pharmacoparameters

Pharmacokinetic Parameters

BLOOD LEVEL DATA(1G Propanamide via IV bolus)

Time (mins) Conc.(mg/100ml)log 10 8.6

20 7.530 6.560 4.280 3.2100 2.4120 1.8

1. Plot the log conc vs time on a semi-log graphing paper.2. Plot the conc vs time on an ordinary graphing paper.3. Plot the log conc vs time on an ordinary graphing paper.

• Is the drug eliminated by zero order kinetics or first order kinetics?

Time of collection (hrs)

Drug A (ug/mL) Drug B (ug/mL)

1 2000 2000

2 1500 1000

3 1000 500

4 500 250

5 0 125

6 0 63

7 0 31

• Which drug is eliminated by first-order kinetics? Which one is zero-order kinetics?

• Which one is concentration-dependent and which one is concentration-independent?

• The rate of a chemical reaction or pharmacokinetic process is the velocity with which it occurs

• The order of a reaction is the way in which the concentration of a drug in a chemical reaction affects the rate

Zero-order reaction

• Drug conc. changes with respect to time at a constant rate

dC/dt = -ko

C = -kot + Co

ko = zero-order rate constant (conc./time)

First-order reaction

• Change in drug conc. with respect to time equals the product rate constant and the concentration of drug remaining

dC/dt = -kC

k = first-order rate constant (reciprocal time)

Integration yields:

C = Coe-kt

ln C = -kt + ln Co

log C = -kt/2.3 + log Co

How did we get the equation?

Biologic half-life (t1/2)

• Time required for the concentration of a drug to decrease by one half

• Formula:

t ½ =

• Half-life is a constant and is related to the first-order rate constant

Biologic half-life (t1/2)

• Unit: mins., sec., hrs.

Elimination rate constant (k or kel)

• Drug elimination is a first-order kinetic process

• Sum of the rate constants for removal of the drug from the body, including the rate constants for renal excretion and metabolism (biotransformation)


• Not affected by the route of administration• Affected by physiologic or pathologic

conditions of the patient (e.g. liver failure, age)


• Formula:

kel = ke + km

ke = rate constant for renal excretion; km =

rate constant for metabolism

kel =

• Unit: reciprocal time (sec-1, mins-1, hrs.-1)

Drug distribution

• Reversible transfer of drug from one location to another within the body

• Most drugs do not distribute uniformly throughout the body

Apparent Volume of Distribution (Vd)

• Hypothetical volume of body fluid in which the drug is dissolved

• Not a true anatomic or physical volume• Is needed to estimate the amount of drug

in the body relative to concentration of drug in the plasma


• Formula:

Vd x Cp = Ab

Vd = apparent volume of distribution (L, mL)

Cp = plasma drug concentration (mg/mL, ug/mL)

Ab = amount of drug in the body (mg, g)


• Reflects the amount of drug in the tissues, not in the plasma

• Inversely proportional in relation to the drug plasma concentration

• Unit: volume (mL, L)


• To calculate the Vd after intravenous bolus injection

Vd = Ab/Cp

Ab = dose of drug given by intravenous bolus (g, mg)

Cp = extrapolated drug concentration at zero time on the y-axis, after the drug equilibrates (ug/mL, mg/mL)


• Influenced by:1. binding affinity of a drug for blood or tissue elements2. blood flow (i.e., delivery of drug to the tissues)3. ability to cross biomembranes4. physicochemical properties (lipophilicity, extent of ionization, pH, pka) that determine partitioning to tissues


• Influenced by:

5. Body weight of the patient

Importance of Vd• Directly proportional to the half-life

prolongs the half-life ___________ duration of action ??

• Used for the computation of the loading dose of a drug

• Determine or predict the distribution of drugs (is it predominantly in the plasma or in the body tissues?)

• Compare the distribution characteristics of various drugs


• A drug which is more bound to plasma proteins than tissue proteins will ___ Cp and ___ Vd

• A drug which has a high affinity for adipose tissues than plasma proteins will ___ Cp and ___ Vd

• Vd of a lipophilic drug is large in an obese patient

Total body clearance (ClT, CL)

• Irreversible removal of drug from the body by an organ of elimination

• Units are flow volume per time (mL/min, L/hr)

• Defined as the volume of blood irreversibly cleared of drug per unit of time

• Influenced by pathologic conditions and age of the patient


• Product of blood flow to the organ (Q) and extraction ratio (ER) of that organ

CL organ = Q x ER• Extraction ratio – fraction of drug that is

irreversibly removed by an organ or tissue as the plasma-containing drug perfuses that tissue


• Drug elimination rate divided by the plasma concentration

ClT = rate of drug elimination

plasma concentration

= dDe/dt

CpdDe/dt = rate of drug elimination (mg/min, g/hr)

Cp = drug plasma conc. (mg/mL)


• According to the concept of clearance, the body contains an apparent volume distribution in which a drug is dissolved (Vd) and a constant portion of this is cleared or removed from the body per unit time (kel or ke)

ClT =


ClT = FDo

AUC

F= absolute bioavailability

Do = amount of drug administered (mg, g)

AUC = area under the curve, rate and extent of drug absorbed in the systemic circulation (mg.hr/mL)

Total body clearance (ClT, CL)• Sum of all clearances of the body

CLT = CLR + CLNR

CLT = total body clearance

CLR = renal clearance

CLNR = non-renal clearance is often equated to hepatic clearance (CLH)

• It is always assumed that the drug is eliminated/cleared by first-order kinetics


• In relation to biologic half-life

ClT = keVd

ClT = 0.693Vd

t 1/2

t ½ = 0.693Vd

ClT

Total body clearance (ClT, CL) is influenced by:

• Body surface area/ body weight• Cardiac output• Drug-drug interactions (renal or hepatic)• Extraction ratio/ blood flow• Genetics• Plasma protein binding• Hepatic and renal function

Importance of ClT

• Computation of the maintenance dose• Determine or predict the duration of action

of a drug good or bad outcome

What is the relationship between…

_____ ClT = _____ t 1/2 = _____ Vd

____ Cp = _____ Vd

Problem Solving

• Following the IV administration of a drug, a patient weighing 70 kg was found to have 70,000 mcg/mL of drug present in the blood. Assuming apparent volume of distribution is 10% of BW, elimination rate constant is 0.231/hr and following first-order kinetics, calculate the plasma conc. after 4 hours. What is the half-life of the drug?

• Immediately after an IV dose of 5 mg, the apparent volume of distribution of chlordiazepoxide has been determined to be 34 liters. Calculate the expected drug plasma concentration of the drug in microgram per milliliter.

• One gram of procainamide was administered to a 75 kg male patient. The initial drug activity after plotting a blood-drug profile was found to be 7.7 mg/L. When the maximum amount in blood is reduced by 26%, what is the corresponding amount in the body?

Are you ready?

• A 50 kg woman was given a single IV dose of an antibacterial drug at a dose level of 6 mg/kg. Blood samples were taken at various time intervals. The concentration of the drug (Cp) was determined in the plasma fraction of each blood sample and the following data were obtained:

t (hr) Cp (ug/mL)

0.25 8.21

0.5 7.87

1.0 7.23

3.0 5.15

6.0 3.09

12.0 1.11

18.0 0.40

• What are the values for Vd, kel, and t ½ for this drug?

• This antibacterial agent is not effective at a plasma concentration of less than 2 ug/mL. What is the duration of activity for this drug?

• A 70 kg volunteer is given an intravenous dose of an antibiotic, and serum conc. were determined at 2 and 5 hr after administration. The concentration were 1.2 and 0.3 ug/mL, respectively. What is the biologic half-life for this drug, assuming first-order kinetics?

• A new drug was given in a single intravenous dose of 200 mg to an 80 kg male. After 6 hrs. the blood concentration of drug was found to be 1.5 mg/100 mL of blood. Assuming that the apparent Vd is 10% of body weight, compute the total amount of drug in the body fluids after 6 hours. What is the half-life of this drug?

• Penicillin has a total body clearance of 15 mL/min. Calculate the elimination rate for penicillin when the plasma drug conc. Is 2 ug/mL and when it reaches 10 ug/mL.

• Determine the total body clearance for a drug in a 70 kg male patient. The drug follows the kinetics of a one-compartment model and has an elimination half-life of 3 hours with an apparent volume of distribution of 100 mL/kg.

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