Human cortical bone intrinsic permeability distribution based on 3D canalicular morphology

Bone permeability is a key parameter that drives osteocyte-based mechanobiological modelling and remodelling. While previous experimental and numerical studies have estimated bone permeability based on the morphology of the lacuno-canalicular network, these studies often relied on simplified geometries. In the current study, bone permeability was characterized using more realistic canalicular geometry for the morphological data. Bone samples harvested from 27 human femoral bones were investigated using synchrotron radiation-based nano-computed tomography with a voxel size of 100 nm. After segmenting the canaliculi and lacunae, each canaliculus was investigated individually by applying a distance map and watershed algorithms. Bone permeability based on canalicular morphology was then assessed using the Kozeny relation, which defines the permeability of a porous medium with capillary-like pores. An averaged intrinsic permeability value of 8.8 10^-18 m² was obtained. It should be noted that this study considered an empty canalicular network, however in vivo, both cellular and peri-cellular matrices decrease space for interstitial fluid flow and thus permeability. Furthermore, a voxel size of 100 nm does not allow for the detection of smaller canaliculi, which may also modify average permeability. With the current data set and the analytic process applied, the results showed a heterogeneous permeability distribution within bone tissue, both when comparing osteonal and interstitial tissues and within an individual osteon. A difference was observed between male and female samples, and permeability appeared to significantly decrease with age. Finally, a significant correlation was found between permeability and canalicular length density, defined as canalicular length per unit bone volume. This study proposes a new form of the Kozeny law to express bone canalicular permeability as a proportional relationship with the canalicular length density. Importantly, this parameter can be directly quantified through confocal fluorescence microcopy, which is more convenient than synchrotron radiation-based nano-computed tomography. In conclusion, the current study confirms that confocal microscopy can be serve as a reliable tool to estimate bone permeability. However, the permeability values calculated here are solely based on canalicular morphology and do not consider cellular and peri-cellular intra-canalicular features.