Mathematical modeling of tumor growth dynamics for personalized therapy selection
Abstract
Purpose of the work: to analyze current approaches to mathematical modeling of tumor growth and prediction of their dynamics using classical deterministic models and machine learning methods, as well as to determine the prospects for their use in modern mathematical oncology and personalized antitumor therapy.
Research methods: analysis and systematization of modern scientific publications on mathematical oncology; use of mathematical modeling methods for tumor growth (exponential, logistic, Gompertz and Bertalanffy models); statistical analysis of clinical data; application of machine learning methods for regression analysis and prediction of tumor growth dynamics based on longitudinal MRI data from the open LUMIERE dataset.
As a result of the study, a review and comparative analysis of classical mathematical models of tumor growth and their modifications used to describe the biological processes of proliferation and restriction of tumor tissue growth was performed. Preliminary processing and analysis of clinical and imaging data, including the volumes of various tumor components, was carried out. Individual tumor growth trajectories were modeled using regression models and ensemble machine learning methods, in particular Random Forest. It was shown that machine learning methods provide more stable and accurate predictions of complex tumor growth dynamics compared to classical models in the case of high data variability.
Conclusions: Combining classical mathematical models of tumor growth with modern machine learning methods is a promising direction for the development of mathematical oncology. This approach improves the accuracy of predicting individual tumor dynamics and creates a basis for developing personalized treatment strategies. The results obtained indicate the feasibility of further use of hybrid models in research on precision medicine and personalized antitumor therapy.
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