Chapter 7: Biomathematical engineering of cell renewal systems: An approach to a biomathematical model of lymphocytopoiesis

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Abstract
Fundamental principles for the development of a biomathematical model of lymphocytopoiesis are presented in this paper. The first step in this modeling approach is the definition of appropriate anatomical compartments in order to identify dominant locations of lymphocytes in the human body, and the definition of functional compartments in order to model different maturation stages. In the second step these compartment structures are combined, and thus form the basis of a dynamical model consisting of linear differential equations. Cell balance equations are used to derive the biomathematical dynamical model which is presented using the tools of modern systems theory. As a result of intensive discussions between engineers and medical doctors, our model of lymphocytopoiesis consists of six anatomical and six functional compartments. Virtual marking technique plays a key role for the interpretation of the simulation results which are in solid agreement with biological observations. Future work is directed towards implementation of radiation damages in order to meet the final goal, namely, the evaluation of our model against the data derived from a group of chronically irradiated uranium miners. Biomathematical model Lymphocytes