Hart R T, Davy D T, Heiple K G
Calcif Tissue Int. 1984;36 Suppl 1:S104-9. doi: 10.1007/BF02406142.
The phenomenon of bone remodeling is a complex biological process which is dependent on genetic, hormonal, metabolic, and age-related factors as well as functional requirements. The possibility of successfully developing a mathematical model to describe and predict the adaptive response of bone to load will be significantly increased after identification of the nature of the transducer(s) which senses functional requirements and provides signals for the cellular processes responsible for bone synthesis and bone removal. In spite of the present limitations in knowledge about the functional dependence of bone remodeling, a phenomenological model has been developed that assumes that the output signal from the (as yet unspecified) transducer is a remodeling potential that can be modulated by genetic, hormonal, and metabolic factors. An attempt has been made to cast the mathematical model in such a form that the constants and variables appearing in the equations are not mere abstractions, but can be related to biological parameters. In order to use the adaptive hypothesis with specific structural model examples, a numerical procedure has been developed to determine the strain distribution, predict the remodeling (assuming that the remodeling rate is related to the strain history), and update the model by changing the geometry and material properties in response to the remodeling. This numerical procedure is repeatedly iterated to determine the structural architecture at subsequent times. The numerical approach allows use of the remodeling concepts with models of irregular geometry, inhomogeneous material distribution, and anisotropic material properties.
骨重塑现象是一个复杂的生物学过程，它取决于遗传、激素、代谢、与年龄相关的因素以及功能需求。在确定能够感知功能需求并为负责骨合成和骨吸收的细胞过程提供信号的传感器的性质之后，成功开发一个数学模型来描述和预测骨对负荷的适应性反应的可能性将显著增加。尽管目前对骨重塑功能依赖性的认识存在局限性，但已经开发出一种唯象模型，该模型假定来自（尚未确定的）传感器的输出信号是一种重塑潜能，可由遗传、激素和代谢因素调节。人们试图将数学模型构建成这样一种形式，即方程中出现的常数和变量不仅仅是抽象概念，而是可以与生物学参数相关联。为了将适应性假设应用于特定的结构模型示例，已开发出一种数值程序来确定应变分布、预测重塑（假设重塑速率与应变历史相关），并通过根据重塑情况改变几何形状和材料特性来更新模型。重复此数值程序以确定后续时间的结构架构。该数值方法允许将重塑概念应用于具有不规则几何形状、非均匀材料分布和各向异性材料特性的模型。
