Angiogenesis, or capillary growth from pre-existing vasculature, is an essential component of several physiological processes, both vital and pathological. These include dermal wound healing and tumour growth that together pose some of the most significant challenges to healthcare systems worldwide. Over the last few decades, mathematical modelling has proven to be a valuable tool for unravelling the complex network of interactions that underlie such processes. Moreover, theoretical frameworks that describe some of the mechanical and chemical aspects of angiogenesis inherent in wound healing and tumour growth have revealed intriguing similarities between the two processes. In this review, we highlight some of the significant contributions made by mathematical models of tumour-induced and wound healing angiogenesis and illustrate how advances in each field have been made using insights from the other. We also detail some open problems that could be addressed through a combination of theoretical and experimental approaches.

中文翻译：

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伤口愈合和肿瘤诱导的血管生成的当前观点

血管生成或来自预先存在的脉管系统的毛细血管生长，是多种生理过程的重要组成部分，包括重要的和病理的。其中包括皮肤伤口愈合和肿瘤生长，它们共同对全球医疗保健系统构成了一些最重大的挑战。在过去的几十年里，数学建模已被证明是解开这些过程背后复杂的相互作用网络的宝贵工具。此外，描述伤口愈合和肿瘤生长中固有的血管生成的一些机械和化学方面的理论框架揭示了这两个过程之间有趣的相似之处。在这次审查中，我们强调了肿瘤诱导和伤口愈合血管生成的数学模型做出的一些重要贡献，并说明了每个领域如何利用另一个领域的见解取得进展。我们还详细介绍了一些可以通过理论和实验方法相结合来解决的开放性问题。