A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone

Abstract

The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching (FRAP) approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis (FEA) approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional (3D) linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform (FEBio) to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces (shear and drag forces) for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.

Figure 1

A multiscale model for loaded bone. (a) The whole-bone FEA model of a murine tibia with 5 112 690 tetra elements and its loading and boundary conditions. A 3 mm segment (20%–40% distal of the proximal end) was used for detailed analysis of strain, pore pressure, and fluid/solute fluxes. (b) The loading profile of cyclic compressive load 3N at 0.5 Hz followed by a 2 s resting periods. (c) The segment biphasic transport model was consisted of ~700 000 tetra elements with its fluid/solute boundary conditions. The site corresponding to the FRAP experiments is shown here. (d) Ultrastructural Brinkman flow model at single canaliculus (adapted from Weinbaum et al. ) was used to predict fluid shear and drag force acting on osteocytes. The three levels of models are physically connected: the displacement outputs from the whole-bone model were used as boundary conditions in the segment transport model that provided fluid/solute flow at the tissue level, which were then converted to the canalicular level scaled with the LCS porosity.

Figure 2

Axial strains from the whole-bone FE model. Only the portion corresponding to the segment model is shown. Due to the combination of compression and bending, the anterior–medial surface (FRAP site) was under tension.

Figure 3

Confocal imaging of the murine cortical LCS. A stack of LCS images (a) was acquired. Individual lacuna (b) and canaliculi (c) were segmented and pore volumes measured.

Figure 4

The tracer concentration (a) and the logarithm of the recovery rate (b) at the FRAP site under non-loaded condition using the segment biphasic model. (c) The model correctly predicted the nearly linear relationship between the transport rate and diffusivity in agreement with theoretical predictions (Wang et al. ).

Figure 5

The tracer concentration (a) and the logarithm of the recovery rate (b) of sodium fluorescein under loaded and non-loaded conditions. A transport enhancement of 1.24 was found for 3 N loading, which is comparable with previous experimental measurements. As anticipated, higher loads (5 N and 7 N) result in greater transport enhancements.

Figure 6

FEBio simulation of fluid pore pressure in the segment model. (a) The pore fluid pressure field at t=3 s at the cross-section containing the FRAP site (location A). (b) The temporal fluid pressure changes at the cortical (A–F) and trabecular sites (G, H) during one loading cycle (Figure 1b).

Figure 7

Load-induced fluid flux at tissue level. (a) The distribution of the fluid flux magnitude and the flow direction at t=2.6 second during the loading phase. (b) The temporal changes of the fluid flux at several selected locations in both cortical (locations A–F) and trabecular sites (locations G–H).