Chapter 7: Biomathematical engineering of cell renewal systems: Modeling of radiogenic responses induced by fractionated irradiation in malignant and normal tissue

The aim of this contribution is to outline how methods of system analysis, control theory and computer science can be applied to simulate malignant and normal cell growth and to optimize cancer treatment. Based on biological observations and cell kinetic data, our group has constructed three types of computer models: 1) A cell cycle model describing the spatial (3D) and temporal growth of tumor spheroids; 2) A compartment model describing the growth of rapidly proliferating normal cells; 3) A compartment model simulating slowly proliferating normal tissues. These growth models have been extended by an irradiation model based on the linear‐quadratic survival function. Different clinical fractionation schemes (standard‐, super‐, hyperfractionation and weekly high single dose) have been applied to the tissues mentioned above. The simulation results show that in the case of irradiating a rapidly growing tumor spheroid the hyperfractionation (3 x 1–1.5 Gy per day) leads to a particularly good anti‐tumor effectiveness. On the other hand, the radiogenic response of rapidly growing normal tissue to a hyperfractionated treatment schedule is severe. The same result is observed when simulating the late reaction on slowly growing parenchymal tissue. Therefore, this therapeutic modality is ensured only if the overall dose is reduced from DTOTAL = 60 Gy to DTOTAL = 50 Gy. Thus, it is possible to study radiation effect on tumors, and on different normal tissues, and to construct treatment schedules via computer simulations with the aim of a maximum tumor cell kill and a minimum radiation effect on normal cells.