Topology of leaf veins: Experimental observation and computational morphogenesis

The unique, hierarchical patterns of leaf veins have attracted extensive attention in recent years. However, it remains unclear how biological and mechanical factors influence the topology of leaf veins. In this paper, we investigate the optimization mechanisms of leaf veins through a combination of experimental measurements and numerical simulations. The topological details of three types of representative plant leaves are measured. The experimental results show that the vein patterns are insensitive to leaf shapes and curvature. The numbers of secondary veins are independent of the length of the main vein, and the total length of veins increases linearly with the leaf perimeter. By integrating biomechanical mechanisms into the topology optimization process, a transdisciplinary computational method is developed to optimize leaf structures. The numerical results show that improving the efficiency of nutrient transport plays a critical role in the morphogenesis of leaf veins. Contrary to the popular belief in the literature, this study shows that the structural performance is not a key factor in determining the venation patterns. The findings provide a deep understanding of the optimization mechanism of leaf veins, which is useful for the design of high-performance shell structures.