Biomathematical Models with State-Dependent Delays for Granulocytopoiesis

The development of a biomathematical model of the human granulopoiesis builds the core of this article. Hereby, the term granulopoiesis specifies the dynamical process of the generation of granulocytes, a subclass of white blood cells. The modeling of this process is based on delay differential equations with state-dependent delays in order to describe non-constant cell maturation times. This model is used to estimate the severeness of radiation damage and, furthermore, to predict the recovery of an irradiated person satisfying real-time requirements. This task is solved by the estimation of the initial conditions of the time delay model since they directly represent the degree of damage to the granulopoietic system harmed by acute radiation exposure. Since it is known that the integration and the parameter estimation for delay differential equations may pose severe difficulties, these problems are analyzed in detail for the model of granulopoiesis and suitable integration and optimization techniques are deduced. Several prediction results for real patient data are presented and show the power of our system in order to estimate an irradiation damage and to predict the recovery of granulopoiesis.