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**PK/PD Modeling of Therapeutic Effects of Erythropoietin**

Wojciech Krzyzanski, PhD, MA Department of Pharmaceutical Sciences University at Buffalo Semiparametric Bayesian Inference: Applications in Pharmacokinetics and Pharmacodynamics SAMSI, Research Triangle Park, July

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**General Model of Hematopiesis**

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

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**Regulation of Erythropoiesis**

Red blood cells (O2-capacity, arterial pO2) pO2-dependent production Kidney Erythropoietin (EPO) Bone marrow + Wolber and Jelkmann., News Physiol. Sci. 17: 6 (2002)

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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

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**Erythropoietin Receptor**

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 ~ pM Internalization rate ~ 0.7 h-1 receptors per erythroid cell Sawyer et al., JBC 262: 5554 (1987); Broudy et al., Blood 77: 2583 (1991)

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**rHuEPO Pharmacokinetics**

Time (hr) 80 160 240 320 400 rHuEPO concentration (IU/l) 1 10 100 1000 10000 300 IU/kg 600 IU/kg 1200 IU/kg 2400 IU/kg SC IV 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 = Slow absorption from the injection site: flip-flop kinetics. Flaharty et al., Clin. Pharmacol. Ther. 47: (1990). Ramakrishnan et al., J. Clin. Pharmacol. 44: (2004).

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**rHuEPO Pharmacodynamics**

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: (2005).

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**PK/PD Modeling Paradigm**

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

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**Receptor Mediated EPO Endocytosis and Degradation**

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

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**Target-Mediated Drug Disposition**

DIV DPO, F•ka Ko, TINF Serum Cp Vc Tissue DT Receptor Complex DR kon koff kel km kpt ktp Free [Rmax-DR] kdeg ksyn + Mager and Jusko. J Pharmacokinet Pharmacodyn. 28: (2001)

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**Erythropoietic Cascade**

Stem Cell BFU-e CFU-e Proerythroblast Erythroblast Reticulocyte RBC EPO responsive cells EPOR-/+ EPOR+++ EPOR+ EPOR- EPOR+/-

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**Lifespan Distribution**

Cell lifespan - time a cell remains in the population Mean lifespan-population mean of the lifespan distribution

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**Lifespan Controlled Cell Loss**

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

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**Basic Model: Stimulation of kin**

Baseline: R0 = kin·TR Krzyzanski and Jusko, JPB 27: 467 (1999).

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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: (2007).

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**TMDD PK/PD Model of rHuEPO**

Woo et al., JPP 34: (2007).

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PK/PD Model Equations Woo et al., JPP 34: (2007).

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PK/PD Model Equations Woo et al., JPP 34: (2007).

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**Initial Conditions , for t < 0, and , for t 0 , for t 0**

Woo et al., JPP 34: (2007).

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Baseline Equations Woo et al., JPP 34: (2007).

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**Residual Error Variance Model**

Parameter estimates were obtained by minimizing the -2LL objective function in ADAPT II. Woo et al., JPP 34: (2007).

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**Parameter Estimates a Parameter was fixed. 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 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: (2007).

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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.

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**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.

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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.

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Acknowledgments Sukyung Woo, PhD. William Jusko, PhD.

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