Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations.

Autor: Wilson N; Department of Mathematics, Toronto Metropolitan University, Toronto, Canada., Drapaca CS; Engineering Science and Mechanics, Pennsylvania State University, University Park, USA., Enderling H; Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, USA.; Department of Radiation Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, USA., Caudell JJ; Department of Radiation Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, USA., Wilkie KP; Department of Mathematics, Toronto Metropolitan University, Toronto, Canada. kpwilkie@torontomu.ca.
Jazyk: angličtina
Zdroj: Bulletin of mathematical biology [Bull Math Biol] 2023 Apr 25; Vol. 85 (6), pp. 47. Date of Electronic Publication: 2023 Apr 25.
DOI: 10.1007/s11538-023-01139-2
Abstrakt: Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but its use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here, we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.
(© 2023. The Author(s).)
Databáze: MEDLINE
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