Parameter estimation for leukocyte dynamics after chemotherapy

Abstract

Leukopenia is one of the most harmful side effects during chemotherapy treatment, since leukocytes (L) are crucial in protecting patients against bacteria and fungi. A personalized mathematical model of dynamics of L would allow a glimpse into the future and the initiation of tailored countermeasures.

We propose such a mathematical model and calibrate it based on a parameter estimation with real world data. For our study we used data of L during and after consolidation chemotherapy treatment (cytarabine) of six patients contracting acute myeloid leukemia. We compare two different ways to treat the unknown initial values of the system of ordinary differential equations, discuss patient-specificity of parameter values, and different scalings of the least squares formulation. These three comparisons are necessary considerations for all modeling approaches to biomedicine, and have thus a methodological scope beyond the specific case of leukopenia. In summary, we show that our approach is able to simulate L dynamics in response to chemotherapy treatment and allows to take patient-specific characteristics into account.