research-article
Authors: Sweta Sinha and Paramjeet Singh
Acta Applicandae Mathematicae, Volume 191, Issue 1
Published: 05 June 2024 Publication History
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Abstract
Tumour growth is a complex process influenced by various factors, including cell proliferation, migration, and chemotaxis. In this study, a biphasic chemotaxis model for tumour growth is considered, and the effect of chemotherapy on the growth process is investigated. We use optimal control theory to derive the optimized treatment strategy that minimises the tumour size while minimising the toxicity associated with chemotherapy. Moreover, the existence, uniqueness, and strong solution estimates for the biphasic chemotaxis model subsystem in one dimension are derived. These results are achieved through semigroup theory and the truncation method. In addition, the research provides evidence of the existence of an optimal pair through the utilization of the minimising sequence technique. It also demonstrates the differentiability of the mapping from control variable to state variable and establishes the first-order necessary optimality condition. Lastly, a sequence of numerical simulations are presented to showcase the impact of chemotherapy and the influence of parameters in restraining tumour growth when applied in an optimized manner. Our results show that optimal control can provide a more effective and personalised treatment for cancer patients, and the approach can be extended to other tumour growth models.
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Published In
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications Volume 191, Issue 1
Jun 2024
345 pages
ISSN:0167-8019
Issue’s Table of Contents
© The Author(s), under exclusive licence to Springer Nature B.V. 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 05 June 2024
Accepted: 23 May 2024
Received: 01 August 2023
Author Tags
- Mathematical modelling
- Biphasic model
- Tumour growth
- Chemotaxis
- Chemotherapy
- Drug transport
- Optimal control
Author Tags
- 92C17
- 35M13
- 49K30
- 92-10
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