Abstract
Mathematical models used in preclinical drug discovery tend to be based on 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
and, in general, are not spatially resolved. This lack of a mechanistic underpinning restricts their
flexibility and inhibits their direct translation across studies.
In this thesis we build on the well-studied continuum approach of modelling cancerous tumour
growth. We present a spatially resolved mathematical model describing tumour growth for the
evaluation of single agent cytotoxic compounds that is based on nutrient di↵usion. Upon assuming
a spherical geometry for the tumour we show that the model can predict spatial distributions of
cell subpopulations, tumour growth fraction, as well as spatial drug distribution within tumours.
Importantly, we demonstrate the model can be reduced to a growth law similar in form to those
currently implemented in pharmaceutical drug development for preclinical trials so that it can be
integrated into the current workflow. By validating this approach for both Cell-derived xenograft
(CDX) and Patient-derived xenograft (PDX) data, we show that our theoretical model fits as
well as the best performing and most widely used models in drug discovery. Our work opens
current preclinical 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.
Utilising the model we explore the Norton-Simon hypothesis of dose scheduling. Alternative
dose schedules are also explored to better reduce the tumour burden and control regrowth while
satisfying current best practice guidelines of the RECIST criteria.
Taking another direction we conduct an initial exploration into the e↵ects of delayed proliferation
of the quiescent cell subpopulation on cytotoxic treatment. We do so by extending the previous
model formulation to incorporate this delay. The result is a system of delay di↵erential equations
which we solve numerically. This additional complexity is considered because cellular quiescence is
thought to provide tumours a mechanism of resistance to treatment. This preliminary work opens
up numerous avenues to investigate strategies to avoid such resistance.