Stochastic Model of the Processe of the Spread of Platinum Drugs in Tumor Tissues

Purpose: The study of the kinetics of the spatio-temporal distribution of cisplatin, as an agent capable of increasing the effectiveness of chemo-radiation therapy of solid tumors. Material and methods: The material was the data of literature on the results of experiments of various groups of authors who studied the content of platinum in tissues on biopsy materials. The method of simulation mathematical modeling (in silico) is used, based on the biological patterns of tumor growth, morphofunctional changes in the structure of tumor cells and tissues. Model is based on reaction-diffusion equation system, coefficients of which are random functions of space and time. The model takes into account the sequence of processes from intravenous administration of cisplatin and its spatial distribution in various tissues, until the excretion of its addicts from the cell. Results: The heterogeneity of the distribution of the concentration of platinum atoms in the tumor is shown. Perhaps this is due to the varying degree of vascularization of tissues, the rate of metabolism of the tumor occurring in the outer layer and in its hypoxic core. These processes lead to significant errors when evaluating the biopsy data obtained in the experiments and the analysis of platinum content in the biopsy. Conclusions: The calculation assessments of the distribution of platinum atoms in the tumor are consistent with the literature on the concentration of cisplatin in biopsy samples for carcinoma. The results of the calculations on the described model are fair, taking into account the morphological type, the size of the tumor and the plan of the administration of the drug. For other conditions (cancer types, treatment regimens, etc.), new calculations are necessary. To increase the efficiency of combined chemo-radiation therapy, cisplatin should be introduced at least 72 hours before the start of radiation therapy.