basics of pharmaco-/ toxicokinetics - ddnz.uzh.ch

Basics of Pharmaco-/ Toxicokinetics

Dr. Robert Doblhoferwww.granzer.biz

Agenda

Introduction

A Absorption (esp. after oral ingestion)

D Distribution

M Metabolism

E Excretion

Concentration in plasma and derived pharmaco-/toxicokinetic parameters

(Possibilities and limitations of pharmaco-/toxicokinetics)

2

Material

Pharmakokinetik: Derendorf, Gramatté, Schäfer

Parameter zur modellunabhängigen PK: Cawello

Arzneimittelwirkungen: Mutschler

Funktionelle Histologie der Haussäugetiere, Liebich

Der Körper des Menschen: Benner

3

4

INTRODUCTION

5

Friedrich Hartmut Dost (Pediatrician), 1953 6

7

8

ABSORPTION

ca. 0,1 m2 > 100 m2

Gastro-Intestinal Tract

9

10

Gain of Surface in the Intestines

10

11

Gain of Surface in the Intestines

11

12

)( ia CCLFDq −⋅⋅=

q = rate of diffusion

D = diffusion-constant

F = membrane surface

L = membrane thickness

Ca = concentration in intestinal lumen

Ci = concentration in intestinal epithelial cell

Fick`s Law (Passive Diffusion)

12

cell membrane

Ca Ci

passive diffusionuncharged, amphiphilic, driven byconcentration gradient Ca > Ci

diffusion through poressmall, hydrophilic

active transportglucose, amino acids, Na+,…

carrier-mediated diffusion

pinocytosis

efflux transporter

phagocytosis

Absorption Processes at the Intestinal Wall

13

solubilitydissolution rate particle size

Substance is dissolved

Substance is uncharged

Substance is amphiphilic

- H+

pka

amphiphilic

intestinal epithelial cell

Bloo

d ca

pilla

ry

Requirements for Passive Diffusion

14

Blood Flow in Villi

15

16

DISTRIBUTION

Total body water (~60%) Blood (~8%)

Plasma proteins Blood cells (esp. erythrocytes) Fatty tissue (highly lipophilic substances, e.g. DDT) Bones (Ca2+-mimetics, e.g. Pb2+, Sr2+)

Distribution Spaces

total body water~42 l (0.6 l/kg)

interstitial water~15 l (0.2 l/kg)

plasma water~3 l (0.04 l/kg)

intracellular water~24 l (0.35 l/kg)

extracellular water~18 l (0.25 l/kg)

17

Examples: blood-brain-barrier kidney, intestines liver

Blood-to-Tissue Transit from Capillaries

A: closed capillary B: fenestrated capillary C: open capillary with discontinuous endothelium

18

19

METABOLISM

Metabolism

Phase I: Activation Mainly CYP450 enzymes Localization of CYPs: Liver Intestines Lung Kidney Skin Blood…

Phase II: Conjugation Glucuronidation Sulphatation Acetylation Conjugation with GSH …

improved aqueous solubility glomerular filtration

20

First-Pass-Effect

CAVE: no/limited FPE after sublingual and rectal administration!21

22

EXCRETION

Biliary Excretion

23

The Kidney

24

The Nephron

25

cut-off: ~70.000 Da (see below)

Glomerular Filtration

26

Glomerular Filtration

27

Glomerular Filtration

28

Pharmacokinetics = ADME

Absorption: uptake into the (blood-)circulation

Distribution: via blood, different types of capillaries

Metabolism: phase I: activationphase II: conjugation (solubility ↑)first-pass-effect after oral administration

Excretion: via urine (glomerular filtration in the kidney)and bile (liver)

Summary Part I

29

30

CONCENTRATION IN PLASMA AND DERIVEDPHARMACO-/TOXICOKINETIC PARAMETERS

tkCtC ⋅−= 00)(

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0

20

40

60

80

100

120

0kdtdC

=−

Zero-Order Kinetics („Saturation“)

31

CkdtdC

⋅=−

eCtC tk ⋅−⋅= 0)(

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0

20

40

60

80

100

120

tkCC ⋅−= 0lnln

tkCC ⋅−=303,2

loglog 0

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0,01

0,1

1

10

100

1000

First-Order Kinetics („Linear PK“)

32

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0

20

40

60

80

100

120

eCtC tk ⋅−⋅= 0)(

tkCC ⋅−= 0lnln

Conc. halved

2/100 ln

2ln tkCC

⋅−=

2/100 ln2lnln tkCC ⋅−=−

kt 2ln

2/1 =

kt 693,0

2/1 =

2/0CC = 2/1tat

The Half-life in First-Order Pharmacokinetics

33

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0,01

0,1

1

10

100

1000

t1/2 = 0,693/kSlope = -k/2,303 (ln/log)

Unit of half-life:t1/2: hk: 1/h resp. h-1

The Half-life in First-Order Pharmacokinetics

34

Vmax = maximum rate of metabolism/elimination

KM = Michaelis-Menten-constant (=C at Vmax/2)

Vd = volume of distribution (for in vivo studies)

dM VCKCV

dtdC

⋅+⋅

=−)(

max

Michaelis-Menten-Kinetics

Non-Linear Pharmacokinetics

35

dM VCKCV

dtdC

⋅+⋅

=−)(

max

C>>KM → (KM+C) ≈ C

dVV

dtdC max

=−

Case 1:high concentration/dose:zero-order kineticssaturation (non-linear)

C<<KM → (KM+C) ≈ KM

CVK

VdtdC

dM⋅

⋅=−

max

Case 2:low concentration/dose:first-order kineticslinear pharmacokinetics!

Michaelis-Menten-Kinetics

36

Michaelis-Menten-Kinetics

37

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0

20

40

60

80

100

120

AUC [µg·h/ml]

The Area under the Curve (AUC)

38

eCtC tk ⋅−⋅= 0)( ∫ ⋅=−

z

z

t

t dttCAUC0

0 )(

)1(00

zz

tkt e

kCAUC ⋅−

− −⋅=

kCAUC 0

0 =∞−

The Area under the Curve (AUC)

39

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0

20

40

60

80

100

120

AUC: The Linear Trapezoidal Rule

40

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0

20

40

60

80

100

120

tz

Cz

AUC0-tz vs. AUC0-∞

41

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0,1

1

10

100

1000

tz

Cz

AUC0-tz

AUC0-tz vs. AUC0-∞

kCAUC z

tz =∞− (max. ~20%)

42

The Volume of Distribution

CXVd =

0CDoseVd =

X = amount of compound present in the body

The amount of compound present in the body (X)is best known immediately after an iv dose.

VXC =

dP V

XC =

X X

CTissue > CPlasma

A: „no distribution“ B: distribution to tissue

43

The Volume of Distribution - Example

3 gC = 1 g/l

0.03 gC = 0.01 g/l

2.97 g

3 g 3 g

Vd = 3 Liter Distribution only

to plasma

44

3 l plasma

Vd = 300 Liter Distribution

to tissue

plasma

fatty tissue

Time0 2 4 6 8 10

Con

cent

ratio

n in

Pla

sma

0,01

0,1

1

10

100

1000

-k/2,303

C0

Vc = Dose/C0

Unit:Vc: l (Liter)

The Volume of Distribution

45

The Volume of Distribution

Reference volumes in the body (70 kg):

total body water~42 l (0.6 l/kg)

interstitial water~15 l (0.2 l/kg)

plasma water~3 l (0.04 l/kg)

intracellular water~24 l (0.35 l/kg)

extracellular water~18 l (0.25 l/kg)

46

rate of elimination: XkdtdE

e ⋅=

AUCDose

CDosekVk

CXk

CCL ede

edtdE

=⋅=⋅=⋅

==0

volume of distribution:0C

DoseCXVd ==

AUC:ek

CAUC 0=

D

X Eke

i.v.

The Clearance

47

AUCDoseVkCL de == [l/h] or [l/h·kg]

Compare:liver blood flow: ~1,5 l/minrenal plasma flow: ~0,6 l/min

hhh QCL ε⋅=

The Clearance

48

Clearance:proportional to: Vd

antiproportional to: AUC; t1/2

D

X Eke

i.v.

Compartments

Time0 2 4 6 8 10

Conc

entra

tion

in P

lasm

a

0,01

0,1

1

10

100

1000

49

D

X Ukr

i.v.

M

km

ke = kr + km

Compartments

Time0 2 4 6 8 10

Conc

entra

tion

in P

lasm

a

0,01

0,1

1

10

100

1000

50

D

Xc Eke

i.v.

Xp

ADosisVz =

Compartments

51

D

X Eke

p.o.

Aka

XkAkdtdX

ea ⋅−⋅=

)()(

tktk

ead

ap

ae eekkV

DFkC ⋅−⋅− −⋅−⋅⋅⋅

=

Bateman-Function

Oral Administration

52

Oral Administration: Bateman-Function

53

Oral Administration: Bateman-Function

Cmax

tmax

54

AUC always identical! Extreme: immediate absorption = iv-curve

CLDFAUC ⋅

= → %)100((%) ⋅=iv

po

AUCAUCF

Oral Administration: Bateman-Function

55

Multiple-Dose PK: „Cumulation“

ss = steady state; sd = single dose; τ = dosing interval

τ(sd)

τ(ss)

AUCAUC

R−

−=0

0„Cumulation“: 2121

1

/tτR

−

−

=

56

Multiple-Dose PK: „Accmulation“

τAUC

C τ(ss)P,ave(ss)

−= 0

„Accumulation“:

10

0 =∞−

−

(sd)

τ(ss)

AUCAUC

10

0 >∞−

−

(sd)

τ(ss)

AUCAUC

(toxicologically relevant!)

57

Linear PK only when saturation does not occur

Very high doses can lead to non-linear PK

First order PK: exponential decrease of CP

t1/2, AUC, Vd und CL

Oral administration: Bateman-Funktion (ka/ke), Cmax, tmax, AUC

Bioavailability F = AUCpo/AUCiv

A high bioavailability does not necessarily lead to high plasmaconcentrations (if the clearance is high)

(Ac-)cumulation is not necessarily of toxicological relevance

Summary Part II

58

Summary Part II

Parameter Meaning iv po

VC / VZ central/apparent volume of distribution X

CL total body clearance X

t1/2 half-life X (X)

AUC0-∞ infinite AUC (extrapolated to infinity) X (X)

AUC0-t observed AUC X X

Cmax highest observed concentration in plasma X

tmax time, at which Cmax is reached X

F (oral) bioavailability X

59

60

Dr. Robert DoblhoferGranzer Regulatory Consulting & Services GmbH

Kistlerhofstraße 172C

81379 München

doblhofer@granzer.biz

Tel: +49 (0)89 780 68 98 - 53

THANK YOU!