<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Dec 21, 2023

Page range: 569 - 581

Received: Nov 11, 2022

Accepted: Jun 30, 2023

DOI: https://doi.org/10.34768/amcs-2023-0041

Keywords
glioma, tumour, generalized model, treatment, partial differential equations, wave solutions, chemotherapy

© 2023 Agnieszka Bartłomiejczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Dec 21, 2023

Page range: 569 - 581

Received: Nov 11, 2022

Accepted: Jun 30, 2023

DOI: https://doi.org/10.34768/amcs-2023-0041

Keywordsglioma, tumour, generalized model, treatment, partial differential equations, wave solutions, chemotherapy

© 2023 Agnieszka Bartłomiejczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
glioma, tumour, generalized model, treatment, partial differential equations, wave solutions, chemotherapy