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.     

Bone remodeling during fracture repair: The cellular picture

Fracture healing is a complex event that involves the coordination of a variety of different processes. Repair is typically characterized by four overlapping stages: the initial inflammatory response, soft callus formation, hard callus formation, initial bony union and bone remodeling. However, repair can also be seen to represent a juxtaposition of two distinct forces: anabolism or tissue formation, and catabolism or remodeling. These anabolic/catabolic concepts are useful for understanding bone repair without giving the false impression of temporally distinct stages that operate independently. They are also relevant when considering intervention. In normal bone development, bone remodeling conventionally refers to the removal of calcified bone tissue by osteoclasts. However, in the context of bone repair there are two phases of tissue catabolism: the removal of the initial cartilaginous soft callus, followed by the eventual remodeling of the bony hard callus. In this review, we have attempted to examine catabolism/remodeling in fractures in a systematic fashion. The first section briefly summarizes the traditional four-stage view of fracture repair in a physiological manner. The second section highlights some of the limitations of using a temporal rather than process-driven model and summarizes the anabolic/catabolic paradigm of fracture repair. The third section examines the cellular participants in soft callus remodeling and in particular the role of the osteoclast in endochondral ossification. Finally, the fourth section examines the effects of delaying osteoclast-dependent hard callus remodeling and also poses questions regarding the crosstalk between anabolism and catabolism in the latter stages of fracture repair.     

Mineral and matrix contributions to rigidity in fracture healing

The purpose of this study was to investigate the relationships among selected properties of fracture callus: bending rigidity, tissue density, mineral density, matrix density and mineral-to-matrix ratio. The experimental model was an osteotomized canine radius in which the development of the fracture callus was modified by electrical stimulation with various levels of direct current. This resulted in a range of values for the selected properties of the callus, determined post mortem at 7 weeks after osteotomy. We found that the rigidity (R) of the bone-callus combination obeyed relationships of the form R = axb, where x is the tissue density, mineral density, matrix density or the mineral-to-matrix ratio of the repair tissue. These are analogous to power-law relationships found in studies of compact and cancellous bone. The results suggest that fracture callus at 7 weeks after osteotomy in canine radius behaves more like immature compact bone than cancellous bone in its mechanical and physicochemical properties. The present study demonstrates the feasibility of developing non-invasive in vivo densitometric methods to monitor fracture healing, since models may be developed that can predict mechanical properties from densitometric data. Further studies are needed to develop a refined model based on experimental data on the mechanical and physicochemical properties and microstructure of fracture callus at different stages of 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.     

Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing

A new quantitative tissue differentiation theory which relates the local tissue formation in a fracture gap to the local stress and strain is presented. Our hypothesis proposes that the amounts of strain and hydrostatic pressure along existing calcified surfaces in the fracture callus determine the differentiation of the callus tissue. The study compares the local strains and stresses in the callus as calculated from a finite element model with histological findings from an animal fracture model. The hypothesis predicts intramembranous bone formation for strains smaller approximately +/- 5% and hydrostatic pressures smaller than +/- 0.15 MPa. Endochondral ossification is associated with compressive pressures larger than about -0.15 MPa and strains smaller than +/- 15%. All other conditions seemed to lead to connective tissue or fibrous cartilage. The hypothesis enables a better understanding of the complex tissue differentiation seen in histological images and the mechanical conditions for healing delayed healing or nonunions.     

Beneficial effects of moderate,early loading and adverse effects of delayed or excessive loading on bone healing

Fracture healing involves the differentiation and proliferation of cells in the callus and the synthesis and degradation of connective, cartilage and bone tissue. These processes are initiated and tightly regulated by growth factors and by the mechanical environment in the callus. In this work we incorporated the effects of mechanical stimulation on cell differentiation and ossification into a previously developed temporal-spatial model of growth factor mediated fracture healing. In particular, the stimulatory and inhibitory effects of dilatational and deviatoric strains were modeled. This predictive model was then calibrated and validated using well-defined in vivo experiments from the literature. As in the experiments, the results of the model demonstrated the beneficial and adverse effects of moderate and excessive loading, respectively, as well as the negative effects of delaying mechanical stimulation of rigidly fixed calluses. In addition, the model examined loading conditions and time points beyond those used in the experiments, providing a more complete and mechanistic characterization of the effects of loading in the biological tissue response associated with fracture healing.     

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.     

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.     

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.     

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.     

Three-dimensional reconstruction of fracture callus morphogenesis.

Rat and mouse femur and tibia fracture calluses were collected over various time increments of healing. Serial sections were produced at spatial segments across the fracture callus. Standard histological methods and in situ hybridization to col1a1 and col2a1 mRNAs were used to define areas of cartilage and bone formation as well as tissue areas undergoing remodeling. Computer-assisted reconstructions of histological sections were used to generate three-dimensional images of the spatial morphogenesis of the fracture calluses. Endochondral bone formation occurred in an asymmetrical manner in both the femur and tibia, with cartilage tissues seen primarily proximal or distal to the fractures in the respective calluses of these bones. Remodeling of the calcified cartilage proceeded from the edges of the callus inward toward the fracture producing an inner-supporting trabecular structure over which a thin outer cortical shell forms. These data suggest that the specific developmental mechanisms that control the asymmetrical pattern of endochondral bone formation in fracture healing recapitulated the original asymmetry of development of a given bone because femur and tibia grow predominantly from their respective distal and proximal physis. These data further show that remodeling of the calcified cartilage produces a trabecular bone structure unique to fracture healing that provides the rapid regain in weight-bearing capacity to the injured bone.     

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.     

Computational simulation of the early stage of bone healing under different configurations of locking compression plates

Flexible fixation or the so-called ‘biological fixation’ has been shown to encourage the formation of fracture callus, leading to better healing outcomes. However, the nature of the relationship between the degree of mechanical stability provided by a flexible fixation and the optimal healing outcomes has not been fully understood. In this study, we have developed a validated quantitative model to predict how cells in fracture callus might respond to change in their mechanical microenvironment due to different configurations of locking compression plate (LCP) in clinical practice, particularly in the early stage of healing. The model predicts that increasing flexibility of the LCP by changing the bone–plate distance (BPD) or the plate working length (WL) could enhance interfragmentary strain in the presence of a relatively large gap size (>3 mm). Furthermore, conventional LCP normally results in asymmetric tissue development during early stage of callus formation, and the increase of BPD or WL is insufficient to alleviate this problem.     

Predicting the external formation of callus tissues in oblique bone fractures: idealised and clinical case studies

It is proposed that the external asymmetric formation of callus tissues that forms naturally about an oblique bone fracture can be predicted computationally. We present an analysis of callus formation for two cases of bone fracture healing: idealised and subject-specific oblique bone fractures. Plane strain finite element (FE) models of the oblique fractures were generated to calculate the compressive strain field experienced by the immature callus tissues due to interfragmentary motion. The external formations of the calluses were phenomenologically simulated using an optimisation style algorithm that iteratively removes tissue that experiences low strains from a large domain. The resultant simulated spatial formation of the healing tissues for the two bone fracture cases showed that the calluses tended to form at an angle equivalent to the angle of the oblique fracture line. The computational results qualitatively correlated with the callus formations found in vivo. Consequently, the proposed methods show potential as a means of predicting callus formation in pre-clinical testing.     

The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing: a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.     

Collagen IX is indispensable for timely maturation of cartilage during fracture repair in mice.

Fracture repair recapitulates in adult organisms the sequence of cell biological events of endochondral ossification during skeletal development and growth. After initial inflammation and deposition of granulation tissue, a cartilaginous callus is formed which, subsequently, is remodeled into bone. In part, bone formation is influenced also by the properties of the extracellular matrix of the cartilaginous callus. Deletion of individual macromolecular components can alter extracellular matrix suprastructures, and hence stability and organization of mesenchymal tissues. Here, we took advantage of the collagen IX knockout mouse model to better understand the role of this collagen for organization, differentiation and maturation of a cartilaginous template during formation of new bone. Although a seemingly crucial component of cartilage fibrils is missing, collagen IX-deficient mice develop normally, but are predisposed to premature joint cartilage degeneration. However, we show here that lack of collagen IX alters the time course of callus differentiation during bone fracture healing. The maturation of cartilage matrix was delayed in collagen IX-deficient mice calli as judged by collagen X expression during the repair phase and the total amount of cartilage matrix was reduced. Entering the remodeling phase of fracture healing, Col9a1(-/-) calli retained a larger percentage of cartilage matrix than in wild type indicating also a delayed formation of new bone. We concluded that endochondral bone formation can occur in collagen IX knockout mice but is impaired under conditions of stress, such as the repair of an unfixed fractured long bone.     

Inter-species investigation of the mechano-regulation of bone healing: comparison of secondary bone healing in sheep and rat

Inter-species differences in regeneration exist in various levels. One aspect is the dynamics of bone regeneration and healing, e.g. small animals show a faster healing response when compared to large animals. Mechanical as well as biological factors are known to play a key role in the process. However, it remains so far unknown whether different animals follow at all comparable mechano-biological rules during tissue regeneration, and in particular during bone healing. In this study, we investigated whether differences observed in vivo in the dynamics of bone healing between rat and sheep are only due to differences in the animal size or whether these animals have a different mechano-biological response during the healing process. Histological sections from in vivo experiments were compared to in silico predictions of a mechano-biological computer model for the simulation of bone healing. Investigations showed that the healing processes in both animal models occur under significantly different levels of mechanical stimuli within the callus region, which could explain histological observations of early intramembranous ossification at the endosteal side. A species-specific adaptation of a mechano-biological model allowed a qualitative match of model predictions with histological observations. Specifically, when keeping cell activity processes at the same rate, the amount of tissue straining defining favorable mechanical conditions for the formation of bone had to be increased in the large animal model, with respect to the small animal, to achieve a qualitative agreement of model predictions with histological data. These findings illustrate that geometrical (size) differences alone cannot explain the distinctions seen in the histological appearance of secondary bone healing in sheep and rat. It can be stated that significant differences in the mechano-biological regulation of the healing process exist between these species. Future investigations should aim towards understanding whether these differences are due to differences in cell behavior, material properties of the newly formed tissues within the callus and/or differences in response to the mechanical environment.     

A 3D computational simulation of fracture callus formation: influence of the stiffness of the external fixator

The stiffness of the external fixation highly influences the fracture healing pattern. In this work we study this aspect by means of a finite element model of a simple transverse mid-diaphyseal fracture of an ovine metatarsus fixed with a bilateral external fixator. In order to simulate the regenerative process, a previously developed mechanobiological model of bone fracture healing was implemented in three dimensions. This model is able to simulate tissue differentiation, bone regeneration, and callus growth. A physiological load of 500 N was applied and three different stiffnesses of the external fixator were simulated (2300, 1725, and 1150 N/mm). The interfragmentary strain and load sharing mechanism between bone and the external fixator were compared to those recorded in previous experimental works. The effects of the stiffness on the callus shape and tissue distributions in the fracture site were also analyzed. We predicted that a lower stiffness of the fixator delays fracture healing and causes a larger callus, in correspondence to well-documented clinical observations.     

The influence of mechanical stimulus on the pattern of tissue differentiation in a long bone fracture--an FEM study

2D, coronal plane, finite elements models (FEMs) were developed from orthogonal radiographs of a diaphyseal tibial fracture and its reparative tissue at four different time points during healing. Each callus was separated into regions of common tissue histology by computerised radiographic analysis. Starting point values of tissue material properties from the literature were refined by the model to simulate exactly the mechanical behaviour of the subject's callus and bone during loading. This was achieved by matching measured inter-fragmentary displacements with calculated inter-fragmentary forces. Stress and strain distributions in the callus and bone were calculated from peak inter-fragmentary displacements measured during natural walking activity, and were correlated with the subsequently observed pattern of tissue differentiation and maturation of the callus. The growth and stiffening of the external callus progressively reduced the inter-fragmentary gap strain. Partial maturation of the gap tissue was apparent only one week before fixator removal. Principal stresses in the callus were compared with 'yield stresses' in corresponding tissue from the literature. This indicated the presence of stress concentrations medial and lateral to the fracture gap, which probably caused tissue damage during normal activity levels. Tissue damage may also have precipitated partial structural failure of the callus, both of which were believed to have delayed healing during the middle third of the fixation period. Had the fixation device provided greater inter-fragmentary support during early healing, this may have prevented callus failure and the consequent delay in healing. A further benefit of this would have been the reduction of the initially high intra-gap tissue strains to a magnitude more conducive to earlier maturation of the bridging tissue that united the bone.     

Molecular signaling in bone fracture healing and distraction osteogenesis

The process of fracture healing has been described in detail in many histological studies. Recent work has focused on the mechanisms by which growth and differentiation factors regulate the fracture healing process. Rapid progress in skeletal cellular and molecular biology has led to the identification of many signaling molecules associated with the formation of skeletal tissues, including members of the transforming growth factor-beta (TGF-beta) superfamily and the insulin-like growth factor (IGF) family. Increasing evidence indicates that they are critical regulators of cellular proliferation, differentiation, extracellular matrix biosynthesis and mineralization. Limb lengthening procedure (distraction osteogenesis) is a relevant model to investigate the in vivo correlation between mechanical stimulation and biological responses as the callus is stretched by a proper rate and rhythm of mechanical strain. This model also provides additional insights into the molecular and cellular events during bone fracture repair. TGF-beta 1 was significantly increased in both the distracted callus and the fracture callus. The increased level of TGF-beta 1, together with a low concentration of calcium and an enhanced level of collagen synthesis, was maintained in the distracted callus as long as mechanical strain was applied. Less mineralization is also associated with a low level of osteocalcin production. These observations provide further insights into the molecular basis for the cellular events during distraction osteogenesis.