Simulation of the chemical stage in water radiolysis with the help of Continuous Petri nets

The final biological effect of ionizing particles may be influenced often strongly by some chemical substances present in cells during irradiation by low-LET radiation. It may occur during the chemical stage of the given process, due to chemical reactions of radicals running in the given process. However, the whole chemical process may be hardly described sufficiently with the help of the usual approach based on the deterministic diffusion-kinetic computations and the stochastic Monte-Carlo simulations. We have proposed already earlier a model describing the processes (i.e., the combined effect of cluster diffusion and chemical reactions) running in individual radical clusters that might be responsible for corresponding damages of DNA molecules (i.e., formation of DSBs). Now a further generalization of the given model (using Continuous Petri nets) will be presented that makes it possible to characterize more detailed behavior of individual radicals in corresponding clusters, which might be useful especially for low-LET radiation when individual radical clusters meet a DNA molecule at different time intervals after their formation; the decreasing presence of individual radicals in corresponding clusters being established. In this paper we shall focus on the design of the corresponding mathematical model and its application; the comparison of corresponding results with experimental data obtained in the case of deoxygenated system will be presented.