Biomechanical assessment and clinical analysis of different intramedullary nailing systems for oblique fractures

The aim of this study is to evaluate the fracture union or non-union for a specific patient that presented oblique fractures in tibia and fibula, using a mechanistic-based bone healing model. Normally, this kind of fractures can be treated through an intramedullary nail using two possible configurations that depends on the mechanical stabilisation: static and dynamic. Both cases are simulated under different fracture geometries in order to understand the effect of the mechanical stabilisation on the fracture healing outcome. The results of both simulations are in good agreement with previous clinical experience. From the results, it is demonstrated that the dynamization of the fracture improves healing in comparison with a static or rigid fixation of the fracture. This work shows the versatility and potential of a mechanistic-based bone healing model to predict the final outcome (union, non-union, delayed union) of realistic 3D fractures where even more than one bone is involved.     

Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing

Most long-bone fractures heal through indirect or secondary fracture healing, a complex process in which endochondral ossification is an essential part and bone is regenerated by tissue differentiation. This process is sensitive to the mechanical environment, and several authors have proposed mechano-regulation algorithms to describe it using strain, pore pressure and/or interstitial fluid velocity as biofeedback variables. The aim of this study was to compare various mechano-regulation algorithms' abilities to describe normal fracture healing in one computational model. Additionally, we hypothesized that tissue differentiation during normal fracture healing could be equally well regulated by the individual mechanical stimuli, e.g. deviatoric strain, pore pressure or fluid velocity. A biphasic finite element model of an ovine tibia with a 3mm fracture gap and callus was used to simulate the course of tissue differentiation during normal fracture healing. The load applied was regulated in a biofeedback loop, where the load magnitude was determined by the interfragmentary movement in the fracture gap. All the previously published mechano-regulation algorithms studied, simulated the course of normal fracture healing correctly. They predicted (1) intramembranous bone formation along the periosteum and callus tip, (2) endochondral ossification within the external callus and cortical gap, and (3) creeping substitution of bone towards the gap from the initial lateral osseous bridge. Some differences between the effects of the algorithms were seen, but they were not significant. None of the volumetric components, i.e. pore pressure or fluid velocity, alone were able to correctly predict spatial or temporal tissue distribution during fracture healing. However, simulation as a function of only deviatoric strain accurately predicted the course of normal fracture healing. This suggests that the deviatoric component may be the most significant mechanical parameter to guide tissue differentiation during indirect fracture healing.     

Prediction of the Time Course of Callus Stiffness as a Function of Mechanical Parameters in Experimental Rat Fracture Healing Studies - A Numerical Study

Numerous experimental fracture healing studies are performed on rats, in which different experimental, mechanical parameters are applied, thereby prohibiting direct comparison between each other. Numerical fracture healing simulation models are able to predict courses of fracture healing and offer support for pre-planning animal experiments and for post-hoc comparison between outcomes of different in vivo studies. The aims of this study are to adapt a pre-existing fracture healing simulation algorithm for sheep and humans to the rat, to corroborate it using the data of numerous different rat experiments, and to provide healing predictions for future rat experiments. First, material properties of different tissue types involved were adjusted by comparing experimentally measured callus stiffness to respective simulated values obtained in three finite element (FE) models. This yielded values for Young’s moduli of cortical bone, woven bone, cartilage, and connective tissue of 15,750 MPa, 1,000 MPa, 5 MPa, and 1 MPa, respectively. Next, thresholds in the underlying mechanoregulatory tissue differentiation rules were calibrated by modifying model parameters so that predicted fracture callus stiffness matched experimental data from a study that used rigid and flexible fixators. This resulted in strain thresholds at higher magnitudes than in models for sheep and humans. The resulting numerical model was then used to simulate numerous fracture healing scenarios from literature, showing a considerable mismatch in only 6 of 21 cases. Based on this corroborated model, a fit curve function was derived which predicts the increase of callus stiffness dependent on bodyweight, fixation stiffness, and fracture gap size. By mathematically predicting the time course of the healing process prior to the animal studies, the data presented in this work provides support for planning new fracture healing experiments in rats. Furthermore, it allows one to transfer and compare new in vivo findings to previously performed studies with differing mechanical parameters.     

Substrate Stiffness and Oxygen as Regulators of Stem Cell Differentiation during Skeletal Tissue Regeneration: A Mechanobiological Model

Extrinsic mechanical signals have been implicated as key regulators of mesenchymal stem cell (MSC) differentiation. It has been possible to test different hypotheses for mechano-regulated MSC differentiation by attempting to simulate regenerative events such as bone fracture repair, where repeatable spatial and temporal patterns of tissue differentiation occur. More recently, in vitro studies have identified other environmental cues such as substrate stiffness and oxygen tension as key regulators of MSC differentiation; however it remains unclear if and how such cues determine stem cell fate in vivo. As part of this study, a computational model was developed to test the hypothesis that substrate stiffness and oxygen tension regulate stem cell differentiation during fracture healing. Rather than assuming mechanical signals act directly on stem cells to determine their differentiation pathway, it is postulated that they act indirectly to regulate angiogenesis and hence partially determine the local oxygen environment within a regenerating tissue. Chondrogenesis of MSCs was hypothesized to occur in low oxygen regions, while in well vascularised regions of the regenerating tissue a soft local substrate was hypothesised to facilitate adipogenesis while a stiff substrate facilitated osteogenesis. Predictions from the model were compared to both experimental data and to predictions of a well established computational mechanobiological model where tissue differentiation is assumed to be regulated directly by the local mechanical environment. The model predicted all the major events of fracture repair, including cartilaginous bridging, endosteal and periosteal bony bridging and bone remodelling. It therefore provides support for the hypothesis that substrate stiffness and oxygen play a key role in regulating MSC fate during regenerative events such as fracture healing.     

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

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.     

Creating Rigidly Stabilized Fractures for Assessing Intramembranous Ossification,Distraction Osteogenesis,or Healing of Critical Sized Defects

Assessing modes of skeletal repair is essential for developing therapies to be used clinically to treat fractures. Mechanical stability plays a large role in healing of bone injuries. In the worst-case scenario mechanical instability can lead to delayed or non-union in humans. However, motion can also stimulate the healing process. In fractures that have motion cartilage forms to stabilize the fracture bone ends, and this cartilage is gradually replaced by bone through recapitulation of the developmental process of endochondral ossification. In contrast, if a bone fracture is rigidly stabilized bone forms directly via intramembranous ossification. Clinically, both endochondral and intramembranous ossification occur simultaneously. To effectively replicate this process investigators insert a pin into the medullary canal of the fractured bone as described by Bonnarens⁴. This experimental method provides excellent lateral stability while allowing rotational instability to persist. However, our understanding of the mechanisms that regulate these two distinct processes can also be enhanced by experimentally isolating each of these processes. We have developed a stabilization protocol that provides rotational and lateral stabilization. In this model, intramembranous ossification is the only mode of healing that is observed, and healing parameters can be compared among different strains of genetically modified mice ^5-7, after application of bioactive molecules ^8,9, after altering physiological parameters of healing ¹⁰, after modifying the amount or time of stabilization ¹¹, after distraction osteogenesis ¹², after creation of a non-union ¹³, or after creation of a critical sized defect. Here, we illustrate how to apply the modified Ilizarov fixators for studying tibial fracture healing and distraction osteogenesis in mice.     

Size Does Matter: An Integrative In Vivo-In Silico Approach for the Treatment of Critical Size Bone Defects

Although bone has a unique restorative capacity, i.e., it has the potential to heal scarlessly, the conditions for spontaneous bone healing are not always present, leading to a delayed union or a non-union. In this work, we use an integrative in vivo - in silico approach to investigate the occurrence of non-unions, as well as to design possible treatment strategies thereof. The gap size of the domain geometry of a previously published mathematical model was enlarged in order to study the complex interplay of blood vessel formation, oxygen supply, growth factors and cell proliferation on the final healing outcome in large bone defects. The multiscale oxygen model was not only able to capture the essential aspects of in vivo non-unions, it also assisted in understanding the underlying mechanisms of action, i.e., the delayed vascularization of the central callus region resulted in harsh hypoxic conditions, cell death and finally disrupted bone healing. Inspired by the importance of a timely vascularization, as well as by the limited biological potential of the fracture hematoma, the influence of the host environment on the bone healing process in critical size defects was explored further. Moreover, dependent on the host environment, several treatment strategies were designed and tested for effectiveness. A qualitative correspondence between the predicted outcomes of certain treatment strategies and experimental observations was obtained, clearly illustrating the model''s potential. In conclusion, the results of this study demonstrate that due to the complex non-linear dynamics of blood vessel formation, oxygen supply, growth factor production and cell proliferation and the interactions thereof with the host environment, an integrative in silico-in vivo approach is a crucial tool to further unravel the occurrence and treatments of challenging critical sized bone defects.     

Computational simulation of bone fracture healing under inverse dynamisation

Adaptive finite element models have allowed researchers to test hypothetical relationships between the local mechanical environment and the healing of bone fractures. However, their predictive power has not yet been demonstrated by testing hypotheses ahead of experimental testing. In this study, an established mechano-biological scheme was used in an iterative finite element simulation of sheep tibial osteotomy healing under a hypothetical fixation regime, “inverse dynamisation”. Tissue distributions, interfragmentary movement and stiffness across the fracture site were compared between stiff and flexible fixation conditions and scenarios in which fixation stiffness was increased at a discrete time-point. The modelling work was conducted blind to the experimental study to be published subsequently. The simulations predicted the fastest and most direct healing under constant stiff fixation, and the slowest healing under flexible fixation. Although low fixation stiffness promoted more callus formation prior to bridging, this conferred little additional stiffness to the fracture in the first 5 weeks. Thus, while switching to stiffer fixation facilitated rapid subsequent bridging of the fracture, no advantage of inverse dynamisation could be demonstrated. In vivo data remains necessary to conclusively test this treatment protocol and this will, in turn, provide an evaluation of the model’s performance. The publication of both hypotheses and their computational simulation, prior to experimental testing, offers an appealing means to test the predictive power of mechano-biological models.     

Impedence osteography: clinical applications of a new method of imaging fractures

Fracture healing usually proceeds without difficulty. However, the diagnosis of delayed or non-union is not simple and can present difficulties in management. Normal fracture healing is briefly reviewed along with some methods of assessing the progress of union. The results of using the technique of impedence osteography in a preliminary study of fracture healing are presented. These indicate that the technique can clearly show a fracture and differentiate between normal bone, a united fracture and a non-union.     

Adjustable Stiffness,External Fixator for the Rat Femur Osteotomy and Segmental Bone Defect Models

The mechanical environment around the healing of broken bone is very important as it determines the way the fracture will heal. Over the past decade there has been great clinical interest in improving bone healing by altering the mechanical environment through the fixation stability around the lesion. One constraint of preclinical animal research in this area is the lack of experimental control over the local mechanical environment within a large segmental defect as well as osteotomies as they heal. In this paper we report on the design and use of an external fixator to study the healing of large segmental bone defects or osteotomies. This device not only allows for controlled axial stiffness on the bone lesion as it heals, but it also enables the change of stiffness during the healing process in vivo. The conducted experiments have shown that the fixators were able to maintain a 5 mm femoral defect gap in rats in vivo during unrestricted cage activity for at least 8 weeks. Likewise, we observed no distortion or infections, including pin infections during the entire healing period. These results demonstrate that our newly developed external fixator was able to achieve reproducible and standardized stabilization, and the alteration of the mechanical environment of in vivo rat large bone defects and various size osteotomies. This confirms that the external fixation device is well suited for preclinical research investigations using a rat model in the field of bone regeneration and repair.     

Spreadsheet method for calculating the induced currents in bone-fracture healing by a low-frequency magnetic field

A commercially available spreadsheet program is used on a microcomputer to calculate the induced current density and electric field patterns produced in a nonhomogeneous, anisotropic model of tissue by a localized, low-frequency magnetic field source. Specific application is made to coils used to promote the healing of bone fractures in limbs. The variation of the conductivity of the fracture gap during healing causes the induced current density pattern to change correspondingly, whereas the induced electric field remains relatively unchanged. Use of more simplified, isotropic models for the bone and for the soft tissue leads to results that differ significantly from those obtained from the full model. The magnetic field beyond the region of the coils contributes little to the induced currents in the fracture gap if the gap is located near the center of the coils. © 1994 Wiley-Liss, Inc.     

Evaluation of residual stresses due to bone callus growth: a computational study

Mechanical environment in callus is determinant for the evolution of bone healing. However, recent mechanobiological computational works have underestimated the effect that growth exerts on the mechanical environment of callus. In the present work, we computationally evaluate the significance of growth-induced stresses, commonly called residual stresses, in callus. We construct a mechanobiological model of a callus in the metatarsus of a sheep in two different stages: one week and four weeks after fracture. The magnitude of stresses generated during callus growth is compared with the magnitude of stresses when only external loads are applied to the callus. We predict that residual stresses are relevant in some areas, mainly located at the periosteal side far from the fracture gap. Therefore, the inclusion of these residual stresses could represent a significant impact on the callus growth and predict a different evolution of biological processes occurring during bone healing.     

Mechanistic,Mathematical Model to Predict the Dynamics of Tissue Genesis in Bone Defects via Mechanical Feedback and Mediation of Biochemical Factors

The link between mechanics and biology in the generation and the adaptation of bone has been well studied in context of skeletal development and fracture healing. Yet, the prediction of tissue genesis within - and the spatiotemporal healing of - postnatal defects, necessitates a quantitative evaluation of mechano-biological interactions using experimental and clinical parameters. To address this current gap in knowledge, this study aims to develop a mechanistic mathematical model of tissue genesis using bone morphogenetic protein (BMP) to represent of a class of factors that may coordinate bone healing. Specifically, we developed a mechanistic, mathematical model to predict the dynamics of tissue genesis by periosteal progenitor cells within a long bone defect surrounded by periosteum and stabilized via an intramedullary nail. The emergent material properties and mechanical environment associated with nascent tissue genesis influence the strain stimulus sensed by progenitor cells within the periosteum. Using a mechanical finite element model, periosteal surface strains are predicted as a function of emergent, nascent tissue properties. Strains are then input to a mechanistic mathematical model, where mechanical regulation of BMP-2 production mediates rates of cellular proliferation, differentiation and tissue production, to predict healing outcomes. A parametric approach enables the spatial and temporal prediction of endochondral tissue regeneration, assessed as areas of cartilage and mineralized bone, as functions of radial distance from the periosteum and time. Comparing model results to histological outcomes from two previous studies of periosteum-mediated bone regeneration in a common ovine model, it was shown that mechanistic models incorporating mechanical feedback successfully predict patterns (spatial) and trends (temporal) of bone tissue regeneration. The novel model framework presented here integrates a mechanistic feedback system based on the mechanosensitivity of periosteal progenitor cells, which allows for modeling and prediction of tissue regeneration on multiple length and time scales. Through combination of computational, physical and engineering science approaches, the model platform provides a means to test new hypotheses in silico and to elucidate conditions conducive to endogenous tissue genesis. Next generation models will serve to unravel intrinsic differences in bone genesis by endochondral and intramembranous mechanisms.     

Longitudinal Analysis of Osteogenic and Angiogenic Signaling Factors in Healing Models Mimicking Atrophic and Hypertrophic Non-Unions in Rats

Impaired bone healing can have devastating consequences for the patient. Clinically relevant animal models are necessary to understand the pathology of impaired bone healing. In this study, two impaired healing models, a hypertrophic and an atrophic non-union, were compared to physiological bone healing in rats. The aim was to provide detailed information about differences in gene expression, vascularization and histology during the healing process. The change from a closed fracture (healing control group) to an open osteotomy (hypertrophy group) led to prolonged healing with reduced mineralized bridging after 42 days. RT-PCR data revealed higher gene expression of most tested osteogenic and angiogenic factors in the hypertrophy group at day 14. After 42 days a significant reduction of gene expression was seen for Bmp4 and Bambi in this group. The inhibition of angiogenesis by Fumagillin (atrophy group) decreased the formation of new blood vessels and led to a non-healing situation with diminished chondrogenesis. RT-PCR results showed an attempt towards overcoming the early perturbance by significant up regulation of the angiogenic regulators Vegfa, Angiopoietin 2 and Fgf1 at day 7 and a further continuous increase of Fgf1, -2 and Angiopoietin 2 over time. However µCT angiograms showed incomplete recovery after 42 days. Furthermore, lower expression values were detected for the Bmps at day 14 and 21. The Bmp antagonists Dan and Twsg1 tended to be higher expressed in the atrophy group at day 42. In conclusion, the investigated animal models are suitable models to mimic human fracture healing complications and can be used for longitudinal studies. Analyzing osteogenic and angiogenic signaling patterns, clear changes in expression were identified between these three healing models, revealing the importance of a coordinated interplay of different factors to allow successful bone healing.     

Predicting the external formation of a bone fracture callus: an optimisation approach

The formation of a fracture callus in vivo tends to form in a structurally efficient manner distributing tissues where mechanical stimulus persists. Therefore, it is proposed that the formation of a fracture callus can be modelled in silico by way of an optimisation algorithm. This was tested by generating a finite element model of a transversal bone fracture embedded in a large tissue domain which was subjected to axial, bending and torsional loads. It was found that the relative fragment motion induced a compressive strain field in the early callus tissue which could be utilised to simulate the formation of external callus structures through an iterative optimisation process of tissue maintenance and removal. The phenomenological results showed a high level of congruence with in vivo healing patterns found in the literature. Consequently, the proposed strategy shows potential as a means of predicting spatial bone healing phenomena for pre-clinical testing.     

A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading

Bone has a capability to repair itself when it is fractured. Repair involves the generation of intermediate tissues, such as fibrous connective tissue, cartilage and woven bone, before final bone healing can occur. The intermediate tissues serve to stabilise the mechanical environment and provide a scaffold for differentiation of new tissues. The repair process is fundamentally affected by mechanical loading and by the geometric configuration of the fracture fragments. Biomechanical analyses of fracture healing have previously computed the stress distribution within the callus and identified the components of the stress tensor favouring or inhibiting differentiation of particular tissue phenotypes. In this paper, a biphasic poroelastic finite element model of a fracture callus is used to simulate the time-course of tissue differentiation during fracture healing. The simulation begins with granulation tissue (post-inflammation phase) and finishes with bone resorption. The biomechanical regulatory model assumes that tissue differentiation is controlled by a combination of shear strain and fluid flow acting within the tissue. High shear strain and fluid flows are assumed to deform the precursor cells stimulating formation of fibrous connective tissue, lower levels stimulate formation of cartilage, and lower again allows ossification. This mechano-regulatory scheme was tested by simulating healing in fractures with different gap sizes and loading magnitudes. The appearance and disappearance of the various tissues found in a callus was similar to histological observation. The effect of gap size and loading magnitude on the rate of reduction of the interfragmentary strain was sufficiently close to confirm the hypothesis that tissue differentiation phenomena could be governed by the proposed mechano-regulation model.     

Stem cell-derived exosomes in bone healing: focusing on their role in angiogenesis

Fractures in bone, a tissue critical in protecting other organs, affect patients’ quality of life and have a heavy economic burden on societies. Based on regenerative medicine and bone tissue engineering approaches, stem cells have become a promising and attractive strategy for repairing bone fractures via differentiation into bone-forming cells and production of favorable mediators. Recent evidence suggests that stem cell-derived exosomes could mediate the therapeutic effects of their counterpart cells and provide a cell-free therapeutic strategy in bone repair. Since bone is a highly vascularized tissue, coupling angiogenesis and osteogenesis is critical in bone fracture healing; thus, developing therapeutic strategies to promote angiogenesis will facilitate bone regeneration and healing. To this end, stem cell-derived exosomes with angiogenic potency have been developed to improve fracture healing. This review summarizes the effects of stem cell-derived exosomes on the repair of bone tissue, focusing on the angiogenesis process.     

Traumatic brain injury and bone healing: radiographic and biomechanical analyses of bone formation and stability in a combined murine trauma model

Introduction:The combination of traumatic brain injury (TBI) and long-bone fractures has previously been reported to lead to exuberant callus formation. The aim of this experimental study was to radiographically and biomechanically study the effect of TBI on bone healing in a mouse model.Materials and methods:138 female C57/Black6N mice were assigned to four groups (fracture (Fx) / TBI / combined trauma (Fx/TBI) / controls). Femoral osteotomy and TBI served as variables: osteotomies were stabilized with external fixators, TBI was induced with controlled cortical impact injury. During an observation period of four weeks, in vivo micro-CT scans of femora were performed on a weekly basis. Biomechanical testing of femora was performed ex vivo.Results:The combined-trauma group showed increased bone volume, higher mineral density, and a higher rate of gap bridging compared to the fracture group. The combined-trauma group showed increased torsional strength at four weeks.Discussion:TBI results in an increased formation of callus and mineral density compared to normal bone healing in mice. This fact combined with a tendency towards accelerated gap bridging leads to increased torsional strength. The present study underscores the empirical clinical evidence that TBI stimulates bone healing. Identification of underlying pathways could lead to new strategies for bone-stimulating approaches in fracture care.     

The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules

During secondary bone healing, different tissue types are formed within the fracture callus depending on the local mechanical and biological environment. Our aim was to understand the temporal succession of these tissue patterns for a normal bone healing progression by means of a basic mechanobiological model. The experimental data stemmed from an extensive, previously published animal experiment on sheep with a 3?mm tibial osteotomy. Using recent experimental data, the development of the hard callus was modelled as a porous material with increasing stiffness and decreasing porosity. A basic phenomenological model was employed with a small number of simulation parameters, which allowed comprehensive parameter studies. The model distinguished between the formation of new bone via endochondral and intramembranous ossification. To evaluate the outcome of the computer simulations, the tissue images of the simulations were compared with experimentally derived tissue images for a normal healing progression in sheep. Parameter studies of the threshold values for the regulation of tissue formation were performed, and the source of the biological stimulation (comprising e.g. stem cells) was varied. It was found that the formation of the hard callus could be reproduced in silico for a wide range of threshold values. However, the bridging of the fracture gap by cartilage on the periosteal side was observed only (i) for a rather specific choice of the threshold values for tissue differentiation and (ii) when assuming a strong source of biological stimulation at the periosteum.     

The role of interfragmentary strain on the rate of bone healing—A new interpretation and mathematical model

It is postulated that there is a causal relationship between mechanical stimulus and the rate of bone healing post fracture. However, despite numerous experimental studies in the literature, no quantifiable relationship has been proposed. It is hypothesized in the present study that the temporal rate of bone fracture healing, measured in terms of callus stiffening per week, can be described mathematically based on the relative motions between bone fragments at the initial stage of the healing process. To test this, a comparative reanalysis of experimental data found in the literature was conducted. These individual data sets described a relationship between an initial intermittently applied peak interfragmentary strain and the change in interfragmentary motion or the increase in callus stiffness over time. The data were converted into a relative increase in stiffness, which normalised the results and reduced inter-study variability. The rates of healing for the various initial strains were compared, and based on this a mathematical phenomenological model was derived. Error analyses were then performed, which showed a high level of congruence between the in-vivo and simulated rates of healing. The results of the comparative analysis revealed that there is a positive correlation between the rate of callus stiffening and interfragmentary strain. Finally, the proposed model has shown for the first time that a quantifiable cause–and–effect relationship exists between the rate of bone healing and mechanical stimulus.