theophyllin, digoxin or tacrolimus).

12.11.1. Determination of pharmacokinetic parameters

Calculate the pharmacokinetic parameters of pharmacon X and draw the plasma curve after oral administration of a single dose (0.25 mg) by using Phoenix WinNonlin software. The therapeutic range of pharmacon X is 0.8-2.5 ng/ml. After this dosage schedule, the following plasma concentrations were measured:

Time (h) Plasma concentration (ng/ml)

0.05 0.66

0.1 1.07

0.15 1.36

0.2 1.57

0.3 1.69

0.4 1.76

0.5 1.80

0.6 1.83

1 1.72

2 1.49

3 1.27

6 0.97

12 0.46

24 0.27

48 0.19

72 0.12

96 0.09

120 0.05

144 0.03

β = ........................................ 1/h

t1/2 = ...................................... h

AUCT = ................................. h ng/ml

ClT = ..................................... l/h

Vd = ....................................... l

Figure 12.9. The plasma curve of pharmacon X after oral administration of a single dose.

Figure 12.10. The absorption part of the plasma curve of pharmacon X after oral administration of a single dose.

After exercise 1, it is clear that pharmacon X has a long half-lifetime, but the plasma concentration decreases very quickly after administration of a single dose, and repeated doses are therefore required.

12.11.2. Calculation of the maintenance dose

Calculate the maintenance dose of pharmacon X, which is able to maintain a steady-state plasma concentration of 1.55 ng/ml.

! =&{' ∙ 44 ∙ 5

9

where 9 is the absorbed fraction (in this exercise f = 0.7).

D = ........................................ mg/ hours

Draw the plasma curve with the above‒calculated maintenance dose. The following plasma concentrations were measured:

Time (h) Plasma concentration (ng/ml)

0.5 1.19

6 0.96

12 0.72

24 0.38

24.5 1.51

36 0.91

48 0.49

48.5 1.61

60 1.03

72 0.51

72.5 1.69

84 1.15

96 0.53

96.5 1.75

108 1.22

120 0.54

120.5 1.82

132 1.32

144 0.55

Figure 12.11. The plasma curve of pharmacon X after repeated doses.

After exercise 2, we know that the time needed to reach the therapeutic range of pharmacon X is too long. To reach the therapeutic plasma level as soon as possible, a loading dose is needed.

12.11.3. Application of the loading dose

On the first day of the therapy, 0.20 mg of drug X is administered every 8 h to the patient as an orally administered loading dose. Draw the plasma curve with the modified dosage scedule. Use the following time and concentration values:

Time (h) Plasma concentration (ng/ml)

0.5 1.11

4 0.75

8 0.46

8.5 1.49

12 1.09

16 0.76

16.5 1.85

20 1.38

24 1.07

24.5 2.56

28 2.01

36 1.72

48 1.24

48.5 2.61

54 1.97

60 1.75

72 1.27

72.5 2.63

84 1.74

96 1.26

96.5 2.65

108 1.74

120 1.28

120.5 2.66

132 1.76

144 1.28

Figure 12.12. The plasma curve of pharmacon X after the loading doses and subsequent repeated doses.

12.11.4. A repeated dosing regimen for the elderly

Using the same dosage schedule, use the Phoenix WinNonlin software to draw the plasma curve in the case of a 78-year-old patient with a weight of 72 kg and a height of 173 cm. What can be observed?

Time (h) Plasma concentration (ng/ml)

(elderly patient)

0.5 1.49

4 1.03

8 0.76

8.5 2.64

12 1.51

16 1.03

16.5 2.76

20 1.85

24 1.35

24.5 3.97

28 3.41

36 2.76

48 1.70

48.5 3.99

54 3.57

60 2.81

72 1.72

72.5 4.02

84 2.83

96 1.75

96.5 4.05

108 2.87

120 1.76

120.5 4.08

132 2.86

144 1.74

Figure 12.13. The plasma curve of pharmacon X after the loading doses and subsequent repeated doses in an elderly patient.

Modify the earlier loading and maintenance doses; reduce both of them by 45%. Draw the plasma curve with the modified doses. What can be observed?

Dloading = ................................ mg

Dmaintenance = .......................... mg

Figure 12.14. The plasma curve of pharmacon X after loading and maintenance doses reduced by 45% in an elderly patient.

12.11.5. A repeated dosing regimen for children

Prepare the dosage schedule of drug X for a 2-year-old child with a body weight of 13.1 kg and a BSA of 0.52 m2. (The previous dosing schedule was for a patient with a body weight of 70 kg and a BSA of 1.8 m2.) Modify the loading and the maintenance doses by taking into account the body weight and the BSA and draw the plasma curve by using Phoenix WinNonlin software. Which calculation gives the better result?

&ℎ! =a�Mvw*u�ℎ0�9 ℎu�Ma�Mvw*u�ℎ0�9PMz�0

∙ PMz�0M�y*

&ℎ! =a�Mvyz�9P *�9 ℎu�Ma�Mvyz�9P *�9PMz�0

∙ PMz�0M�y*

Adult dose ChD modified by body weight ChD modified by BSA

Loading dose

Maintenance dose

Figure 12.15. The plasma curve of pharmacon X used in children on the basis of adult doses.

Figure 12.16. The plasma curve of pharmacon X used in children on the basis of the body weight modification.

Figure 12.17. The plasma curve of pharmacon X used in children on the basis of the BSA modification.

12.12. Questions

1. How can the pharmacokinetics of lipophilic drugs be influenced by obesity (a higher proportion of adipose tissue)?

2. How can the absorption of pharmacons be influenced by old age? How can the pharmacokinetic parameters be changed?

3. Choose the correct answers. (multiple choices)

A. In neonates, the activity of oxidation is lower than that of in adults. B. The levels of phase 1 enzymes exceed those in adults until the 2nd year. C. In neonates, the level of sulfate conjugation is lower. D. In neonates, the glucuronidation is lower. E. The level of alcohol dehydrogenase exceeds that in adults until the 5th year.

4. Calculate the dose of theophylline for a child (2 years old, 87 cm tall, 12.7 kg), if the dose for an adult (70 kg, 170 cm) is 250 mg/day.

5. Give two examples of metabolic differences caused by gender.

6. How can the distribution of drugs be influenced during pregnancy?

7. Choose the true answers. (multiple choices)

A. The degree of renal impairment can be determined via the creatinine clearance. B. The elimination half-life times of drugs that are excreted via the kidneys are lower,

and the elimination is therefore faster. C. The GFR never changes. D. The elimination of drugs that are excreted via the kidneys is diminished in the case

of renal disease. E. Depending on the degree of renal impairment, the plasma concentrations of some

pharmacons can be increased. 8. Give an example of how the pharmacokinetics of a drug can be influenced by the velocity

of acetylation.

9. Give two examples of how the pharmacokinetics of drugs can be influenced by smoking.

10. How can the absorption of lipophilic drugs from the gut be influenced by a high‒fat diet?

13. Nonlinear pharmacokinetics

The pharmacokinetic processes discussed so far follow firstorder elimination, for example,the rate of elimination also increases, i.e., the amount of drug eliminated over a given time changes, but the fraction of drug that is eliminated remains constant. For firstthe elimination rate constant ((ClT) remain constant even when the dose is changed. The plasma concentration and increase proportionally as the dose increases (Fig. 13.1, blue line). 95clinical situations are eliminated by firstfirst-order processes are known as linear or dose

Figure 13.1. The dose dependence of

For some drugs, however, the relationships between the drug dose and the plasma concentration and AUCT are not linear. As the drug dose is increased, the peak concentration and the resulting AUCT do not increase propordrugs are therefore said to follow non(i.e. the pharmacokinetics changes with the dose given). Nonto saturation of one of the pharmacokinetic processes in which enzymes or carrier molecules take part: absorption, protein binding, the hepatic metabolism or active renal transport of the drug. Many drugs exhibit mixedpharmacokinetics at low drug concentrations, but switch to zeroconcentrations. This usually occurs in the case of overdosing, but for some drugs dosedependent kinetics is also typical at therapeutic concentrations.

If the absorption of a drug is a saturable process, then above a certain concentration at the absorption site, there will be no further increase in the rate of absorption due to the sauration of the carrier molecules. The plasma concentration and the bioavailability of the drug therefore decrease disproportionately less relative to the increase of the dose. For example, the

Nonlinear pharmacokinetics

The pharmacokinetic processes discussed so far follow first-order kinetics.order elimination, for example, as the dose and the plasma concentration of the drug increase, the rate of elimination also increases, i.e., the amount of drug eliminated over a given time changes, but the fraction of drug that is eliminated remains constant. For firstthe elimination rate constant (ke), the volume of distribution (Vd) and the total body clearance

) remain constant even when the dose is changed. The plasma concentration and increase proportionally as the dose increases (Fig. 13.1, blue line). 95% of the drugs used in clinical situations are eliminated by first-order kinetics in therapeutic doses. In pharmacology,

order processes are known as linear or dose-independent processes.

The dose dependence of css and AUCT for linear and non-linear kinetics

For some drugs, however, the relationships between the drug dose and the plasma are not linear. As the drug dose is increased, the peak concentration

do not increase proportionally (Fig. 13.1, red and green lines). Such drugs are therefore said to follow non-linear, zero-order, or dose-dependent pharmacokinetics (i.e. the pharmacokinetics changes with the dose given). Non-linear pharmacokinetics is due

f the pharmacokinetic processes in which enzymes or carrier molecules take part: absorption, protein binding, the hepatic metabolism or active renal transport of the drug. Many drugs exhibit mixed-order pharmacokinetics, displaying first

tics at low drug concentrations, but switch to zero-order kinetics at high concentrations. This usually occurs in the case of overdosing, but for some drugs dosedependent kinetics is also typical at therapeutic concentrations.

is a saturable process, then above a certain concentration at the absorption site, there will be no further increase in the rate of absorption due to the sauration of the carrier molecules. The plasma concentration and the bioavailability of the drug

efore decrease disproportionately less relative to the increase of the dose. For example, the

In the case of first-as the dose and the plasma concentration of the drug increase,

the rate of elimination also increases, i.e., the amount of drug eliminated over a given time changes, but the fraction of drug that is eliminated remains constant. For first-order processes,

) and the total body clearance ) remain constant even when the dose is changed. The plasma concentration and AUCT

% of the drugs used in order kinetics in therapeutic doses. In pharmacology,

linear kinetics.

For some drugs, however, the relationships between the drug dose and the plasma are not linear. As the drug dose is increased, the peak concentration

tionally (Fig. 13.1, red and green lines). Such dependent pharmacokinetics

linear pharmacokinetics is due f the pharmacokinetic processes in which enzymes or carrier molecules

take part: absorption, protein binding, the hepatic metabolism or active renal transport of the order pharmacokinetics, displaying first-order

order kinetics at high concentrations. This usually occurs in the case of overdosing, but for some drugs dose-

is a saturable process, then above a certain concentration at the absorption site, there will be no further increase in the rate of absorption due to the sauration of the carrier molecules. The plasma concentration and the bioavailability of the drug

efore decrease disproportionately less relative to the increase of the dose. For example, the

absorption of amoxicillin by active and facilitated transport from the gastrointestinal tract is a saturable process.

If the plasma protein binding or active renal reabsorption is saturable, then above a certain dose the protein binding or the drug rebasorption in the renal tubules tends to reach the maximum capacity. This leads to a disproportionate increase in the rate of elimination with increasing doses, while AUCT decreases to a lower extent than directly proportional. As an example, the plasma protein binding of dizopyramide is saturable at therapeutic concentrations, which leads to a disproportionate increase in the volume of distribution with increasing dose.

When the hepatic metabolism or renal secretion of a drug is saturable, the rate of elimination tends to reach the maximum capacity and there is no further increase in elimination with increasing dose. The drug clearance therefore decreases and the bioavailability of the drug increases more than proportionally way. The active secretion of dicloxacillin and the hepatic metabolism of ethanol, phenytoin or acetylsalicylic acid are saturable processes.

13.1. Michaelis–Menten kinetics

Saturable processes, and mainly metabolic processes may be quantified by Michaelis–Menten kinetics. The system describes the relationship of an enzyme to the substrate (in this case, the drug molecule). The basic equation of the enzyme-catalysed reaction is:

� + r ⇌ �r → e + �

The enzyme (E) and the substrate (S) form an enzyme-substrate complex (ES), in a reversible step. The complex ES then dissociates to a product (P), and the enzyme is regenerated. The product formation is a quick and irreversible step.

The velocity of the reaction is equal to the rate of drug concentration decline in unit time:

� =M�r�M0

=�����r��� + �r�

where vmax is the maximum velocity of the system, i.e. the maximum rate of drug metabolism, or the maximum amount of drug that can be eliminated in the given time period [mg/h], KM is the Michaelis–Menten constant [mg/l] and [S] is the substrate concentration [mg/l].

The exact concentration of the drug at the site of the metabolism is usually not known. However, since the blood circulation carries the drug to this site, it is reasonable to assume that [S] is equal to the drug concentration in the plasma [cp], which is readily measured by taking blood samples. The Michaelis–Menten equation can therefore be written as follows:

� =M�r�M0

=M )M0

=���� ∙ )�� + )

If the drug concentrations are plotted against the velocity of the system, the curve will be a typical saturation curve (Fig. 13.2).

Figure 13.2. Plot of substrate concentration vs. the velocity of the system

The velocity first increases in proportion to the increasing substrate concentrations. The rate of increase in the velocity then slows down until a maximum velocity is reached, limited by the enzyme concentration. At the maximum velocity (present in enzyme–substrate complexes; the capacity of the enzyme is saturated.

The Michaelis–Menten equation can be rearranged to give an equation that expresses the drug concentration at 50% of vmax. Thus, if

After rearrangement:

The Michaelis–Menten constant is the drug concentration at which the rate of elimination is half of vmax. In simplified terms, metabolism is presumable.

When the substrate concentration is low, simplifies to:

�

Plot of substrate concentration vs. the velocity of the system.

in proportion to the increasing substrate concentrations. The rate of increase in the velocity then slows down until a maximum velocity is reached, limited by the enzyme concentration. At the maximum velocity (vmax), every single enzyme

substrate complexes; the capacity of the enzyme is saturated.

Menten equation can be rearranged to give an equation that expresses the drug . Thus, if vmax = 2 and v = 1, the following equation is obtai

1 =2 ∙ )

�� + )

�� + ) = 2 ∙ )

�� = )

Menten constant is the drug concentration at which the rate of elimination is . In simplified terms, KM is the concentration above which saturation of the drug

When the substrate concentration is low, cp << KM, and the Michaelis

� =���� ∙ )

��

=����

��

∙ ) = �′ ∙ )

in proportion to the increasing substrate concentrations. The rate of increase in the velocity then slows down until a maximum velocity is reached, limited by

enzyme molecule is substrate complexes; the capacity of the enzyme is saturated.

Menten equation can be rearranged to give an equation that expresses the drug = 1, the following equation is obtained:

Menten constant is the drug concentration at which the rate of elimination is is the concentration above which saturation of the drug

, and the Michaelis–Menten equation

Since vmax and KM are constants, their quotient (k') is also constant. At low plasma concentrations of the drug, therefore the velocity of the metabolism is directly proportional to the plasma drug concentration and can be described as a first-order process. The therapeutic doses of most drugs remain below KM and the elimination of such drugs follows first-order kinetics.

If the plasma drug concentration is high so that cp >> KM, the rate of metabolism becomes:

� =���� ∙ )

)= ����

In other words, the velocity has reached the maximum that the available enzyme molecules can handle; the enzyme system is saturated. The rate of metabolism is independent of the drug concentration; this is a characteristic of a zero-order process. This means any additional drug in the plasma (e.g. as a result of a higher dose) will not be metabolized until more enzyme molecules become available. Such a situation can result in the accumulation of drug and higher plasma concentrations than expected. The concentration of ethanol responsible for the pharmacologic effect is appreciably higher than its KM value, and the metabolism of ethanol is therefore a first-order process. Phenytoin is an example of a drug that switches the order of its kinetics at therapeutic concentrations.

For drugs that have saturable elimination, maintenance doses can be predicted through the following equation:

! = ����

LL

LL + ��

5

where css is the steady-state concentration of the drug [mg/l].

For dose predictions, it is necessary to estimate vmax and KM. Without computers, the curve fitting of hyperbolic plots would be difficult, and would resulted in inaccurate determinations of vmax and KM. To overcome this difficulty, several transformations of the Michaelis–Menten equation have been made in order to linearize the curve fitting and permit the graphical determination of the kinetic parameters.

The Lineweaver–Burk or double reciprocal plot is a common transfomation. This is produced by taking the reciprocals of both sides of the Michaelis–Menten equation:

1

�=

�� + )

���� ∙ )=

��

����

∙1

)+

1

����

A plotting of @

f against

@

�� produces a straight line, with a y-intercept equivalent to

@

f�/� and

and a slope of ��

f�/� (Fig. 13.3). The method has the disadvantage that it gives a non-uniform

distribution of data points; the less precisely determined points are those obtained at low values of cp, whereas the more accurate points are obtained at high values of cp and this leads to inaccurate line fitting.

Figure 13.3. Lineweaver–Burk plotting method.

A more accurate linear plotting method is the Hanes–Woolf (or Hanes–Langmuir) method. The equation here is obtained by multiplying the reciprocal form of the Michaelis–Menten equation by cp:

)

�=

��

����

+1

����

∙ )

A plot of ��

f against cp will yield a straight line. The intercept of the line on the y-axis is

��

f�/�

and the slope of the line is @

f�/�. This eliminates some of the previously mentioned errors

because the method provides a more uniform distribution of data points (Fig. 13.4).

Figure 13.4. Hanes–Woolf plotting method.

1/v

1/Cp

cp/v

cp

Nowadays, however, computer programs are available for the non-linear regression of the data, and these are significantly more accurate than the graphical methods.

13.2. Computer simulation

Many drugs exhibit mixed-order pharmacokinetics, displaying first-order pharmacokinetics at low drug concentrations and zero-order pharmacokinetics at high concentrations. It is important to know the drug concentration at which a drug switches from first- to zero-order. In these cases, the elimination of the drug deviates from the expected behaviour and the pharmacokinetic parameters cannot be applied to calculate the multidose schedule. A model that has been used to describe the kinetics of saturable elimination, known as Michaelis–Menten kinetics, allows the prediction of doses for multiple administration.

Drug X is taken as an example of a drug that participates in saturable elimination.

13.2.1. Calculation of pharmacokinetic parameters

Examine the plasma concentration and the kinetic parameters of drug X, after the oral doses of 100 mg, 400 mg and 1000 mg.

Record the values in the table.

Kinetic parameter Dose of drug X

100 mg 400 mg 1000 mg

ke (1/h)

t½ (h)

AUCT (h mg/l)

ClT (l/h)

ClR (l/h)

What is the difference between the shapes of the curves?

How does the elimination half-life of drug X change with increasing dose?

What relation exists between the AUCT values and increasing doses?

How does the total clearaence of the drug change?

How does the renal clearance of the drug change with increasing dose?

How can you explain the results?

13.2.2. Planning of the dosage for a multiple regimen on the assumption of first order kinetics

Calculate the repeated daily oral dose of drug X required to maintain a plasma concentration of 15 mg/l during 6 days. Use the kinetic parameters calculated for a single oral dose of 400 mg.

D = .............................. mg/24 h

Draw the plasma curve with the help of the WinNonlin software. Calculate the corresponding time points to produce an adequate plasma curve.

Observe the therapeutic range of drug X:

minimum effective concentration: ................... mg/l

maximum tolerated concentration: ................... mg/l

What do you think about the dosing calculated according to first-order elimination?

13.2.3. Calculation of a repeated dose by Michaelis–Menten kinetics

This type of elimination requires a different dose calculation from that for first-order elimination.

The parameters for the dose calculation:

vmax = 18 mg/h

KM = 5.7 mg/l

css = 15 mg/l

For prediction of the maintenance dose, use the following equation:

! = ���� ∙ 44

44 + ��∙ 5

D = .............................. mg/24 h

Plot the plasma curve of drug X for 6 days using the maintenance dose calculated according to Michaelis–Menten kinetics.

What do you think about the therapy?

13.2.4. Administration of the loading dose

It is necessary to reach the desired 15 mg/ml plasma level as quickly as possible because of the long half-life of the drug. The patient is given 600 mg of drug X in two portions during the first day of the therapy, and the treatment is then followed by the maintenance dose calculated in section 13.2.3.

Modify the time points according to the dosing interval of the loading doses.

Draw the plasma curve again in this case and give your opinion about the therapy with the loading doses.

13.3. Questions

1. What does the first-order elimination mean?

2. How do the pharmacokinetic parameters (t½, ke, Vd, ClT) change with increasing dose in the case of first-order elimination?

3. How do the AUCT and the css change with increasing dose in the case of first-order elimination?

4. What does the zero-order elimination mean?

5. How does the css change with increasing dose in the case of zero-order elimination?

6. How does the AUCT change with insreasing dose in the case of saturable hepatic metabolism?

7. What are the reasons of the non-linear kinetics?

8. What is the Michaelis–Menten constant?

9. Explain how the velocity of enzyme-catalysed reaction changes at high substrate concentrations (cp >> KM).

10. What methods do you know for the graphical determination of KM and vmax? Which is the more accurate method and why?

14. A brief review of Phoenix WinNonlin software – The basic user manual

From 2015 our institute will use the Certara Phoenix platform to analyse pharmacokinetic (PK) and pharmacodynamic (PD) data for educational purposes.

Phoenix WinNonlin (WNL) is one of the most popular pharmacokinetic software packages; it is a part of the Certara Phoenix platform. As stated by Certara, WNL is the industry standard for PK/PD modelling and simulation, non-compartmental analysis and bioequivalence analysis.

The Certara Phoenix platform is a very complex software package, and a detailed description of it is beyond the scope of this publication. Our aim is merely to describe the basic features of WNL that are required in your practical work.

In this guide, we analyse data, relating to the intravenous administration of a single dose of a drug.

14.1. Start a new project

Projects contain all the imported binary objects and all the operational objects that are used to perform an analysis. Two of the benefits of Phoenix projects are that they allow the analysis work to be easily organized and saved. Users can save projects as Phoenix project files (*.phxproj). The Phoenix project contains the following items:

– Data folder, for worksheets – Code folder (not used in this course) – BQL rules (not used in this course) – Documents folder (not used in this course) – Workflow object, for operational objects (models)

1. Start the Phoenix platform from the Windows Start menu, choose the Pharsight folder and click on the Phoenix icon. Alternatively, the software can be started from the desktop by clicking on the Phoenix icon.

2. Create a new project from the File menu (File/New Project) or press Ctrl+N, and then name the project to Test project (Fig. 14.1.). The saved file name of the project is automatically the name of the project. The left panel contains the folders discussed above.

Figure 14.1. Creating a new project.

14.2. Create data tables

We usually perform pharmacokinetic analyses, and concentration, time and dose specification is therefore required. The data are stored in worksheets in Data folder.

1. To create a new worksheet, click (right mouse button) on the the Data folder, and then choose New option, and next Worksheet (Fig. 14.2.).

Figure 14.2. Creating a new worksheet.

2. Name the worksheet (e.g. dose) as your project requires. Usually you need two worksheets in a PK study: one for the dose and one for the time vs. concentration pairs.

3. Create another worksheet, repeating step 2, and name it concentration.

14.3. Complete the data tables – adding the columns

1. Click on the dose worksheet, and then check the lower part of the right panel. Here you can find the specifications of the worksheet columns.

2. Under the Columns field, click on the Add button to create the first column of your worksheet. Choose the type of the column (numerical or text), name it (dose) and then click the OK button (Fig. 14.3.). Next specify the unit of the dose, which is usually mg. Repeat this step to create the time column and the unit (Fig. 14.4.). If you give appropriate names for the columns the software later associates the setup fields with the proper columns. For example, the time column may be named time, and the concentration concentration and not cc.

Figure 14.3. Name the columns in the worksheet.

Figure 14.4. Specifying units of columns.

14.4. Complete the data tables – adding the missing data

When your data are stored in an MS Excel file or a text file, you can copy and paste them into your worksheets. If not, you can click on a cell of the worksheet and write in the data one by one (Fig. 14.5.). Do NOT use a comma (,) to separate decimal numbers. In the dose worksheet, two cells must be filled; the dose, which is the amount of the drug, and the time when the dose was given. In the case of a single dose administration, the time is zero (0).

Figure 14.5. Filling in the worksheets with time and concentration data.

DO NOT FORGET TO SAVE YOUR PROJECT, because there is no autosave function in

Phoenix.

14.5. Choose and set up your PK model

The next step is to choose an appropriate model for your data.

1. After saving your project, click on the Workflow folder (right click), then choose New menu next WNL Classic Modeling and finally click on the PK Model option.

2. Name your model (e.g. single dose iv).

3. The right panel is changed. The upper part contains the Setup, Results and Verification tabs and related fields. The lower panel consists of five different tabs: Model Selection, Weighting/Dosing Options, Parameter Options, Engine Settings and Plots.

4. First, in the Model Selection tab, choose your model: number 1, IV Bolus (Fig. 14.6.). On the left side of this panel, the compartment model and the equation of the plasma concentration vs. time function can be seen.

Figure 14.6. Model Selection tab.

5. Setup tab (upper panel). The right-side panel contains four different folders: Main,

Dosing, Internal Estimates, and Units. The right-side panel of the Setup tab changes when the folders are chosen.

a. When the Main folder is active, the data involved in the analysis can be specified. There are four icons (Fig. 14.7.). The first is the “Select source” function. Click on it and choose the “concentration” worksheet. If your columns are named correctly the appropriate association has been done (Fig. 14.8.). Otherwise, you have to choose the column that contains time data and concentration data.

Figure 14.7. Icons of the Main folder.

Figure 14.8. Automatic data association.

b. After saving your project, click on the Dosing folder, and then repeat step “a”.

c. In this model, the Initial Estimates and Units folders should not be modified.

6. The Weighting/Dosing Options, Parameter Options and Engine Settings options rarely

change during our course. If it is required, the project description will mention it.

7. In the last tab (Plots) you can choose the plots that must be generated by the software.

14.6. Run the analysis

When the set up has been completed, there is a possibility to verify your setting. In the first icon row (Fig. 14.9.), the fourth icon from the right is the Verify icon. If the model is misconfigured, a popup window sends a message and the verification notes can be read in the Verification tab (besides the Results tab).

Figure 14.9. Position of the Verification icon.

After verification, the chosen model can be executed by clicking on the icon to the right-hand side of the verification icon. When the analysis has been completed, the results are summarized under the Results tab.

There are three folders under the Results tab: Output Data, Plots and Text Output. Check the Final Parameters and Secondary Parameters tables for calculated values of the elimination rate constant, the volume of distribution, AUC, MRT, etc.

In the Plots folder, you can see the chosen plots. The blood concentration vs. time curve is represented in the “Observed Y and Predicted Y” figure (Fig. 14.10.).

Figure 14.10. Blood concentration vs. time curve fitted by the chosen model.

DO NOT FORGET TO SAVE YOUR PROJECT!