Modelling the response of spatially structured tumours to chemotherapy: Drug kinetics

In this paper we consider the effects of a single anticancer agent on the growth of a solid tumour in the context of a simple mathematical model for the latter. The tumour is assumed to comprise a single cell population which reproduces and dies at a rate dependent on the local drug concentration. This causes cell movement and so establishes a velocity field within the tumour. We investigate the action of a single chemotherapeutic drug on the tumour and explore how different drug kinetics and treatment regimes may affect the final treatment outcome. A single infusion of drug is shown to be more effective than repeated short applications. We are able to construct asymptotic solutions to the model in the limit of a small drug degradation rate; these closely match solutions obtained numerically and provide additional insight into the behaviour of the tumour, in particular allowing the prediction of the strength of drug required to achieve tumour regression.