Abstract
AbstractFractional 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.
Funder
Natural Sciences and Engineering Research Council of Canada
NIH National Cancer Institute
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Agricultural and Biological Sciences,Pharmacology,General Environmental Science,General Biochemistry, Genetics and Molecular Biology,General Mathematics,Immunology,General Neuroscience