Multi-scale mathematical modelling of tumour growth and microenvironments in anti-angiogenic therapy

Yan Cai, Jie Zhang, Zhiyong Li

Angiogenesis, a process of generation of new blood vessels from the pre-existing vasculature, has been demonstrated to be a basic prerequisite for sustainable growth and proliferation of tumour. Anti-angiogenic treatments show normalization of tumour vasculature and microenvironment at least transiently in both preclinical and clinical settings. In this study, we proposed a multi-scale mathematical model to simulate the dynamic changes of tumour microvasculature and microenvironment in response to anti-angiogenic drug endostatin (ES). We incorporated tumour growth, angiogenesis and vessel remodelling at tissue level, by coupling tumour cell phenotypes and endothelial cell behaviour in response to local chemical and haemodynamical microenvironment. Computational simulation results showed the tumour morphology and growth curves in general tumour progression and following different anti-angiogenic drug strategies. Furthermore, different anti-angiogenic drug strategies were designed to test the influence of ES on tumour growth and morphology. The largest reduction of tumour size was found when ES is injected at simulation time 100, which was concomitant with the emergence of angiogenesis phase. The proposed model not only can predict detailed information of chemicals distribution and vessel remodelling, but also has the potential to specific anti-angiogenic drugs by modifying certain functional modules.