A spatially resolved mechanistic growth law for cancer drug development

Mathematical models used in pre-clinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumour volume, however, they typically have little connection with the underlying physiological processes. This lack of a mechanistic underpinning restricts their flexibility and inhibits their direct translation across studies including from animal to human. Here we present a mathematical model describing tumour growth for the evaluation of single agent cytotoxic compounds that is based on mechanistic principles. The model can predict spatial distributions of cell subpopulations, tumour growth fraction as well as include spatial drug distribution effects within tumours. Importantly, we demonstrate the model can be reduced to a growth law similar in form to the ones currently implemented in pharmaceutical drug development for pre-clinical trials so that it can integrated into the current workflow. We validate this approach for both cell-derived xenograft (CDX) and patient-derived xenograft (PDX) data. This shows that our theoretical model fits as well as the best performing and most widely used models. Our work opens up current pre-clinical modelling studies to also incorporating spatially resolved and multi-modal data without significant added complexity and creates the opportunity to improve translation and tumour response predictions. SignificanceA mechanistic model is presented that has the same growth law structure as currently used models for cancer drug development. However, deriving from the mechanistic framework the model is shown to also predict necrotic and growth fractions in the tumour as well as account for variations in spatial drug distribution.