Travelling Waves for Low–Grade Glioma Growth and Response to A Chemotherapy Model

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

International Journal of Applied Mathematics and Computer Science Pub Date : 2023-12-01 DOI:10.34768/amcs-2023-0041

Agnieszka Bartłomiejczyk, Marek Bodnar, Magdalena U. Bogdańska, M. Piotrowska

引用次数: 0

Abstract

Abstract Low-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the existence of travelling wave solutions in the framework of Fenichel’s invariant manifold theory. The estimates of the minimum speeds of the travelling wave solutions are provided. The obtained analytical results are illustrated by numerical simulations.

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低级别胶质瘤生长和对化疗模型反应的游走波

摘要低级别胶质瘤（LGGs）是一种原发性脑肿瘤，其发展速度非常缓慢，但不可避免地会导致患者死亡。在本文中，我们考虑了之前提出的 ODE 模型的 PDE 版本，该模型描述了功能存活的 LGGs 细胞和因化疗而不可逆转地受损的细胞的密度变化。除了模型的基本数学特性外，我们还在费尼切尔不变流形理论的框架内研究了行波解存在的可能性。我们提供了行波解的最小速度估计值。我们通过数值模拟来说明所获得的分析结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Applied Mathematics and Computer Science 工程技术-计算机：人工智能

CiteScore

4.10

自引率

21.10%

发文量

审稿时长

4.2 months

期刊介绍： The International Journal of Applied Mathematics and Computer Science is a quarterly published in Poland since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland (Sciendo) and Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences. The journal strives to meet the demand for the presentation of interdisciplinary research in various fields related to control theory, applied mathematics, scientific computing and computer science. In particular, it publishes high quality original research results in the following areas: -modern control theory and practice- artificial intelligence methods and their applications- applied mathematics and mathematical optimisation techniques- mathematical methods in engineering, computer science, and biology.