Comparison of solid and fluid constitutive models of bone marrow during trabecular bone compression

Fluid-solid coupling numerical simulation of the effects of different doses of verapamil on cancellous bone in type 2 diabetic rats

BACKGROUND

The purpose of this study was to investigate the effects of four different doses of verapamil on the mechanical behaviors of solid and the characteristics of fluid flow in cancellous bone of distal femur of type 2 diabetes rats under dynamic external load.

METHODS

Based on the micro-CT images, the finite element models of cancellous bones and fluids at distal femurs of rats in control group, diabetes group, treatment groups VER 4, VER 12, VER 24, and VER 48 (verapamil doses of 4, 12, 24, and 48 mg/kg/day, respectively) were constructed. A sinusoidal time-varying displacement load with an amplitude of 0.8 μm and a period of 1s was applied to the upper surface of the solid region. Then, fluid-solid coupling numerical simulation method was used to analyze the magnitudes and distributions of von Mises stress, flow velocity, and fluid shear stress of cancellous bone models in each group.

RESULTS

The results for mean values of von Mises stress, flow velocity and FSS (t = 0.25s) were as follows: their values in control group were lower than those in diabetes group; the three parameters varied with the dose of verapamil; in the four treatment groups, the values of VER 48 group were the lowest, they were the closest to control group, and they were smaller than diabetes group. Among the four treatment groups, VER 48 group had the highest proportion of the nodes with FSS = 1-3 Pa on the surface of cancellous bone, and more areas in VER 48 group were subjected to fluid shear stress of 1-3 Pa for more than half of the time.

CONCLUSION

It could be seen that among the four treatment groups, osteoblasts on the cancellous bone surface in the highest dose group (VER 48 group) were more easily activated by mechanical loading, and the treatment effect was the best. This study might help in understanding the mechanism of verapamil's effect on the bone of type 2 diabetes mellitus, and provide theoretical guidance for the selection of verapamil dose in the clinical treatment of type 2 diabetes mellitus.

Fluid-solid coupling numerical simulation of entire rat caudal vertebrae under dynamic loading

Trabeculae bone undergoes directional growth along the applied force under physiological loading. The growth of bone structure relies on the coordinated interplay among osteocytes, osteoblasts, and osteoclasts. Under normal circumstances, bone remodeling maintains a state of equilibrium. Excessive bone formation can lead to osteosclerosis, while excessive bone resorption can result in osteoporosis and osteonecrosis. The investigation of the structural characteristics of trabeculae and the mechanotransduction between bone cells plays a vital role in the treatment of bone-related diseases. In this study, a fluid-solid coupling model of the entire vertebral bone was established based on micro-CT images obtained from rat tail vertebrae subjected to tensile loading experiments. The flow characteristics of bone marrow and the mechanical response of osteocytes in different regions under physiological loading were investigated. The results revealed a U-shaped distribution of wall fluid shear stress (FSS) along the longitudinal axis in trabecular bone, with higher FSS regions exhibiting greater mechanical stimulation on osteocytes. These findings elucidate a positive correlation between the mechanical microenvironment among osteocytes, osteoblasts, and osteoclasts, providing potential strategies for the prevention and treatment of bone diseases.

Numerical simulations of fluid flow in trabecular-lacunar cavities under cyclic loading

BACKGROUND

Under external loading, the fluid shear stress (FSS) in the porous structures of bones, such as trabecular or lacunar-canalicular cavity, can influence the biological response of bone cells. However, few studies have considered both cavities. The present study investigated the characteristics of fluid flow at different scales in cancellous bone in rat femurs, as well as the effects of osteoporosis and loading frequency.

METHODS

Sprague Dawley rats (3 months old) were divided into normal and osteoporotic groups. A multiscale 3D fluid-solid coupling finite element model considering trabecular system and lacunar-canalicular system was established. Cyclic displacement loadings with frequencies of 1, 2, and 4 Hz were applied.

FINDINGS

Results showed that the wall FSS around the adhesion complexes of osteocyte on the canaliculi was higher than that on the osteocyte body. Under the same loading conditions, the wall FSS of the osteoporotic group was smaller than that of the normal group. The fluid velocity and FSS in trabecular pores exhibited a linear relationship with loading frequency. Similarly, the FSS around osteocytes also showed the loading frequency-dependent phenomenon.

INTERPRETATION

The high cadence in movement can effectively increase the FSS level on osteocytes for osteoporotic bone, i.e., expand the space within the bone with physiological load. This study might help in understanding the process of bone remodeling under cyclic loading and provide the fundamental data for the development of strategies for osteoporosis treatment.

The role of bone marrow on the mechanical properties of trabecular bone: a systematic review

Background

Accurate evaluation of the mechanical properties of trabecular bone is important, in which the internal bone marrow plays an important role. The aim of this systematic review is to investigate the roles of bone marrow on the mechanical properties of trabecular bone to better support clinical work and laboratory research.

Methods

A systematic review of the literature published up to June 2022 regarding the role of bone marrow on the mechanical properties of trabecular bone was performed, using PubMed and Web of Science databases. The journal language was limited to English. A total of 431 articles were selected from PubMed (n = 186), Web of Science (n = 244) databases, and other sources (n = 1).

Results

After checking, 38 articles were finally included in this study. Among them, 27 articles discussed the subject regarding the hydraulic stiffening of trabecular bone due to the presence of bone marrow. Nine of them investigated the effects of bone marrow on compression tests with different settings, i.e., in vitro experiments under unconfined and confined conditions, and computer model simulations. Relatively few controlled studies reported the influence of bone marrow on the shear properties of trabecular bone.

Conclusion

Bone marrow plays a non-neglectable role in the mechanical properties of trabecular bone, its contribution varies depending on the different loading types and test settings. To obtain the mechanical properties of trabecular bone comprehensively and accurately, the solid matrix (trabeculae) and fluid-like component (bone marrow) should be considered in parallel rather than tested separately.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12938-022-01051-1.

Integration of mechanics and biology in computer simulation of bone remodeling

Bone remodeling is a complex physiological process that spans across multiple spatial and temporal scales and is regulated by both mechanical and hormonal cues. An imbalance between bone resorption and bone formation in the process of bone remodeling may lead to various bone pathologies. One powerful and non-invasive approach to gain new insights into mechano-adaptive bone remodeling is computer modeling and simulation. Recent findings in bone physiology and advances in computer modeling have provided a unique opportunity to study the integration of mechanics and biology in bone remodeling. Our objective in this review is to critically appraise recent advances and developments and discuss future research opportunities in computational bone remodeling approaches that enable integration of mechanics and cellular and molecular pathways. Based on the critical appraisal of the relevant recent published literature, we conclude that multiscale in silico integration of personalized bone mechanics and mechanobiology combined with data science and analytics techniques offer the potential to deepen our knowledge of bone remodeling and provide ample opportunities for future research.

Fluid-solid coupling numerical simulation of trabecular bone under cyclic loading in different directions

The structure of a bone tissue is capable of adapting to mechanical loading through the process of bone remodeling, which is regulated by osteoblasts and osteoclasts. Fluid flow within trabecular porosity under cyclic loading is one of the factors stimulating the biological response of osteoblasts and osteoclasts. However, the relation between loading directions and interstitial fluid flow was seldom studied. In the present study, a finite element model based on micro-computed tomographic reconstructions is built by using a mouse femur. Results from the fluid-solid coupling numerical simulation indicate that the loading in different directions generates a distinct distribution of von Mises stress in the bone matrix and a fluid shear stress (FSS) in the bone marrow. The loading along the physiological direction leads to a more uniform distribution of solid stress and produces an FSS level beneficial to the biological response of osteoblasts and osteoclasts compared with those along the non-physiological direction. There was a minimum threshold line of wall FSS with a specific solid stress at the bone surface, suggesting that the wall FSS is mainly induced by the solid strain. These results may offer fundamental data in understanding the mechanical environment around osteoblasts and osteoclasts and the cellular and molecular mechanisms of mechanical loading-induced bone remodeling.

Mechanical Heterogeneity in the Bone Microenvironment as Characterized by Atomic Force Microscopy

Bones are structurally heterogeneous organs with diverse functions that undergo mechanical stimuli across multiple length scales. Mechanical characterization of the bone microenvironment is important for understanding how bones function in health and disease. Here, we describe the mechanical architecture of cortical bone, the growth plate, metaphysis, and marrow in fresh murine bones, probed using atomic force microscopy in physiological buffer. Both elastic and viscoelastic properties are found to be highly heterogeneous with moduli ranging over three to five orders of magnitude, both within and across regions. All regions include extremely compliant areas, with moduli of a few pascal and viscosities as low as tens of Pa·s. Aging impacts the viscoelasticity of the bone marrow strongly but has a limited effect on the other regions studied. Our approach provides the opportunity to explore the mechanical properties of complex tissues at the length scale relevant to cellular processes and how these impact aging and disease.

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

BACKGROUND

Bone 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.

METHODS

To 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.

RESULTS

FE 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.

CONCLUSION

Based 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.

Physicochemical Niche Conditions and Mechanosensing by Osteocytes and Myocytes

PURPOSE OF REVIEW

Bone and muscle mass increase in response to mechanical loading and biochemical cues. Bone-forming osteoblasts differentiate into early osteocytes which ultimately mature into late osteocytes encapsulated in stiff calcified matrix. Increased muscle mass originates from muscle stem cells (MuSCs) enclosed between their plasma membrane and basal lamina. Stem cell fate and function are strongly determined by physical and chemical properties of their microenvironment, i.e., the cell niche.

RECENT FINDINGS

The cellular niche is a three-dimensional structure consisting of extracellular matrix components, signaling molecules, and/or other cells. Via mechanical interaction with their niche, osteocytes and MuSCs are subjected to mechanical loads causing deformations of membrane, cytoskeleton, and/or nucleus, which elicit biochemical responses and secretion of signaling molecules into the niche. The latter may modulate metabolism, morphology, and mechanosensitivity of the secreting cells, or signal to neighboring cells and cells at a distance. Little is known about how mechanical loading of bone and muscle tissue affects osteocytes and MuSCs within their niches. This review provides an overview of physicochemical niche conditions of (early) osteocytes and MuSCs and how these are sensed and determine cell fate and function. Moreover, we discuss how state-of-the-art imaging techniques may enhance our understanding of these conditions and mechanisms.

Effects of mechanobiological signaling in bone marrow on skeletal health

Bone marrow is a cellular tissue that forms within the pore space and hollow diaphysis of bones. As a tissue, its primary function is to support the hematopoietic progenitor cells that maintain the populations of both erythroid and myeloid lineage cells in the bone marrow, making it an essential element of normal mammalian physiology. However, bone's primary function is load bearing, and deformations induced by external forces are transmitted to the encapsulated marrow. Understanding the effects of these mechanical inputs on marrow function and adaptation requires knowledge of the material behavior of the marrow at multiple scales, the loads that are applied, and the mechanobiology of the cells. This paper reviews the current state of knowledge of each of these factors. Characterization of the marrow mechanical environment and its role in skeletal health and other marrow functions remains incomplete, but research on the topic is increasing, driven by interest in skeletal adaptation and the mechanobiology of cancer metastasis.

Mechanical Stimuli in the Local In Vivo Environment in Bone: Computational Approaches Linking Organ-Scale Loads to Cellular Signals

PURPOSE OF REVIEW

Connecting organ-scale loads to cellular signals in their local in vivo environment is a current challenge in the field of bone (re)modelling. Understanding this critical missing link would greatly improve our ability to anticipate mechanotransduction during different modes of stimuli and the resultant cellular responses. This review characterises computational approaches that could enable coupling links across the multiple scales of bone.

RECENT FINDINGS

Current approaches using strain and fluid shear stress concepts have begun to link organ-scale loads to cellular signals; however, these approaches fail to capture localised micro-structural heterogeneities. Furthermore, models that incorporate downstream communication from osteocytes to osteoclasts, bone-lining cells and osteoblasts, will help improve the understanding of (re)modelling activities. Incorporating this potentially key information in the local in vivo environment will aid in developing multiscale models of mechanotransduction that can predict or help describe resultant biological events related to bone (re)modelling. Progress towards multiscale determination of the cell mechanical environment from organ-scale loads remains elusive. Construction of organ-, tissue- and cell-scale computational models that include localised environmental variation, strain amplification and intercellular communication mechanisms will ultimately help couple the hierarchal levels of bone.

Thermal analysis of the dentine tubule under hot and cold stimuli using fluid-structure interaction simulation

The objective of this study is to compare the thermal stress changes in the tooth microstructures and the hydrodynamic changes of the dental fluid under hot and cold stimuli. The dimension of the microstructures of eleven cats' teeth was measured by scanning electron microscopy, and the changes in thermal stress during cold and hot stimulation were calculated by 3D fluid-structure interaction modeling. Evaluation of results, following data validation, indicated that the maximum velocities in cold and hot stimuli were - 410.2 ± 17.6 and + 205.1 ± 8.7 µm/s, respectively. The corresponding data for maximum thermal stress were - 20.27 ± 0.79 and + 10.13 ± 0.24 cmHg, respectively. The thermal stress caused by cold stimulus could influence almost 2.9 times faster than that caused by hot stimulus, and the durability of the thermal stress caused by hot stimulus was 71% greater than that by cold stimulus under similar conditions. The maximum stress was on the tip of the odontoblast, while the stress in lateral walls of the odontoblast and terminal fibril was very weak. There is hence a higher possibility of pain transmission with activation of stress-sensitive ion channels at the tip of the odontoblast. The maximum thermal stress resulted from the cold stimulus is double that produced by the hot stimulus. There is a higher possibility of pain transmission in the lateral walls of the odontoblast and terminal fibril by releasing mediators during the cold stimulation than the hot stimulation. These two reasons can be associated with a greater pain sensation due to intake of cold liquids.