Ph d iPharmacodynamicsPharmacokinetic - PharmacodynamicPharmacokinetic Pharmacodynamic

modeling

Peter De PaepeHeymans Institute of Pharmacology

Dose effect

Pharmocokinetic processesPharmocokinetic processes

Resorption

Tissues BiotransformationFree

Bound

Bile

UrineExcretion

PharmacodynamicsPharmacodynamics

PharmacodynamicsPharmacodynamics1. Emax-model

Emax Ce

EC50 + CeE =

50

E : effectE : maximum effectEmax : maximum effect Ce : biophase concentrationEC50 : biophase concentration

required to produce 50% of Emax (potency)

Unbound concentration of propranolol, mg/L Unbound concentration of propranolol, mg/L

(Lalonde et al J Pharmacokin Biopharm 1987; 15: 569)(Lalonde et al, J Pharmacokin Biopharm 1987; 15: 569)

2. Sigmoid Emax-modelg max

Emax Cen

EC50n + CenE = n : shape factor

EC50 + Ce

Sigmoid Emax model

(Laurijssens & Greenblatt Clin Pharmacol Ther 1989; 45: 356)(Laurijssens & Greenblatt, Clin Pharmacol Ther 1989; 45: 356)

3. Linear model E CCe < EC50

E C

Emax Ce

EC50 + CeE =

Emax Ce

EC50E = = SCe Linear relationship :

plasma concentration

Linear model

(Holford et al Br J Clin Pharmacol 1981; 11: 187)(Holford et al, Br J Clin Pharmacol 1981; 11: 187)

4. Log-linear modelg

E = S log Ce

log CEffect compartment concentration (mg 1-1) of oxazepam

(Dingemanse et al, Br J Pharmacol 1990; 99: 53-58)

Concentration(C)-effect(E) relationship

Region 1 : Cp < EC20E declines exponentially C declines exponentiallyC declines exponentially Linear relationship between E and C

Region 2 : EC20 < Cp < EC80E d li li lE declines linearlyC declines exponentially Linear relationship between E and logClogC

Region 3 : Cp > EC80E remains almost constant and

i lmaximalC declines exponentially Little influence of C on E

M th d lMethodology

• Measurement of plasma concentrations in function of timefunction of time

• Measurement of effect in function of timeMeasurement of effect in function of time (surrogate effects)

• PK-PD modeling

Comparison of potency and efficacy between different benzodiazepinesComparison of potency and efficacy between different benzodiazepines

(Mandema et al., J Pharmacol Exp Ther 1991; 257: 472)

Pl ( /L)Plasma conc. (mg/L)

Why studying "concentration-effect relationships"?

• Better understanding of factors influencing drug effect:• Better understanding of factors influencing drug effect:‣ Formation of active metabolites‣ Development of acute tolerance‣ Influence of illnesses

• Scientific explanation for TDMp• Development of concentration-time profiles to achieve

the desired time course of effect• Potential in vivo measure for the sensitivity to a drug

Pharmacokinetic-pharmacodynamic modelingPharmacokinetic pharmacodynamic modeling (PK/PD modeling)

Direct link models• Measured plasma concentrations

are directly related to the effectare directly related to the effect-site concentrations

• Rapid equilibration between bothRapid equilibration between both concentrations

• Measured plasma concentrations can be used in the pharmacodynamic model

• No hysteresis• No hysteresis

Indirect link modelsIndirect link models• A temporary shift is observed

between the time course of the l t ti d thplasma concentrations and the

time course of the effect (mostly due to a slow distribution to the effect site)effect-site)

• Sometimes distribution of the drug to the effect-site parallels the distribution to a peripheral compartment; concentrations of this compartment can be used in h h d i d lthe pharmacodynamic model

• Sometimes an effect compartment is used

Direct effect versus indirect effect• Direct effect : The effect is determined by the concentration

t th ff t it ith t l ti h iat the effect-site without a lag time; a change in concentration is immediately followed by a change in effect. Indirect effect : The effect can be the result of different• Indirect effect : The effect can be the result of different processes from which only one is influenced by the drug (e.g. where the production or degradation of a mediator is ( g p ginvolved). In these circumstances there is no direct relationship between concentration and effect.

(Clin Pharmacol Ther 1969; 10: 22-35)

DD DaysDays

Time course of the effectTime course of the effectA. Plasma and biophase in the same compartment

E S l C I l C E – IE = S logC + I (log-linear model) logC = E IS

k tk

⇒

logC = logCo ke t2.303

k tE I E I

C=C0.e-kt ⇒

ke t2.303

E – IS

Eo – IS= ⇒

E = Eo S ke t2.303⇒

I fl f d d T½ th d ti f th ff tInfluence of dose and T½ on the duration of the effect

lnCeff = lnCo - keteff

Co = D/Vd

lnCeff = ln(D/Vd ) - keteff⇒o d

keteff = ln(D/Vd) - lnCeff

t = 1ln

D/Vd

⇔

⇔ teff = keln Ceff

ke = 0.693/T½

⇔

teff = 1.44 T½ ln ( )DVdCeff

⇔d eff

Succinylcholine (0 5 mg/kg IV)Succinylcholine (0.5 mg/kg, IV)

Time course of the effectTime course of the effect B. Biophase in tissue compartment

Time course of the effect

• Shift of the effect-time curve with regard to the plasma concentration-

Time course of the effect C. Plasma and biophase in different compartments

g ptime curve: slow equilibration between plasma concentration and biophase concentration

• Relationship between plasma concentration and effect: counterclockwise hysteresis loop

Tetrahydrocannabinol

(Chiang and Barnett, Clin Pharmacol Ther 1984; 36: 234)

Effect-compartmentp

Concept• The time course of the effect can be used to determine the time

f h ff (bi h ) i Fcourse of the effect compartment (biophase) concentration. From this, the distribution rate to the effect compartment can be calculated

• The central compartment of the pharmacokinetic model is linked to the effect compartment (K1e)

Effect-compartment (cont.)p ( )

Concept• Negligible amounts of drug distribute to the effect compartment;

therefore the subsequent loss of this negligible mass from the effecttherefore the subsequent loss of this negligible mass from the effect compartment is conveniently be taken to be to the outside rather than back into the systemK is a first order rate constant controlling the loss of drug from the• Ke0 is a first-order rate constant controlling the loss of drug from the effect compartment and controls the equilibration time between plasma concentration and effect

• If the plasma concentration immediately increases from zero to a steady-state concentration C, than the effect will increaseto a steady state concentration C, than the effect will increase proportionally to the biophase concentration until equilibration is reached between plasma and biophase concentration

• If the uptake and loss of drug from the effect compartment is t ll d b t diff t fi t d t t t (K K ) thcontrolled by two different first-order rate constants (K1e en Ke0), than

the rate by which the effect increases to steady-state is determined by the rate constant controlling the loss of drug from the effect compartment (K ) (analogous to IV infusion: steady state after 4 timescompartment (Ke0) (analogous to IV infusion: steady-state after 4 times T½, dependent on Ke)

• The time needed to reach 50% of the effect at steady-state is the yequilibration T½ for the effect and is determined by 0.693/Ke0 (T½ke0: half-life for equilibration between plasma and biophase)

T½ke0 is determined by :T½ke0 is determined by :

• Perfusion of the biophase• Diffusion in the biophase• Time needed to interact with the receptorsp• Time needed to generate a receptor mediated responsemediated response

One compartmental model with IV bolusOne compartmental model with IV bolus

Central compartment Effect compartment

Rate of change in the amount of drug (Ae) in het effect compartment :dA = k1eA1 – ke0Ae (1)dAedt

Ae en A1 = amount of drug in effect and central compartmente 1 g p

K1e en Ke0 = first-order rate constants

Ae = (e-ket – e )-ke0tk1eDk k

(2)ke0 – ke

Dividing by Ve, the volume of the effect compartmentk DCe = (e-ket – e )k1eD

Ve (ke0 – ke)-ke0t

(3)

At steady state :At steady state : k1eA1 = ke0Ae (4)

(5)k1eV1C1 = ke0VeCe

V1 = distribution volume of central compartment

If K = C /C1 (K = partition coefficient between plasma en effect-siteIf Kp Ce/C1 (Kp partition coefficient between plasma en effect site concentration at equilibrium)

k1eV1K kVe = (6)Kpke0e ( )

Substitution of (6) in (3) :

k DKCe = (e – e )ke0DKpV1 (ke0 – ke)

-ke0t (7)-ket

k DC(8)ke0D

V1 (ke0 – ke)-ke0t-ket= (e – e )Ce

Kp

(9)E = Emax Ce/KpEC50 + Ce/Kp

This equation is fitted to the effect versus time data from which ke0, EC50 and Emax can be determined

Lorazepam

LLorazepam

SWAY OPENSWAY OPEN

T½ (Ke,o) hr 0.52 + 0.03( , )

EC50 (ng/ml) 32.2 + 11.2

N 6.2 + 0.7

Emax 416 + 36.1

Factors influencing pharmacodynamic effects

1 T l1. Tolerance

2. Active metabolites

3. Stereoisomers

4. Interactions

5 Age5. Age

…

1. Tolerance1. ToleranceEffect decreases with time (clockwise hysteresis loop)( y p)Examples: cocaïne, nicotine, nitroglycerine

(Van Dyke et al, Science 1978; 200:211)

2. Active metabolites2. Active metabolites

Oral IV

Higher concentrations of active metabolite after oral administration

(Coltart & Shand, BMJ 1970; 3: 731)

metabolite after oral administration

3 Stereoselectivity3. Stereoselectivity• Difference in pharmacodynamics

and pharmacokinetics between enantiomers

• Concentration-effect relationships using total (racemic) concentrations may lead to wrong conclusions

• Example: Verapamil p pConcentration-effect relationship dependent on the route of administration Active enantiomer exhibits lower bioavailability compared to the less active enantiomer

(Eichelbaum et al, Klin Wochenschr 1980; 58: 919)

4 Interactions4. InteractionsExample: Flumazenil (antagonist) and midazolam (agonist)

o midazolam 10 mg/kgmidazolam 10 mg/kg +flumazenil 1 mg/kg/hr

5. AgeExample: Thiopental

pent

al

p p

Thi

op

(Homer & Stanski, Anesthesiology 1985; 62: 714)