Study on the biomechanical responses of the loaded bone in macroscale and mesoscale by multiscale poroelastic FE analysis

Abstract

BackgroundBone is a hierarchically structured composite material, and different hierarchical levels exhibit diverse material properties and functions. The stress and strain distribution and fluid flow in bone play an important role in the realization of mechanotransduction and bone remodeling.MethodsTo investigate the mechanotransduction and fluid behaviors in loaded bone, a multiscale method was developed. Based on poroelastic theory, we established the theoretical and FE model of a segment bone to provide basis for researching more complex bone model. The COMSOL Multiphysics software was used to establish different scales of bone models, and the properties of mechanical and fluid behaviors in each scale were investigated.ResultsFE results correlated very well with analytical in macroscopic scale, and the results for the mesoscopic models were about less than 2% different compared to that in the macro–mesoscale models, verifying the correctness of the modeling. In macro–mesoscale, results demonstrated that variations in fluid pressure (FP), fluid velocity (FV), von Mises stress (VMS), and maximum principal strain (MPS) in the position of endosteum, periosteum, osteon, and interstitial bone and these variations can be considerable (up to 10, 8, 4 and 3.5 times difference in maximum FP, FV, VMS, and MPS between the highest and the lowest regions, respectively). With the changing of Young’s modulus (E) in each osteon lamella, the strain and stress concentration occurred in different positions and given rise to microscale spatial variations in the fluid pressure field. The heterogeneous distribution of lacunar–canalicular permeability (klcp) in each osteon lamella had various influence on the FP and FV, but had little effect on VMS and MPS.ConclusionBased on the idealized model presented in this article, the presence of endosteum and periosteum has an important influence on the fluid flow in bone. With the hypothetical parameter values in osteon lamellae, the bone material parameters have effect on the propagation of stress and fluid flow in bone. The model can also incorporate alternative material parameters obtained from different individuals. The suggested method is expected to provide dependable biological information for better understanding the bone mechanotransduction and signal transduction.

Closing the osteon: Do osteocytes sense strain rate rather than fluid flow?

“…We tested whether a permeable cement line would alter our results, but this was not the case because interstitial fluid always drains towards the Haversian canal and fluid will only flow from a depth of about 100 microns. [31,95] Such a limited role of cement line permeability was also shown by Nguyen and colleagues. [56] Along with the aligned network of osteocytes and their radial processes, there is also a strong anisotropy of the bone matrix.…”

“…[ 22 ] This concept was confirmed in a dynamic model of bone remodelling [ 104 ] and is now implemented in many recent osteon models. [ 56,95,102,105–107 ]…”

“…Others already pointed out that spatial gradients of permeability do not cause an obvious variation in radial fluid velocity distribution. [95,102] The continuity of matrix tissue also applies to the unmineralized layer of osteoid deposited by the osteoblasts. The youngest, presumably most mechanosensitive osteocytes [74] are located in this layer that has a much lower Young's modulus.…”

“…[22] This concept was confirmed in a dynamic model of bone remodelling [104] and is now implemented in many recent osteon models. [56,95,102,[105][106][107] Yet there are deviations from osteon alignment along the lines of principal stress: osteons do not align perfectly in parallel and there are Volkmann's canals that connect adjacent osteons. [19,21] What could be the origin of this?…”

Cortical Bone Model With a Microcrack Under Tensile Loading

“…Through hundreds of million years of evolution, biological materials have evolved with outstanding performance and efficiency [1,2]. Biological material can achieve diverse mechanical, biological and chemical functions through its composite hierarchical structures [2,3]. As a biological material, bone consists of cortical and trabecular bone.…”