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

Numerical Simulation of Fluid Shear Stress Distribution in Microcracks of Trabecular Bone

Bone is one of the hardest tissues in the human body, but it can undergo microcracks under long-term and periodic mechanical loads. The Newton iterative method was used to calculate the steady state, and the effects of different inlet and outlet pressures, trabecular gap width and height, and microcrack's depth and width on the fluid shear stress (FSS) were studied, and the gradient of FSS inside the microcrack was analyzed. The results show that the pressure difference and trabecular gap heigh are positively correlated with the FSS (the linear correlation coefficients R 2 were 0.9768 and 0.96542, respectively). When the trabecular gap width was 100 μm, the peak of FSS decreased by 28.57% compared with 800 and 400 μm, and the gradient of FSS inside the microcrack was 0.1-0.4 Pa/mm. This study can help people more intuitively understand the internal fluid distribution of trabecular bone and provide a reliable theoretical basis for the subsequent construction of gradient FSS devices in vitro.

Comparing the bone regeneration potential between a trabecular bone and a porous scaffold through osteoblast migration and differentiation: A multiscale approach

Both cell migration and osteogenic differentiation are critical for successful bone regeneration. Therefore, understanding the mechanobiological aspects that govern these two processes is essential in designing effective scaffolds that promote faster bone regeneration. Studying these two factors at different locations is necessary to manage bone regeneration in various sections of a scaffold. Hence, a multiscale computational model was used to observe the mechanical responses of osteoblasts placed in different positions of the trabecular bone and gyroid scaffold. Fluid shear stresses in scaffolds at cell seeded locations (representing osteogenic differentiation) and strain energy densities in cells at cell substrate interface (representing cell migration) were observed as mechanical response parameters in this study. Comparison of these responses, as two critical factors for bone regeneration, between the trabecular bone and gyroid scaffold at different locations, is the overall goal of the study. This study reveals that the gyroid scaffold exhibits higher osteogenic differentiation and cell migration potential compared to the trabecular bone. However, the responses in the gyroid only mimic the trabecular bone in two out of nine positions. These findings can guide us in predicting the ideal cell seeded sites within a scaffold for better bone regeneration and in replicating a replaced bone condition by altering the physical parameters of a scaffold.

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.

A Numerical Study on Mechanical Effects of Low-Intensity Pulsed Ultrasound on Trabecular Bone and Osteoblasts

The lack of sufficient mechanical stimulation to the human bone, results in disuse osteoporosis. Low-intensity pulsed ultrasound (LIPUS) promotes fracture healing and the treatment of disuse osteoporosis, but its biomechanical mechanism remains unknown. Simulative research on the mechanical effects of LIPUS on disuse trabecular bone and osteoblasts have been performed. The von Mises stress of disuse trabecular bone and osteoblasts obviously increased under LIPUS irradiation. The average von Mises stress of osteoblasts were two orders of magnitude higher under the irradiation of simulant LIPUS than that without LIPUS irradiation, and the von Mises stress of osteoblasts was positively correlated with the amplitude of sound pressure excitation. The results showed that LIPUS irradiation could obviously improve the mechanical micro-environment of trabecular bone and osteoblasts to alleviate the lack of mechanical stimulation. The results of the research can reveal the biomechanical mechanism of LIPUS in the treatment of disuse osteoporosis to some extent and provide theoretical guidance for clinical treatment of disuse osteoporosis through physical methods.

Combined computational analysis and cytology show limited depth osteogenic effect on bone defects in negative pressure wound therapy

Background: The treatment of bone defects remains a clinical challenge. The effect of negative pressure wound therapy (NPWT) on osteogenesis in bone defects has been recognized; however, bone marrow fluid dynamics under negative pressure (NP) remain unknown. In this study, we aimed to examine the marrow fluid mechanics within trabeculae by computational fluid dynamics (CFD), and to verify osteogenic gene expression, osteogenic differentiation to investigate the osteogenic depth under NP. Methods: The human femoral head is scanned using micro-CT to segment the volume of interest (VOI) trabeculae. The VOI trabeculae CFD model simulating the bone marrow cavity is developed by combining the Hypermesh and ANSYS software. The effect of trabecular anisotropy is investigated, and bone regeneration effects are simulated under NP scales of -80, -120, -160, and -200 mmHg. The working distance (WD) is proposed to describe the suction depth of the NP. Finally, gene sequence analysis, cytological experiments including bone mesenchymal stem cells (BMSCs) proliferation and osteogenic differentiation are conducted after the BMSCs are cultured under the same NP scale. Results: The pressure, shear stress on trabeculae, and marrow fluid velocity decrease exponentially with an increase in WD. The hydromechanics of fluid at any WD inside the marrow cavity can be theoretically quantified. The NP scale significantly affects the fluid properties, especially those fluid close to the NP source; however, the effect of the NP scale become marginal as WD deepens. Anisotropy of trabecular structure coupled with the anisotropic hydrodynamic behavior of bone marrow; An NP of -120 mmHg demonstrates the majority of bone formation-related genes, as well as the most effective proliferation and osteogenic differentiation of BMSCs compared to the other NP scales. Conclusion: An NP of -120 mmHg may have the optimal activated ability to promote osteogenesis, but the effective WD may be limited to a certain depth. These findings help improve the understanding of fluid mechanisms behind NPWT in treating bone defects.

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons—where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers—up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford’s law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium–long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm.