A Numerical Method for Structured Population Equations Modeling Control of Erythropoiesis

Population equations with more than one structuring attribute play an essential role in modeling cell populations important for the process of erythropoiesis. Attributes in this case are cell age, iron content of cells and number of transferrin receptors on the cell membrane. The system is controlled via a feedback control using the oxygen carrying capacity of blood (which is determined by the number of red blood cells) as input for the controller and erythropoietin secreted by the kidneys as control for the system. The numerical algorithm is based on Trotter-Kato type approximations of the system state by system states of high order ordinary differential equations on finite dimensional subspaces of the state space of the system. These finite dimensional subspaces are generated by Legendre polynomials.