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.