PK/PD Modeling of Therapeutic Effects of Erythropoietin

Wojciech Krzyzanski, PhD, MADepartment of Pharmaceutical Sciences

University at Buffalo

Semiparametric Bayesian Inference: Applications in Pharmacokinetics and Pharmacodynamics

SAMSI, Research Triangle Park, July 14 2010

General Model of Hematopiesis

From Kaushansky, N. Engl. J. Med. 354:2034 (2006).

Regulation of Erythropoiesis

Wolber and Jelkmann., News Physiol. Sci. 17: 6 (2002)

Red blood cells(O2-capacity, arterial pO2)

pO2-dependent production

Kidney

Erythropoietin(EPO)

Bone marrow

+

Erythropoietin

EPO is a 30.4 kD glycoprotein responsible for survival, proliferation, and maturation of erythroid cells.

EPO is produced by peritubal cells in the kidneys in response to tissue hypoxia.

Indications for rHuEPO:

- Anemia of chronic renal failure - Chemotherapy induced anemia - Anemia of prematurity

Erythropoietin Receptor

Sawyer et al., JBC 262: 5554 (1987); Broudy et al., Blood 77: 2583 (1991)

EPOR is a 185 kD member of the class 1 cytokine receptor superfamily.

Expressed on erythroid progenitor cells, epicardium, neurons, liver, gut, endothelium.

Upon binding to EPO homodimerizes and activates JAK2 tyrosine kinase.

EPO-EPOR complex is internalized and degraded by the endosome-lysosome pathway.

KD ~ 100-200 pM

Internalization rate ~ 0.7 h-1

300- 1000 receptors per erythroid cell

Time (hr)0 80 160 240 320 400

rHu

EP

O c

on

cen

trat

ion

(IU

/l)

1

10

100

1000

10000300 IU/kg600 IU/kg1200 IU/kg2400 IU/kg

rHuEPO Pharmacokinetics

Ramakrishnan et al., J. Clin. Pharmacol. 44:991-1002 (2004).

Time, hr

0 10 20 30 40

rHuE

PO

Ser

um C

onc.

IU/L

100

1000

10000

10000010 IU/kg50 IU/kg150 IU/kg500 IU/kg1000 IU/kg

IV SC

Flaharty et al., Clin. Pharmacol. Ther. 47: 557-64 (1990).

Distribution: Vd = 3-5 L. Moderate nonlinear clearance: t1/2 = 4-11 hr. Minimal renal and hepatic clearance. Receptor binding, internalization, and degradation in bone marrow.

Dose dependent bioavailability: F = 0.4-1. Slow absorption from the injection site: flip-flop kinetics.

rHuEPO Pharmacodynamics

0 5 10 15 20 25

Ret

icu

locy

tes,

%

1

2

3

4

5

0 5 10 15 20 25

RB

C C

ou

nt,

10

12 c

ells

/L

4.5

4.8

5.1

5.4

Time, days

0 5 10 15 20 25

Hem

og

lob

in,

g/d

L

14

15

16

Time, days

0 7 14 21 28

Ser

um

EP

O, I

U/L

10

100

rHuEPO was administered SC to healthy subjects 150 IU/kg t.i.w for four weeks.

rHuEPO pharmacodynamic responses

Reticuloctyte count RBC Hemoglobin concentration

Krzyzanski et al., EJPS 26:295-306 (2005).

PK/PD Modeling Paradigm

Mager and Jusko, Clin. Pharmacol. Ther. 70:210-16 (2001).

Receptor Mediated EPO Endocytosis and Degradation

Gross and Lodish, J. Biol. Chem. 281:2024 (2006).

DIV

DPO, F•kaKo, TINF

SerumCpVc

TissueDT

ReceptorComplex

DR

kon

koff

kel km

kpt

ktp

FreeReceptor[Rmax-DR]

kdeg

ksyn

+

Target-Mediated Drug Disposition

DRkkCpDRRkdt

dDR

DRkCpDRRkVc

DkCpkk)t(In

dt

dCp

moffmaxon

offmaxonT

tpptel

Mager and Jusko. J Pharmacokinet Pharmacodyn. 28:507-32 (2001)

Erythropoietic Cascade

Stem CellStem Cell

BFU-eBFU-e

CFU-eCFU-eProerythroblastProerythroblast ErythroblastErythroblast

ReticulocyteReticulocyte

RBCRBC

EPO responsive cellsEPO responsive cells

EPOR-/EPOR-/++

EPOR++EPOR++++

EPOR+EPOR+

EPOR-EPOR-

EPOR+/-EPOR+/-

EPOR-EPOR-

EPOR-EPOR-

Lifespan Distribution

Lifespan0 2 4 6 8 10

Pro

bab

ility

Den

sity

0

1

Tmean

Cell lifespan - time a cell remains in the population

Mean lifespan-population mean of the lifespan distribution

0

mean dt)t(tT

Lifespan Controlled Cell Loss

Rkin(t) (kin*)(t)

0

inin (z)dzz)(tk)(t)*(k

Point Lifespan Distribution: (t) = (t-TR)

(kin* )(t) = kin(t-TR)

kin

S(t)

Rkin

S(t-TR)

C(t)

)Tt(Sk)t(Skdt

dRRinin

)Tt(Sk)t(Skdt

dRRinin

γγ50

γmax

C(t)SC

C(t)S1S(t)

Basic Model: Stimulation of kin

Baseline: R0 = kin·TR

Krzyzanski and Jusko, JPB 27: 467 (1999).

PK/PD of rHuEPO in Rats

Mean serum rHuEPO concentrations, reticulocyte, and hemoglobin levels following IV bolus administration of 10, 100, 450, 1350, and 4050 IU/kg in rats.

Woo et al., JPP 34:849-68 (2007).

TMDD PK/PD Model of rHuEPO

Woo et al., JPP 34:849-68 (2007).

PK/PD Model Equations

pTtppteloffonEPO VAkCkkRCkCRkkdt

dC

TtppptT AkVCk

dt

dA

RkRCkCRkkdt

dRdegoffonsyn

)TTTt(I)TTt(S)TTTt(Sk

)TTt(I)Tt(S)TTt(Skdt

dRET

RET2P1PRET2PRET2P1Pin

2P1P2P2P1Pin

)TTTTt(I

)TTTt(S)TTTTt(Sk

)TTTt(I)TTt(S)TTTt(Skdt

dRBC

RBCRET2P1P

RBCRET2PRBCRET2P1Pin

RET2P1PRET2PRET2P1PinM

Woo et al., JPP 34:849-68 (2007).

RCkkCRkdt

dRCintoffon

PK/PD Model Equations

)t(RCSC

)t(RCS1)t(S

50

max

)t(HbIC

)t(HbI1)t(I

50

max

)0(Hb)t(Hb)t(Hb

)t(RBCMCH)t(Hb

)t(RBC)t(RET)t(RBC M

Woo et al., JPP 34:849-68 (2007).

Initial Conditions

0C)t(C p

IV0 V

DC)0(C , for t < 0, and

tp

p0ptT k

VCk)t(A

, for t 0

0R)t(R , for t 0

0RC)t(RC

0RET)t(RET

00M RETRBC)t(RBC

, for t 0

, for t 0

, for t 0

Woo et al., JPP 34:849-68 (2007).

Baseline Equations

intoff

00on0 kk

CRkRC

0int0elEPO RCkCkk

0int0degsyn RCkRkk

RBCRET

0RET0 TT

RBCTRET

Donoff Kkk

Woo et al., JPP 34:849-68 (2007).

Residual Error Variance Model

CC)C(Var Cobs

RETRET)RET(Var RETobs

RBCRBC)RBC(Var RBCobs

HbHb)Hb(Var Hbobs

Parameter estimates were obtained by minimizing the -2LL objective function in ADAPT II.

Woo et al., JPP 34:849-68 (2007).

Parameter Estimates Parameter Estimate CV%

Vp (ml/kg) 56.94 1

kel (h-1) 0.2256 2

kpt (h-1) 0.2092 6

ktp (h-1) 0.1721 6

kint (h-1) 0.8228 66

kdeg (h-1) 0.1133 58

kon (nM-1h-1) 11.32 80

KD (nM) 1.297 70

R0 (nM) 0.0632 43

C0 (nM) 0a

RBC0 (106 cells/l) 6.128a

MCH (pg/cell) 20.0a

TP1 (h) 42.97 8

TP2 (h) 3.02 75

TRET (h) 72.33 4

TRBC (h) 1440a

Smax 3.48 7

SC50 (pM) 1.7 35

Imax 1.0a

IC50 (g/dl) 1.79 10

a Parameter was fixed. Woo et al., JPP 34:849-68 (2007).

Numerical Challenges

• Stiffness: Receptor binding (kon, R0) is typically much faster than distribution and elimination (kel,ktp,kpt).

• Delay differential equations: Lifespan based PD model requires a DDE solver.

Parameter Estimability

• Large number of model parameters.• Observable data (blood compartments) are poorly

informative about processes occurring in the bone marrow: receptor binding, cell maturation, negative feedback.

• Large values of SE of corresponding parameter estimates, correlations, singularity of covariance matrix.

• Necessary reduction of the number of model parameters:

- fixing at known physiological values. - simplifying assumptions: quasi steady-state etc.

Conclusions

• rHuEPO nonlinear PK can be explained by receptor mediated disposition.

• PD response is significantly delayed with respect to PK exposure.

• PK/PD model exhibits stiffness and requires DDE solver.

• System large dimension and data based on blood measurements lead to parameter estimability problems.

Acknowledgments

• Sukyung Woo, PhD.

• William Jusko, PhD.