A computational model to explore the role of angiogenic impairment on endochondral ossification during fracture healing

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.

An in silico micro-multiphysics agent-based approach for simulating bone regeneration in a mouse femur defect model

Bone defects represent a challenging clinical problem as they can lead to non-union. In silico models are well suited to study bone regeneration under varying conditions by linking both cellular and systems scales. This paper presents an in silico micro-multiphysics agent-based (micro-MPA) model for bone regeneration following an osteotomy. The model includes vasculature, bone, and immune cells, as well as their interaction with the local environment. The model was calibrated by time-lapsed micro-computed tomography data of femoral osteotomies in C57Bl/6J mice, and the differences between predicted bone volume fractions and the longitudinal in vivo measurements were quantitatively evaluated using root mean square error (RMSE). The model performed well in simulating bone regeneration across the osteotomy gap, with no difference (5.5% RMSE, p = 0.68) between the in silico and in vivo groups for the 5-week healing period - from the inflammatory phase to the remodelling phase - in the volume spanning the osteotomy gap. Overall, the proposed micro-MPA model was able to simulate the influence of the local mechanical environment on bone regeneration, and both this environment and cytokine concentrations were found to be key factors in promoting bone regeneration. Further, the validated model matched clinical observations that larger gap sizes correlate with worse healing outcomes and ultimately simulated non-union. This model could help design and guide future experimental studies in bone repair, by identifying which are the most critical in vivo experiments to perform.

External mechanical loading overrules cell-cell mechanical communication in sprouting angiogenesis during early bone regeneration

Sprouting angiogenesis plays a key role during bone regeneration. For example, insufficient early revascularization of the injured site can lead to delayed or non-healing. During sprouting, endothelial cells are known to be mechano-sensitive and respond to local mechanical stimuli. Endothelial cells interact and communicate mechanically with their surroundings, such as outer-vascular stromal cells, through cell-induced traction forces. In addition, external physiological loads act at the healing site, resulting in tissue deformations and impacting cellular arrangements. How these two distinct mechanical cues (cell-induced and external) impact angiogenesis and sprout patterning in early bone healing remains however largely unknown. Therefore, the aim of this study was to investigate the relative role of externally applied and cell-induced mechanical signals in driving sprout patterning at the onset of bone healing. To investigate cellular self-organisation in early bone healing, an in silico model accounting for the mechano-regulation of sprouting angiogenesis and stromal cell organization was developed. Computer model predictions were compared to in vivo experiments of a mouse osteotomy model stabilized with a rigid or a semirigid fixation system. We found that the magnitude and orientation of principal strains within the healing region can explain experimentally observed sprout patterning, under both fixation conditions. Furthermore, upon simulating the selective inhibition of either cell-induced or externally applied mechanical cues, external mechanical signals appear to overrule the mechanical communication acting on a cell-cell interaction level. Such findings illustrate the relevance of external mechanical signals over the local cell-mediated mechanical cues and could be used in the design of fracture treatment strategies for bone regeneration.

Development of numerical model-based machine learning algorithms for different healing stages of distal radius fracture healing

BACKGROUND AND OBJECTIVES

Early therapeutic exercises are vital for the healing of distal radius fractures (DRFs) treated with the volar locking plate. However, current development of rehabilitation plans using computational simulation is normally time-consuming and requires high computational power. Thus, there is a clear need for developing machine learning (ML) based algorithms that are easy for end-users to implement in daily clinical practice. The purpose of the present study is to develop optimal ML algorithms for designing effective DRF physiotherapy programs at different stages of healing.

METHOD

First, a three-dimensional computational model for the healing of DRF was developed by integrating mechano-regulated cell differentiation, tissue formation and angiogenesis. The model is capable of predicting time-dependant healing outcomes based on different physiologically relevant loading conditions, fracture geometries, gap sizes, and healing time. After being validated using available clinical data, the developed computational model was implemented to generate a total of 3600 clinical data for training the ML models. Finally, the optimal ML algorithm for each healing stage was identified.

RESULTS

The selection of the optimal ML algorithm depends on the healing stage. The results from this study show that cubic support vector machine (SVM) has the best performance in predicting the healing outcomes at the early stage of healing, while trilayered ANN outperforms other ML algorithms in the late stage of healing. The outcomes from the developed optimal ML algorithms indicate that Smith fractures with medium gap sizes could enhance the healing of DRF by inducing larger cartilaginous callus, while Colles fractures with large gap sizes may lead to delayed healing by bringing excessive fibrous tissues.

CONCLUSIONS

ML represents a promising approach for developing efficient and effective patient-specific rehabilitation strategies. However, ML algorithms at different healing stages need to be carefully chosen before being implemented in clinical applications.

The effects of mechanical instability on PDGF mediated inflammatory response at early stage of fracture healing under diabetic condition

BACKGROUND AND OBJECTIVE

Mechanical stability plays an important role in fracture healing process. Excessive interfragmentary movement will continuously damage the tissue and newly formed capillaries at the fracture site, which leads to overproduction of platelet-derived growth factor (PDGF) that attracts more macrophages into fracture callus, ultimately persistent and enhanced inflammatory response happens. For diabetic condition, the impact of mechanical instability of fracture site on inflammatory response could be further compliciated and the relevant research in this field is relatively limited.

METHODS

Building on previous experimental studies, this study presents a numerical model consisting of a system of reactive-transport equations representing the transport as well as interactions of different cells and cytokines within the fracture callus. The model is initially validated by available experimental data, and then implemented to investigate the role of mechanical stability of fracture site in inflammatory response during early stage of healing. It is assumed that there is an increased release of PDGF due to the rupture of blood vessels resulting from mechanical instability, which leads to increased production of inflammatory cytokines (i.e., TNF-α). The bone healing process under three different conditions were investigated, i.e., mechanically stable condition with normal inflammatory response (Control, Case 1), mechanically unstable condition with normal inflammatory response (Case 2) and mechanically unstable condition with diabetes (Case 3).

RESULTS

Mechanical instability can promote the macrophage infiltration and thus induce an enhanced and prolonged inflammatory response, which could impede the MSCs proliferation during the early fracture healing stage (e.g., compared with the control condition, the MSCs concentration in unstable fracture with normal inflammatory response can be reduced by 3.2% and 5.2% on day 2 and day 10 post-fracture, respectively). Under diabetic condition, the mechanical instability of fracture site could lead to a significant increase of TNF-α concentration in fracture callus (Case 3) in comparison to control (Case 1) (e.g., three-fold increase in TNF-α concentration compared to control). In addition, the results show that the mechanical instability affects the cell differentiation and proliferation in fracture callus in a spatially dependent manner, e.g., for diabetic fracture patients, the mechanical instability could potentially decrease the concentration of MSCs, osteoblasts and chondrocytes by around 39%, 30% and 29% in cortical callus, respectively, in comparison to control.

CONCLUSION

The mechanical instability together with diabetic condition can significantly affect the natural resolution of inflammation during early stage of healing by turning acute inflammation into chronic inflammation which is characterized by a continuously upregulated TNF-α pathway.

Effect of Intramedullary Nailing Patterns on Interfragmentary Strain in a Mouse Femur Fracture: A Parametric Finite Element Analysis

Delayed long bone fracture healing and nonunion continue to be a significant socioeconomic burden. While mechanical stimulation is known to be an important determinant of the bone repair process, understanding how the magnitude, mode, and commencement of interfragmentary strain (IFS) affect fracture healing can guide new therapeutic strategies to prevent delayed healing or nonunion. Mouse models provide a means to investigate the molecular and cellular aspects of fracture repair, yet there is only one commercially available, clinically-relevant, locking intramedullary nail (IMN) currently available for studying long bone fractures in rodents. Having access to alternative IMNs would allow a variety of mechanical environments at the fracture site to be evaluated, and the purpose of this proof-of-concept finite element analysis study is to identify which IMN design parameters have the largest impact on IFS in a murine transverse femoral osteotomy model. Using the dimensions of the clinically relevant IMN as a guide, the nail material, distance between interlocking screws, and clearance between the nail and endosteal surface were varied between simulations. Of these parameters, changing the nail material from stainless steel (SS) to polyetheretherketone (PEEK) had the largest impact on IFS. Reducing the distance between the proximal and distal interlocking screws substantially affected IFS only when nail modulus was low. Therefore, IMNs with low modulus (e.g., PEEK) can be used alongside commercially available SS nails to investigate the effect of initial IFS or stability on fracture healing with respect to different biological conditions of repair in rodents.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

Towards in silico Models of the Inflammatory Response in Bone Fracture Healing

In silico modeling is a powerful strategy to investigate the biological events occurring at tissue, cellular and subcellular level during bone fracture healing. However, most current models do not consider the impact of the inflammatory response on the later stages of bone repair. Indeed, as initiator of the healing process, this early phase can alter the regenerative outcome: if the inflammatory response is too strongly down- or upregulated, the fracture can result in a non-union. This review covers the fundamental information on fracture healing, in silico modeling and experimental validation. It starts with a description of the biology of fracture healing, paying particular attention to the inflammatory phase and its cellular and subcellular components. We then discuss the current state-of-the-art regarding in silico models of the immune response in different tissues as well as the bone regeneration process at the later stages of fracture healing. Combining the aforementioned biological and computational state-of-the-art, continuous, discrete and hybrid modeling technologies are discussed in light of their suitability to capture adequately the multiscale course of the inflammatory phase and its overall role in the healing outcome. Both in the establishment of models as in their validation step, experimental data is required. Hence, this review provides an overview of the different in vitro and in vivo set-ups that can be used to quantify cell- and tissue-scale properties and provide necessary input for model credibility assessment. In conclusion, this review aims to provide hands-on guidance for scientists interested in building in silico models as an additional tool to investigate the critical role of the inflammatory phase in bone regeneration.

Optimal time-dependent levels of weight-bearing for bone fracture healing under Ilizarov circular fixators

It is known that weight-bearing exercises under Ilizarov circular fixators (ICF) could enhance bone fracture healing by mechano-regulation. However, interfragmentary movements at the fracture site induced by weight-bearing may inhibit angiogenesis and ultimately delay the healing process. To tackle this challenge, a computational model is presented in this study which considers the spatial and temporal changes in mechanical properties of fracture callus to predict optimal levels of weight-bearing during fracture healing under ICF. The study takes sheep fractures as example and shows that the developed model has the capability of predicting patient specific, time-dependent optimal levels of weight-bearing which enhances mechano-regulation mediated healing without hindering the angiogenesis process. The results demonstrate that allowable level of weight-bearing and timings depend on fracture gap size. For normal body weights (BW) and moderate fracture gap sizes (e.g. 3 mm), weight-bearing with 30% BW could start by week 4 post-operation and gradually increase to 100% BW by week 11. In contrast, for relatively large fracture gap sizes (i.e. 6 mm), weight-bearing is recommended to commence in later stages of healing (e.g. week 11 post-operation). Furthermore, increasing ICF stiffness (e.g. using half pins instead of pretension wires) can increase the level of weight-bearing significantly in the early stages up to a certain time point (e.g. week 8 post-operation) beyond which no noticeable benefits could be achieved. The findings of this study have potential applications in designing post-operative weight bearing exercises.

The Effect of External Fixator Configurations on the Dynamic Compression Load: An Experimental and Numerical Study

(1) Objective: External fixation systems are commonly used by surgeons to ensure stabilization and consolidation of bone fractures, especially in patients who are at high risk for systematic complications. Both rigid and elastic external fixations are important in the fracture healing process. This study aims to evaluate the behavior of the Orthofix Limb Reconstruction System (LRS)® in the dynamic compression mode. (2) Methods: Experimental and numerical setups were developed using a simplified model of a human tibia which consisted of a nylon bar with a diameter of 30 mm. The bone callus was included in both setups by means of a load cell-based system, which consisted of two carbon epoxy laminated composite plates with a final stiffness of 220 N/mm. The system was evaluated experimentally and numerically, considering different numbers of pins and comparing distances between the external fixator frame and the bone, achieving a good correlation between experimental and numerical results. (3) Results: The results identified and quantified the percental load transferred to the fracture and its sensibility to the distance between the external fixator and bone. Additionally, LRS locking stiffness was evaluated which resulted from the clamp-rail clearances. The results show that the blocking effects of the free clamp movement are directly related to the fixator configuration and are responsible for changes in the amount of load that crosses the bone callus. (4) Conclusions: From the biomechanical point of view, the results suggest that the average bending span of Schanz pins and the weights of the patients should be included into clinical studies of external fixators comparisons purpose.

The potential of exosomes in the therapy of the cartilage and bone complications; emphasis on osteoarthritis

Osteoarthritis is a prevalent worldwide joint disease, which demonstrates a remarkable adverse effect on the patients' life modality. Medicinal agents, exclusively nonsteroidal anti-inflammatory drugs (NSAIDs), have been routinely applied in the clinic. But, their effects are restricted to pain control with insignificant effects on cartilage renovation, which would finally lead to cartilage destruction. In the field of regenerative medicine, many researchers have tried to use stem cells to repair tissues and other human organs. However, in recent years, with the discovery of extracellular microvesicles, especially exosomes, researchers have been able to offer more exciting alternatives on the subject. Exosomes and microvesicles are derived from different types of bone cells such as mesenchymal stem cells, osteoblasts, and osteoclasts. They are also recognized to play substantial roles in bone remodeling processes including osteogenesis, osteoclastogenesis, and angiogenesis. Specifically, exosomes derived from a mesenchymal stem cell have shown a great potential for the desired purpose. Exosomal products include miRNA, DNA, proteins, and other factors. At present, if it is possible to extract exosomes from various stem cells effectively and load certain products or drugs into them, they can be used in diseases, such as rheumatoid arthritis, osteoarthritis, bone fractures, and other diseases. Of course, to achieve proper clinical use, advances have to be made to establish a promising regenerative ability for microvesicles for treatment purposes in the orthopedic disorders. In this review, we describe the exosomes biogenesis and bone cell derived exosomes in the regenerate process of bone and cartilage remodeling.

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.

Regeneration of Osteochondral Defects Using Developmentally Inspired Cartilaginous Templates

IMPACT STATEMENT

Successfully treating osteochondral defects involves regenerating both the damaged articular cartilage and the underlying subchondral bone, in addition to the complex interface that separates these tissues. In this study, we demonstrate that a cartilage template, engineered using bone marrow-derived mesenchymal stem cells, can enhance the regeneration of such defects and promote the development of a more mechanically functional repair tissue. We also use a computational mechanobiological model to understand how joint-specific environmental factors, specifically oxygen levels and tissue strains, regulate the conversion of the engineered template into cartilage and bone in vivo.

Harnessing extracellular vesicles to direct endochondral repair of large bone defects

Large bone defects remain a tremendous clinical challenge. There is growing evidence in support of treatment strategies that direct defect repair through an endochondral route, involving a cartilage intermediate. While culture-expanded stem/progenitor cells are being evaluated for this purpose, these cells would compete with endogenous repair cells for limited oxygen and nutrients within ischaemic defects. Alternatively, it may be possible to employ extracellular vesicles (EVs) secreted by culture-expanded cells for overcoming key bottlenecks to endochondral repair, such as defect vascularization, chondrogenesis, and osseous remodelling. While mesenchymal stromal/stem cells are a promising source of therapeutic EVs, other donor cells should also be considered. The efficacy of an EV-based therapeutic will likely depend on the design of companion scaffolds for controlled delivery to specific target cells. Ultimately, the knowledge gained from studies of EVs could one day inform the long-term development of synthetic, engineered nanovesicles. In the meantime, EVs harnessed from in vitro cell culture have near-term promise for use in bone regenerative medicine. This narrative review presents a rationale for using EVs to improve the repair of large bone defects, highlights promising cell sources and likely therapeutic targets for directing repair through an endochondral pathway, and discusses current barriers to clinical translation. Cite this article: E. Ferreira, R. M. Porter. Harnessing extracellular vesicles to direct endochondral repair of large bone defects. Bone Joint Res 2018;7:263-273. DOI: 10.1302/2046-3758.74.BJR-2018-0006.

Simulation enabled search for explanatory mechanisms of the fracture healing process

A significant portion of bone fractures fail to heal properly, increasing healthcare costs. Advances in fracture management have slowed because translation barriers have limited generation of mechanism-based explanations for the healing process. When uncertainties are numerous, analogical modeling can be an effective strategy for developing plausible explanations of complex phenomena. We demonstrate the feasibility of engineering analogical models in software to facilitate discovery of biomimetic explanations for how fracture healing may progress. Concrete analogical models—Callus Analogs—were created using the MASON simulation toolkit. We designated a Target Region initial state within a characteristic tissue section of mouse tibia fracture at day-7 and posited a corresponding day-10 Target Region final state. The goal was to discover a coarse-grain analog mechanism that would enable the discretized initial state to transform itself into the corresponding Target Region final state, thereby providing an alternative way to study the healing process. One of nine quasi-autonomous Tissue Unit types is assigned to each grid space, which maps to an 80×80 μm region of the tissue section. All Tissue Units have an opportunity each time step to act based on individualized logic, probabilities, and information about adjacent neighbors. Action causes transition from one Tissue Unit type to another, and simulation through several thousand time steps generates a coarse-grain analog—a theory—of the healing process. We prespecified a minimum measure of success: simulated and actual Target Region states achieve ≥ 70% Similarity. We used an iterative refinement protocol to explore many combinations of Tissue Unit logic and action constraints. Workflows progressed through four stages of analog mechanisms. Similarities of 73–90% were achieved for Mechanisms 2–4. The range of Upper-Level similarities increased to 83–94% when we allowed for uncertainty about two Tissue Unit designations. We have demonstrated how Callus Analog experiments provide domain experts with a fresh medium and tools for thinking about and understanding the fracture healing process.

Translation barriers have limited the generation of mechanism-based explanations of fracture healing processes. Those barriers help explain why, to date, biological therapeutics have had only a minor impact on fracture management. Alternative approaches are needed, and we present one that is intended to help develop incrementally better mechanism-based explanations of fracture healing phenomena. We created virtual Callus Analogs to simulate how the histologic appearance of a mouse fracture callus may transition from day-7 to day-10. Callus Analogs use software-based model mechanisms, and simulation experiments enable challenging and improving those model mechanisms. During execution, model mechanism operation provides a coarse-grain explanation (a theory) of a four-day portion of the healing process. Simulated day-10 callus histologic images achieved 73–94% Similarity to a corresponding day-10 fracture callus image, thus demonstrating feasibility. Simulated healing provides an alternative perspective on the actual healing process and an alternative way of thinking about plausible fracture healing mechanisms. Our working hypothesis is that the approach can be extended to cover more of the healing process while making features of simulated and actual fracture healing increasingly analogous. The methods presented are intended to be extensible to other research areas that use histologic analysis to investigate and explain tissue level phenomena.

Influence of functionally graded pores on bone ingrowth in cementless hip prosthesis: a finite element study using mechano-regulatory algorithm

Cementless hip prostheses with porous outer coating are commonly used to repair the proximally damaged femurs. It has been demonstrated that stability of prosthesis is also highly dependent on the bone ingrowth into the porous texture. Bone ingrowth is influenced by the mechanical environment produced in the callus. In this study, bone ingrowth into the porous structure was predicted by using a mechano-regulatory model. Homogenously distributed pores (200 and 800 [Formula: see text]m in diameter) and functionally graded pores along the length of the prosthesis were introduced as a porous coating. Bone ingrowth was simulated using 25 and 12 [Formula: see text]m micromovements. Load control simulations were carried out instead of traditionally used displacement control. Spatial and temporal distributions of tissues were predicted in all cases. Functionally graded pore decreasing models gave the most homogenous bone distribution, the highest bone ingrowth (98%) with highest average Young's modulus of all tissue phenotypes approximately 4.1 GPa. Besides this, the volume of the initial callus increased to 8.33% in functionally graded pores as compared to the 200 [Formula: see text]m pore size models which increased the bone volume. These findings indicate that functionally graded porous surface promote bone ingrowth efficiently which can be considered to design of surface texture of hip prosthesis.

Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach

Bone is a living part of the body that can, in most situations, heal itself after fracture. However, in some situations, healing may fail. Compromised conditions, such as large bone defects, aging, immuno-deficiency, or genetic disorders, might lead to delayed or non-unions. Treatment strategies for those conditions remain a clinical challenge, emphasizing the need to better understand the mechanisms behind endogenous bone regeneration. Bone healing is a complex process that involves the coordination of multiple events at different length and time scales. Computer models have been able to provide great insights into the interactions occurring within and across the different scales (organ, tissue, cellular, intracellular) using different modeling approaches [partial differential equations (PDEs), agent-based models, and finite element techniques]. In this review, we summarize the latest advances in computer models of bone healing with a focus on multiscale approaches and how they have contributed to understand the emergence of tissue formation patterns as a result of processes taking place at the lower length scales.

Stimulating Fracture Healing in Ischemic Environments: Does Oxygen Direct Stem Cell Fate during Fracture Healing?

Bone fractures represent an enormous societal and economic burden as one of the most prevalent causes of disability worldwide. Each year, nearly 15 million people are affected by fractures in the United States alone. Data indicate that the blood supply is critical for fracture healing; as data indicate that concomitant bone and vascular injury are major risk factors for non-union. However, the various role(s) that the vasculature plays remains speculative. Fracture stabilization dictates stem cell fate choices during repair. In stabilized fractures stem cells differentiate directly into osteoblasts and heal the injury by intramembranous ossification. In contrast, in non-stable fractures stem cells differentiate into chondrocytes and the bone heals through endochondral ossification, where a cartilage template transforms into bone as the chondrocytes transform into osteoblasts. One suggested role of the vasculature has been to participate in the stem cell fate decisions due to delivery of oxygen. In stable fractures, the blood vessels are thought to remain intact and promote osteogenesis, while in non-stable fractures, continual disruption of the vasculature creates hypoxia that favors formation of cartilage, which is avascular. However, recent data suggests that non-stable fractures are more vascularized than stable fractures, that oxygen does not appear associated with differentiation of stem cells into chondrocytes and osteoblasts, that cartilage is not hypoxic, and that oxygen, not sustained hypoxia, is required for angiogenesis. These unexpected results, which contrast other published studies, are indicative of the need to better understand the complex, spatio-temporal regulation of vascularization and oxygenation in fracture healing. This work has also revealed that oxygen, along with the promotion of angiogenesis, may be novel adjuvants that can stimulate healing in select patient populations.