e-book_basic concepts of pharmacokinetics

7/31/2019 E-Book_Basic Concepts of Pharmacokinetics

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Gent, 24 August 2007/avpeer1

Basic Conceptsof Pharmacokinetics

Achiel Van Peer, Ph.D.Clinical Pharmacology


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Some introductory Examples


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15 mg of Drug X in a slow release OROS capsuleadministered in fasting en fed conditions

in comparison to 15 mg in solution fasting


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Prediction of drug plasma concentrations

before the first dose in a humanNOAEL in female rat

NOAEL in male rat

NOAEL in female dog

NOAEL in male dog

First dose 5 mgFabs 100%Fabs 50%Fabs 20%


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Allometric Scaling


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Pharmacokinetics:Time Profile of Drug Amounts

Drug at absorption site

Drug in body

Metabolites

Excreted drug

Time (arbitrary units)

Per

centofdose

Row land and Tozer,Clin ical Pharmacokinet ics: Concepts and Applicat ions, 3rd Ed. 1995


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Definition of Pharmacokinetics ?

Pharmacokinetics is the science describing drug

absorption from the administration sitedistribution to tissues,

target sites of desired and/or undesired activity

metabolism

excretion

PK= ADME


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We will cover

Some introductory Examples

Model-independent ApproachCompartmental Approaches

Drug Distribution and Elimination

Multiple-Dose Pharmacokinetics

Drug Absorption and Oral Bioavailability

Role of Pharmacokinetics


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Cmax, Tmax and AUC inBioavailability and Bioequivalence Studies

Absolute bioavailability (Fabs) compares the amount in the systemic circulation

after intravenous (reference) and extravascular (usually oral) dosing

Fabs = AUCpo/AUCiv for the same dose

between 0 and 100% (occasionally >100%)

Relative bioavailability (Frel) compares one drug product (e.g. tablet)

relative to another drug product (solution)

Bioequivalence (BE): a particular FrelTwo drug products with the same absorption rate (Cmax, Tmax)

and the same extent (AUC) of absorption(90% confidence intervals for Frel between 80-125%)


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Absolute oral bioavailability

flunarizine, J&J data on file

Other example: nebivolol:

10% in extensive metabolisers; 100% in poor metabolisers


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Area under the curve

)12).(2

21(AUC t2-t1 ttCC +=

Trapezoidal rule: divide the plasma concentration-time profileto several trapezoids, and add the AUCs of these trapezoids

Conc

Time

z

ClastlatedAUCextrapo

=

0

0

Units, e.g. ng.h/mL


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Elimination half-life ?

Half- l i fe (t 1/ 2) : t ime the drug concent rationneeds

to decrease by 50%


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visual inspection


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visual inspection or alternatives ?

Half- l i fe ( t 1/ 2) : t ime to decrease by 50%

T1/ 2 = 6 hrs

Derived from

a semi log plot

T1/ 2 = 0.693/ z


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From Whole-Body PhysiologicallybasedPharmacokinetics to CompartmentalModels

Poggesi et al., Nerviano Medical Science


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Compartmental Approach

One-compart ment PK model

Bodycompartment

DrugAbsorption

Drug Elim inat ion

drug distributes very rapidly to all tissuesvia the systemic circulation

an equilibrium is rapidly established between the bloodand the tissues, the body behaves like

one (lumped) compartment

does not mean that the concentrations in the differenttissues are the same


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One compartment behaviourmore often observed after oral drug intake

1

10

100

1000

0 8 16 24 32 40 48

Time, hours

Poor metabolisers

Extensive metabolisers


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Intravenous dose of 0.2 mg Levocabastine(J&J data on file)


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Depending on rate of equilibration with

the systemic circulation, lumping tissues together,and simplification is possible

Mult i-Tissue or Mult i-CompartmentWhole Body Pharm acokinet ic model

Tri-compart ment model

Tw o-compart ment model

One-compart ment model


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Zero-order rate drug administrationand first-order rate drug elimination

I nfusion ratemg/ m in

Rat e of eliminat ion isproport ional t o

the Amount

in blood/ plasma

dDose/ dt = Ko = mg/ min

dA/ dt = -k.A

Amount Ain blood, plasma

[ Oft en K= Kel= K10]


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First-order rate of drug disappearance

Intravenousbolus

Amount A[ or Concent rat ion C]

in blood, plasma

Rate of eliminat ionis proport ional t o

the Amount or

Concent rat ion inblood, plasma

dA/ dt = -k.A = -k.Vd.C

If A = Amount in plasma, then V= Plasma volume

If A = Remaining amount in the body, thenVd= Total volume of distribution


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A single iv dose of 5 mgfor a drug with immediate equilibration

(one compartment behaviour)

dC/dt = -k10.C

dA/dt = -k10.A = -k10.V.C

dA/dt = -k10.A = -CL.C

C = C0. e-k10.t


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A single iv dose of 5 mg

C = C0 e-k10.t

lnC = lnC0 - k10.t

Remark for log10

scale:slope = k10/2.303


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ln C = lnC0 - k10.t

12693.0

122ln1ln10

ttttCCk

=

=

C2= half ofC1

Slope= k10= the elimination rat e constant

Half-l ife =

0.693/ k10


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Vd = volume of dist r ibut ion,

relates t he drug concent rat ion

t o the drug amountin t he body

LmLng

ng9.30

/162

5000000

Cpo

doseVd ===


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One-Compartment modelafter intravenous administration

Vd = volume of dist r ibut ion,

relat es t he drug concent rat ion at a part icular t ime

t o the drug amount in the body at t hat t ime

k10= ( f irst -order) el imination rate const ant

Clearance (CL) = Vd.K10

The volume of drug in t he body cleared per unit t ime

Half- l ife = 0.693 . Vd/ CL

Compartmental Approach


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Compartmental Approachafter intravenous dosing

Rapidly equilibrat ing t issues:plasma, red blood cells, liver , kidney,

Slow er equilibrating:

adipose t issues, muscle,

Usually peripheral compart ment

Slow ly redist ribu t ion reason

for long t erm inal half- l i f e

Elimination

Distribution

Re-distribution

Centralcompartment

Peripheralcompartment


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Intravenous dose of 0.2 mg levocabastine

V1 = 44 L V2 = 35 L

K12= 0.84 h-1

K21= 1.05 h-

1

K10 = 0.4 h-1


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V1 = 44 L V2 = 35 L

Cld= k12.V1= 36.7 L/ h

Cld= k21.V2= 36.7 L/ h

Cl= K10 .V1= Dose/ AUC= 1.77 L/ h= 30 mL/ min

Vdss = V1 + V2


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Rates of drug exchange

DAp/dt = - K10.Vc.Cp - K12.Vc.Cp + K21.Vt.Ct

DAt/dt = K12.Vc.Cp - k12.Vt.Ct

Initially very fast decay due to distribution to tissues andelimination (distribution phase) until equilibrium is

reached (influx into and efflux from tissue is equal)

After a pseudo-equilibrium is reached, there is only loss ofdrug from the body (elimination phase), but is in fact

combination of redistribution from tissues and elimination

Rate of redistribution may differ significantly across drugs;long terminal half-life is compounds sticks somewhere


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Cp= A.e- .t+ B.e- .t

Cp= 2.1.e-1.91 .t+ 2.5.e- 0.0224.t

h

h

tt term 31

10224.0

693.02/12/1 =

=0.693

==

Vd = CL/=Dose/(AUC. )=Vdarea


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Two-compartmental model

Central

Compartment

Vc

Peripheral

CompartmentVt

K10

K12

K21

K10, K12, K21 are f irst order rate const ants

hybrid first-order rate constants and for the so-calleddistribution phase and elimination phases, T1/2 and T1/2

Vc, Vdss, Vd or Vdarea are Vd of

cent ral compartment , at steady-state, dur ing eliminat ion phase

Compartmental approach


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Compartmental approachafter intravenous dosing

Centralcompartment

Shallow Peripheralcompartment

Deep Peripheralcompartment

Compartments serveas reservoirs with different drug amounts (concentrations),

different volumes, anddifferent rates of exchange of drug with the central compartment.

The shape of the plasma concentration-time profile

empirically defines the number of compartmentsl


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IntravenousSufentanil

Gepts et al., Anest hesiology,83:1194-1204, 1995

Three compartmental model


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Three compartmental modelSufentanil Pharmacokinetics

Gepts et al., Anest hesiology, 83:1194-1204, 1995

Mixed-effects Population PK analysis(N =23)

PopulationAverage

CV (%)

Volume of distribution (L)Central (V1) 14.6 22

Rapidly equilibrating (V2) 66 31

Slowly equilibrating (V3) 608 76At steady-state 689

Clearance (L/min)

Systemic (CL or CL1) 0.88 23

Rapid distribution (CL2) 1.7 48

Slow distribution (CL3) 0.67 78

Three compartmental model


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Three compartmental modelSufentanil Pharmacokinetics

Gepts et al., Anest hesiology, 83:1194-1204, 1995

FractionalCoefficients

Rate constants(min-1)

A 0.94 K10 0.06

B 0.058 K12 0.11

C 0.0048 K13 0.05

K21 0.025

K31 0.0011

Exponents (min-1) Half-lives (min)

0.24 t1/2 2.9

0.012 t1/2 59

0.0006 t1/2 1129

Compartmental approach


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Compartmental approachafter intravenous dosing

Centralcompartment

Shallow Peripheralcompartment

Central

compartment

Deep Peripheralcompartment

Peripheral

compartment

Ef fect sit e


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Shafer and Varvel,Anesthesiology 74:53-63, 1991

Time profile of opioid concentrationsin plasma and the predicted

concentrations at the effect sitebased upon an effect compartment

PK-PD model

(expressed as percentage of theinitial plasma concentration)

Effect site concentration profilereflect difference

in onset time of analgesia


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Rate of Drug Distribution

perfusion-limitedtissue distribution

immediate equilibrium of drug in blood and in

tissue only limited by blood flow

highly perfused : liver, kidneys, lung, brain

poorly perfused : skin, fat, bone, muscle

Permeability rate limitations or membrane barriers

blood-brain barrier (BBB)

blood-testis barrier (BTB)

placenta


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Unbound Fraction and Drug Disposition

Plasma Tissue

Protein-bound

drug

Protein-bound

drug

Free drug

(non-ionized)

Free drug

(non-ionized)

Ionized drug(free)

Ionized drug(free)

Cellmembrane

Receptor-bounddrug

Pka-pH, affinity for plasma and tissue proteins,permeability,

Ph i h i PK d EEG PD


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Physicochemistry, PK and EEG PDof narcotic analgesics

Alfen tan il F en tan yl S u fen tan il

pK a 6.5 8 .43 8.01

% u n io n ized at p H 7 .4 89 8 10

P o ct/w ater 130 810 1750

% u n b o u n d in p lasm a 8 16 8

V d ss (L ) 23 358 541

C l (L /m in ) 0 .20 0.62 1.2

t1 /2 keo E E G (m in ) 1 .1 6 .6 6 .2

C e50, E E G (ng /m l) 520 8.1 0 .68

C e50, u n b (ng /m l) 41 1.2 0 .05 1

K i (n g /m l) 7 .9 0 .54 0.039

Shafer SL, Varvel JR: Pharmacokinetics, pharmacodynamics, and rational opioid selection.Anesthesiology 1991; 74:53-63; DR Stanski, J Mandema (diverse papers)

Localisation and Role of Drug Transporters


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Localisation and Role of Drug TransportersZhang et al., FDA web site and Mol. Pharmaceutics 3, 62-69, 2006

Apparent Volume


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Apparent Volumeof Distribution

Vd = Amount of drug inbody/concentration in plasma

Minimum Vd for any drug is ~3L, theplasma volume in an adult, for ethanol:equal to body water

For most basic drugs very high due to

sequestering in specific organs (liver,muscle, fat, etc.)

Row land and Tozer,Clin ical Pharmacokinet ics: Concepts and Applicat ions,

3rd

Ed., 1995


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Vd (L/kg) after iv dosingin rat and human (J&J data)


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Multiple DosingConcepts


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Dosing to Steady-stateOn continued drug administration, the amount in the bodywill initially increase but attain a steady-state, when the rate of elimination(drug loss per unit time) equals the amount administered per unit time

Amount A in body

Cplasma.Vdss

mg/ dayFract ional loss of A or Cp

First -order rate- K.A; - CL.Cp

1. I nit ial increase w hen k o > -K10.Abody

2. Steady st ate when ko = K.Abody= CL.C

3. Ass or Css constantas long k o const ant and CL constant


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Time to steady-stateHalf-life of 24 hr and dosing interval of 24 hrs

St eady-state w hen drug loss per dayequals drug in t ake per day


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Cmax

Cmin

Cavg,ss

Cavg,ss = AUCss /

AUC at steady st ate = AUC single doseAUC ss/ AUC first dose= Accumulation I ndex


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Steady-state

The amount in the body at steady-state (Ass)

Kel

KoAss =

The plasma concentration at steady-state (Css,Cavgss)

Cl

Ko

Kel.Vdss

Ko

Cpss ==

Css is proportional to the dosing rate (zero-order input)

andinversely proportional to the first-order elimination rate

or clearance


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Cmax

Cmin

Cavg,ss

C=Css(1-e-k.t)

5-6 half-lives to reach steady-state


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An effect ive half -l ife reflect s drug accumulat ion

Drug A: A=20 ng/mL; B=80 ng/mL; T1/2=3 h; T1/2=24 hDrug B: A=80 ng/mL; B=20 ng/mL; T1/2=3 h; T1/2=24 h


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An effect ive half -l ife reflect s drug accumulat ion

).exp(1

1

0

AUCss,ratioonAccumulati

KeffAUC ==

C=Css(1-e-keff.t)

Drug A: T1/2eff= 20 h

Drug B: T1/2eff= 10 h

Boxenbaum, J Clin Pharmcol 35:763-766, 1995


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Mean residence time = MRT

MRT is the time the drug, on average,

resides in the body.

MRT = Vdss/Cl


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Loading and Maintenance Dose

Maintenance Dose= desired Css x CL

Loading Dose= desired Css X Vd

Loading dose can be high fordrugs with large Vd,then LD divided

over various administrations

(J&J data on file)


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Total body clearance (CL)

CL= Dose / AUCplasma

CL = k10.Vc = z.Vdz= MRT.Vdss

A measure of the efficiency of all eliminating organsto metabolize or excrete the drug

Volume of plasma/blood cleared from drug per unit time


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Physiological approach to Clearance

Rate in

Q.Cpa

Amount Aor Concentration C

in blood Rate outQ.Cpv

Clearance = QE

Low hepat ic clearanceif ext ract ion rat io E < < 1

eg. Risperidone (Fabs 85% )

High hepat ic clearanceif E 1

eg. Nebivolol (Fabs 10% )

fu.ClintQ

fu.Clint

.QCpa

Cpv)-Q(Cpa

Clearance +==


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Bioavailability F

After oral administration,

not all drug may reach the systemic circulation

The fraction of the administered dose

that reaches the systemic circulationis called the bioavailability F

Oral drug absorption,


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g pInflux and Efflux Transporters, Drug Loss by First-pass

Gutlumen

PortalVein

LiverGut wall

MetabolismHepatic Metabolism

Biliary secretion

Uptake and effluxtransportersInto

faeces

Tabletdisintegration

Drugdissolution

Systemiccirculation

Uptake and efflux

transporters

F= Fabsorbed.(1-Egut).(1-Eliver)


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Grapefruit inhibits gut-wall metabolism(J&J data on file)

0

20

40

60

80

100

120

140

0 8 16 24 32 40 48

Time after morning dose on day 6 (hours)

Plasmacisapr

ideconc.

(ng/m

L)

Cisapride 10 mg q.i.d./waterCisapride 10 mg q.i.d./GFJ

Mean (N=13)


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Total body clearance (CL)

CL= Dose / AUCiv

Cl = k10.Vc = z.Vdz = MRT.Vdss

I nt ravenous clearance

Apparent oral clearance

Oral clearance CL/F= Dose / AUCoral


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High Solubility Low Solubility

High

Permeabil

ity

Low

Permeab

ility

Amidon et al., Pharm Res 12: 413-420, 1995; www.fda.gov

Class 2Low SolubilityHigh Permeability

Class 1High SolubilityHigh PermeabilityRapid Dissolution

Class 3

High SolubilityLow Permeability

Class 4

Low SolubilityLow Permeability

Biopharmaceutical Classification

Predicting Drug Disposition via BCS


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High

Permeabil

ity

Low

Permeab

ility

Class 1Transportereffects minimal

Class 3

Absorptivetransportereffectspredominate

Class 4

Absorptive andefflux transportereffects could beimportant

Predicting Drug Disposition via BCSWu and Benet, Pharm Res 22:11-23, 2005

Class 2Efflux transportereffectspredominate

Predicting Drug Disposition via BCS


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High

Permeabil

ity

Low

Permeab

ility

Class 1Metabolism

Class 3

Renal & BiliaryElimination ofUnchanged Drug

Class 4

Renal & BiliaryElimination ofUnchanged Drug

Predicting Drug Disposition via BCSWu and Benet, Pharm Res 22:11-23, 2005

Class 2Metabolism


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Biliary Excretion: Enterohepatic Recycling

The drug in the GI t ractis deplet ed.

Biliary excreted drugis reabsorbed

Drugin blood

Conjugatein bile Conjugatein int est ine

Drug inIntestine

Excretionin urine

Conjugate

inLiver

Metabolism

Dumpedfrom

gall bladder

Enzymaticbreakdownof glucuronide

Re-absorption

Excretionin feces

Hi hl i bl d d d d t


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Highly variable drugs and drug products

Drugs with high within-subject variabilityin Cmax and AUC (> 30% coefficient ofvariation) are called highly-variable drugs

Highly-variable drug products are

pharmaceutical products inwhich the drug is not highly variable, but theproduct is of poor pharmaceutical quality

From PK to relevant information for the patient


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Compound X

Tablets and oral solution

Pharmacokinetics: The estimated mean SD half-life

at steady-state of compound X after intravenousinfusion was 35.4 29.4 hours.

Renal impairment: The oral bioavailability ofcompound X may be lower in patients with renal

insufficiency. A dose adjustment may be considered.Other medicines: Do not combine compound X withcertain medicines called azoles that are given for fungalinfections. Examples of azoles are ketoconazole,itraconazole, miconazole and fluconazole.

You should not take compound X with grapefruit juice.

U f l M t i l


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Useful Material

HandbooksPharmacokinetics, 2nd Ed., by Milo Gibaldi

Clinical Pharmacokinetics, Concepts and Applications,

3rd

Ed., by Malcolm Rowland and Thomas N. TozerPharmacokinetic & Pharmacodynamic Data Analysis:Concepts and Applications, 4th Ed.,by Johan Gabrielsson and Dan Weiner

WinNonLin software, Pharsight

Noncompartmental and Compartmental analysis

Pharmacokinetic-pharmacodynamic analysis

Statistical Bioequivalence analysis

In vitro-in vivo Correlation for drug products


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Thank for your attention !

Rates and Orders


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Rates and Ordersof pharmacokinetic processes

The rate of a process is the speed at which it occurs

The rate of drug elimination representsthe amount (A) of drug absorbed, distributed oreliminated per unit time

Zero-order process or rate: constant amount per unit time

Input rate of infusion: mg per h dA/dt = ko = zero order rate constant

First-order process or rate: rate is proportional to theamount of drug available for the process

dA/dt = - k.A = -k.Volume.Concentration

R t f d g h g


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Rates of drug exchange

Change of the drug amount in central compartment

DAplasma/dt = - K10. Aplasma - K12. Aplasma + K21. AperipheralDAplasma/dt = - K10.Vc.Cplasma - K12.Vc.Cplasma + K21.Vt.Cperipheral

DAplasma/dt = - CL.Cplasma - CLd.Cplasma + CLd.CperipheralDCp/dt = - K10.Cplasma - K12.Cplasma + K21.Cperipheral

Change of the drug amount in peripheral compartment

DAperipheral/dt = - K12.Vc.Cplasma + K21.Vt.Cperipheral

DAperipheral/dt = - CLd.Cplasma + CLd.CperipheralDCperipheral/dt = - K12.Cplasma + K21.Cperipheral

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