Dynamic permeability of the lacunar-canalicular system in human cortical bone

Abstract

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar-canalicular permeability [Formula: see text] in bone. The interest in the permeability of the lacunar-canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from [Formula: see text] to [Formula: see text]. However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the [Formula: see text] to be on the order of [Formula: see text] for human osteonal bone. It was found that the [Formula: see text] has a linear dependence on loading frequency, decreasing at a rate of [Formula: see text]/Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the [Formula: see text] variability.

Fig. 1

a The loss tangent (mean ± SD) versus time for a period of 5 h. b The loss tangent (mean ± SD) versus time for a duration of 5 days (* p<0.05, nine loaded osteons in each analysis)

Fig. 2

Curve fitting of the analytical model and experimental data of the loss tangent to evaluate the average lacunar–canalicular permeability, K_rr = (2.34 ± 0.33) × 10⁻²²m²(^* p < 0.05, sixty loaded osteons)

Fig. 3

Lacunar–canalicular permeability versus frequency, K_rr = (3.27 − 0.02 f ) × 10⁻²²m²(^* p < 0.05, sixty loaded osteons) from inverse poroelastic model of K_rr

Fig. 4

Loss tangent, tan [δ(ω = 2π)], measured at 1 Hz cyclic loading of isolated human osteons versus lacunar–canalicular porosity, φ_LC (sixty loaded osteons)

Fig. 5

Lacunar–canalicular permeability in the radial direction of isolated human osteons, K_rr, versus lacunar–canalicular porosity, φ_LC (sixty loaded osteons)