植物叶片中轴图式的形态机理研究

Research on the Morphology Mechanism of the Medial Axis Pattern of Plant Leaf

中轴图式是生物组织一个普遍而显著的特征.为探讨植物叶片中轴图式的形态机理,采集了双子叶植物叶片的坐标数据并生成了叶片模型.依数学与形态的关系计算了叶片边缘与叶脉之间的角度,从理论上分析出叶脉其实是一个完美的等角坐标系.叶脉在结构上实际上是一种对称特征,在传递养料方面路径是最短且最有效的,完全符合路径最短与对称原理.建立了叶脉的分枝模型,分析了叶片主脉两侧生长的力学平衡关系.由于环境应力的不对称性使得叶片左右两侧的生长速度并不相等,但差异并不大.对侧脉的角度测量表明,叶脉分布体现了叶脉传输物质路径的最短形式,与其保持自身的能量稳定性有很大关系,植物叶片在生长过程中是符合最大生长率与系统最小势能的生态学约束关系的.

The medial axis pattern is one of a common and significant features of biological tissue.In order to reveal the morphology mechanism of medial axis pattern of plant leaf,some plant leaf models were generated according to the coordinate data of the dicot leaf.The angle between the edge of the plant leaf and the vein is calculated according to the relationship between mathematics and morphology,and the vein is actually a perfect equiangular coordinate system by theoretical analysis.In actually,the vein in the structure is a symmetric feature,and the nutrient transfer path is the shortest and the most effective,which is conform to the shortest path and the principle of symmetry completely.A branch vein model was established and the mechanical equilibrium relationship of growth on both sides of main leaf veins was analyzed.The growth rate of the left and right sides of the leaf is not equal because of the asymmetry of the environmental stress,but the difference in size is slight.The angle measurement of lateral veins show that the vein distribution reflects the shortest form of transport path,which has a great relationship with its energy stability.The growth process of plant leaves is consistent with the maximum growth rate and the minimum potential energy of the system in ecological constraints.