Abstract
AbstractThe study of vascular network morphology is of great significance for the analysis and treatment of diseases. However, the mechanism of vascular network formation during angiogenesis is still not fully understood. The mathematical model of angiogenesis is an important means to study the formation and morphology of vascular network. It is an important way to reveal the underlying principles of biology through mathematical equations. Over the past 30 years, models of vascular network morphology have achieved great advances. Different from other studies, we reviewed the vascular network mathematical models in the process of development, and established a new model constructure system based on the reaction diffusion theory, phase field theory, and the cellular automata theory. The key discrete factors in the construction of the mathematical model for the morphology of the vascular network were also explored. Moreover, we concluded the characteristic application fields of the vascular network mathematical models. Finally, we summarized the deficiency and improvement thoughts of the mathematical model of vascular construction, and analyzed the development ideas and prospects of mathematical role in the field of vascular research.KeywordsMathematical modelVascular network morphologyAngiogenesis
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