PDF(Pubmed)
Abstract：
Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.
摘要：
在过去的40年里,人们一直非常关注血管生成数学模型的发展，虽然发育重塑很少受到数学界的关注。发芽的血管生成可以被视为一种非常粗糙的方法来布置原始的血管网络（原材料），在改造时(被理解为修剪多余的船只，直径控制,以及船舶身份和层次结构的建立）是将原始网络转变为功能网络的关键。这种多尺度问题在功能性脉管系统的发展中至关重要。此外,有缺陷的重塑（在发育重塑过程中或由于受伤引起的重塑计划的重新激活）与许多疾病有关。在这次审查中,我们讨论了现有的发育重塑的数学模型，并探讨了这些模型对血管发育领域的重要贡献。这些数学模型可有效地用于研究和预测血管发育，并能够重现实验可观察到的结果。此外，这些模型提供了一种有用的假设生成手段，并且可以解释驱动观察到的结构和功能网络发展的潜在机制。然而,发育性血管重塑在数学生物学中仍然是一个相对较新的领域，许多生物学问题仍然没有答案。在这次审查中,我们介绍了现有的建模范式，并定义了该领域的关键挑战。
