Influence of high-frequency cyclical stimulation on the bone fracture-healing process: mathematical and experimental models

Computational models of bone fracture healing and applications: a review

Fracture healing is a very complex physiological process involving multiple events at different temporal and spatial scales, such as cell migration and tissue differentiation, in which mechanical stimuli and biochemical factors assume key roles. With the continuous improvement of computer technology in recent years, computer models have provided excellent solutions for studying the complex process of bone healing. These models not only provide profound insights into the mechanisms of fracture healing, but also have important implications for clinical treatment strategies. In this review, we first provide an overview of research in the field of computational models of fracture healing based on CiteSpace software, followed by a summary of recent advances, and a discussion of the limitations of these models and future directions for improvement. Finally, we provide a systematic summary of the application of computational models of fracture healing in three areas: bone tissue engineering, fixator optimization and clinical treatment strategies. The application of computational models of bone healing in clinical treatment is immature, but an inevitable trend, and as these models become more refined, their role in guiding clinical treatment will become more prominent.

Significance of mechanical loading in bone fracture healing, bone regeneration, and vascularization

In 1892, J.L. Wolff proposed that bone could respond to mechanical and biophysical stimuli as a dynamic organ. This theory presents a unique opportunity for investigations on bone and its potential to aid in tissue repair. Routine activities such as exercise or machinery application can exert mechanical loads on bone. Previous research has demonstrated that mechanical loading can affect the differentiation and development of mesenchymal tissue. However, the extent to which mechanical stimulation can help repair or generate bone tissue and the related mechanisms remain unclear. Four key cell types in bone tissue, including osteoblasts, osteoclasts, bone lining cells, and osteocytes, play critical roles in responding to mechanical stimuli, while other cell lineages such as myocytes, platelets, fibroblasts, endothelial cells, and chondrocytes also exhibit mechanosensitivity. Mechanical loading can regulate the biological functions of bone tissue through the mechanosensor of bone cells intraosseously, making it a potential target for fracture healing and bone regeneration. This review aims to clarify these issues and explain bone remodeling, structure dynamics, and mechano-transduction processes in response to mechanical loading. Loading of different magnitudes, frequencies, and types, such as dynamic versus static loads, are analyzed to determine the effects of mechanical stimulation on bone tissue structure and cellular function. Finally, the importance of vascularization in nutrient supply for bone healing and regeneration was further discussed.

Multiscale modeling of bone tissue mechanobiology

Mechanical environment has a crucial role in our organism at the different levels, ranging from cells to tissues and our own organs. This regulatory role is especially relevant for bones, given their importance as load-transmitting elements that allow the movement of our body as well as the protection of vital organs from load impacts. Therefore bone, as living tissue, is continuously adapting its properties, shape and repairing itself, being the mechanical loads one of the main regulatory stimuli that modulate this adaptive behavior. Here we review some key results of bone mechanobiology from computational models, describing the effect that changes associated to the mechanical environment induce in bone response, implant design and scaffold-driven bone regeneration.

Mechano-Regulation of Trabecular Bone Adaptation Is Controlled by the Local in vivo Environment and Logarithmically Dependent on Loading Frequency

It is well-established that cyclic, but not static, mechanical loading has anabolic effects on bone. However, the function describing the relationship between the loading frequency and the amount of bone adaptation remains unclear. Using a combined experimental and computational approach, this study aimed to investigate whether trabecular bone mechano-regulation is controlled by mechanical signals in the local in vivo environment and dependent on loading frequency. Specifically, by combining in vivo micro-computed tomography (micro-CT) imaging with micro-finite element (micro-FE) analysis, we monitored the changes in microstructural as well as the mechanical in vivo environment [strain energy density (SED) and SED gradient] of mouse caudal vertebrae over 4 weeks of either cyclic loading at varying frequencies of 2, 5, or 10 Hz, respectively, or static loading. Higher values of SED and SED gradient on the local tissue level led to an increased probability of trabecular bone formation and a decreased probability of trabecular bone resorption. In all loading groups, the SED gradient was superior in the determination of local bone formation and resorption events as compared to SED. Cyclic loading induced positive net (re)modeling rates when compared to sham and static loading, mainly due to an increase in mineralizing surface and a decrease in eroded surface. Consequently, bone volume fraction increased over time in 2, 5, and 10 Hz (+15%, +21% and +24%, p ≤ 0.0001), while static loading led to a decrease in bone volume fraction (-9%, p ≤ 0.001). Furthermore, regression analysis revealed a logarithmic relationship between loading frequency and the net change in bone volume fraction over the 4 week observation period (R 2 = 0.74). In conclusion, these results suggest that trabecular bone adaptation is regulated by mechanical signals in the local in vivo environment and furthermore, that mechano-regulation is logarithmically dependent on loading frequency with frequencies below a certain threshold having catabolic effects, and those above anabolic effects. This study thereby provides valuable insights toward a better understanding of the mechanical signals influencing trabecular bone formation and resorption in the local in vivo environment.

Real-Time Wireless Platform for In Vivo Monitoring of Bone Regeneration

For the monitoring of bone regeneration processes, the instrumentation of the fixation is an increasingly common technique to indirectly measure the evolution of bone formation instead of ex vivo measurements or traditional in vivo techniques, such as X-ray or visual review. A versatile instrumented external fixator capable of adapting to multiple bone regeneration processes was designed, as well as a wireless acquisition system for the data collection. The design and implementation of the overall architecture of such a system is described in this work, including the hardware, firmware, and mechanical components. The measurements are conditioned and subsequently sent to a PC via wireless communication to be in vivo displayed and analyzed using a developed real-time monitoring application. Moreover, a model for the in vivo estimation of the bone callus stiffness from collected data was defined. This model was validated in vitro using elastic springs, reporting promising results with respect to previous equipment, with average errors and uncertainties below 6.7% and 14.04%. The devices were also validated in vivo performing a bone lengthening treatment on a sheep metatarsus. The resulting system allowed the in vivo mechanical characterization of the bone callus during experimentation, providing a low-cost, simple, and highly reliable solution.

Matrix architecture plays a pivotal role in 3D osteoblast migration: The effect of interstitial fluid flow

Osteoblast migration is a crucial process in bone regeneration, which is strongly regulated by interstitial fluid flow. However, the exact role that such flow exerts on osteoblast migration is still unclear. To deepen the understanding of this phenomenon, we cultured human osteoblasts on 3D microfluidic devices under different fluid flow regimes. Our results show that a slow fluid flow rate by itself is not able to alter the 3D migratory patterns of osteoblasts in collagen-based gels but that at higher fluid flow rates (increased flow velocity) may indirectly influence cell movement by altering the collagen microstructure. In fact, we observed that high fluid flow rates (1 µl/min) are able to alter the collagen matrix architecture and to indirectly modulate the migration pattern. However, when these collagen scaffolds were crosslinked with a chemical crosslinker, specifically, transglutaminase II, we did not find significant alterations in the scaffold architecture or in osteoblast movement. Therefore, our data suggest that high interstitial fluid flow rates can regulate osteoblast migration by means of modifying the orientation of collagen fibers. Together, these results highlight the crucial role of the matrix architecture in 3D osteoblast migration. In addition, we show that interstitial fluid flow in conjunction with the matrix architecture regulates the osteoblast morphology in 3D.

Analysis of the Impact of Configuration of the Stabilisation System for Femoral Diaphyseal Fractures on the State of Stresses and Displacements

Introduction

The treatment of femoral diaphyseal fractures by intramedullary nailing has become a common procedure in orthopaedic surgery. The purpose of this numerical simulation was to present how the changes in configuration of the stabilisation system can affect the stress and displacement state in the bone tissue and implanted device.

Material and Methods

The numerical comparison of the stabilisation variants for the type 32-A2 femoral diaphyseal fracture (according to the AO classification) performed by using the Charfix2 (ChM®) anatomical nail locked in a number of chosen ways. The displacement and the stress distributions both in the bone and implant were obtained and analysed by computational simulation.

Results

In all models, there was the same characteristic distribution, which shows there were minimal rotational movements of the bone around the anatomical axis. In all cases, stress concentrations were generated in the nail material in the area of the fracture gap.

Conclusions

The obtained results indicate that there is a visible advantage to one-plane distal stabilisation in the reduction of stresses regardless of the type of proximal stabilisation. The results of calculations indicate that the use of proximal stabilisation with a neck screw reduces the possibility of damage to the implant.

Effects of continuous or intermittent low-magnitude high-frequency vibration on fracture healing in sheep

PURPOSE

Vibration therapy has been shown to improve fracture healing. In this study, we investigated the effects of continuous or different intermittent vibration regimens on fracture healing in sheep models on the basis of radiographs, mechanical, and biochemical testing.

METHODS

The 63 right-hind metatarsals from 63 sheep (12-month-old) were osteotomized; followed by surgical fixation with a steel plate. Two weeks after the surgery, the sheep with right-hind metatarsal fractures were randomly divided into seven groups (n=9/group): control (no vibration treated), continuous vibration (CV), one, three, five, seven and 14-day intermittent vibration (named IV-1, -3, -5, -7, and -14, respectively) groups, which represented a cycle of the successive n-day vibration and successive n-day break. Vibration stimulation (F=35 Hz, a=0.25 g) lasted 15 minutes each treatment. After eight weeks with/without vibration treatment, the sheep were euthanized with intravenous anesthetic. The callus formation, mechanical properties, and biochemical compositions of fracture metatarsals were analyzed.

RESULTS

In CV and IV-7 groups, X-ray images showed an increased callus volume around the fracture area. The bone elastic modulus and the concentrations of Ca, P, and Ca/P ratio of the area at 15 and 25 mm away from the fracture centerline were higher in CV and IV-7 groups compared with the other groups.

CONCLUSIONS

Our results demonstrate that both CV and IV-7 vibration patterns showed better improvement of fracture healing.

Computational Investigation on the Biomechanical Responses of the Osteocytes to the Compressive Stimulus: A Poroelastic Model

Osteocytes, the major type of bone cells embedded in the bone matrix and surrounded by the lacunar and canalicular system, can serve as biomechanosensors and biomechanotranducers of the bone. Theoretical analytical methods have been employed to investigate the biomechanical responses of osteocytes in vivo; the poroelastic properties have not been taken into consideration in the three-dimensional (3D) finite element model. In this study, a 3D poroelastic idealized finite element model was developed and was used to predict biomechanical behaviours (maximal principal strain, pore pressure, and fluid velocity) of the osteocyte-lacunar-canalicular system under 150-, 1000-, 3000-, and 5000-microstrain compressive loads, respectively, representing disuse, physiological, overuse, and pathological overload loading stimuli. The highest local strain, pore pressure, and fluid velocity were found to be highest at the proximal region of cell processes. These data suggest that the strain, pore pressure, and fluid velocity of the osteocyte-lacunar-canalicular system increase with the global loading and that the poroelastic material property affects the biomechanical responses to the compressive stimulus. This new model can be used to predict the mechanobiological behaviours of osteocytes under the four different compressive loadings and may provide an insight into the mechanisms of mechanosensation and mechanotransduction of the bone.

Cyclic mechanical loading enables solute transport and oxygen supply in bone healing: an in vitro investigation

Bone healing is a complex process with an increased metabolic activity and consequently high demand for oxygen. In the hematoma phase, inflammatory cells and mesenchymal stromal cells (MSCs) are initially cut off from direct nutritional supply via blood vessels. Cyclic mechanical loading that occurs, for example, during walking is expected to have an impact on the biophysical environment of the cells but meaningful quantitative experimental data are still missing. In this study, the hypothesis that cyclic mechanical loading within a physiological range significantly contributes to oxygen transport into the fracture hematoma was investigated by an in vitro approach. MSCs were embedded in a fibrin matrix to mimic the hematoma phase during bone healing. Construct geometry, culture conditions, and parameters of mechanical loading in a bioreactor system were chosen to resemble the in vivo situation based on data from human studies and a well-characterized large animal model. Oxygen tension was measured before and after mechanical loading intervals by a chemical optical microsensor. The increase in oxygen tension at the center of the constructs was significant and depended on loading time with maximal values of 9.9%±5.1%, 14.8%±4.9%, and 25.3%±7.2% of normal atmospheric oxygen tension for 5, 15, and 30 min of cyclic loading respectively. Histological staining of hypoxic cells after 48 h of incubation confirmed sensor measurements by showing an increased number of normoxic cells with intermittent cyclic compression compared with unloaded controls. The present study demonstrates that moderate cyclic mechanical loading leads to an increased oxygen transport and thus to substantially enhanced supply conditions for cells entrapped in the hematoma. This link between mechanical conditions and nutrition supply in the early regenerative phases could be employed to improve the environmental conditions for cell metabolism and consequently prevent necrosis.