A theoretical model to predict distribution of the fabric tensor and apparent density in cancellous bone

Zong Ping Luo, Kai Nan An

研究成果: Article同行評審

16 引文 斯高帕斯(Scopus)

摘要

The adaptation of cancellous bone to mechanical forces is well recognized. Theoretical models for predicting cancellous bone architecture have been developed and have mainly focused on the distribution of trabecular mass or the apparent density. The purpose of this study was to develop a theoretical model which can simultaneously predict the distribution of trabecular orthotropy/orientation, as represented by the fabric tensor, along with apparent density. Two sets of equations were derived under the assumption that cancellous bone is a biological self-optimizing material which tends to minimize strain energy. The first set of equations provide the relationship between the fabric tensor and stress tensor, and have been verified to be consistent with Wolff's law of trabecular architecture, that is, the principal directions of the fabric tensor coincide with the principal stress trajectories. The second set of equations yield the apparent density from the stress tensor, which was shown to be identical to those obtained based on local optimization with strain energy density of true bone tissue as the objective function. These two sets of equations, together with elasticity field equations, provide a complete mathematical formulation for the adaptation of cancellous bone.

原文English
頁(從 - 到)557-568
頁數12
期刊Journal of Mathematical Biology
36
發行號6
DOIs
出版狀態Published - 1998 六月

All Science Journal Classification (ASJC) codes

  • 建模與模擬
  • 農業與生物科學(雜項)
  • 應用數學

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