Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

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.

Influence of implant base material on secondary bone healing: an in silico study

The implant material at the fracture site influences fracture healing not only from biological perspective but also from mechanical perspective. Biodegradable implants such as magnesium (Mg) based alloys have shown faster secondary bone healing properties as compared to bioinert implants such as titanium (Ti). The general reasoning behind this is the benefit of Mg from biocompatibility perspectives. We studied the effect of Ti and Mg as base materials for implants from mechanical perspectives, where we focused on the displacements at the fracture site of the tibia and their influence on the stimulus for bone healing. We found out that in comparison to Ti, Mg implants have minimal stress shielding problem, only which led to better mechanical stimulus at the fracture site.

Experimental and virtual testing of bone-implant systems equipped with the AO Fracture Monitor with regard to interfragmentary movement

Introduction: The management of fractured bones is a key domain within orthopedic trauma surgery, with the prevention of delayed healing and non-unions forming a core challenge. This study evaluates the efficacy of the AO Fracture Monitor in conjunction with biomechanical simulations to better understand the local mechanics of fracture gaps, which is crucial for comprehending mechanotransduction, a key factor in bone healing. Through a series of experiments and corresponding simulations, the study tests four hypotheses to determine the relationship between physical measurements and the predictive power of biomechanical models. Methods: Employing the AO Fracture Monitor and Digital Image Correlation techniques, the study demonstrates a significant correlation between the surface strain of implants and interfragmentary movements. This provides a foundation for utilizing one-dimensional AO Fracture Monitor measurements to predict three-dimensional fracture behavior, thereby linking mechanical loading with fracture gap dynamics. Moreover, the research establishes that finite element simulations of bone-implant systems can be effectively validated using experimental data, underpinning the accuracy of simulations in replicating physical behaviors. Results and Discussion: The findings endorse the combined use of monitoring technologies and simulations to infer the local mechanical conditions at the fracture site, offering a potential leap in personalized therapy for bone healing. Clinically, this approach can enhance treatment outcomes by refining the assessment precision in trauma trials, fostering the early detection of healing disturbances, and guiding improvements in future implant design. Ultimately, this study paves the way for more sophisticated patient monitoring and tailored interventions, promising to elevate the standard of care in orthopedic trauma surgery.

Effect of different composite plates on the healing of femoral fractures

In this paper, the effects of different composite plates on the healing of femoral fractures were studied by numerical simulation. The healing model of femoral fracture was established by ABAQUS display solver. Based on the fuzzy logic theory, the process of callus differentiation at femoral fracture was considered under the joint action of biological variables and mechanical stimulation, and the healing process of femur was simulated. Compare the stress on the screw, concentration of callus bone and cartilage, and callus healing performance of the carbon/epoxy composite (WSN3k) plate, glass/polypropylene composite (Twintex) plate, and stainless steel plate at various stages of bone healing, and investigate the impact of composite plates on the bone healing process. The results showed that the modulus of the plate had a notable impact on bone healing. Compared to stainless steel plate, the composite plate (due to its lower stiffness) exhibiting superior healing performance. Altering the sequence of composite laminates may modify the bone healing efficiency, and the wsn3k [0]18 composite plate exhibits superior healing performance.

Reappraisal of clinical trauma trials: the critical impact of anthropometric parameters on fracture gap micro-mechanics-observations from a simulation-based study

The evidence base of surgical fracture care is extremely sparse with only few sound RCTs available. It is hypothesized that anthropometric factors relevantly influence mechanical conditions in the fracture gap, thereby interfering with the mechanoinduction of fracture healing. Development of a finite element model of a tibia fracture, which is the basis of an in silico population (n = 300) by systematic variation of anthropometric parameters. Simulations of the stance phase and correlation between anthropometric parameters and the mechanical stimulus in the fracture gap. Analysis of the influence of anthropometric parameters on statistical dispersion between in silico trial cohorts with respect to the probability to generate two, with respect to anthropometric parameters statistically different trial cohorts, given the same power assumptions. The mechanical impact in the fracture gap correlates with anthropometric parameters; confirming the hypothesis that anthropometric factors are a relevant entity. On a cohort level simulation of a fracture trial showed that given an adequate power the principle of randomization successfully levels out the impact of anthropometric factors. From a clinical perspective these group sizes are difficult to achieve, especially when considering that the trials takes advantage of a "laboratory approach ", i.e. the fracture type has not been varied, such that in real world trials the cohort size have to be even larger to level out the different configurations of fractures gaps. Anthropometric parameters have a significant impact on the fracture gap mechanics. The cohort sizes necessary to level out this effect are difficult or unrealistic to achieve in RCTs, which is the reason for sparse evidence in orthotrauma. New approaches to clinical trials taking advantage of modelling and simulation techniques need to be developed and explored.

Effects of dynamization timing and degree on bone healing of different fracture types

Dynamization, that is, increasing interfragmentary movement (IFM) by reducing fixation stiffness from a rigid to a more flexible state, has been successfully used in clinical practice to promote fracture healing. However, it remains unclear how dynamization timing and degree affect bone healing of different fracture types. Finite element models of tibial fractures based on the OTA/AO classification (Simple: A1-Spiral, A2-Oblique, A3-Transverse; Wedge: B2-Spiral, B3-Fragmented; Complex: C2-Segment, C3-Irregular), in combination with fuzzy logic-based mechano-regulatory tissue differentiation algorithms, were used to simulate the healing process when dynamization of varied degrees (dynamization coefficient or DC = 0-0.9; 0.9 represents 90% reduction in the fixation stiffness relative to a rigid fixation) were applied at different time points after fracture. The fuzzy logic-based algorithms have been validated with a preclinical animal model. The results showed that the healing responses of type A fractures were more sensitive to the changes in dynamization degree and timing comparing with type B or C fractures. Additionally, the optimal dynamization regime for each fracture type was different. For type A fractures, a moderate dynamization degree (e.g., DC = 0.5) applied after Week 1 promoted the recovery of biomechanical integrity. For type B and C fractures, the effective dynamization included a greater dynamization degree (DC = 0.7) applied after Week 2. Our results further demonstrated that the fracture morphology affected interfragmentary strain environments within the callus, leading to varied healing results for different fracture types. These results suggest that the effects of dynamization are highly dependent of the fracture types. Therefore, specific dynamization strategies should be chosen for different fracture types to achieve optimal healing outcomes.

Finite element analysis of a customized implant in PMMA coupled with the cranial bone

This computational study investigates the effect of the Von Misses stresses and deformations distribution generated by coupling a customized cranial implant with its fixation system for anchoring in the cranial bone of a specific patient. Three simulations were carried out under static loads, in different areas of the implant and during the rest-activity; and another three simulations were considered preset maximum intracranial pressures. Anatomical models were obtained by computed tomography. The design of the device to be implanted was carried out by applying reverse engineering processes, from the corresponding computer-aided design (CAD) model of the bone structure of interest. Likewise, the anchoring system was modeled in detail. Loads were applied at three points on the custom implant. The stress distribution on the artificial plate and the implant-natural bone interface was analyzed. The distribution of the stresses caused by the internal load states on the plate and the anchoring system was also studied. The neurocranial reconstruction with the customized polymethylmethacrylate (PMMA)-based implant and the finite element analysis demonstrated that the fixation and coupling system of the bone-implant interface guarantees adequate protection for the internal structures of the restored area. In addition, the custom-designed and placed implant will not cause non-physiological harm to the patient. Nor will failures occur in the anchoring system.

Computer-Based Mechanobiological Fracture Healing Model Predicts Non-Union of Surgically Treated Diaphyseal Femur Fractures

As non-unions are still common, a predictive assessment of healing complications could enable immediate intervention before negative impacts for the patient occur. The aim of this pilot study was to predict consolidation with the help of a numerical simulation model. A total of 32 simulations of patients with closed diaphyseal femoral shaft fractures treated by intramedullary nailing (PFNA long, FRN, LFN, and DePuy Synthes) were performed by creating 3D volume models based on biplanar postoperative radiographs. An established fracture healing model, which describes the changes in tissue distribution at the fracture site, was used to predict the individual healing process based on the surgical treatment performed and full weight bearing. The assumed consolidation as well as the bridging dates were retrospectively correlated with the clinical and radiological healing processes. The simulation correctly predicted 23 uncomplicated healing fractures. Three patients showed healing potential according to the simulation, but clinically turned out to be non-unions. Four out of six non-unions were correctly detected as non-unions by the simulation, and two simulations were wrongfully diagnosed as non-unions. Further adjustments of the simulation algorithm for human fracture healing and a larger cohort are necessary. However, these first results show a promising approach towards an individualized prognosis of fracture healing based on biomechanical factors.

Computational model of articular cartilage regeneration induced by scaffold implantation in vivo

Computational models allow to explain phenomena that cannot be observed through an animal model, such as the strain and stress states which can highly influence regeneration of the tissue. For this purpose, we have developed a simulation tool to determine the mechanical conditions provided by the polymeric scaffold. The computational model considered the articular cartilage, the subchondral bone, and the scaffold. All materials were modeled as poroelastic, and the cartilage had linear-elastic oriented collagen fibers. This model was able to explain the remodeling process that subchondral bone goes through, and how the scaffold allowed the conditions for cartilage regeneration. These results suggest that the use of scaffolds might lead the cartilaginous tissue growth in vivo by providing a better mechanical environment. Moreover, the developed computational model demonstrated to be useful as a tool prior experimental in vivo studies, by predicting the possible outcome of newly proposed treatments allowing to discard approaches that might not bring good results.

Design and performance analysis of 3D-printed stiffness gradient femoral scaffold

Studies on 3D-printed porous bone scaffolds mostly focus on materials or structural parameters, while the repair of large femoral defects needs to select appropriate structural parameters according to the needs of different parts. In this paper, a kind of stiffness gradient scaffold design idea is proposed. Different structures are selected according to the different functions of different parts of the scaffold. At the same time, an integrated fixation device is designed to fix the scaffold. Finite element method was used to analyze the stress and strain of homogeneous scaffolds and the stiffness gradient scaffolds, and the relative displacement and stress between stiffness gradient scaffolds and bone in the case of integrated fixation and steel plate fixation. The results showed that the stress distribution of the stiffness gradient scaffolds was more uniform, and the strain of host bone tissue was changed greatly, which was beneficial to the growth of bone tissue. The integrated fixation method is more stable, less stress and evenly distributed. Therefore, the integrated fixation device combined with the design of stiffness gradient can repair the large femoral bone defect well.

Three-Dimensional Computational Model Simulating the Initial Callus Growth during Fracture Healing in Long Bones: Application to Different Fracture Types

Bone fractures are among the most common and potentially serious injuries to the skeleton, femoral shaft fractures being especially severe. Thanks to recent advances in the area of in silico analysis, several approximations of the bone healing process have been achieved. In this context, the objective of this work was to simulate the initial phase of callus formation in long bones, without a pre-meshed domain in the 3D space. A finite element approach was computationally implemented to obtain the values of the cell concentrations along the whole domain and evaluate the areas where the biological quantities reached the thresholds necessary to trigger callus growth. A voxel model was used to obtain the 3D domain of the bone fragments and callus. A mesh growth algorithm controlled the addition of new elements to the domain at each step of the iterative procedure until complete callus formation. The implemented approach is able to reproduce the generation of the primary callus, which corresponds to the initial phase of fracture healing, independently of the fracture type and complexity, even in the case of several bone fragments. The proposed approach can be applied to the most complex bone fractures such as oblique, severely comminuted or spiral-type fractures, whose simulation remains hardly possible by means of the different existing approaches available to date.

Enhanced bone formation in locally-optimised, low-stiffness additive manufactured titanium implants: An in silico and in vivo tibial advancement study

A tibial tuberosity advancement (TTA), used to treat lameness in the canine stifle, provides a framework to investigate implant performance within an uneven loading environment due to the dominating patellar tendon. The purpose of this study was to reassess how we design orthopaedic implants in a load-bearing model to investigate potential for improved osseointegration capacity of fully-scaffolded mechanically-matched additive manufactured (AM) implants. While the mechanobiological nature of bone is well known, we have identified a lower limit in the literature where investigation into exceedingly soft scaffolds relative to trabecular bone ceases due to the trade-off in mechanical strength. We developed a finite element model of the sheep stifle to assess the stresses and strains of homogeneous and locally-optimised TTA implant designs. Using additive manufacturing, we printed three different low-stiffness Ti-6Al-4 V TTA implants: 0.8 GPa (Ti1), 0.6 GPa (Ti2) and an optimised design with a 0.3 GPa cortex and 0.1 GPa centre (Ti3), for implantation in a 12-week in vivo ovine pilot study. Static histomorphometry demonstrated uniform bone ingrowth in optimised low-modulus Ti3 samples compared to homogeneous designs (Ti1 and Ti2), and greater bone-implant contact. Mineralising surfaces were apparent in all implants, though mineral apposition rate was only consistent throughout Ti3. The greatest bone formation scores were seen in Ti3, followed by Ti2 and Ti1. Results from our study suggest lower stiffnesses and higher strain ranges improve early bone formation, and that by accounting for loading environments through rational design, implants can be optimised to improve uniform osseointegration. STATEMENT OF SIGNIFICANCE: The effect of different strain ranges on bone healing has been traditionally investigated and characterised through computational models, with much of the literature suggesting higher strain ranges being favourable. However, little has been done to incorporate strain-optimisation into porous orthopaedic implants due to the trade-off in mechanical strength required to induce these microenvironments. In this study, we used finite element analysis to optimise the design of additive manufactured (AM) titanium orthopaedic implants for different strain ranges, using a clinically-relevant surgical model. Our research suggests that there is potential for locally-optimised AM scaffolds in the use of orthopaedic devices to induce higher strains, which in turn encourages de novo bone formation and uniform osseointegration.

Simulation-based prediction of bone healing and treatment recommendations for lower leg fractures: Effects of motion, weight-bearing and fibular mechanics

Despite recent experimental and clinical progress in the treatment of tibial and fibular fractures, in clinical practice rates of delayed bone healing and non-union remain high. The aim of this study was to simulate and compare different mechanical conditions after lower leg fractures to assess the effects of postoperative motion, weight-bearing restrictions and fibular mechanics on the strain distribution and the clinical course. Based on the computed tomography (CT) data set of a real clinical case with a distal diaphyseal tibial fracture, a proximal and a distal fibular fracture, finite element simulations were run. Early postoperative motion data, recorded via an inertial measuring unit system and pressure insoles were recorded and processed to study strain. The simulations were used to compute interfragmentary strain and the von Mises stress distribution of the intramedullary nail for different treatments of the fibula, as well as several walking velocities (1.0 km/h; 1.5 km/h; 2.0 km/h) and levels of weight-bearing restriction. The simulation of the real treatment was compared to the clinical course. The results show that a high postoperative walking speed was associated with higher loads in the fracture zone. In addition, a larger number of areas in the fracture gap with forces that exceeded beneficial mechanical properties longer was observed. Moreover, the simulations showed that surgical treatment of the distal fibular fracture had an impact on the healing course, whereas the proximal fibular fracture barely mattered. Weight-bearing restrictions were beneficial in reducing excessive mechanical conditions, while it is known that it is difficult for patients to adhere to partial weight-bearing recommendations. In conclusion, it is likely that motion, weight bearing and fibular mechanics influence the biomechanical milieu in the fracture gap. Simulations may improve decisions on the choice and location of surgical implants, as well as give recommendations for loading in the postoperative course of the individual patient.

Biodegradable interbody cages for lumbar spine fusion: Current concepts and future directions

Lumbar fusion often remains the last treatment option for various acute and chronic spinal conditions, including infectious and degenerative diseases. Placement of a cage in the intervertebral space has become a routine clinical treatment for spinal fusion surgery to provide sufficient biomechanical stability, which is required to achieve bony ingrowth of the implant. Routinely used cages for clinical application are made of titanium (Ti) or polyetheretherketone (PEEK). Ti has been used since the 1980s; however, its shortcomings, such as impaired radiographical opacity and higher elastic modulus compared to bone, have led to the development of PEEK cages, which are associated with reduced stress shielding as well as no radiographical artefacts. Since PEEK is bioinert, its osteointegration capacity is limited, which in turn enhances fibrotic tissue formation and peri-implant infections. To address shortcomings of both of these biomaterials, interdisciplinary teams have developed biodegradable cages. Rooted in promising preclinical large animal studies, a hollow cylindrical cage (Hydrosorb™) made of 70:30 poly-l-lactide-co-d, l-lactide acid (PLDLLA) was clinically studied. However, reduced bony integration and unfavourable long-term clinical outcomes prohibited its routine clinical application. More recently, scaffold-guided bone regeneration (SGBR) with application of highly porous biodegradable constructs is emerging. Advancements in additive manufacturing technology now allow the cage designs that match requirements, such as stiffness of surrounding tissues, while providing long-term biomechanical stability. A favourable clinical outcome has been observed in the treatment of various bone defects, particularly for 3D-printed composite scaffolds made of medical-grade polycaprolactone (mPCL) in combination with a ceramic filler material. Therefore, advanced cage design made of mPCL and ceramic may also carry initial high spinal forces up to the time of bony fusion and subsequently resorb without clinical side effects. Furthermore, surface modification of implants is an effective approach to simultaneously reduce microbial infection and improve tissue integration. We present a design concept for a scaffold surface which result in osteoconductive and antimicrobial properties that have the potential to achieve higher rates of fusion and less clinical complications. In this review, we explore the preclinical and clinical studies which used bioresorbable cages. Furthermore, we critically discuss the need for a cutting-edge research program that includes comprehensive preclinical in vitro and in vivo studies to enable successful translation from bench to bedside. We develop such a conceptual framework by examining the state-of-the-art literature and posing the questions that will guide this field in the coming years.

[Movement analysis and musculoskeletal simulation in non-union treatment-Experiences and first clinical results]

BACKGROUND

The mechanical boundary conditions of the non-union and osteosynthetic construct are a key determinant of fracture healing after revision surgery. Aim of this study was to introduce a movement analysis and simulation workflow to determine the mechanical conditions during non-union healing in vivo.

MATERIAL AND METHODS

On an individual case basis after non-union revision surgery we performed an accelerometry-based movement analysis. The results were then used as input for a musculoskeletal simulation of the non-union, osteosynthetic construct as well as adjacent joints mechanical boundary conditions.

RESULTS

A total of 13 patients were analyzed with our new workflow. The introduced protocol allows an in vivo determination of the mechanical boundary conditions. On clinical follow-up all patients showed radiographic consolidation of the non-union.

CONCLUSION

The introduced workflow allows a clinically applicable determination of the mechanical boundary conditions of fracture and non-union healing. Further studies can now determine the effect of the introduced technique for mechanically optimized postoperative aftercare regimes as well as biomechanically adapted surgical treatment.

A preclinical model of post-surgery secondary bone healing for subtrochanteric femoral fracture based on fuzzy interpretations

Mechanobiology plays an essential role in secondary bone fracture healing. While the introduction of newer type of plates, e.g. locking plate (LP), is becoming increasingly popular for complex femoral fractures, the conventional technique involving dynamic compression plate (DCP) remains the standard choice. The difference between the two techniques lies primarily in their screw fixation mechanisms. The present study applied 3D dynamic fracture healing scheme modelled on a subtrochanteric femur fracture, regulated by both finite element (FE) analysis and Fuzzy logic control in order to understand the spatio-temporal healing phenomena for both LP and DCP. The study further examined the influence of the two screw fixation mechanisms in determining the comparative progression of fracture healing. The problem was solved iteratively in several healing steps running in loop and accordingly, the local tissue concentrations and material properties were updated. The predicted results accorded well with various previous experimental observations. The study found an initial delay in healing associated with DCP. However, as the healing progressed, there was no significant difference in overall callus modulus. The presented preclinical model may further help predict bone healing for different implantation techniques, and thus can serve as a non-invasive tool for evaluating relative merits of extramedullary plating techniques.

Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures

Background: The purpose of this study was to demonstrate the usefulness of 3D image-based virtual reduction by validating the evaluation criteria according to guidelines suggested by the AO Surgery Reference. Methods: For this experiment, 19 intact radial ORTHObones (ORTHObones radius, 3B Scientific, Germany, Hamburg) without any fractures were prepared. All ORTHObones with six cortical marking holes (three points on the distal part and three points on the proximal part) were scanned using a CT scanner twice (before/after intentional fracture of the ORTHObone). After the virtual reduction of all 19 ORTHObones, accuracy evaluations using the four criteria (length variation, apposition variation, alignment variation, Rotation Variation) suggested in the AO Surgery Reference were performed. Results: The mean (M) length variation was 0.42 mm, with 0.01 mm standard deviation (SD). The M apposition variation was 0.48 mm, with 0.40 mm SD. The M AP angulation variation (for alignment variation) was 3.24°, with 2.95° SD. The M lateral angulation variation (for alignment variation) was 0.09°, with 0.13° SD. The M angle of axial rotation was 1.27° with SD: 1.19°. Conclusions: The method of accuracy evaluation used in this study can be helpful in establishing a reliable plan.

In vivo and in silico monitoring bone regeneration during distraction osteogenesis of the mouse femur

BACKGROUND AND OBJECTIVE

Distraction osteogenesis (DO) is a mechanobiological process of producing new bone by gradual and controlled distraction of the surgically separated bone segments. Mice have been increasingly used to study the role of relevant biological factors in regulating bone regeneration during DO. However, there remains a lack of in silico DO models and related mechano-regulatory tissue differentiation algorithms for mouse bone. This study sought to establish an in silico model based on in vivo experimental data to simulate the bone regeneration process during DO of the mouse femur.

METHODS

In vivo micro-CT, including time-lapse morphometry was performed to monitor the bone regeneration in the distraction gap. A 2D axisymmetric finite element model, with a geometry originating from the experimental data, was created. Bone regeneration was simulated with a fuzzy logic-based two-stage (distraction and consolidation) mechano-regulatory tissue differentiation algorithm, which was adjusted from that used for fracture healing based on our in vivo experimental data. The predictive potential of the model was further tested with varied distraction frequencies and distraction rates.

RESULTS

The computational simulations showed similar bone regeneration patterns to those observed in the micro-CT data from the experiment throughout the DO process. This consisted of rapid bone formation during the first 10 days of the consolidation phase, followed by callus reshaping via bone remodeling. In addition, the computational model predicted a faster and more robust bone healing response as the model's distraction frequency was increased, whereas higher or lower distraction rates were not conducive to healing.

CONCLUSIONS

This in silico model could be used to investigate basic mechanobiological mechanisms involved in bone regeneration or to optimize DO strategies for potential clinical applications.

The combined effects of dynamization time and degree on bone healing

Dynamization, increasing the interfragmentary movement (IFM) by reducing the fixation stiffness from a rigid to a more flexible condition, is widely used clinically to promote fracture healing. However, it remains unknown how dynamization degree (relative change in fixation stiffness/IFM from a rigid to a flexible fixation) affects bone healing at various stages. To address this issue, we used a fuzzy logic-based mechano-regulated tissue differentiation algorithm on published experimental data from a sheep osteotomy healing model. We applied a varied degree of dynamization, from 0 (fully rigid fixation) to 0.9 (90% reduction in stiffness relative to the rigid fixation) after 1, 2, 3, and 4 weeks of osteotomy (R1wF, R2wF, R3wF, and R4wF) and computationally evaluated bone regeneration and biomechanical integrity over the healing process of 8 weeks. Compared with the constant rigid fixation, early dynamization (R1wF and R2wF) led to delays in bone bridging and biomechanical recovery of the osteotomized bone. However, the effect of early dynamization on healing was dependent of the degree of dynamization. Specifically, a higher dynamization degree (e.g., 0.9 for R1wF) led to a prolonged delay in bone bridging and largely unrecovered bending stiffness (48% relative to the intact bone), whereas a moderate degree of dynamization (e.g., 0.5 or 0.7) significantly enhanced bone formation and biomechanical properties of the osteotomized bone. These results suggest that dynamization degree and timing interactively affect the healing process. A combination of early dynamization with a moderate degree could enhance the ultimate biomechanical recovery of the fractured bone.

Bone Ingrowth Around an Uncemented Femoral Implant Using Mechanoregulatory Algorithm: A Multiscale Finite Element Analysis

The primary fixation and long-term stability of a cementless femoral implant depend on bone ingrowth within the porous coating. Although attempts were made to quantify the peri-implant bone ingrowth using the finite element (FE) analysis and mechanoregulatory principles, the tissue differentiation patterns on a porous-coated hip stem have scarcely been investigated. The objective of this study is to predict the spatial distribution of evolutionary bone ingrowth around an uncemented hip stem, using a three-dimensional (3D) multiscale mechanobiology-based numerical framework. Multiple load cases representing a variety of daily living activities, including walking, stair climbing, sitting down, and standing up from a chair, were used as applied loading conditions. The study accounted for the local variations in host bone material properties and implant-bone relative displacements of the macroscale implanted FE model, in order to predict bone ingrowth in microscale representative volume elements (RVEs) of 12 interfacial regions. In majority RVEs, 20-70% bone tissue (immature and mature) was predicted after 2 months, contributing toward a progressive increase in average Young's modulus (1200-3000 MPa) of the interbead tissue layer. Higher bone ingrowth (mostly greater than 60%) was predicted in the anterolateral regions of the implant, as compared to the posteromedial side (20-50%). New bone tissue was formed deeper inside the interbead spacing, adhering to the implant surface. The study helps to gain an insight into the degree of osseointegration of a porous-coated femoral implant.

Image-based radiodensity profilometry measures early remodeling at the bone-callus interface in sheep

Bone healing has been traditionally described as a four-phase process: inflammatory response, soft callus formation, hard callus development, and remodeling. The remodeling phase has been largely neglected in most numerical mechanoregulation models of fracture repair in favor of capturing early healing using a pre-defined callus domain. However, in vivo evidence suggests that remodeling occurs concurrently with repair and causes changes in cortical bone adjacent to callus that are typically neglected in numerical models of bone healing. The objective of this study was to use image processing techniques to quantify this early-stage remodeling in ovine osteotomies. To accomplish this, we developed a numerical method for radiodensity profilometry with optimization-based curve fitting to mathematically model the bone density gradients in the radial direction across the cortical wall and callus. After assessing data from 26 sheep, we defined a dimensionless density fitting function that revealed significant remodeling occurring in the cortical wall adjacent to callus during early healing, a 23% average reduction in density compared to intact. This fitting function is robust for modeling radial density gradients in both intact bone and fracture repair scenarios and can capture a wide variety of the healing responses. The fitting function can also be scaled easily for comparison to numerical model predictions and may be useful for validating future mechanoregulatory models of coupled fracture repair and remodeling.

Individualized Determination of the Mechanical Fracture Environment After Tibial Exchange Nailing-A Simulation-Based Feasibility Study

Non-union rate after tibial fractures remains high. Apart from largely uncontrollable biologic, injury, and patient-specific factors, the mechanical fracture environment is a key determinant of healing. Our aim was to establish a patient-specific simulation workflow to determine the mechanical fracture environment and allow for an estimation of its healing potential. In a referred patient with failed nail-osteosynthesis after tibial-shaft fracture exchange nailing was performed. Post-operative CT-scans were used to construct a three-dimensional model of the treatment situation in an image processing and computer-aided design system. Resulting forces, computed in a simulation-driven workflow based on patient monitoring and motion capturing were used to simulate the mechanical fracture environment before and after exchange nailing. Implant stresses for the initial and revision situation, as well as interfragmentary movement, resulting hydrostatic, and octahedral shear strain were calculated and compared to the clinical course. The simulation model was able to adequately predict hardware stresses in the initial situation where mechanical implant failure occurred. Furthermore, hydrostatic and octahedral shear strain of the revision situation were calculated to be within published healing boundaries—accordingly the fracture healed uneventfully. Our workflow is able to determine the mechanical environment of a fracture fixation, calculate implant stresses, interfragmentary movement, and the resulting strain. Critical mechanical boundary conditions for fracture healing can be determined in relation to individual loading parameters. Based on this individualized treatment recommendations during the early post-operative phase in lower leg fractures are possible in order to prevent implant failure and non-union development.

A new approach for initial callus growth during fracture healing in long bones

The incidence of bone fracture has become a major clinical problem on a worldwide scale. In the past two decades there has been an increase in the use of computational tools to analyse the bone fracture problem. In several works, various study cases have been analysed to compare human and animal bone fracture healing. Unfortunately, there are not many publications about computational advances in this field and the existing approaches to the problem are usually similar. In this context, the objective of this work is the application of a diffusion problem in the model of the bone fragments resulting from fracture, working together with a mesh-growing algorithm that allows free growth of the callus depending on the established conditions, without a pre-meshed domain. The diffusion problem concerns the different biological magnitudes controlling the callus growth, among which Mesenchymal Stem Cells and chondrocytes concentrations were chosen, together with Tumour Necrosis Factor α and Bone Morphogenetic Protein as the factors influencing the velocity in the callus formation. A Finite Element approach was used to solve the corresponding diffusion problems, obtaining the concentration values along the entire domain and allowing detecting the zones in which biological magnitudes reach the necessary thresholds for callus growth. The callus growth is guided by a geometrical algorithm which performs an additional mesh generation process (self-added mesh) at each step of the iterative procedure until complete callus formation. The proposed approach was applied to different types of diaphyseal femoral fractures treated by means of intramedullary nailing. Axisymmetric models based on triangular quadratic elements were used, obtaining results in good agreement with clinical evidence of these kinds of fractures. The algorithm proposed has the advantage of a natural callus growth, without the existence of a previous mesh that may affect the conditions and direction of growth. The approach is intended for the initial phase of callus growth. Future work will address the implementation of the corresponding formulations for tissue transformation and bone remodelling in order to achieve complete fracture healing.

Domain-independent simulation of physiologically relevant callus shape in mechanoregulated models of fracture healing

Mechanoregulatory models have been used to predict the progression of bone fracture healing for more than two decades. However, many published studies share the same fundamental limitation: callus development proceeds within a pre-defined domain that both restricts and directs healing and leads to some non-physiologic healing patterns. To address this limitation, we added two spatial proximity functions to an existing mechanoregulatory model of fracture healing to control the localization of callus within the healing domain. We tested the performance of the new model in an idealized ovine tibial osteotomy with medial plate fixation using three sizes of healing domains and multiple variations of the spatial proximity functions. All model variations produced outward callus growth and bridging weighted toward the far cortex, which is consistent with in vivo healing. With and without the proximity functions, there were marked differences in the predicted callus volume and shape. With no proximity functions, the callus produced was strongly domain dependent, with a 15% difference in volume between the smallest and largest initialization domains. With proximity function control, callus growth was restricted to near the fracture line and there was only 2% difference in volume between domain sizes. Superimposing both proximity functions - one to control outward growth and one representing a decay in periosteal activity away from the fracture - produced a predicted callus size that was within the physiologic range for sheep and had a realistic morphology when compared with fluorescent dye co-localization with calcium deposition over time and histology.

The interplay between bone healing and remodeling around dental implants

Long-term bone healing/adaptation after a dental implant treatment starts with diffusion of mesenchymal stem cells to the wounded region and their subsequent differentiation. The healing phase is followed by the bone-remodeling phase. In this work, a mechano-regulatory cellular differentiation model was used to simulate tissue healing around an immediately loaded dental implant. All tissue types were modeled as poroelastic in the healing phase. Material properties of the healing region were updated after each loading cycle for 30 cycles (days). The tissue distribution in the healed state was then used as the initial condition for the remodeling phase during which regions healed into bone adapt their apparent density with respect to a homeostatic remodeling stimulus. The short- (bone healing) and long-term (bone remodeling) effects of initial implant micromotion during the healing phase were studied. Development of soft tissue was observed both in the coronal region due to high fluid velocity, and on the vertical sides of the healing-gap due to high shear stress. In cases with small implant micromotion, tissue between the implant threads differentiated into bone during the healing phase but resorbed during remodeling. In cases with large implant micromotion, higher percentage of the healing region differentiated into soft tissue resulting in smaller volume of bone tissue available for remodeling. However, the remaining bone region developed higher density bone tissue. It was concluded that an optimal range of initial implant micromotion could be designed for a specific patient in order to achieve the desired long-term functional properties.

Stability of femoral neck fracture fixation: A finite element analysis

Femoral neck fractures represent a relatively uncommon injury in the non-elderly population often resulting from high-energy trauma. Clinical outcome in these patients can be improved by optimizing surgical procedures and selecting appropriate fixation methods. The aim of this study was to develop a numerical fracture model to investigate the influence of critical mechanical factors on the stability of fixation methods for femoral neck fractures. The mechanical stability of fracture fixation was assessed through employing finite element models and simulating progressive consolidation of the fracture for a vertical femoral neck fracture (i.e. Pauwels type III in which the angle between the fracture line and the horizontal plane is greater than 70°). Mechanical performance was compared among three different fixation methods (cannulated screws, dynamic hip screw with de-rotational screw, and proximal femoral locking plate). Axial femoral head displacement varied from 2.3 mm for cannulated screws to 1.12 mm for proximal femoral locking plate, although dynamic hip screw with de-rotational screw indicated a value of 0.94 mm. Considering a consolidated fracture and full weight-bearing load case, average displacements of fracture fragments were obtained of about 1.5, 3 and 70 µm for dynamic hip screw with de-rotational screw, proximal femoral locking plate and cannulated screws methods, respectively. In terms of interfragmentary movements at the fracture site, outcomes of this study demonstrated that, in agreement with our previous experimental research, the dynamic hip screw with de-rotational screw implant is a more effective choice than cannulated screws and proximal femoral locking plate techniques for vertical femoral neck fractures in young patients. Thus, one may conclude that the use of dynamic hip screw with de-rotational screw, particularly during the early stages of bone healing, could provide suitable mechanical environments that facilitate direct bone formation and shorter healing times.

Localizing the osseous boundaries of micro-osteoperforations

INTRODUCTION

The aim of this work was to determine how far the effects of micro-osteoperforations (MOPs) extend within bone by quantifying the damage caused and the short-term bony adaptations that occur in and around the injury site.

METHODS

With the use of a split-mouth design, 34 MOPs (Propel) were randomly placed in the mandibular furcal bone of 13 beagle dogs either 2 or 4 weeks before killing them. The control side received no treatment. Vickers hardness microindentation, microscopic computed tomography, and histologic analyses were performed to evaluate the bone surrounding the MOPs.

RESULTS

Microfractures produced during insertion extended ∼0.6 mm from the MOP sites. Cortical and trabecular bone were significantly less dense on the experimental than on the control side up to 4.2 mm from the edge of the MOP, but side differences were small (<5%) beyond 1.5 mm from the MOP. Experimental cortical bone was significantly softer than the control bone up to 0.8 mm from the MOP after 2 weeks of healing, and up to 0.5 mm from the MOP after 4 weeks of healing. Hematoxylin and eosin stained sections of cortical and trabecular bone showed small areas of woven bone within the MOP sites after 2 weeks, and acellular areas of bone extending ∼0.5 mm from the MOP. After 4 weeks of healing, there were greater amounts of woven bone, as well as early signs of lamellar bone, in and around the MOP sites. Markedly increased TRAP activity extending up to 2.5 mm from the MOP was evident after 2 weeks, but not after 4 weeks. Vital fluorescence staining showed diffuse bone deposition on the experimental side up to 1.5 mm from the MOP margin.

CONCLUSIONS

When MOPs are performed in beagle dogs, demineralization is transient and healing of the injured area, as well as remineralization of bone affected by MOP placement, begins during the first 2 weeks. Although the transient effects extend farther, the principal effects extend only ∼1.5 mm from the MOP site.

Numerical simulations of bone remodelling and formation following nucleotomy

Nucleotomy is the gold standard treatment for disc herniation and has proven ability to restore stability by creating a bony bridge without any additional fixation. However, the evolution of mineral density in the extant and new bone after nucleotomy and fixation techniques has to date not been investigated in detail. The main goal of this study is to determine possible mechanisms that may trigger the bone remodelling and formation processes. With that purpose, a finite element model of the L4-L5 spinal segment was used. Bone mineral density (BMD), new tissue composition, and endplate deflection were determined as indicators of lumbar fusion. A bone-remodelling algorithm and a tissue-healing algorithm, both mechanically driven, were implemented to predict vertebral bone alterations and fusion patterns after nucleotomy, internal fixation, and anterior plate placement. When considering an intact disc height, neither nucleotomy nor internal fixation were able to provide the necessary stability to promote bony fusion. However, when 75% of the disc height was considered, bone fusion was predicted for both techniques. By contrast, an anterior plate allowed bone fusion at all disc heights. A 50% disc-height reduction led to osteophyte formation in all cases. Changes in the intervertebral disc tissue caused BMD alterations in the endplates. From this observations it can be drawn that fusion may be self-induced by controlling the mechanical stabilisation without the need of additional fixation. The amount of tissue to be removed to achieve this stabilisation remains to be determined.

Mechanobiologically optimized 3D titanium-mesh scaffolds enhance bone regeneration in critical segmental defects in sheep

Three-dimensional (3D) titanium-mesh scaffolds offer many advantages over autologous bone grafting for the regeneration of challenging large segmental bone defects. Our study supports the hypothesis that endogenous bone defect regeneration can be promoted by mechanobiologically optimized Ti-mesh scaffolds. Using finite element techniques, two mechanically distinct Ti-mesh scaffolds were designed in a honeycomb-like configuration to minimize stress shielding while ensuring resistance against mechanical failure. Scaffold stiffness was altered through small changes in the strut diameter only. Honeycombs were aligned to form three differently oriented channels (axial, perpendicular, and tilted) to guide the bone regeneration process. The soft scaffold (0.84 GPa stiffness) and a 3.5-fold stiffer scaffold (2.88 GPa) were tested in a critical size bone defect model in vivo in sheep. To verify that local scaffold stiffness could enhance healing, defects were stabilized with either a common locking compression plate that allowed dynamic loading of the 4-cm defect or a rigid custom-made plate that mechanically shielded the defect. Lower stress shielding led to earlier defect bridging, increased endochondral bone formation, and advanced bony regeneration of the critical size defect. This study demonstrates that mechanobiological optimization of 3D additive manufactured Ti-mesh scaffolds can enhance bone regeneration in a translational large animal study.

Effect of ultrasound on bone fracture healing: A computational mechanobioregulatory model

Bone healing process is a complicated phenomenon regulated by biochemical and mechanical signals. Experimental studies have shown that ultrasound (US) accelerates bone ossification and has a multiple influence on cell differentiation and angiogenesis. In a recent work of the authors, a bioregulatory model for providing bone-healing predictions was addressed, taking into account for the first time the salutary effect of US on the involved angiogenesis. In the present work, a mechanobioregulatory model of bone solidification under the US presence incorporating also the mechanical environment on the regeneration process, which is known to affect cellular processes, is presented. An iterative procedure is adopted, where the finite element method is employed to compute the mechanical stimuli at the linear elastic phases of the poroelastic callus region and a coupled system of partial differential equations to simulate the enhancement by the US cell angiogenesis process and thus the oxygen concentration in the fractured area. Numerical simulations with and without the presence of US that illustrate the influence of progenitor cells' origin in the healing pattern and the healing rate and simultaneously demonstrate the salutary effect of US on bone repair are presented and discussed.

Acceleration of Bone Defect Healing and Regeneration by Low-Intensity Ultrasound Radiation Force in a Rat Tibial Model

The objective was to evaluate the effect of low-intensity pulsed ultrasound (LIPUS)-induced acoustic radiation force on trabecular bone defect repair and healing in a rat tibial model. A uniform surgical defect, 3.5 mm in diameter, was generated in the proximal bilateral tibial region of rats (N = 20). LIPUS was applied to the defects in the left tibia for 20 min every day for 2 wk. Contralateral defects in the right tibia served as a control without active LIPUS treatment. The micro-computed tomography data revealed that LIPUS-treated tibia exhibited higher bone volume/total volume, connectivity density, trabecular number, and bone mineral density and significantly lower trabecular separation. Histomorphometry analysis indicated a similar trend. Mechanical testing data revealed that LIPUS treatment significantly increased bone stiffness relative to that of the control group. Short-term (2-wk) LIPUS therapy initiated trabecular bone repair and regeneration in large trabecular bone defects, whereas cortical bone remained in the initial non-mineralization stage.

Three-dimensional computational model simulating the fracture healing process with both biphasic poroelastic finite element analysis and fuzzy logic control

A dynamic model regulated by both biphasic poroelastic finite element analysis and fuzzy logic control was established. Fuzzy logic control was an easy and comprehensive way to simulate the tissue differentiation process, and it is convenient for researchers and medical experts to communicate with one another to change the fuzzy logic rules and improve the simulation of the tissue differentiation process. In this study, a three-dimensional fracture healing model with two different interfragmentary movements (case A: 0.25 mm and case B: 1.25 mm) was analysed with the new set-up computational model. As the healing process proceeded, both simulated interfragmentary movements predicted a decrease and the time that the decrease started for case B was later than that for case A. Compared with experimental results, both cases corresponded with experimental data well. The newly established dynamic model can simulate the healing process under different mechanical environments and has the potential to extend to the multiscale healing model, which is essential for reducing the animal experiments and helping to characterise the complex dynamic interaction between tissue differentiations within the callus region.

Differences in 3D vs. 2D analysis in lumbar spinal fusion simulations

Lumbar interbody fusion is currently the gold standard in treating patients with disc degeneration or segmental instability. Despite it having been used for several decades, the non-union rate remains high. A failed fusion is frequently attributed to an inadequate mechanical environment after instrumentation. Finite element (FE) models can provide insights into the mechanics of the fusion process. Previous fusion simulations using FE models showed that the geometries and material of the cage can greatly influence the fusion outcome. However, these studies used axisymmetric models which lacked realistic spinal geometries. Therefore, different modeling approaches were evaluated to understand the bone-formation process. Three FE models of the lumbar motion segment (L4-L5) were developed: 2D, Sym-3D and Nonsym-3D. The fusion process based on existing mechano-regulation algorithms using the FE simulations to evaluate the mechanical environment was then integrated into these models. In addition, the influence of different lordotic angles (5, 10 and 15°) was investigated. The volume of newly formed bone, the axial stiffness of the whole segment and bone distribution inside and surrounding the cage were evaluated. In contrast to the Nonsym-3D, the 2D and Sym-3D models predicted excessive bone formation prior to bridging (peak values with 36 and 9% higher than in equilibrium, respectively). The 3D models predicted a more uniform bone distribution compared to the 2D model. The current results demonstrate the crucial role of the realistic 3D geometry of the lumbar motion segment in predicting bone formation after lumbar spinal fusion.

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.

Simulating lateral distraction osteogenesis

Distraction osteogenesis is an effective method for generating large amounts of bone in situ for treating pathologies such as large bone defects or skeletal malformations, for instance leg-length discrepancies. While an optimized distraction procedure might have the potential to reduce the rate of complications significantly, our knowledge of the underlying mechanobiological processes is still insufficient for systematic optimization of treatment parameters such as distraction rate or fixation stiffness. We present a novel numerical model of lateral distraction osteogenesis, based on a mechanically well-controlled in vivo experiment. This model extends an existing numerical model of callus healing with viscoplastic material properties for describing stress relaxation and stimuli history-dependent tissue differentiation, incorporating delay and memory effects. A reformulation of appositional growth based non-local biological stimuli in terms of spatial convolution as well as remeshing and solution-mapping procedures allow the model to cope with severe mesh distortions associated with large plastic deformations. With these enhancements, our model is capable of replicating the in vivo observations for lateral distraction osteogenesis in sheep using the same differentiation rules and the same set of parameters that successfully describes callus healing in sheep, indicating that tissue differentiation hypotheses originally developed for fracture healing scenarios might indeed be applicable to distraction as well. The response of the model to modified distraction parameters corresponds to existing studies, although the currently available data is insufficient for rigorous validation. As such, this study provides a first step towards developing models that can serve as tools for identifying both interesting research questions and, eventually, even optimizing clinical procedures once better data for calibration and validation becomes available.

Phase-field boundary conditions for the voxel finite cell method: Surface-free stress analysis of CT-based bone structures

The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field-based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then used to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, ie, the interface width of the phase field, the voxel spacing, and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body.

Microscale poroelastic metamodel for efficient mesoscale bone remodelling simulations

Bone functional tissue adaptation is a multiaspect physiological process driven by interrelated mechanical and biological stimuli which requires the combined activity of osteoclasts and osteoblasts. In previous work, the authors developed a phenomenological mesoscale structural modelling approach capable of predicting internal structure of the femur based on daily activity loading, which relied on the iterative update of the cross-sectional areas of truss and shell elements representative of trabecular and cortical bones, respectively. The objective of this study was to introduce trabecular reorientation in the phenomenological model at limited computational cost. To this aim, a metamodel derived from poroelastic microscale continuum simulations was used to predict the functional adaptation of a simplified proximal structural femur model. Clear smooth trabecular tracts are predicted to form in the regions corresponding to the main trabecular groups identified in literature, at minimal computational cost.

Finite-element modelling of mechanobiological factors influencing sesamoid tissue morphology in the patellar tendon of an ostrich

The appearance and shape of sesamoid bones within a tendon or ligament wrapping around a joint are understood to be influenced by both genetic and epigenetic factors. Ostriches (Struthio camelus) possess two sesamoid patellae (kneecaps), one of which (the distal patella) is unique to their lineage, making them a good model for investigating sesamoid tissue development and evolution. Here we used finite-element modelling to test the hypothesis that specific mechanical cues in the ostrich patellar tendon favour the formation of multiple patellae. Using three-dimensional models that allow application of loading conditions in which all muscles, or only distal or only proximal muscles to be activated, we found that there were multiple regions within the tendon where transformation from soft tissue to fibrocartilage was favourable and therefore a potential for multiple patellae based solely upon mechanical stimuli. While more studies are needed to better understand universal mechanobiological principles as well as full developmental processes, our findings suggest that a tissue differentiation algorithm using shear strain and compressive strain as inputs may be a roughly effective predictor of the tissue differentiation required for sesamoid development.

Bone fracture healing in mechanobiological modeling: A review of principles and methods

Bone fracture is a very common body injury. The healing process is physiologically complex, involving both biological and mechanical aspects. Following a fracture, cell migration, cell/tissue differentiation, tissue synthesis, and cytokine and growth factor release occur, regulated by the mechanical environment. Over the past decade, bone healing simulation and modeling has been employed to understand its details and mechanisms, to investigate specific clinical questions, and to design healing strategies. The goal of this effort is to review the history and the most recent work in bone healing simulations with an emphasis on both biological and mechanical properties. Therefore, we provide a brief review of the biology of bone fracture repair, followed by an outline of the key growth factors and mechanical factors influencing it. We then compare different methodologies of bone healing simulation, including conceptual modeling (qualitative modeling of bone healing to understand the general mechanisms), biological modeling (considering only the biological factors and processes), and mechanobiological modeling (considering both biological aspects and mechanical environment). Finally we evaluate different components and clinical applications of bone healing simulation such as mechanical stimuli, phases of bone healing, and angiogenesis.

In silico bone mechanobiology: modeling a multifaceted biological system

Mechanobiology, the study of the influence of mechanical loads on biological processes through signaling to cells, is fundamental to the inherent ability of bone tissue to adapt its structure in response to mechanical stimulation. The immense contribution of computational modeling to the nascent field of bone mechanobiology is indisputable, having aided in the interpretation of experimental findings and identified new avenues of inquiry. Indeed, advances in computational modeling have spurred the development of this field, shedding new light on problems ranging from the mechanical response to loading by individual cells to tissue differentiation during events such as fracture healing. To date, in silico bone mechanobiology has generally taken a reductive approach in attempting to answer discrete biological research questions, with research in the field broadly separated into two streams: (1) mechanoregulation algorithms for predicting mechanobiological changes to bone tissue and (2) models investigating cell mechanobiology. Future models will likely take advantage of advances in computational power and techniques, allowing multiscale and multiphysics modeling to tie the many separate but related biological responses to loading together as part of a larger systems biology approach to shed further light on bone mechanobiology. Finally, although the ever‐increasing complexity of computational mechanobiology models will inevitably move the field toward patient‐specific models in the clinic, the determination of the context in which they can be used safely for clinical purpose will still require an extensive combination of computational and experimental techniques applied to in vitro and in vivo applications. WIREs Syst Biol Med 2016, 8:485–505. doi: 10.1002/wsbm.1356

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Estimation of Local Bone Loads for the Volume of Interest

Computational bone remodeling simulations have recently received significant attention with the aid of state-of-the-art high-resolution imaging modalities. They have been performed using localized finite element (FE) models rather than full FE models due to the excessive computational costs of full FE models. However, these localized bone remodeling simulations remain to be investigated in more depth. In particular, applying simplified loading conditions (e.g., uniform and unidirectional loads) to localized FE models have a severe limitation in a reliable subject-specific assessment. In order to effectively determine the physiological local bone loads for the volume of interest (VOI), this paper proposes a novel method of estimating the local loads when the global musculoskeletal loads are given. The proposed method is verified for the three VOI in a proximal femur in terms of force equilibrium, displacement field, and strain energy density (SED) distribution. The effect of the global load deviation on the local load estimation is also investigated by perturbing a hip joint contact force (HCF) in the femoral head. Deviation in force magnitude exhibits the greatest absolute changes in a SED distribution due to its own greatest deviation, whereas angular deviation perpendicular to a HCF provides the greatest relative change. With further in vivo force measurements and high-resolution clinical imaging modalities, the proposed method will contribute to the development of reliable patient-specific localized FE models, which can provide enhanced computational efficiency for iterative computing processes such as bone remodeling simulations.

Establishment of a preclinical ovine screening model for the investigation of bone tissue engineering strategies in cancellous and cortical bone defects

Background

New tissue engineering strategies for bone regeneration need to be investigated in a relevant preclinical large animal model before making the translation into human patients. Therefore, our interdisciplinary group established a simplified large animal screening model for intramembranous bone defect regeneration in cancellous and cortical bone.

Methods

Related to a well-established model of cancellous drill hole defect regeneration in sheep, both the proximal and distal epimetaphyseal regions of the femur and the humerus were used bilaterally for eight drill hole cancellous defects (Ø 6 mm, 15 mm depth). Several improvements of the surgical procedure and equipment for an easier harvest of samples were invented. For the inclusion of cortical defect regeneration, a total of eight unicortical diaphyseal drill holes (6 mm Ø) were placed in the proximal-lateral and distal-medial parts of the metacarpal (MC) and metatarsal (MT) diaphyseal bone bilaterally. Acting moments within a normal gait cycle in the musculoskeletal lower limb model were compared with the results of the biomechanical in vitro torsion test until failure to ensure a low accidental fracture risk of utilized bones (ANOVA, p < 0.05). The model was tested in vivo, using thirteen adult, female, black-face sheep (Ø 66 kg; ± 5 kg; age ≥ 2.5 years). In a two-step surgical procedure 16 drill holes were performed for the investigation of two different time points within one animal. Defects were left empty, augmented with autologous cancellous bone or soft bone graft substitutes.

Results

The in vitro tests confirmed this model a high comparability between drilled MC and MT bones and a high safety margin until fracture. The exclusion of one animal from the in vivo study, due to a spiral fracture of the left MC bone led to a tolerable failure rate of 8 %.

Conclusions

As a screening tool, promising biomaterials can be tested in this cancellous and cortical bone defect model prior to the application in a more complex treatment site.