On assessing quality of therapy in non-linear distributed mathematical models for brain tumor growth dynamics

Mathematical analysis on a diffusion model describing the compatibility between two types of tumor cells

“…The spatiotemporal dynamics of a model of cancer invasion was explored by Domschke et al [22], where the change of adhesion properties during cancer growth and development was investigated through time-dependent adhesion characteristics; the computational simulation results demonstrate a range of heterogeneous dynamics which were qualitatively similar to the invasive growth patterns observed in a number of different types of cancer. Bratus et al [23] presented a mathematical model for glioma therapy with nonlinear spatially varying diffusion depending on a parameter. To find a good estimate for the lower bound of the cost function, the quality of the optimal strategy of treatment with the quality of another one was compared.…”

Simulation analysis for tumor radiotherapy based on three‐component mathematical models

“…The metabolic process of cancer is so complicate that its mechanism is still not revealed completely until now. Researchers try their best to develop many models for clinical treatment of cancer including mathematical models, which were proposed in the early 1900s and deepened in this century with the development of computer . In these models, the features of tumor growth have been deduced into some basic mathematical theories such as signal processing, image analysis, and stochastic field theory, then, all the models were formulated mathematically according to the different theories and fitted with huge experimental or clinical data for tumor growth prediction and effective evaluation of tumor treatment…”

Survival task for the mathematical model of glioma therapy with blood-brain barrier

“…Создание достоверной математической модели терапии глиомы позволит, во-первых, охватить весь объем возможных вариантов комбинаций терапевтического воздействия, во-вторых, решить задачу оптимального управления, подобрав наилучшую стратегию лечения, останавливающую рост опухоли. Предложенная математическая модель продолжает наши работы [Bratus et al, 2014;. При построении математической модели и идентификации параметров учитывалось состояние экспериментальных групп крыс, а именно объем гломы в определенные моменты времени и срок жизни животного.…”