Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations
- Resource Type
- Authors
- Nicole Wilson; Corina S. Drapaca; Heiko Enderling; Jimmy J. Caudell; Kathleen P. Wilkie
- Source
- Bulletin of Mathematical Biology. 85
- Subject
- Pharmacology
Computational Theory and Mathematics
General Mathematics
General Neuroscience
Immunology
General Agricultural and Biological Sciences
General Biochemistry, Genetics and Molecular Biology
General Environmental Science
- Language
- ISSN
- 1522-9602
0092-8240
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.