A comparison and verification of computational methods to determine the permeability of vertebral trabecular bone

Abstract

Fluid flow in the intertrabecular spaces of vertebral bone has been implicated in a number of physiological phenomena. Despite the potential clinical significance of the flow of various fluids through the intertrabecular cavities, the intrinsic permeability of trabecular bone is not fully characterized or understood. Furthermore, very little is known about the interdependence of permeability and morphological parameters. The main purpose of this study is to characterize computational methods to determine intrinsic bone permeability from three-dimensional computed tomography (CT) image stacks that were, depending on the underlying algorithm of each model, acquired at a spatial resolution ranging from the order of 500 μm (macroscale) up to 10 μm (microscale). A Finite Element formulation of the steady-state Stokes flow and an in house developed pore network modeling approach compute permeability on the microscopic length scale. To approximate the geometry of the trabecular bone network, a cellular model is used to map morphological information into intrinsic permeability by means of a log-linear regression equation. If the image resolution is too low for the quantification of the trabecular bone architecture, permeability is directly derived by fitting a simplified version of the log-linear regression equation to the CT Hounsfield values. Depending on the resolution of the raw image data and the chosen model, permeability value correlations are 0.31 ≤ R² ≤ 0.90 compared to the Finite Element method, that is referred to as the baseline for any comparisons in this study. Furthermore, we found no significant dependence of the intrinsic permeability on the trabecular thickness parameter.