| Mathematical modeling can help providing better understanding of the nature and characteristics of regulatory processes in hematology. We first review different mathematical approaches used for modeling so-called dynamical hematological diseases, which are characterized by oscillations in one or more blood cell lines. Then, we present two delay differential equation (DDE) models of the hematopoietic system designed for the study of the effects of Granulocyte-Colony Stimulating Factor (G-CSF) administration. G-CSF is used clinically for treating subjects presenting low numbers of white blood cells, a condition referred to as neutropenia that can result from different causes. However, even though G-CSF is widely used in clinical practice, it is not clear whether the standard G-CSF administration schedule is optimal. The aim of this work is to study alternative treatment regimens that would optimize the use of C-CSF using a mathematical modeling approach. The first model we propose is a comprehensive model that considers C-CSF administration for cyclical neutropenia, a dynamical disorder characterized by oscillations in the circulating neutrophil count. The second model focuses on the effects of two recombinant forms of G-CSF (filgrastim and pegfilgrastim) for the treatment of chemotherapy-induced neutropenia. For each model, we use a combination of mathematical analysis and numerical simulations to study alternative G-CSF treatment regimens that would be efficient while reducing the amount of drug. We found that the dynamical properties of the model could be exploited for designing better G-CSF treatment strategies. |
