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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

A numerical approach to the biomechanical analysis of bone fracture healing

Investigations are reported in the literature, by means of experimental, analytical and numerical methods, concerning the biomechanical properties of bone. However, the evolutionary phenomena of bone fracture healing does not have a large reference literature. This work investigates and describes the behaviour of inclined human femur fractures with external fixation up to complete healing. A numerical formulation based on the finite element method has been adopted. Geometric configuration is defined using data from a magnetic resonance process applied to a femur in vivo. A three dimensional model has been developed by adopting an orthotropic material law for cortical bone and an isotropic law for the fracture gap zone. Stress and strain reponses of the bone and fixation device are investigated with reference to the evolutionary behaviour of the healing tissue.     

Assessment of a mechano-regulation theory of skeletal tissue differentiation in an in vivo model of mechanically induced cartilage formation

Mechanical cues are known to regulate tissue differentiation during skeletal healing. Quantitative characterization of this mechano-regulatory effect has great therapeutic potential. This study tested an existing theory that shear strain and interstitial fluid flow govern skeletal tissue differentiation by applying this theory to a scenario in which a bending motion applied to a healing transverse osteotomy results in cartilage, rather than bone, formation. A 3-D finite element mesh was created from micro-computed tomography images of a bending-stimulated callus and was used to estimate the mechanical conditions present in the callus during the mechanical stimulation. Predictions regarding the patterns of tissues—cartilage, fibrous tissue, and bone—that formed were made based on the distributions of fluid velocity and octahedral shear strain. These predictions were compared to histological sections obtained from a previous study. The mechano-regulation theory correctly predicted formation of large volumes of cartilage within the osteotomy gap and many, though not all patterns of tissue formation observed throughout the callus. The results support the concept that interstitial fluid velocity and tissue shear strain are key mec- hanical stimuli for the differentiation of skeletal tissues.     

A comparison of stereology, structural rigidity and a novel 3D failure surface analysis method in the assessment of torsional strength and stiffness in a mouse tibia fracture model

In attempting to develop non-invasive image based measures for the determination of the biomechanical integrity of healing fractures, traditional μCT based measurements have been limited. This study presents the development and evaluation of a tool for assessment of fracture callus mechanical properties through determination of the geometric characteristics of the fracture callus, specifically along the surface of failure identified during destructive mechanical testing. Fractures were created in tibias of ten male mice and subjected to μCT imaging and biomechanical torsion testing. Failure surface analysis, along with previously described image based measures was calculated using the μCT image data, and correlated with mechanical strength and stiffness. Three-dimensional measures along the surface of failure, specifically the surface area and torsional rigidity of bone, were shown to be significantly correlating with mechanical strength and stiffness. It was also shown that surface area of bone along the failure surface exhibits stronger correlations with both strength and stiffness than measures of average and minimum torsional rigidity of the entire callus. Failure surfaces observed in this study were generally oriented at 45° to the long axis of the bone, and were not contained exclusively within the callus. This work represents a proof of concept study, and shows the potential utility of failure surface analysis in the assessment of fracture callus stability.     

Correlations between local strains and tissue phenotypes in an experimental model of skeletal healing

Defining how mechanical cues regulate tissue differentiation during skeletal healing can benefit treatment of orthopaedic injuries and may also provide insight into the influence of the mechanical environment on skeletal development. Different global (i.e., organ-level) mechanical loads applied to bone fractures or osteotomies are known to result in different healing outcomes. However, the local stimuli that promote formation of different skeletal tissues have yet to be established. Finite element analyses can estimate local stresses and strains but require many assumptions regarding tissue material properties and boundary conditions. This study used an experimental approach to investigate relationships between the strains experienced by tissues in a mechanically stimulated osteotomy gap and the patterns of tissue differentiation that occur during healing. Strains induced by the applied, global mechanical loads were quantified on the mid-sagittal plane of the callus using digital image correlation. Strain fields were then compared to the distribution of tissue phenotypes, as quantified by histomorphometry, using logistic regression. Significant and consistent associations were found between the strains experienced by a region of the callus and the tissue type present in that region. Specifically, the probability of encountering cartilage increased, and that of encountering woven bone decreased, with increasing octahedral shear strain and, to a lesser extent, maximum principal strain. Volumetric strain was the least consistent predictor of tissue type, although towards the end of the four-week stimulation timecourse, cartilage was associated with increasingly negative volumetric strains. These results indicate that shear strain may be an important regulator of tissue fate during skeletal healing.     

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.     

Sustained expression of transforming growth factor-beta1 by distraction during distraction osteogenesis

Distraction osteogenesis is a well-established clinical treatment for limb length discrepancy and skeletal deformities. In our previous studies, we have shown that the tension at the distraction gap correlated with the plasma bone specific alkaline phosphatase activity during distraction. Transforming growth factor-beta1 (TGF-beta1) has been shown to have a regulatory role in alkaline phosphatase activity during fracture healing. This study is to investigate the expression of TGF-beta1 during distraction as a biological response to mechanically stimulated osteoblastic activity by immunohistochemistry. The expression of TGF-beta1 in the distraction callus was compared with that in the fracture callus. During the distraction phase, the osteoblasts and osteocytes expressed a high level of TGF-beta1. Moderate expression of TGF-beta1 was observed in fibroblast-like cells in the fibrous zone of the distraction callus. After the distraction stopped, the expression of TGF-beta1 in different cell types decreased. In fracture healing, the strong expression of TGF-beta1 declined after the first week. Our results showed that the mechanical force induced and sustained TGF-beta1 expression in osteoblasts and fibroblasts-like cells of the distraction callus. Transforming growth factor-beta1 may play a role in transducing mechanical stimulation to biological tissue during in distraction osteogenesis.     

A fuzzy logic model of fracture healing

A quantitative biomechanical model describes the tissue transformation during healing of a transverse osteotomy of a sheep metatarsal. The model predicts bridging of the bone ends through cartilage, followed by the growth of a callus cuff, and finally, the resorption of callus after ossification of the interfragmentary gap. We suggest bone density or the modulus of elasticity do not sufficiently characterize healing tissue for predictive purposes. In addition to the stimulus reflected by strain energy density we introduce a new osteogenic factor based upon stress gradients and which predicts areas of a high osteogenic capacity. Our model distinguishes three basic types of tissue, namely bone, cartilage and fibrous tissue. A fuzzy controller is proposed to model the tissue reaction. A set of fuzzy rules derived from medical knowledge has been implemented to describe tissue transformation such as intramembraneous or chondral ossification, atrophy or destruction. Fuzzy logic is able to model tissue transformation processes within the numerical simulation of remodeling processes. This approach improves the simulation tools and affords the potential to optimize planning of animal experiments and conduct parametric studies.