Widmer René P, Ferguson Stephen J
a Institute for Biomechanics, ETH Zurich , Zurich , Switzerland.
Comput Methods Biomech Biomed Engin. 2013;16(8):908-22. doi: 10.1080/10255842.2011.643787. Epub 2012 Jan 30.
To characterise the flow of a fluid through a uniform porous medium, the medium may be completely described by its permeability, a measure of flow resistance. Fluid flow in the intertrabecular spaces of cancellous bone has been recognised as an important factor in a number of physical phenomena. In order to investigate the interdependence of permeability, porosity and the structural parameters, we adapted a morphological model and systematically varied its structural parameters. By simulating a viscous Stokes flow regime, we were able to estimate the anisotropic permeability tensor and performed an extensive, stepwise multivariate regression analysis to establish empirical relationships between the morphological parameters and the permeability for the anatomical directions individually. The regression analysis indicated high values of determination coefficients [0.88 < R(2) < 0.89 (transversal directions) and R(2) = 0.60 (longitudinal direction), porosity-based prediction and R(2) = 0.98 for all directions and information presented to the regression model]. We conclude that a pooled set of structural parameters may explain up to 98% of the permeability variability, the regression model predicts permeability values that match experimental data, and a good prediction performance could be achieved by only incorporating the porosity and either the degree of anisotropy (0.89 < R(2) < 0.91) or the trabecular spacing predictor (0.96 < R(2) < 0.97). These conclusions imply that trabecular thickness and shape parameters only play a minor role in the determination of vertebral trabecular bone permeability. However, a major limitation of the model is that it reflects an idealisation of the real, regionally varying structure of trabecular bone. Therefore, the goodness-of-fit estimates we are presenting should be considered as an upper bound limitation regarding the prediction performance.
为了描述流体在均匀多孔介质中的流动，该介质可以通过其渗透率来完全描述，渗透率是流动阻力的一种度量。松质骨小梁间隙中的流体流动已被认为是许多物理现象中的一个重要因素。为了研究渗透率、孔隙率和结构参数之间的相互依存关系，我们采用了一个形态学模型，并系统地改变其结构参数。通过模拟粘性斯托克斯流态，我们能够估计各向异性渗透率张量，并进行了广泛的逐步多元回归分析，以分别建立形态学参数与解剖方向渗透率之间的经验关系。回归分析表明，决定系数的值较高[横向方向为0.88 < R(2) < 0.89，纵向方向为R(2) = 0.60，基于孔隙率的预测，所有方向以及提供给回归模型的信息的R(2) = 0.98]。我们得出结论，一组综合的结构参数可以解释高达98%的渗透率变异性，回归模型预测的渗透率值与实验数据相符，并且仅通过纳入孔隙率和各向异性程度(0.89 < R(2) < 0.91)或小梁间距预测因子(0.96 < R(2) < 0.97)就能实现良好的预测性能。这些结论意味着小梁厚度和形状参数在椎骨小梁骨渗透率的测定中仅起次要作用。然而，该模型的一个主要局限性在于它反映了小梁骨真实的、区域变化结构的理想化情况。因此，我们给出的拟合优度估计应被视为预测性能的上限限制。
