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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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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.8) 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.
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fig1: 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.8) 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.

Mentions: An intact mouse tibia from an adult C57BL/6J male mouse was imaged by a Scanco μCT35 scanner (Scanco USA, Inc., Wayne, PA, USA) using a standard protocol (55 keV, 145 μA, 200 ms integration time, 3 600 projections, and 20 μm voxel size). The raw image slices (998 slices) were imported in the DICOM format into ScanIP (Simpleware, Chantilly, VA, USA), with which the entire tibia, including the cortical and trabecular bone, was thresholded and meshed with 5 112 690 tetra elements (Figure 1a). In Hypermesh (Altair/HyperWorks; http://www.altairhyperworks.com/), fixed displacement constraints were imposed at the elements of the proximal tibial plateau. Similar to our experimental setup,27 a 3 N compressive load was applied to the distal end of the tibia (Figure 1a). Assuming bone elements to be an elastic material with 20 GPa Young’s modulus and 0.33 Poisson’s ratio,8 the strain field was obtained using OptiStruct, a FEA linear solver in the HyperWork software package. The average strain of a 1×3 mm area on the medial–anterior surface that was 20%–40% distal from the tibial proximal end was compared with the strain measurement of a similar area in our previous studies.27,35 Good agreement between the comparisons would validate the material properties and boundary conditions assigned to the whole-bone FEA model.


A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone
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.8) 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.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig1: 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.8) 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.
Mentions: An intact mouse tibia from an adult C57BL/6J male mouse was imaged by a Scanco μCT35 scanner (Scanco USA, Inc., Wayne, PA, USA) using a standard protocol (55 keV, 145 μA, 200 ms integration time, 3 600 projections, and 20 μm voxel size). The raw image slices (998 slices) were imported in the DICOM format into ScanIP (Simpleware, Chantilly, VA, USA), with which the entire tibia, including the cortical and trabecular bone, was thresholded and meshed with 5 112 690 tetra elements (Figure 1a). In Hypermesh (Altair/HyperWorks; http://www.altairhyperworks.com/), fixed displacement constraints were imposed at the elements of the proximal tibial plateau. Similar to our experimental setup,27 a 3 N compressive load was applied to the distal end of the tibia (Figure 1a). Assuming bone elements to be an elastic material with 20 GPa Young’s modulus and 0.33 Poisson’s ratio,8 the strain field was obtained using OptiStruct, a FEA linear solver in the HyperWork software package. The average strain of a 1×3 mm area on the medial–anterior surface that was 20%–40% distal from the tibial proximal end was compared with the strain measurement of a similar area in our previous studies.27,35 Good agreement between the comparisons would validate the material properties and boundary conditions assigned to the whole-bone FEA model.

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