ANALYTICAL DESCRIPTION OF GROWTH
ANALYTICAL DESCRIPTION OF GROWTH
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DOI：
10.1016/0022-5193(82)90301-0
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发表时间：
1982-01-01
影响因子：
2
通讯作者：
VILMANN, H
中科院分区：
文献类型：
--
作者：
SKALAK, R;DASGUPTA, G;VILMANN, H
生长的数学描述的方法进行了审查和扩展。描述的主要模式是识别构成动物或植物的质点的物质点路径（在时空中）。动物基本粒子的空间位置和质量被认为在时空中是连续的。位移函数中允许不连续性，以允许滑动，如膝关节;在表面的突然粘附或不粘附的意义上，以及在拓扑结构中，如环的完成或打开，也允许不连续性。当细胞在整个过程中增殖或萎缩时，组织生长被认为是时空中的分布式源或汇。骨表面的沉积或吸收被认为是时空中质量源或质量汇的表面分布。所涉及的数学描述的理想化的例子说明的理论框架。
Methods for the mathematical description of growth are reviewed and extended. The main mode of description is that of identifying the material point paths (in space-time) of the mass points which make up the animal or plant. Spatial location and mass of the elementary particles of the animal are considered to be continuous in space-time. Discontinuities are allowed in displacement functions to allow for slip, as in a knee joint; discontinuities are also allowed in material properties in the sense of sudden adhesion or non-adhesion of surfaces and in topology, such as the completion or opening of a ring. When cells proliferate or atrophy throughout, tissue growth is considered as distributed sources or sinks in space-time. Deposition or resorption on the surface of a bone is considered to be a surface distribution of mass sources or sinks in space-time. The theoretical framework is illustrated by idealized examples of mathematical descriptions involved.