AbstractThe aim of this article is to show how a tumor can modify energy substrates fluxes in the brain to support its own growth. To address this question we use a modeling approach to explain brain nutrient kinetics. In particular we set up a system of 17 equations for oxygen, lactate, glucose concentrations and cells number in the brain. We prove the existence and uniqueness of nonnegative solutions and give bounds on the solutions. We also provide numerical simulations.

中文翻译：

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脑中底物通量和肿瘤生长的数学建模

摘要本文的目的是展示肿瘤如何改变大脑中的能量底物通量以支持其自身的生长。为了解决这个问题，我们使用建模方法来解释大脑营养动力学。特别是，我们为大脑中的氧气、乳酸、葡萄糖浓度和细胞数量建立了一个由 17 个方程组成的系统。我们证明了非负解的存在性和唯一性，并给出了解的界限。我们还提供数值模拟。