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Excessive tumour growth results in a hypoxic environment around cancer cells, thus inducing tumour angiogenesis, which refers to the generation of new blood vessels from pre-existing vessels. This mechanism is biologically and physically complex, with various mathematical simulation models proposing to reproduce its formation. However, although temporary vessel regression is clinically known, few models succeed in reproducing this phenomenon. Here, we developed a three-dimensional simulation model encompassing both angiogenesis and tumour growth, specifically including angiopoietin. Angiopoietin regulates both adhesion and migration between vascular endothelial cells and wall cells, thus inhibiting the cell-to-cell adhesion required for angiogenesis initiation. Simulation results showed a regression, i.e. transient decrease, in the overall length of new vessels during vascular network formation. Using our model, we also evaluated the efficacy of administering the drug bevacizumab. The results highlighted differences in treatment efficacy: (1) earlier administration showed higher efficacy in inhibiting tumour growth, and (2) efficacy depended on the treatment interval even with the administration of the same dose. After thorough validation in the future, these results will contribute to the design of angiogenesis treatment protocols.

Mathematical simulation of tumour angiogenesis: angiopoietin balance is a key factor in vessel growth and regression