Meshwork pattern transformed from branching pattern in spherical shell domain

Abstract

The alveolar microvascular network is significant for the lung development of vertebrates, which is consisted of tree-like main veins and interconnected capillaries between the main veins. However, it is still unclear how the meshwork pattern is formed by the multigenerational branches.Based on the reaction-diffusion model, we find that the meshwork pattern is transformed from the branching pattern in a spherical shell domain. Furthermore, we find that it is the branch tip fusion that facilitates the meshwork pattern formation, which is guided by the activator peak fusion, and it is the insufficient space for branch tip growth that promotes the branch tip fusion. In addition, we notice that the consumption rate of substrate regulates the meshwork pattern formation and an asymmetric shell domain composed of prolate and oblate hemi-ellipsoidal shell facilitates the dense meshwork pattern formation.Our model provides a qualitative understanding of how the vascular system remodels from the branching pattern to the meshwork pattern and how to make a dense meshwork pattern.Both researches associated with branching and network morphogenesis can benefit from our work.