Effects of microcracks on the poroelastic behaviors of a single osteon

It has been suggested that microcracks do play a key role in the triggering of the bone remodeling process. In order to evaluate the influence of microcracks on the poroelastic behaviors of an osteon, a finite element model is established and investigated by using the Comsol Multiphysics software. The findings show that the presence of a microcrack in the osteon wall strongly modifies (enlarges) its local fluid pressure and velocity. Especially, the pressure and velocity amplitudes produced in the microcracked region are larger than those of the non-cracked region. Thus, this study can also be used for proposing a likely mechanism that bone can sense the changes of surrounding mechanical environments.     

Laser polarimetry of the orientation structure of bone tissue osteons

A matrix method is proposed for describing polarization properties of biological tissues as an aggregate of uniaxial crystal structures. We investigated 25 μm-thick histological sections of compact bone tissue which provided single light scattering. It is shown that in this case there exists a unique relationship between the polarization parameters of the boundary laser field and the parameters of anisotropy and orientation of the structural elements of biological tissue. On this basis, contactless methods of laser polarimetry of histological sections of bone tissue have been proposed. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 52–55, January–February, 2000.     

一种骨小管中液体流动产生的流量及切应力模型

骨组织受力变形后其内部液体就会流动,同时在其微观结构——骨单元壁中扩散,并进一步产生一系列与骨液流动相关的物理效应,如流体剪切应力、流动电位等,这些物理效应被细胞感知并做出破骨或成骨等反应,来使骨适应外部载荷环境.鉴于骨组织产生的内部液体流动很难实验测定,理论模拟是目前的主要研究手段.基于骨单元的多孔弹性性质建立了骨小管内部液体的流动模型,该模型将骨单元所受的外部载荷与骨小管内部液体的压力、流速、流量和切应力联系起来,并进一步可以研究其力传导与力电传导机制.骨小管模型的建立分别基于中空和考虑哈弗液体的骨单元模型,并考虑了骨单元外壁的弹性约束和刚性位移约束两种边界条件.最终得到骨单元在外部轴向载荷作用下,骨小管内部液体的流量及流体切应力的解析解.结果表明:骨小管中的液体流量与流体切应力都正比于应变载荷幅值和频率,并由载荷的应变率决定.因此应变率可以作为控制流量和流体切应力的一种生理载荷因素.流量随着骨小管半径的增大而非线性增大,而流体切应力则随着骨小管半径的增大而线性增大.此外,在相同的载荷下,含哈弗液体的骨单元的模型中,骨小管中液体的流量和切应力均大于中空骨单元模型.     

Fluid flow and fluid shear stress in canaliculi induced by external mechanical loading and blood pressure oscillation

The paper studies the problem of fluid flow and fluid shear stress in canaliculi when the osteon is subject to external mechanical loading and blood pressure oscillation. The single osteon is modeled as a saturated poroelastic cylinder. Solid skeleton is regarded as a poroelastic transversely isotropic material. To get near-realistic results, both the interstitial fluid and the solid matrix are regarded as compressible. Blood pressure oscillation in the Haverian canal is considered. Using the poroelasticity theory, an analytical solution of the pore fluid pressure is obtained. Assuming the fluid in canaliculi is incompressible, analytical solutions of fluid flow velocity and fluid shear stress with the Navier-Stokes equations of incompressible fluid are obtained. The effect of various parameters on the fluid flow velocity and fluid shear stress is studied.     

骨陷窝-骨细胞形状和方向对骨单元内液体流动行为的影响

骨组织内的流体流动不仅为骨细胞的生存提供了充足营养供应及代谢物排放途径,也在骨重建过程中起到关键作用. 为了更精确地阐明骨内液体流动的具体形式,这项研究利用骨陷窝-骨细胞的密度,形态和方向等参数来计算骨单元内液体的流动行为. 首先,计算出不同形状和方向的骨陷窝周围骨小管的数量及分布情况,其次利用算出的参数以及骨组织其他微结构数据来估计骨组织的渗透率和孔隙率等参数,最后根据计算所得的参数建立骨单元的多孔弹性力学有限元模型,并分析了在轴向位移载荷作用下骨陷窝形状和方向对骨单元内液体渗流行为的影响. 结果表明,在所研究的参数范围内不同骨单元模型的相同区域上,骨陷窝形状影响下的骨单元最大压力和流速比最小的分别增加了86%和18%;骨陷窝方向影响下的最大压力和流速比最小的分别增加了125%和56%. 伸长形骨陷窝对单个骨单元局部压力的影响远大于扁平形和圆形骨陷窝. 骨陷窝从0°绕$x$轴旋转到90°过程中压力是逐渐降低的,且30°,45°和60°的模型对骨单元内局部流速有显著影响. 该模型表示骨陷窝的形状和方向以及骨小管的三维分布对骨单元内液体压力和流速幅值及沿不同方向的流动差异有显著的影响. 这项研究将有助于精确量化描述骨内液体的流体行为.      

Polarization-Phase Visualization and Processing of Coherent Images of Fractal Structures of Biotissues

A polarization-phase method of visualization of optically anisotropic inhomogeneities of biotissues, which is based on multifractal modeling of biotissue properties, is proposed. An algorithm for obtaining topograms of orientations of the fractal domains of a visualized architectonic net of a biotissue is developed and realized experimentally.     

Mathematical osteon model for examining poroelastic behaviors

An extended and reasonable stress boundary condition at an osteon exterior wall is presented to solve the model proposed by Rémond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. (i) Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. (ii) In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. (iii) At the osteon scale, the pressure is strongly affected by the permeability variations, whereas the fluid velocity is not.     

人的密质骨的力学性能

本文把骨组织看作是一种材料和骨骼系统的粘弹性结构元件,评述了它们的力学性能.首先描述了骨的结构,包括宏观结构、微结构和超微结构.随后是骨的力学性能.第三部分介绍了哈弗氏骨的力学模型.笔者指出,单个哈弗氏骨可考虑为正交铺设的胶原纤维增强的粘弹性厚壁筒.最后讨论了哈弗氏骨的应力-应变关系.显然,简单的弹性关系是不可用于实际的.