Mathematical optimization of a thrombopoiesis quantitative systems pharmacology (QSP) model
Authors: Ruiz-Martinez Alvaro , Dasika Krishnakant , Hurez Vincent , Reed Michael 
Published: February 2025

Objectives: Several models have been developed over the years to understand platelet dynamics and regulation of thrombopoiesis. Some reproduce observed oscillations in the platelet counts of normal humans, while others explored platelet dynamics in response to chemotherapy in cancer patients. Most of these models use complex mathematical representation, e.g., integro-differential equations [1,2]. Here, we optimized a recent QSP model of thrombocytopenia, finding the minimal model structure still able to reproduce experimental data. We set three goals: simplification of parameters and equations, calibration to match platelets data, and evaluation of response to chemotherapy of a reference virtual patient (VP) with normal platelet levels and a thrombocytopenic VP corresponding to acute myeloid leukemia (AML) patients.Methods: We researched previously published thrombopoiesis models and identified a recent QSP model [3] as the reference for this work. We developed a simpler fit-for-purpose thrombopoiesis QSP model using MATLAB’s SimBiology software. The model includes bone marrow (BM) and blood compartments with production and differentiation of megakaryocytes and platelets, regulated by TPO. The model also includes pharmacokinetics of two chemotherapy drugs. Platelet levels in blood is the primary clinical endpoint. Most parameter values were derived from literature. A few parameters were calibrated using test protocols to match published TPO bolus dose and chemotherapy data.Results: Compared to the original published QSP model, we reduced the number of BM megakaryocyte progenitor species from 28 to 8 while still being able to capture the complex dynamics of platelet levels. The implementation of TPO dynamics was simplified and its effect on megakaryopoiesis was corrected. In addition, chemotherapies were represented using simple expressions and non-regime-dependent parameters, unlike some previous models [4,5], which allows for simulating therapy protocols in a wide range of clinical settings. Simulations of azacitidine (AZA) monotherapy and AZA + venetoclax combinations in the reference VP matched the reduction in platelet levels measured in various studies. AZA + venetoclax combination was predicted to induce grade 3 to 4 thrombocytopenia and doubled blood and bone marrow TPO levels. The effect of AZA + venetoclax on TPO was consistent with the doubling of blood TPO levels reported with induction chemotherapy in AML patients [6]. We also confirmed that further reductions in the number of BM species fail to reproduce the platelet dynamics, indicating that an optimal model size has been achieved.Conclusions: We present an efficient fit-for-purpose thrombopoiesis QSP model that tackles the mathematical challenges of simulating megakaryopoiesis and platelet dynamics. Both the timing of the processes and the TPO dynamics are accurately represented. The model has been successfully tested for AZA monotherapy and AZA + venetoclax combination therapy.Citations: [1] R. Apostu and M.C. Mackey. J Theor Biol (2008) 251 (2) 297-316[2] G.P. Langlois et al. J Math Biol (2017) 75 (6-7) 1411-1462[3] R. Shimizu et al. Cpt Pharmacometrics Sys Pharmacol (2021) 10 (5) 489-499[4] M. Scholz et al. J Math Biol (2010) 264 (2) 287-300[5] Y. Kheifetz and M. Scholz. PLoS Comput Biol (2019) 15 (3):e1006775[6] C. Gonen et al. Platelets 16 (1):31-7