Modelling tumour-induced angiogenesis: A review of individual-based models and multiscale approaches

A non-technical review of the main developments of the last 10 years in mathematical modelling of tumour-induced angiogenesis is presented. This field has seen much progress in recent times, therefore, for the sake of concreteness and brevity, we will focus on hybrid models in which the progression of the vascular network, described in terms of individual-based models, is coupled to blood flow and/or external factors due to the dynamics of its sorrounding tissue. The interest of such models is twofold: whilst they constitute the state-of-the-art as far as (potential) predictive power and clinical applicability is concerned, their analysis and numerical implementation also offer remarkable mathematical challenges.