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.     

Identification of tissue differentiation rates in a mechanobiological model of fracture healing

As a basis for model-based analysis of the processes in secondary fracture healing, a dynamical model is presented that characterises the physiological status in the fracture area by the location-dependent composition of tissues. Five types of tissue are distinguished: connective tissue, cartilage, bone, haematoma and avascular bone. A rule base is given that describes dynamical tissue differentiation processes. The rules consider not only a mechanical stimulus but also osteogenic and a vasculative factors as biological stimuli. Within this model structure, it is possible, e.g., to distinguish intramembranous from endochondral ossification processes. An objective function is introduced to assess accordance between the model-based simulation results and reference healing stages. By minimising this objective function, relevant tissue differentiation rates can be determined. For a reference process of secondary fracture healing it could be shown that the intramembranous ossification rate of 0.313%/day (from connective tissue to bone) is much smaller than the endochondral ossification rate of 1.136%/day (from cartilage to bone). In order to verify the model approach, it is transferred to simulate long bone distraction. Results show that healing patterns of bone distraction can be predicted. Using this method, it is possible to identify model parameters for individual subjects. This will allow a patient-specific analysis of tissue healing processes in future.     

A hybrid bioregulatory model of angiogenesis during bone fracture healing

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.     

Influence of fracture gap size on the pattern of long bone healing: a computational study

Following fractures, bones restore their original structural integrity through a complex process in which several cellular events are involved. Among other factors, this process is highly influenced by the mechanical environment of the fracture site. In this study, we present a mathematical model to simulate the effect of mechanical stimuli on most of the cellular processes that occur during fracture healing, namely proliferation, migration and differentiation. On the basis of these three processes, the model then simulates the evolution of geometry, distributions of cell types and elastic properties inside a healing fracture. The three processes were implemented in a Finite Element code as a combination of three coupled analysis stages: a biphasic, a diffusion and a thermoelastic step. We tested the mechano-biological regulatory model thus created by simulating the healing patterns of fractures with different gap sizes and different mechanical stimuli. The callus geometry, tissue differentiation patterns and fracture stiffness predicted by the model were similar to experimental observations for every analysed situation.     

A numerical model of the fracture healing process that describes tissue development and revascularisation

A dynamic model was developed to simulate complex interactions of mechanical stability, revascularisation and tissue differentiation in secondary fracture healing. Unlike previous models, blood perfusion was included as a spatio-temporal state variable to simulate the revascularisation process. A 2D, axisymmetrical finite element model described fracture callus mechanics. Fuzzy logic rules described the following biological processes: angiogenesis, intramembranous ossification, chondrogenesis, cartilage calcification and endochondral ossification, all of which depended on local strain state and local blood perfusion. In order to evaluate how the predicted revascularisation depended on the mechanical environment, we simulated two different healing cases according to two groups of transverse metatarsal osteotomies in sheep with different axial stability. The model predicted slower revascularisation and delayed bony bridging for the less stable case, which corresponded well to the experimental observations. A revascularisation sensitivity analysis demonstrated the potential of the model to account for different conditions regarding the blood supply.     

A numerical model of the fracture healing process that describes tissue development and revascularisation

A dynamic model was developed to simulate complex interactions of mechanical stability, revascularisation and tissue differentiation in secondary fracture healing. Unlike previous models, blood perfusion was included as a spatio-temporal state variable to simulate the revascularisation process. A 2D, axisymmetrical finite element model described fracture callus mechanics. Fuzzy logic rules described the following biological processes: angiogenesis, intramembranous ossification, chondrogenesis, cartilage calcification and endochondral ossification, all of which depended on local strain state and local blood perfusion. In order to evaluate how the predicted revascularisation depended on the mechanical environment, we simulated two different healing cases according to two groups of transverse metatarsal osteotomies in sheep with different axial stability. The model predicted slower revascularisation and delayed bony bridging for the less stable case, which corresponded well to the experimental observations. A revascularisation sensitivity analysis demonstrated the potential of the model to account for different conditions regarding the blood supply.     

Dynamic analysis of a simplified bone model during the process of fracture healing

The dynamic analysis of fracture healing is tackled numerically by means of a bone model which uses the finite element method. The model is of non-uniform cross-sectional area and moment of inertia. Shear and rotatory inertia are taken into account. Considerable variation of the upper natural frequencies is observed as the healing process progresses. The practical implications, as well as present limitations, of the technique are examined.     

Myofibroblasts and mechano-regulation of connective tissue remodelling

During the past 20 years, it has become generally accepted that the modulation of fibroblastic cells towards the myofibroblastic phenotype, with acquisition of specialized contractile features, is essential for connective-tissue remodelling during normal and pathological wound healing. Yet the myofibroblast still remains one of the most enigmatic of cells, not least owing to its transient appearance in association with connective-tissue injury and to the difficulties in establishing its role in the production of tissue contracture. It is clear that our understanding of the myofibroblast its origins, functions and molecular regulation will have a profound influence on the future effectiveness not only of tissue engineering but also of regenerative medicine generally.     

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.     

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.     

Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells

Modelling the course of healing of a long bone subjected to loading has been the subject of several investigations. These have succeeded in predicting the differentiation of tissues in the callus in response to a static mechanical load and the diffusion of biological factors. In this paper an approach is presented which includes both mechanoregulation of tissue differentiation and the diffusion and proliferation of cell populations (mesenchymal stem cells, fibroblasts, chondrocytes, and osteoblasts). This is achieved in a three-dimensional poroelastic finite element model which, being poroelastic, can model the effect of the frequency of dynamic loading. Given the number of parameters involved in the simulation, a parameter variation study is reported, and final parameters are selected based on comparison with an in vivo experiment. The model predicts that asymmetric loading creates an asymmetric distribution of tissues in the callus, but only for high bending moments. Furthermore the frequency of loading is predicted to have an effect. In conclusion, a numerical algorithm is presented incorporating both mechanoregulation and evolution of cell populations, and it proves capable of predicting realistic difference in bone healing in a 3D fracture callus.     

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.     

Sensitivity of tissue differentiation and bone healing predictions to tissue properties

Computational models are employed as tools to investigate possible mechano-regulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The aim was to clarify the importance of the assumed tissue material properties in a computational model of tissue differentiation during bone healing. An established mechano-biological model was employed together with a statistical approach. The model included an adaptive 2D finite element model of a fractured long bone. Four outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at specific time points, (3) total time until healing, and (4) mechanical stability at specific time points. Statistical analysis based on fractional factorial designs first involved a screening experiment to identify the most significant tissue material properties. These seven properties were studied further with response surface methodology in a three-level Box–Behnken design. Generally, the sequential events were not significantly influenced by any properties, whereas rate-dependent outcome criteria and mechanical stability were significantly influenced by Young's modulus and permeability. Poisson's ratio and porosity had minor effects. The amount of bone formation at early, mid and late phases of healing, the time until complete healing and the mechanical stability were all mostly dependent on three material properties; permeability of granulation tissue, Young's modulus of cartilage and permeability of immature bone. The consistency between effects of the most influential parameters was high. To increase accuracy and predictive capacity of computational models of bone healing, the most influential tissue mechanical properties should be accurately quantified.     

A finite element inverse analysis to assess functional improvement during the fracture healing process

Assessment of the restoration of load-bearing function is the central goal in the study of fracture healing process. During the fracture healing, two critical aspects affect its analysis: (1) material properties of the callus components, and (2) the spatio-temporal architecture of the callus with respect to cartilage and new bone formation. In this study, an inverse problem methodology is used which takes into account both features and yields material property estimates that can analyze the healing changes. Six stabilized fractured mouse tibias are obtained at two time points during the most active phase of the healing process, respectively 10 days (n=3), and 14 days (n=3) after fracture. Under the same displacement conditions, the inverse procedure estimations of the callus material properties are generated and compared to other fracture healing metrics. The FEA estimated property is the only metric shown to be statistically significant (p=0.0194) in detecting the changes in the stiffness that occur during the healing time points. In addition, simulation studies regarding sensitivity to initial guess and noise are presented; as well as the influence of callus architecture on the FEA estimated material property metric. The finite element model inverse analysis developed can be used to determine the effects of genetics or therapeutic manipulations on fracture healing in rodents.     

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

While it is well established that an adequate blood supply is critical to successful bone regeneration, it remains poorly understood how progenitor cell fate is affected by the altered conditions present in fractures with disrupted vasculature. In this study, computational models were used to explore how angiogenic impairment impacts oxygen availability within a fracture callus and hence regulates mesenchymal stem cell (MSC) differentiation and bone regeneration. Tissue differentiation was predicted using a previously developed algorithm which assumed that MSC fate is governed by oxygen tension and substrate stiffness. This model was updated based on the hypothesis that cell death, chondrocyte hypertrophy and endochondral ossification are regulated by oxygen availability. To test this, the updated model was used to simulate the time course of normal fracture healing, where it successfully predicted the observed quantity and spatial distribution of bone and cartilage at 10 and 20 days post-fracture (dpf). It also predicted the ratio of cartilage which had become hypertrophic at 10 dpf. Following this, three models of fracture healing with increasing levels of angiogenic impairment were developed. Under mild impairment, the model predicted experimentally observed reductions in hypertrophic cartilage at 10 dpf as well as the persistence of cartilage at 20 dpf. Models of more severe impairment predicted apoptosis and the development of fibrous tissue. These results provide insight into how factors specific to an ischemic callus regulate tissue regeneration and provide support for the hypothesis that chondrocyte hypertrophy and endochondral ossification during tissue regeneration are inhibited by low oxygen.     

Dynamic gap junctional communication: a delimiting model for tissue responses.

Gap junctions are aqueous intercellular channels formed by a diverse class of membrane-spanning proteins, known as connexins. These aqueous pores provide partial cytoplasmic continuity between cells in most tissues, and are freely permeable to a host of physiologically relevant second messenger molecules/ionic species (e.g., Ca2+, IP3, cAMP, cGMP). Despite the fact that these second messenger molecules/ionic species have been shown to alter junctional patency, there is no clear basis for understanding how dynamic and transient changes in the intracellular concentration of second messenger molecules might modulate the extent of intercellular communication among coupled cells. Thus, we have modified the tissue monolayer model of Ramanan and Brink (1990) to account for both the up-regulatory and down-regulatory effects on junctions by second messenger molecules that diffuse through gap junctions. We have chosen the vascular wall as our morphological correlate because of its anisotropy and large investment of gap junctions. The model allows us to illustrate the putative behavior of gap junctions under a variety of physiologically relevant conditions. The modeling studies demonstrated that transient alterations in intracellular second messenger concentrations are capable of producing 50-125% changes in the number of cells recruited into a functional syncytial unit, after activation of a single cell. Moreover, the model conditions required to demonstrate such physiologically relevant changes in intercellular diffusion among coupled cells are commonly observed in intact tissues and cultured cells.     

Collagen deposition in the subcutaneous tissue during wound healing in humans: a model evaluation

Wound healing encompasses coagulation, inflammation, angiogenesis, fibroplasia, contraction, epithelialisation and remodeling. A granulation tissue is produced following incision of tissue such as skin, abdominal wall or the gastrointestinal tract, and the strength of the wound is determined primarily by the collagen content early in the healing course. Few models are available to study wound healing in man. The percutaneous insertion of expanded poly-tetrafluoroethylene tubes (ePTFE) into the subcutaneous tissue has been an established model for 20 years. The procedure is performed using a local anesthesia. The model has a diameter of 2.5 mm, a length of 5-10 cm and a pore size of 90-120 microns which is substantially more than that of vascular grafts. The polymer accumulates granulation tissue, the architecture of which resembles that of a normal surgical wound. Previous studies on the use of the ePTFE model in wound healing research are summarized in detail. Histological and immunohistochemical analyses of the granulation tissue deposited in the model were undertaken. The content of amino acids following hydrolysis of the granulation tissue was determined applying spectrophotometric or HPLC assays. Collagen amounts accumulated in the model are expressed as hydroxyproline per length of ePTFE or per total protein. Following a study in rats we examined 85 healthy volunteers and 158 surgical patients in the studies. Higher contents of hydroxyproline were found 10 days after implantation as compared to 5 days with considerable inter-person variation. Regarding median values there was a 25% difference between two measurements performed on two distinct ePTFE tubes from the same person, and a 12% difference between values obtained from two different pieces of the same ePTFE. Higher accumulation levels of hydroxyproline did not result in higher variability. Deposition of proline in the model correlated closely to total protein content. The ePTFE and a modified PVA model were compared in surgical patients. No reproducible measurements of hydroxyproline deposition were obtained with the PVA model as opposed to the ePTFE model. It is concluded that the modified PVA model is inadequate for determination of collagen deposition in subcutaneous granulation tissue. We found no correlation between collagen deposition levels obtained with placement of the ePTFE model in the subcutaneous tissue of the arm and in an uncomplicated surgical wound of the groin in the same patient, respectively. Significantly higher collagen deposition levels in the model were found in the surgical wound. Conversely, there was a significant correlation between protein deposition levels obtained at the two sites. Patients undergoing minor surgery (groin hernia repair) did not differ from healthy non-traumatized volunteers as regards deposition of collagen in subcutaneous tissue of the arm, whereas patients subjected to major general surgery demonstrated a significant decline during the postoperative phase compared to a preoperative evaluation. This decline was enhanced in patients who had infectious complications. Non-smoking volunteers were found to specifically accumulate more collagen (median value 82%) than smokers matched for age and gender. Irrespective of the smoking status women accumulated significantly more collagen in the model than men. These findings were re-tested in a prospective series leading to the same conclusion. Matrix metalloproteinases (MMP-2 and MMP-9) were determined in wound fluid obtained from the subcutaneous cavities of herniotomy wounds 24 and 48 h after operation. A significant and inverse correlation was demonstrated between MMP-9 after 24 h and accumulation levels of collagen in the ePTFE tube 10 days after implantation in the wound. Finally, it was demonstrated that local application of granulocyte-macrophage colony-stimulating factor into the ePTFE model during implantation specifically and dose-dependently reduced the number of fibroblasts and deposition of collagen. The doses chosen for the experiments resulted in both a local and a systemic effect. It is concluded that the minimally invasive ePTFE model, despite a certain level of variability, presently provides one of the best possibilities of evaluation of the wound healing potential in both volunteers and patients under various conditions. We found the model convenient for the assessment of both matrix deposition during wound healing and the influence of several factors including demographic characteristics, trauma, tobacco smoking, drugs and tissue degrading components of the wound.     

The expression of the fibrillar collagen genes during fracture healing: heterogeneity of the matrices and differentiation of the osteoprogenitor cells

The cells that express the genes for the fibrillar collagens, types I, II, III and V, during callus development in rabbit tibial fractures healing under stable and unstable mechanical conditions were localized. The fibroblast-like cells in the initial fibrous matrix express types I, III and V collagen mRNAs. Osteoblasts, and osteocytes in the newly formed membranous bone under the periosteum, express the mRNAs for types I, III and V collagens, but osteocytes in the mature trabeculae express none of these mRNAs. Cartilage formation starts at 7 days in calluses forming under unstable mechanical conditions. The differentiating chondrocytes express both types I and II collagen mRNAs, but later they cease expression of type I collagen mRNA. Both types I and II collagens were located in the cartilaginous areas. The hypertrophic chondrocytes express neither type I, nor type II, collagen mRNA. Osteocalcin protein was located in the bone and in some cartilaginous regions. At 21 days, irrespective of the mechanical conditions, the callus consists of a layer of bone; only a few osteoblasts lining the cavities now express type I collagen mRNA.We suggest that osteoprogenitor cells in the periosteal tissue can differentiate into either osteoblasts or chondrocytes and that some cells may exhibit an intermediate phenotype between osteoblasts and chondrocytes for a short period. The finding that hypertrophic chondrocytes do not express type I collagen mRNA suggests that they do not transdifferentiate into osteoblasts during endochondral ossification in fracture callus.     

Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity

Corroboration of mechano-regulation algorithms is difficult, partly because repeatable experimental outcomes under a controlled mechanical environment are necessary, but rarely available. In distraction osteogenesis (DO), a controlled displacement is used to regenerate large volumes of new bone, with predictable and reproducible outcomes, allowing to computationally study the potential mechanisms that stimulate bone formation. We hypothesized that mechano-regulation by octahedral shear strain and fluid velocity can predict the spatial and temporal tissue distributions seen during experimental DO. Variations in predicted tissue distributions due to alterations in distraction rate and frequency could then also be studied. An in vivo ovine tibia experiment evaluating bone-segment transport (distraction, 1 mm/day) over an intramedullary nail was used for comparison. A 2D axisymmetric finite element model, with a geometry originating from the experimental data, was created and included into a previously developed model of tissue differentiation. Cells migrated and proliferated into the callus, differentiating into fibroblasts, chondrocytes or osteoblasts, dependent on the biophysical stimuli. Matrix production was modelled with an osmotic swelling model to allow tissues to grow at individual rates. The temporal and spatial tissue distributions predicted by the computational model agreed well with those seen experimentally. In addition, it was observed that decreased distraction rate (0.5 mm/d vs. 0.25 mm/d) increased the overall time needed for complete bone regeneration, whereas increased distraction frequency (0.5 mm/12 h vs. 0.25 mm/6 h) stimulated faster bone regeneration, as found in experimental findings by others. Thus, the algorithm regulated by octahedral shear strain and fluid velocity was able to predict the bone regeneration patterns dependent on distraction rate and frequency during DO.