A spatio-temporal evolution mathematical model of glioma growth: The influence of cellular and nutrient interactions on the tumor microenvironment

BackgroundGliomas are primary tumors originating in the brain parenchyma known for their aggressive and diffusive behavior. The diagnosis is based on pathological anatomy that consists of morphological, immunohistochemical and molecular analysis. Simulating the behavior of gliomas in mathematical modeling is a powerful tool in evaluating tumor growth, as well as assisting in therapeutic decision-making.MethodsWe propose a mathematical model of continuous evolution of glioma that seeks to predict its spatio-temporal evolution through interactions of cell populations (concentration (C) of cancer cells “C_C� and dead cells “C_m�) with microenvironment (Mev) nutrients (nutrient C “ C_n�). As it is a complex phenomenon, this model takes into account the process of cell division (proliferation), death and motility. The cell division rate is assumed to follow a logistic model where the proliferation coefficient “r(C_C, C_n)� will be evaluated depending on the C of diseased cells (C_C) and nutrients (oxygen - C_n). The motility coefficient (D_c) and the Mev support capacity (C_Tmax) vary spatially as presented in the literature. For the cell death rate, it was considered that this is a function of the nutrient concentration “k_cm (C_n)� in the Mev. The non-linear system of partial differential equations, for the variables Cc (t,x), Cm (t,x), and Cn (t,x),was solved by the Method of Lines (MOL).ResultsIn table we present some results for the average tumor cell population (Nc - Cells) as a function of time (in the limit cases when kn and kcm are very small and a = 0, 62.5) and comparisons with literature data. Nc - Cells for a = 0 and a = 62.5. Table: 485P t (days) a = 0 a = 62.5 Present Ref. [1] Ref. [2] Present Ref. [1] Ref. [2] 1080 1710 — 1752 3116 3134 3126 ConclusionsResults for C, Nc - Cells, average tumor size and growth rate were obtained and compared to those available in the literature, showing that the presente model, with contributions that make it more rigorous and complex, appears to be physically coherent and capable of evaluating the spatio-temporal tumor growth.Legal entity responsible for the studyThe authors.FundingHas not received any funding.DisclosureAll authors have declared no conflicts of interest.