Mathematical modelling has proven to be a valuable tool in predicting the delivery and efficacy of molecular, antibody-based, nano and cellular therapy in solid tumours. Mathematical models based on our understanding of the biological processes at subcellular, cellular and tissue level are known as mechanistic models that, in turn, are divided into continuous and discrete models. Continuous models are further divided into lumped parameter models — for describing the temporal distribution of medicine in tumours and normal organs — and distributed parameter models — for studying the spatiotemporal distribution of therapy in tumours. Discrete models capture interactions at the cellular and subcellular levels. Collectively, these models are useful for optimizing the delivery and efficacy of molecular, nanoscale and cellular therapy in tumours by incorporating the biological characteristics of tumours, the physicochemical properties of drugs, the interactions among drugs, cancer cells and various components of the tumour microenvironment, and for enabling patient-specific predictions when combined with medical imaging. Artificial intelligence-based methods, such as machine learning, have ushered in a new era in oncology. These data-driven approaches complement mechanistic models and have immense potential for improving cancer detection, treatment and drug discovery. Here we review these diverse approaches and suggest ways to combine mechanistic and artificial intelligence-based models to further improve patient treatment outcomes.
