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.     

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.     

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.     

The effect of roughness on biophysical stimuli at the bone-cartilage interface

Numerical simulations are often used to investigate the effect of mechanical environment on fracture healing. Although these models exhibit biologically relevant mechanical parameters at the bone-callus interface, this interface is modelled as perfectly smooth when in fact it is rough. In this study, a macro-micro-two-scale finite element model was used to determine if roughness significantly alters calculated local mechanical parameters. An idealized fracture healing poroelastic model with a small micro-modelled sub-domain of cartilaginous callus adjacent to rough bone was subjected to cyclic loading. The shear stress, tangential fluid velocity, and pore pressure were investigated. With roughness similar to that at the growth plate, solid matrix shear stress differed substantially with interface roughness, whereas interstitial fluid velocity and pore pressure were only slightly affected. Hence, when modelling local micro-mechanical environments near hard-soft tissue interfaces, interface roughness should be considered.     

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.     

Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair

A number of mechano-regulation theories have been proposed that relate the differentiation pathway of mesenchymal stem cells (MSCs) to their local biomechanical environment. During spontaneous repair processes in skeletal tissues, the organisation of the extracellular matrix is a key determinant of its mechanical fitness. In this paper, we extend the mechano-regulation theory proposed by Prendergast et al. (J Biomech 30(6):539–548, 1997) to include the role of the mechanical environment on the collagen architecture in regenerating soft tissues. A large strain anisotropic poroelastic material model is used in a simulation of tissue differentiation in a fracture subject to cyclic bending (Cullinane et al. in J Orthop Res 20(3):579–586, 2002). The model predicts non-union with cartilage and fibrous tissue formation in the defect. Predicted collagen fibre angles, as determined by the principal decomposition of strain- and stress-type tensors, are similar to the architecture seen in native articular cartilage and neoarthroses induced by bending of mid-femoral defects in rats. Both stress and strain-based remodelling stimuli successfully predicted the general patterns of collagen fibre organisation observed in vivo. This provides further evidence that collagen organisation during tissue differentiation is determined by the mechanical environment. It is envisioned that such predictive models can play a key role in optimising MSC-based skeletal repair therapies where recapitulation of the normal tissue architecture is critical to successful repair.     

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.     

A dynamical study of the mechanical stimuli and tissue differentiation within a CaP scaffold based on micro-CT finite element models

The control of the mechanical stimuli transmitted to the cells is critical for the design of functional scaffolds for tissue engineering. The objective of this study was to investigate the dynamics of the mechanical stimuli transmitted to the cells during tissue differentiation in an irregular morphology scaffold under compressive load and perfusion flow. A calcium phosphate-based glass porous scaffold was used. The solid phase and the fluid flow within the pores were modeled as linear elastic solid material and Newtonian fluid, respectively. In the fluid model, different levels of viscosity were used to simulate tissue differentiation. Compressive strain of 0.5% and fluid flow with constant inlet velocity of 10 μm/s or constant inlet pressure of 3 Pa were applied. Octahedral shear strain and fluid shear stress were used as mechano-regulatory stimuli. For constant inlet velocity, stimuli equivalent to bone were predicted in 80% of pore volume for the case of low tissue viscosity. For the cases of high viscosity, fluctuations between stimuli equivalent to tissue formation and cell death were predicted due to the increase in the fluid shear stress when tissue started to fill pores. When constant pressure was applied, stimuli equivalent to bone were predicted in 62% of pore volume when low tissue viscosity was used and 42% when high tissue viscosity was used. This study predicted critical variations of fluid shear stress when cells differentiated. If these variations are not controlled in vitro, they can impede the formation of new matured tissue.     

Modelling cartilage mechanobiology

The growth, maintenance and ossification of cartilage are fundamental to skeletal development and are regulated throughout life by the mechanical cues that are imposed by physical activities. Finite element computer analyses have been used to study the role of local tissue mechanics on endochondral ossification patterns, skeletal morphology and articular cartilage thickness distributions. Using single-phase continuum material representations of cartilage, the results have indicated that local intermittent hydrostatic pressure promotes cartilage maintenance. Cyclic tensile strains (or shear), however, promote cartilage growth and ossification. Because single-phase material models cannot capture fluid exudation in articular cartilage, poroelastic (or biphasic) solid/fluid models are often implemented to study joint mechanics. In the middle and deep layers of articular cartilage where poroelastic analyses predict little fluid exudation, the cartilage phenotype is maintained by cyclic fluid pressure (consistent with the single-phase theory). In superficial articular layers the chondrocytes are exposed to tangential tensile strain in addition to the high fluid pressure. Furthermore, there is fluid exudation and matrix consolidation, leading to cell 'flattening'. As a result, the superficial layer assumes an altered, more fibrous phenotype. These computer model predictions of cartilage mechanobiology are consistent with results of in vitro cell and tissue and molecular biology experiments.     

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.     

Computational simulation of fracture healing: influence of interfragmentary movement on the callus growth

Bone fractures heal through a complex process involving several cellular events. This healing process can serve to study factors that control tissue growth and differentiation from mesenchymal stem cells. The mechanical environment at the fracture site is one of the factors influencing the healing process and controls size and differentiation patterns in the newly formed tissue. Mathematical models can be useful to unravel the complex relation between mechanical environment and tissue formation. In this study, we present a mathematical model that predicts tissue growth and differentiation patterns from local mechanical signals. Our aim was to investigate whether mechanical stimuli, through their influence on stem cell proliferation and chondrocyte hypertrophy, predict characteristic features of callus size and geometry. We found that the model predicted several geometric features of fracture calluses. For instance, callus size was predicted to increase with increasing movement. Also, increases in size were predicted to occur through increase in callus diameter but not callus length. These features agree with experimental observations. In addition, spatial and temporal tissue differentiation patterns were in qualitative agreement with well-known experimental results. We therefore conclude that local mechanical signals can probably explain the shape and size of fracture calluses.     

A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 microm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 microm/s of inlet fluid velocity and 1.45 Pas viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5)Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.     

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.     

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.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

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.     

Immunolocalization of myostatin (GDF-8) following musculoskeletal injury and the effects of exogenous myostatin on muscle and bone healing

The time course and cellular localization of myostatin expression following musculoskeletal injury are not well understood; therefore, the authors evaluated the temporal and spatial localization of myostatin during muscle and bone repair following deep penetrant injury in a mouse model. They then used hydrogel delivery of exogenous myostatin in the same injury model to determine the effects of myostatin exposure on muscle and bone healing. Results showed that a "pool" of intense myostatin staining was observed among injured skeletal muscle fibers 12-24 hr postsurgery and that myostatin was also expressed in the soft callus chondrocytes 4 days following osteotomy. Hydrogel delivery of 10 or 100 μg/ml recombinant myostatin decreased fracture callus cartilage area relative to total callus area in a dose-dependent manner by 41% and 80% (p<0.05), respectively, compared to vehicle treatment. Myostatin treatment also decreased fracture callus total bone volume by 30.6% and 38.8% (p<0.05), with the higher dose of recombinant myostatin yielding the greatest decrease in callus bone volume. Finally, exogenous myostatin treatment caused a significant dose-dependent increase in fibrous tissue formation in skeletal muscle. Together, these findings suggest that early pharmacological inhibition of myostatin is likely to improve the regenerative potential of both muscle and bone following deep penetrant musculoskeletal injury.     

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.     

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.