Optimum experimental design for patient specific mathematical Leukopenia models

Abstract

Mathematical models are essential for simulation-driven decision support for clinical doctors. For an estimation of parameters for patient specific models, values such as the number of certain blood cells need to be measured. In this paper we focus on leukopenia, a clinically important side effect arising from the treatment of leukemia with chemotherapy. A mathematical leukopenia model is presented describing the dynamics of leukocytes and we show that the standard deviations of the parameter estimates depend strongly on the timing of the measurements. We discuss the issue of measurement time points for two patients being in the consolidation phase of acute myeloid leukemia and provide optimal solutions. Optimized measurement time points and the thus enabled accurate simulations have a large impact: drug treatments can be adapted individually and patients may safely leave the hospital for longer and more convenient time intervals. The dynamics of leukocytes are modeled by a system of ordinary differential equations and the chemotherapy with cytarabine is described by a pharmacokinetics/pharmacodynamics model consisting of two compartments and a log-linear function representing the drug effect. The measurement time points are optimized by optimal experimental design. With optimal experimental design an average parameter uncertainty reduction of 57% (Patient 1 ) and 80% (Patient 2 ) can be achieved compared to the clinical experimental designs, with the same total number of measurements. These enco