Chapter 3 Pharmacokinetics

Chapter 3Chapter 3

PharmacokineticsPharmacokinetics

PK process in the bodyPK process in the body

Kinetic processesKinetic processes

Part APart A Pharmacokinetic ProcessesPharmacokinetic Processes

1 Overview1 Overview

2 2 Transport of Drug in the BodyTransport of Drug in the Body

3 Pharmacokinetic Processes of the Drug3 Pharmacokinetic Processes of the Drug in the Bodyin the Body

1.1. OverviewOverview

ADMEADMEof the drug inof the drug in

human bodyhuman body

2.2. Transport of Drug in the Body Transport of Drug in the Body

2.1 Transmembrane Transport of 2.1 Transmembrane Transport of DrugsDrugs

(1) Passive Transport(1) Passive Transport Simple diffusionSimple diffusion （简单扩散）（简单扩散） FiltrationFiltration （滤过）（滤过）


Characteristics of Passive TransportCharacteristics of Passive Transport

not involving specific carriers not involving specific carriers Energy-independentEnergy-independent no saturabilityno saturability no competition with other drugsno competition with other drugs Concentration gradient (down-hill)Concentration gradient (down-hill)


(2) Active Transport(2) Active Transport

Characteristics of active transportCharacteristics of active transport

Involving specific carrier Involving specific carrier Energy-dependentEnergy-dependent SaturabilitySaturability Competition at same carrierCompetition at same carrier Moving against concentration gradient (up-hill)Moving against concentration gradient (up-hill)


(3) Others(3) Others

Filtration through poresFiltration through pores （膜孔滤过）（膜孔滤过） Facilitated diffusionFacilitated diffusion （易化扩散）（易化扩散） EndocytosisEndocytosis （内吞）（内吞） PinocytosisPinocytosis （胞饮）（胞饮） Ion-pair transportIon-pair transport （离子对转运）（离子对转运）


Three types of functional membrane proteins.Three types of functional membrane proteins.

Transporters Transporters of drugs in PK of drugs in PK processesprocesses

Simple diffusionSimple diffusion


Determinants of simple diffusionDeterminants of simple diffusion

For most drugs of small molecules (usually aFor most drugs of small molecules (usually are weak acids or weak bases):re weak acids or weak bases):

Lipid-soluble or un-ionized formsLipid-soluble or un-ionized forms

pKa pKa of the drug andof the drug and pHpH of the body fluidof the body fluid

The The pKapKa is that pH at which the concentrations of tis that pH at which the concentrations of the ionized and un-ionized forms are equal.he ionized and un-ionized forms are equal.


Henderson-Hasselbalch equationHenderson-Hasselbalch equation

Weak acid drugs: Weak acid drugs: ppH - H - ppKa = log ( [AKa = log ( [A--] / [HA] )] / [HA] ) ppKa - Ka - ppH = log ( [HA] / [AH = log ( [HA] / [A--] )] )

Weak base drugs:Weak base drugs: ppKa - Ka - ppH = log ( [BHH = log ( [BH++] / [B] )] / [B] ) ppH - H - ppKa = log ( [B] / [BHKa = log ( [B] / [BH++] )] )



ppHH ppKaKaun-ionized un-ionized

formformlipid-lipid-solublesoluble

Simple Simple diffusiondiffusion

Weak Weak acidsacids

Weak Weak basesbases

And / orAnd / or

And / orAnd / or

And / orAnd / or

And / orAnd / or

pH < pKa:pH < pKa: HA and BHHA and BH+ + are predominantare predominant

pH > pKa:pH > pKa: AA －－ and B are predominantand B are predominant

ImplicationsImplications

Absorption Absorption

DistributionDistribution

ExcretionExcretion


2.2 Free and Bound Forms2.2 Free and Bound Forms

Plasma protein bindingPlasma protein binding

Tissue / organ affinityTissue / organ affinity


3.3. Fate of the drug in the body Fate of the drug in the body

AbsorptionAbsorption DistributionDistribution BiotransformationBiotransformation ( metabolism)( metabolism) ExcretionExcretion －－ ADMEADME


3.1 Absorption3.1 AbsorptionAbsorption is the transfer of a drug from its site of aAbsorption is the transfer of a drug from its site of a

dministration to the blood stream.dministration to the blood stream.

Gastrointestinal tractGastrointestinal tract Parenteral injection Parenteral injection im. sc.im. sc. InhalationInhalation Transdermal Transdermal


(1) Gastrointestinal tract(1) Gastrointestinal tract

Route:Route: OralOral SublingualSublingual RectalRectal


Factors influencing absorption:Factors influencing absorption:

blood flow to the absorption siteblood flow to the absorption site total surface area available for absorptiontotal surface area available for absorption contact time at the absorption surfacecontact time at the absorption surface physic-chemical properties of the drugphysic-chemical properties of the drug first-pass eliminationfirst-pass elimination


First-pass elimination First-pass elimination

When a drug is absorbed across the GI tract, When a drug is absorbed across the GI tract, it enters the portal circulation before entering it enters the portal circulation before entering the systemic circulation. If the drug is rapidly the systemic circulation. If the drug is rapidly metabolized by the liver, the amount of metabolized by the liver, the amount of unchanged drug that gains access to the unchanged drug that gains access to the systemic circulation is decreased.systemic circulation is decreased.


First-pass First-pass eliminationelimination

(2) Parenteral injection(2) Parenteral injection

intramuscular injection ( im ) intramuscular injection ( im ) subcutaneous injection ( sc )subcutaneous injection ( sc )

DeterminantsDeterminants Local blood flowLocal blood flow Solubility of the drug Solubility of the drug


(3) Others(3) Others

InhalationInhalation IntranasalIntranasal Transdermal Transdermal Topical Topical


3.2 Distribution3.2 Distribution

Drug distribution is the process by which a drDrug distribution is the process by which a drug reversibly leaves the blood stream and enteug reversibly leaves the blood stream and enters the interstitium (extracellular fluid) and / or rs the interstitium (extracellular fluid) and / or the cells of the tissues.the cells of the tissues.


Body fluid Body fluid volume:volume:

Sites of drug Sites of drug

distributiondistribution

(1) Binding of drug to plasma proteins(1) Binding of drug to plasma proteins

Bound drug: Bound drug: Inactive temporilyInactive temporily can not distributioncan not distribution reversible (storage form)reversible (storage form) percentage of bindingpercentage of binding competitively displacement competitively displacement


competitively displacementcompetitively displacement Class I drugs:Class I drugs: Dose less than available binding Dose less than available binding

sites. sites. Most drug molecules are bound to the protMost drug molecules are bound to the proteins and free drug concentration is low.eins and free drug concentration is low.

Class II drugs:Class II drugs: Dose greater than available bin Dose greater than available binding sites. ding sites. Most proteins contain a bound drug aMost proteins contain a bound drug and free drug concentration is significant.nd free drug concentration is significant.

Class I + Class II drugs:Class I + Class II drugs: Displacement of Clas Displacement of Class I drug occures when a Class II drug is administs I drug occures when a Class II drug is administered simultaneously.ered simultaneously.


(2) Physic-chemical properties of the drug(2) Physic-chemical properties of the drug

(3) Blood flow and re-distribution(3) Blood flow and re-distribution

(4) Affinity to organs or tissues(4) Affinity to organs or tissues

(5) Barriers(5) Barriers

Blood-brain barrier (BBB)Blood-brain barrier (BBB)

Placental barrierPlacental barrier

Blood-eye barrier Blood-eye barrier


Blood-brain barrier (BBB)Blood-brain barrier (BBB)

Able to pass throughAble to pass through Unable to pass throughUnable to pass through

Small moleculesSmall molecules Large moleculesLarge molecules

Lipid-solubleLipid-soluble Water-solubleWater-soluble

Transporter-mediation Transporter-mediation

Structure of liver Structure of liver capillary and brain capillary and brain

capillarycapillary

Amount of drug passing through blood-braiAmount of drug passing through blood-brain barriern barrier

Percentage of drug in Percentage of drug in c.s.f.c.s.f.

Increases whenIncreases when

InflammationInflammation

Larger doses usedLarger doses used


BBB BBB permeability permeability increases in increases in

inflammationinflammation

Placental barrier:Placental barrier:

More permeableMore permeable

3.3 Biotransformation (drug metabolism)3.3 Biotransformation (drug metabolism)

(1) Biotransformation sites(1) Biotransformation sites

Liver:Liver: most of the drugsmost of the drugs Other organs/tissues:Other organs/tissues: intestine, kidney, lunintestine, kidney, lun

g, plasma, etc.g, plasma, etc.


(2) Phases of biotransformation(2) Phases of biotransformation

Phase I: Phase I: Oxidation reduction hydrolysisOxidation reduction hydrolysis most drugs are inactivatedmost drugs are inactivated few (few (prodrugsprodrugs) are activated) are activated

Phase II: Phase II: ConjugationConjugation inactivatedinactivated

Metabolites: Metabolites: more water-soluble more water-soluble easier to excreteeasier to excrete


Drugs or other substancesDrugs or other substances Phase IPhase I

inactivatedinactivated （（ few: activatedfew: activated ）） Phase IIPhase II

inactivatedinactivated

ExcretionExcretion


(3) Enzymes in biotransformation(3) Enzymes in biotransformation

Enzymes in Phase I: Enzymes in Phase I: cytochrome-P450cytochrome-P450 many other enzymesmany other enzymes

Enzymes in Phase II: Enzymes in Phase II: acetylase acetylase glucuronosyltransferaseglucuronosyltransferase etc.etc.


Superfamily of cytoSuperfamily of cytochrome-P450chrome-P450

CYP3A4CYP3A4（（ cytochrome / familcytochrome / family / subfamily / memby / subfamily / memb

erer ））

(4) Hepatic enzymes of drug metabolism(4) Hepatic enzymes of drug metabolism

hepatic microsomal mixed function oxidase shepatic microsomal mixed function oxidase system ystem （肝药酶）（肝药酶）

Extraction > 0.7: Extraction > 0.7: hepatic blood flow dependenthepatic blood flow dependent －－ nitroglucerin, propranolol, …nitroglucerin, propranolol, …Extraction < 0.3: Extraction < 0.3: hepatic enzyme dependenthepatic enzyme dependent －－ diazepam, phenobarbital, …diazepam, phenobarbital, …


Induction of hepatic enzymes by drugsInduction of hepatic enzymes by drugs example: example: phenobarbitalphenobarbital －－ steroids, warfarinsteroids, warfarin

Inhibition of hepatic enzymes by drugsInhibition of hepatic enzymes by drugs example: example: cimetidinecimetidine －－ diazepamdiazepam


肝药酶诱导剂对双香豆素血浓度及凝血作用的影响肝药酶诱导剂对双香豆素血浓度及凝血作用的影响

3.4 Excretion3.4 Excretion

(1) Excretion routes(1) Excretion routes KidneyKidney BileBile LungLung GI tractGI tract MilkMilk Secretion glandsSecretion glands


(2) Renal excretion(2) Renal excretion

Glomerular filtrattionGlomerular filtrattion renal blood flowrenal blood flow

Active tubule secretionActive tubule secretion specific carriers / competitionspecific carriers / competition

Passive tubule reabsorptionPassive tubule reabsorption urine pH, urine flowurine pH, urine flow


Renal excretionRenal excretion

Glumerular fitrationGlumerular fitration

Active secretionActive secretion

Passive reabsorptionPassive reabsorption

(3) Bile excretion(3) Bile excretion

Carrier-mediated activeCarrier-mediated active

transporttransport

Hepato-enteral circulationHepato-enteral circulation


3.5 Elimination and Accumulation3.5 Elimination and Accumulation

Elimination:Elimination: BiotransformationBiotransformation ExccretionExccretion Distribution (stored in fat, hair, etc)Distribution (stored in fat, hair, etc)

Accumulation:Accumulation: Dosing rate > elimination rate Dosing rate > elimination rate


Part BPart B Kinetic ProcessesKinetic Processes

1 Drug concentration-time curve1 Drug concentration-time curve

2 Kinetic rate processes2 Kinetic rate processes

3 Pharmacokinetic models3 Pharmacokinetic models

4 Pharmacokinetic parameters and 4 Pharmacokinetic parameters and implicationsimplications

5 Multiple dosing5 Multiple dosing


1.1. Drug concentration-time curve Drug concentration-time curve (C-T curve)(C-T curve)

Maximal (peak) concentration:Maximal (peak) concentration: CCmaxmax C Cpp

Time to maximal concentration (Peak time ) :Time to maximal concentration (Peak time ) : TTmaxmax T Tpp

Area under the curve:Area under the curve: AUCAUC Multiple dosing (steady state): Multiple dosing (steady state):

CCssss max max C Css minss min C Cssss

t

C

i.m.i.m.

s.c.s.c.

OralOral

i.v.i.v.

←

←

←

←

CCmaxmax

CCpp

↑ ↑ ↑TTmax, max, TTpp

TTmaxmax 、、 CCmaxmax and AUC and AUC

↑Tmax

←Cmax

AUC↙

C-T curve after multiple dosing C-T curve after multiple dosing （（ sasame dose and intervalme dose and interval ））

Temporal characteristics of drug effect and relaTemporal characteristics of drug effect and relattionship to therapeutic windowttionship to therapeutic window

2. 2. Kinetic rate processesKinetic rate processes

dC / dt dC / dt ＝＝ KCKCnn


2.1 Zero order kinetics2.1 Zero order kinetics

n n ＝＝ 00 dC / dt dC / dt ＝－＝－ KK CCt t ＝＝ CC00 －－ K tK t CC00 －－ Ct Ct ＝＝ K tK t when Cwhen Ctt ＝＝ 1/2 C1/2 C00,,

then then t = tt = t1/21/2, 0.5 C, 0.5 C00 ＝＝ K tK t1/2 1/2

tt1/21/2 ＝＝ 0.5 C0.5 C0 0 / K/ K


Zero order kineticsZero order kinetics

A.A. same amounts of drug are same amounts of drug are eliminated per unit timeeliminated per unit time

B. B. t t1/21/2 is not a constant is not a constant

C. C. C-T curve is linear C-T curve is linear

D. D. no Css theoretically no Css theoretically


Kinetic properties of C-T curves after Kinetic properties of C-T curves after single bolus injection of drugsingle bolus injection of drug

2.2 First order kinetics2.2 First order kinetics n n ＝＝ 11 dC / dt dC / dt ＝－＝－ KCKC CCt t ＝＝ CC00ee －－ KtKt lnClnCt t ＝＝ lnClnC00 －－ Kt Kt KtKt ＝＝ lnClnC00 －－ lnClnCtt ＝＝ ln(Cln(C00 / C / Ctt)) when Cwhen Ctt ＝＝ 1/2C1/2C00 ，， tt ＝＝ tt1/21/2 ，， tt1/21/2 ＝＝ ln2/Kln2/K ＝＝ 0.693/K0.693/K


First order kineticsFirst order kinetics

A.A. eliminated at same rate per unit time eliminated at same rate per unit time

B.B. t t1/21/2 is a constant is a constant

C.C. logC-T curve is linear logC-T curve is linear

D.D. steady state (Css) after 4-5 t steady state (Css) after 4-5 t1/21/2


2.3 Non-linear kinetics2.3 Non-linear kinetics

Higher concentration (or dose):Higher concentration (or dose): zero order kineticszero order kineticsLowerconcentration (or dose):Lowerconcentration (or dose): first order kineticsfirst order kinetics

Because of limits in elimination capacity Because of limits in elimination capacity Examples:Examples: aspirin, phenytoin, ethanolaspirin, phenytoin, ethanol


Michaelis-Menten kineticsMichaelis-Menten kinetics

dC / dt = VdC / dt = Vmax max C / (KC / (Kmm + C) + C) if if Km >> C Km >> C dC / dt = VdC / dt = Vmax max C / KC / Kmm

VVmaxmax / K / Kmm = K = Ke e －－ First orderFirst order

ifif C >> Km C >> Km dC / dt = VdC / dt = Vmax max C / CC / C dC / dt = -VdC / dt = -Vmaxmax －－ Zero orderZero order


3 3 Pharmacokinetic modelsPharmacokinetic models

2.1 One-compartment model2.1 One-compartment model

If the drug rapidly distributed in the body If the drug rapidly distributed in the body after administration, then eliminated at samafter administration, then eliminated at same rate.e rate.


One-compartment modelOne-compartment model

BodyBody logC

t

iv


D E

2.2 Two-compartment model2.2 Two-compartment model

D → → E D → → E

↑↓ ↑↓

PeripheralPeripheral

CentralCentral

First, enter the centralFirst, enter the central

compartmentcompartment

Then, distributed to peripThen, distributed to peripheral compartment, and elheral compartment, and eliminnatediminnated

CentralCentral



D → → E

↑↓logC

t

iv

α β

βα

Distribution over, Distribution over, and eliminationand elimination

C-T curveC-T curve

CentralCentral


DistributionDistribution EliminationElimination


2.3 Other models2.3 Other models

Physiological pharmacokinetic modelPhysiological pharmacokinetic model

Combined pharmacokinetic-Combined pharmacokinetic- pharmacodynamic modelpharmacodynamic model

Statistical momentStatistical moment


4. 4. Pharmacokinetic parameters and Pharmacokinetic parameters and their implicationstheir implications

4.1 Bioavailability 4.1 Bioavailability ( F )( F )

Bioavailability is the fraction of adminBioavailability is the fraction of administered drug (oral) that reaches the systeistered drug (oral) that reaches the systemic circulationmic circulation


Absolute bioavailabilityAbsolute bioavailability

F = AUCF = AUC(po, sc, im)(po, sc, im) / AUC / AUC (iv)(iv)

Relative bioavailabilityRelative bioavailability

F = AUCF = AUC(tested)(tested) / AUC / AUC(standard)(standard)

Implication:Implication: Evaluation for absorption a Evaluation for absorption and drug quality controlnd drug quality control


4.2 Apparent volume of distribution (4.2 Apparent volume of distribution (VdVd))

The volume of distribution (Vd) relates the amThe volume of distribution (Vd) relates the amount of drug in the body to the concentration of ount of drug in the body to the concentration of drug (C) in the blood or plasma.drug (C) in the blood or plasma. iv iv Vd = D / C Vd = D / C popo Vd = FD / C Vd = FD / C


Implications of VImplications of Vdd

Ratio of drug amount and plasma drug Ratio of drug amount and plasma drug concentrationconcentration

Properties of drug distributionProperties of drug distribution

Used for pharmacokinetic calculationUsed for pharmacokinetic calculation


4.3 Half-life (4.3 Half-life (tt1/21/2))

The half-life (tThe half-life (t1/21/2) is the time takes for the plas) is the time takes for the plasma concentration or the amount of drug in the bma concentration or the amount of drug in the body reduced by 50%.ody reduced by 50%.

tt1/21/2 = 0.693 / Ke = 0.693 / Ke ＝＝ Vd / ClVd / Cl


Implications of Implications of tt1/21/2

Elimination rateElimination rate

Estimating the times of fully elimination and Estimating the times of fully elimination and reaching steady statereaching steady state

Classifying short- and long-acting drugsClassifying short- and long-acting drugs

Adjusting dosage regimens for patients with Adjusting dosage regimens for patients with hepatic or renal failureshepatic or renal failures


Elimination of single dose and accumulation after multiple dosing (at same dose and interval) of a first order kinetic drug

Elimination after single dosingElimination after single dosing

t1/2 0 100%

1 50%

2 25%

3 12.5%

4 6.25%

5 3.13%

6 1.57%

…………

Accumulation after multiple doAccumulation after multiple dosing at same dose and intervalsing at same dose and interval（（ tt1/21/2))

t1/2 0 0 ～ 100%

1 50 ～ 150%

2 75 ～ 175%

3 87.5 ～ 187.5%

4 93.8 ～ 193.8%

5 96.9 ～ 196.9%

6 98.4 ～ 198.4%

…………

4.4 Clearance (Cl)4.4 Clearance (Cl)

A A constant fractionconstant fraction of drug in the body is eliminated of drug in the body is eliminated per unit of time (per unit of time (first-order kineticsfirst-order kinetics).).

Cl = Ke Cl = Ke Vd Vd A A constant amountconstant amount of drug in the body is eliminated of drug in the body is eliminated per unit of time (per unit of time (zero-order kineticszero-order kinetics).).

4.5 Elimination rate constant (Ke)4.5 Elimination rate constant (Ke)

KeKe = 0.693 / = 0.693 / tt1/21/2 ＝＝ Cl / VdCl / Vd


tt (min)(min)

lnClnCtt

lnClnCtt = lnC = lnC00 －－ KKee

tt

slope = - Kslope = - Kee

tt1/21/2 = 0.693 / K = 0.693 / Kee

VVdd = D / C = D / C00

Cl = VCl = Vdd × K × Kee

lnClnC00

slope = - Kslope = - Kee

First order kineticsFirst order kinetics

One compartment modelOne compartment model

Intravenous administrationIntravenous administration

5.5. Multiple dosing Multiple dosing

Steady state: 4Steady state: 4 ～～ 5 5 tt1/21/2

Varying according to dose and inVarying according to dose and intervalstervals


Same dose and different intervalsSame dose and different intervals

Different doses and same intervalDifferent doses and same interval

Same total doses and different intervalsSame total doses and different intervals

Same dose and same interval, but first Same dose and same interval, but first dose × 2dose × 2

C-T curves of drug after multiple dosing at same C-T curves of drug after multiple dosing at same

interval and same doseinterval and same dose

Loading dose (DLoading dose (DLL)) DDLL = target C = target Cssss VVd ssd ss / F / F

Maintenance doseMaintenance dose raterate (DDm m )) DDmm ＝＝ target Ctarget Cssss CL / FCL / F


Chapter 3 Pharmacokinetics

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