A model of vascular tumour growth in mice combining longitudinal tumour size data with histological biomarkers

Optimising the delivery of antiangiogenic drugs requires the development of drug-disease models of vascular tumour growth that incorporate histological data indicative of cytostatic action. In this study, we formulated a model to analyse the dynamics of tumour progression in nude mice xenografted with HT29 or HCT116 colorectal cancer cells. In 30 mice, tumour size was periodically measured, and percentages of hypoxic and necrotic tissue were assessed using immunohistochemistry techniques on tumour samples after euthanasia. The simultaneous analysis of histological data together with longitudinal tumour size data prompted the development of a semi-mechanistic model integrating random effects of parameters. In this model, the peripheral non-hypoxic tissue proliferates according to a generalised-logistic equation where the maximal tumour size is represented by a variable called 'carrying capacity'. The ratio of the whole tumour size to the carrying capacity was used to define the hypoxic stress. As this stress increases, non-hypoxic tissue turns hypoxic. Hypoxic tissue does not stop proliferating, but hypoxia constitutes a transient stage before the tissue becomes necrotic. As the tumour grows, the carrying capacity increases owing to the process of angiogenesis. The model is shown to correctly predict tumour growth dynamics as well as percentages of necrotic and hypoxic tissues within the tumour. We show how the model can be used as a theoretical tool to investigate the effects of antiangiogenic treatments on tumour growth. This model provides a tool to analyse tumour size data in combination with histological biomarkers such as the percentages of hypoxic and necrotic tissue and is shown to be useful for gaining insight into the effects of antiangiogenic drugs on tumour growth and composition.