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

View Article: PubMed Central - PubMed

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.

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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.16).
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fig4: 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.16).

Mentions: For the non-loaded condition, the solute concentration at the FRAP site was shown to increase with time and the rate of increase varied with diffusivity (Figure 4a). The transport rate, K, shown as the slope of ln[(C−C0)/(Cb−C0)] vs time curve (Figure 4b), was slightly higher initially and gradually reached a steady state (constant slope). This steady-state transport rate (Kdiff) was nearly linearly proportional to the solute diffusivity (Kdiff=4.11×10−4×D, Figure 4c). In particular, a diffusivity of 31.8 μm2·s−1 in the 3D porous model was found to best match the experimentally observed Kdiff=0.017 s−1 of sodium fluorescein (376 Da).27


A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone
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.16).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037578&req=5

fig4: 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.16).
Mentions: For the non-loaded condition, the solute concentration at the FRAP site was shown to increase with time and the rate of increase varied with diffusivity (Figure 4a). The transport rate, K, shown as the slope of ln[(C−C0)/(Cb−C0)] vs time curve (Figure 4b), was slightly higher initially and gradually reached a steady state (constant slope). This steady-state transport rate (Kdiff) was nearly linearly proportional to the solute diffusivity (Kdiff=4.11×10−4×D, Figure 4c). In particular, a diffusivity of 31.8 μm2·s−1 in the 3D porous model was found to best match the experimentally observed Kdiff=0.017 s−1 of sodium fluorescein (376 Da).27

View Article: PubMed Central - PubMed

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.

No MeSH data available.


Related in: MedlinePlus