On the interrelationship of permeability and structural parameters of vertebral trabecular bone: a parametric...

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.