Modelling radiation cancer treatment with ordinary and fractional differential equations
- June 1 (Thu) at 10:00 - 11:00, 2023 (JST)
- Dr. Kathleen Wilkie (Associate Professor, Department of Mathematics, Toronto Metropolitan University, Canada)
- via Zoom
- Catherine Beauchemin
Fractional calculus has recently been applied to 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.
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