Department of Mechanical Engineering, Faculty of Systems Science and Technology, Akita Prefectural University, Akita, 015-0055, Japan.
Graduate School of Science and Technology, Nara Institute of Science and Technology, Nara, 630-0192, Japan.
Sci Rep. 2022 Mar 8;12(1):4054. doi: 10.1038/s41598-022-08030-5.
Trees are thought to have acquired a mechanically optimized shape through evolution, but a scientific methodology to investigate the mechanical rationality of tree morphology remains to be established. The aim of this study was to develop a new method for 3D reconstruction of actual tree shape and to establish a theoretical formulation for elucidating the structure and function of tree branches. We obtained 3D point cloud data of tree shape of Japanese zelkova (Zelkova serrata) and Japanese larch (Larix kaempferi) using the NavVis Lidar scanner, then applied a cylinder structure extraction from point cloud data with error estimation. We then formulated the mechanical stress of branches under gravity using the elastic theory, and performed finite element method simulations to evaluate the mechanical characteristics. Subsequently, we constructed a mechanics-based theoretical formulation of branch development that ensures constant bending stress produces various branching patterns depending on growth properties. The derived theory recapitulates the trade-off among branch growth anisotropy, stress-gravity length, and branch shape, which may open the quantitative way to evaluate mechanical and morphological rationality of tree branches.
树木的形态被认为是通过进化而获得了机械优化，但仍需要建立一种科学的方法来研究树木形态的机械合理性。本研究旨在开发一种新的方法来重建实际树木形态的 3D 结构，并建立一个用于阐明树木分支的结构和功能的理论公式。我们使用 NavVis Lidar 扫描仪获取了日本榉树（Zelkova serrata）和日本落叶松（Larix kaempferi）的树木形状的 3D 点云数据，然后对点云数据进行了圆柱结构提取，并进行了误差估计。接着，我们使用弹性理论来描述树枝在重力作用下的机械应力，并进行了有限元方法模拟以评估其力学特性。随后，我们构建了一个基于力学的分支发育理论公式，该公式确保恒定的弯曲应力会根据生长特性产生各种分支模式。所得到的理论可以概括分支生长各向异性、应力-重力长度和分支形状之间的权衡关系，这可能为评估树木分支的力学和形态合理性提供了一种定量方法。
