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Modeling Delays in Chemotherapy Induced Hematological Toxicities

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Modeling Delays in Chemotherapy Induced Hematological Toxicities Modeling Delays in Chemotherapy Induced Hematological Toxicities Wojciech Krzyzanski, PhD, MA University at Buffalo Virtual Symposium by National Capital Area Chapter of the Society of Toxicology June 25th 2020 1 Outline • Mechanisms of chemotherapy-induced hematological toxicities • Examples of neutropenia, thrombocytopenia, and anemia caused by anti-cancer agents • General structure of pharmacodynamic model of myelosuppression • Models of delays - Transit compartments - Distributed delays - Lifespan • Conclusions 2 Thymocyte THelper Hematopoietic IL-7 IL-1, IL-2, IL-7 T Progenitor Cell Cascade TKiller IL-2, IL-4, IL-5, IL-6 IL-3, IL-7 Lymphoid Stem Cell B Cell B Progenitor Cell IL-3 Pluripotent Stem Cell GM-CSF IL-3, G-CSF, GM-CSF Monocyte GM-CSF, G-CSF IL-3, IL-6, GM-CSF Granulocyte Monocyte Progenitor Cell Neutrophil Myeloid Stem Cell IL-3, GM-CSF IL-5, GM-CSF IL-3, GM-CSF Eosinophil Eosinophil Progenitor Cell IL-3, IL-11, EPO, IL-4, GM-CSF TPO, GM-CSF IL-3, GM-CSF,EPO Basophil Basophil Progenitor Cell IL-9 Mast Cell Megakaryocyte IL-6, EPO, TPO, GM-CSF Platelets Erthyroid Progenitor Cell EPO Red Blood Cell 3 Mould. (2005) Chapter: “Using Pharmacometrics in the Development of Biological Therapeutic Biological Agents”. Hematological Toxicities • Chemotherapy arrests cell cycle and/or induces apoptosis in proliferating progenitors cells in the bone marrow • This results in decrease in production of blood cells (myelosuppression): - white blood cells (leukopenia) - red blood cells (anemia) - platelets (thrombocytopenia) • Myelosuppression is common dose limiting toxicity for anticancer drugs • The time between administration of the drug and onset of this toxicity varies from 12 h to 8 weeks, depending on drug, dose, and schedule 4 Pharmacodynamic Models of Chemotherapy- Induced Hematological Toxicities • Quantify toxicity outcomes of clinical trials • Translate pre-clinical experiments to humans • Select maximum tolerable dose • Design of optimal treatment regimen • Predict risk of cytopenia Testart-Paillet et al., Critical Reviews in Oncology/Hematology 63 (2007) 1–11 5 Cytotoxic Effect of Cytarabine on Platelets Time course of platelet count (o) and thrombopoietin plasma concentration (•) in a AML patient following a high-dose cytarabine and idarubicin treatment. 6 Bernstein et al., J. Clin. Pharmacol. 42: 501-11 (2002). Cytotoxic Effect of Etoposide on Leukocytes Leukocyte counts during and after 72 hr infusion of 150 mg/m2 of etoposide. The leukocyte counts represent the mean of the population of 71 patients. 7 Krzyzanski and Jusko, J Pharmacokinet Biopharm 29: 311 (2002). Cytotoxic Effect of Carboplatin on RBCs in Rats Time course of reticulocytes (a), RBC (b), hemoglobin (c), and endogenous rat EPO (d) profiles after single i.v. administration of either saline (o) or 60 mg/kg carboplatin (•) in rats at day 0. 8 Woo et al., Cancer Chemother Pharmacol (2008) 62:123–133 Signature Profile of Blood Cell Response to Chemotherapy Maturation Onset Nadir Offset Rebound 9 Model of Chemotherapy-Induced Myelosuppression Fornali et al. Clin. Pharmacol. Ther. 104:4 (2018). 10 Transit Compartments Model of Chemotherapy-Induced Myelosuppression Prol= proliferative cells in bone marrow sensitive to drug. Transit = maturating cells in bone marrow. Circ = circulation observed blood cells. Friberg et al. J. Clin. Oncol. 20:4713 (2002). 11 Model of Chemotherapy-induced Myelosuppression d Pr ol Circ = k Pr ol 0 − k Pr ol − SlopeCProl prol tr Pr ol( 0 ) = Circ dt Circ 0 dTrans1 = k (Pr ol −Trans ) Trans1 ( 0 ) = Circ0 dt tr 1 dTrans2 = ktr (Trans1 −Trans2 ) dt Trans2 ( 0 ) = Circ0 dTrans 3 = k (Trans −Trans ) Trans ( 0 ) = Circ dt tr 2 3 3 0 dCirc = k Trans − k Circ Circ( 0 ) = Circ dt tr 3 circ 0 Friberg et al. J. Clin. Oncol. 20:4713 (2002). 12 Erlang Distribution 1 (t / t)n−1 (t) = e−t / t t (n −1)! Signal transduction: T = n·τ 0.5 mean t = mean transit time SD2 = n·τ2 0.4 n =1 t=2 dA1 1 1 = − A1, A1(0) = dt t t 0.3 dA 1 2 = A − A , A (0) = 0 ( 1 2 ) 2 P.D.F dt t 0.2 : 2 : dA 1 5 N = (A − A ), A (0) = 0 0.1 10 dt t N−1 N N 15 25 1 (t / t)N−1 0.0 A (t) = e−t / t 0 20 40 60 80 100 N t (N −1)! t Sun and Jusko, J. Pharm. Sci. 87:732 (1998) 13 Vinflunine-Induced Neutropenia Individual predicted profiles (lines) and observations (symbols) for the time course of neutrophils in 3 patients with different dose regimens of vinflunine. Arrows denote times of administration. 14 Friberg et al. J. Clin. Oncol. 20:4713 (2002). Distribution of Delays Input(t) Output(t) P P – population of cells that have assigned maturation times (delays, lifespans) :P→ [0,) random variable assigning every cell its lifespan ℓ(흉) – probability density function for distribution of 푶풖풕풑풖풕 풕 = ∞ 푰풏풑풖풕 풕 − 흉 ℓ 흉 풅흉 푰풏풑풖풕 ∗ ℓ(풕) = ׬ퟎ 15 Example: Convolution of Rectangular Input 퐼푛푝푢푡(푡) ℓ(휏) 퐼푛푝푢푡 ∗ ℓ(푡) 16 Gamma Distribution 0.10 = = 0.08 = 0.06 P.D.F. 0.04 0.02 0.00 0 20 40 60 80 100 t 푘 푔휈 휏 = 푘휏 휈−1푒푥푝 −푘휏 푘 Γ(휈) 휈 Mean: 푀푇푇 = 휈 > 0 -shape parameter 푘 푣 푘- rate parameter Standard deviation: 푆퐷 = 푘 1/푘 -scale parameter 휈−1 Mode: , 휈 > 1 Γ(휈) – Euler gamma function 푘 ∞ Γ 휈 = 푡휈−1푒−푡푑푡 Γ 푛 = 푛 − 1 ! 푛 = 1,2, … ׬0 for 17 Model of Myelosuppression with Distributed Delay Circ 0 Circ kprol k ktr Pr ol* g ,ktr circ Prol Circ SlopeC d Pr ol Circ0 = k prol Pr ol − ktr Pr ol − SlopeC Pr ol dt Circ dCirc = k Pr ol* g − k Circ dt tr ,ktr circ Circ( 0 ) = Circ0 Pr ol( t ) = Circ0 , t 0 Krzyzanski W, Hu S, Dunlavey M, J. Pharmacokinet Pharmacodyn (2018) WBC Response to 5-Fluorouracil in Rats • Four groups of rats received IV bolus doses of 5FU: Placebo, Single (127 mg/kg on day 0), Double (63 mg/kg on day 0 and 2), and Triple (49 mg/kg on day 0, 2, and 4). WBC counts were measured up to 25 days following first dose. • Lines represent fitting the data by distributed delays (blue) and transit compartment (red)models 19 Krzyzanski W, Hu S, Dunlavey M, J. Pharmacokinet Pharmacodyn (2018) Friberg et al. JPET 295:734–740 (2000) Lifespan Model of Hematologic Effects of Anticancer Agents k in T TM T P P M R R f(C) loss rateP(t) = killing rate(t) + conversion rate(t) killing rate(t) = f(C(t))·P(t) t conversion rate(t) = k exp− f(C(z))dz in t−TP 20 Krzyzanski and Jusko, J Pharmacokinet Biopharm 29: 311 (2002). Cell Count in the Circulation Pool dR = k SF(t − T ) − k SF(t − T − T ) dt in M in M R t SF(t) = exp− f(C(z))dz Surviving Fraction: t-TP Linear Cytotoxicity: f(C) = k·C KmaxC Nonlinear killing: f (C) = KC50 + C 21 Krzyzanski and Jusko, J Pharmacokinet Biopharm 29: 311 (2002). Role of Dose and Cell Cytotoxicity Function 1000 100 C0=1000 10 k 1 100 in 0.1 T TM T 10P R 0.01P M R 0.001 1 Concentration C 0 50 100 150 200 250 100 80 f(C) 60 f(C) = k·C 40 Response R Response 20 0 0 50 100 150 200 250 100 80 K C f(C) = max 60 KC50 + C Response R Response 40 0 50 100 150 200 250 Time 22 Krzyzanski and Jusko, J Pharmacokinet Biopharm 29: 311 (2002). Cytotoxic Effect of Paclitaxel on Neutrophils Bulitta et al., Cancer Chemother. Pharmacol. 63:1035-48 (2009). 23 Cytotoxic Effect of Paclitaxel on Neutrophils The time course of neutropenia in cancer patients following treatment with a tocopherol-based Cremophor-free formulation (Tocosol) and Cremophor EL-formulated paclitaxel. In a randomized two-way crossover trial patients received 175 mg/m2 paclitaxel as either 15 min (Tocosol) or 3 h (Taxol) intravenous infusions. The plot shows the median, 10, 25, 75, and 90% percentiles of the simulated ANC profiles plotted on top of the individual observations. 24 Bulitta et al., Cancer Chemother. Pharmacol. 63:1035-48 (2009). Conclusions • Major mechanism for chemotherapy-induced hematological toxicities is suppression of myeloid precursor cells in the bone marrow • Delays in cell blood response to chemotherapy are caused by time necessary for bone marrow cells to mature and differentiate before release into the circulation • Mathematical models of delays include ordinary differential equations (transit compartments), integral-differential equations (distributed delays), and delay differential equations (lifespan) • Most pharmacometric software is equipped with solvers for ODEs and DDEs. Convolution integrals are implemented in Phoenix (Certara) 25.
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