Parameter identification for population equations modeling erythropoiesis

Abstract

Physiological models explaining the anemia of chronic kidney disease have become more complicated over the last years. Identification of model parameters poses difficulties as measurements are very limited. A model for erythropoiesis, consisting of coupled partial differential equations, is adapted to individual patients. The numerical approximations make use of evolution operators and are based on the theory of abstract Cauchy problems. The abstract Cauchy problems corresponding to the model equations are approximated by Cauchy problems on finite-dimensional subspaces of the state space of the original problem. A low approximation dimension suffices to obtain accurate numerical solutions and estimates for the parameters. An example of (locally) well identifiable parameters expressing numerical convergence for increasing dimensions of the finite dimensional approximating system is discussed. Moreover, it is demonstrated that a clever choice of cost-functionals can reduce the observation time needed for parameter identification from 150 to 90 days.