Multiscale models of compact bone  

作　　者：Junfeng Li Shugang Li 

机构地区：[1]School of Mathematics and Statistics Central China Normal University Wuhan 430079, P. R. China

出　　处：《International Journal of Biomathematics》2016年第3期271-292,共22页生物数学学报（英文版）

摘　　要：This work is concerned about multiscale models of compact bone. We focus on the lacuna-canalicular system. The interstitial fluid and the ions in it are regarded as sol- vent and others are treated as solute. The system has the characteristic of solvation process as well as non-equilibrium dynamics. The differential geometry theory of sur- faces is adopted. We use this theory to separate the macroscopic domain of solvent from the microscopic domain of solute. We also use it to couple continuum and discrete descriptions. The energy functionals are constructed and then the variational principle is applied to the energy functionals so as to derive desirable governing equations. We consider both long-range polar interactions and short-range nonpolar interactions. The solution of governing equations leads to the minimization of the total energy.

关 键 词：Compact bone lacuna-canalicular system multiscale Laplace-Beltramiequation Poisson Boltzmann equation. 

分 类 号：O189.11[理学—数学] TP391.4[理学—基础数学]