Analyzing the impact of proliferation and treatment parameters on low-grade glioma growth using mathematical models

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-02-01 DOI:10.1016/j.physd.2024.134491

M. Bodnar , M. Vela-Pérez , A. Tryniecka-Maciążek

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引用次数: 0

Abstract

Low-grade gliomas (LGGs) are characterized by their slow growth and infiltrative nature, making complete surgical resection challenging and often resulting in the need for adjunctive therapies. This study introduces a mathematical model appeared in Ribba et al. (2012) aimed at elucidating the growth patterns of LGGs and their response to chemotherapy. Our model undergoes validation against clinical data, demonstrating its efficacy in accurately describing real patient data. Through mathematical analysis, we establish the existence of a unique non-negative solution and delve into the stability of steady-state solutions. Notably, we establish the global stability of a tumor-free equilibrium under conditions of sufficiently robust constant and asymptotically dynamics in the case of periodic treatment. Additionally, a sensitivity analysis highlights the proliferation rate as the primary determinant of model outcomes. Finally, numerical simulations are employed to explore the stability of the fitting procedure.

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.