485P - A spatio-temporal evolution mathematical model of glioma growth: The influence of cellular and nutrient interactions on the tumor microenvironment

Background

Gliomas 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.

Methods

We 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 C_c (t,x), C_m (t,x), and C_n (t,x),was solved by the Method of Lines (MOL).

Results

In table we present some results for the average tumor cell population (N_c - Cells) as a function of time (in the limit cases when k_n and k_cm are very small and a = 0, 62.5) and comparisons with literature data. N_c - Cells for a = 0 and a = 62.5. Table: 485P

Conclusions

Results 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.

Clinical trial identification

Editorial acknowledgement

Legal entity responsible for the study

The authors.

Funding

Has not received any funding.

Disclosure

All authors have declared no conflicts of interest.