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 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.     

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.     

Inelastic strain accumulation in cortical bone during rapid transient tensile loading

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of +/- 420 MPa/s. Loads were reversed at pre selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.     

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.     

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.     

Material characterization of human medial collateral ligament.

The objectives of this study were to determine the longitudinal and transverse material properties of the human medial collateral ligament (MCL) and to evaluate the ability of three existing constitutive models to describe the material behavior of MCL. Uniaxial test specimens were punched from ten human cadaveric MCLs and tensile tested along and transverse to the collagen fiber direction. Using load and optical strain analysis information, the tangent modulus, tensile strength and ultimate strain were determined. The material coefficients for each constitutive model were determined using nonlinear regression. All specimens failed within the substance of the tissue. Specimens tested along the collagen fiber direction exhibited the typical nonlinear behavior reported for ligaments. This behavior was absent from the stress-strain curves of the transverse specimens. The average tensile strength, ultimate strain, and tangent modulus for the longitudinal specimens was 38.6 +/- 4.8 MPa, 17.1 +/- 1.5 percent, and 332.2 +/- 58.3 MPa, respectively. The average tensile strength, ultimate strain, and tangent modulus for the transverse specimens was 1.7 +/- 0.5 MPa, 11.7 +/- 0.9 percent, and 11.0 +/- 3.6 MPa, respectively. All three constitutive models described the longitudinal behavior of the ligament equally well. However, the ability of the models to describe the transverse behavior of the ligament varied.     

Effects of spaceflight on rat humerus geometry, biomechanics, and biochemistry

The effects of a 12.5-day spaceflight (Cosmos 1887 biosatellite) on the geometric, biomechanical, and biochemical characteristics of humeri of male specific pathogen-free rats were examined. Humeri of age-matched basal control, synchronous control, and vivarium control rats were contrasted with the flight bones to examine the influence of growth and space environment on bone development. Lack of humerus longitudinal growth occurred during the 12.5 days in spaceflight. In addition, the normal mid-diaphysial periosteal appositional growth was affected; compared with their controls, the spaceflight humeri had less cortical cross-sectional area, smaller periosteal circumferences, smaller anterior-posterior periosteal diameters, and smaller second moments of area with respect to the bending and nonbending axes. The flexural rigidity of the flight humeri was comparable to that of the younger basal control rats and significantly less than that of the synchronous and vivarium controls; the elastic moduli of all four groups, nonetheless, were not significantly different. Generally, the matrix biochemistry of the mid-diaphysial cross sections showed no differences among groups. Thus, the spaceflight differences in humeral mechanical strength and flexural rigidity were probably a result of the differences in humeral geometry rather than material properties.     

Gene expression of TGF-beta, TGF-beta receptor, and extracellular matrix proteins during membranous bone healing in rats

Poorly healing mandibular fractures and osteotomies can be troublesome complications of craniomaxillofacial trauma and reconstructive surgery. Gene therapy may offer ways of enhancing bone formation by altering the expression of desired growth factors and extracellular matrix molecules. The elucidation of suitable candidate genes for therapeutic intervention necessitates investigation of the endogenously expressed patterns of growth factors during normal (i.e., successful) fracture repair. Transforming growth factor beta1 (TGF-beta1), its receptor (Tbeta-RII), and the extracellular matrix proteins osteocalcin and type I collagen are thought to be important in long-bone (endochondral) formation, fracture healing, and osteoblast proliferation. However, the spatial and temporal expression patterns of these molecules during membranous bone repair remain unknown. In this study, 24 adult rats underwent mandibular osteotomy with rigid external fixation. In addition, four identically treated rats that underwent sham operation (i.e., no osteotomy) were used as controls. Four experimental animals were then killed at each time point (3, 5, 7, 9, 23, and 37 days after the procedure) to examine gene expression of TGF-beta1 and Tbeta-RII, osteocalcin, and type I collagen. Northern blot analysis was used to compare gene expression of these molecules in experimental animals with that in control animals (i.e., nonosteotomized; n = 4). In addition, TGF-beta1 and T-RII proteins were immunolocalized in an additional group of nine animals killed on postoperative days 3, 7, and 37. The results of Northern blot analysis demonstrated a moderate increase (1.7 times) in TGF-beta1 expression 7 days postoperatively; TGF-beta1 expression returned thereafter to near baseline levels. Tbeta-RII mRNA expression was downregulated shortly after osteotomy but then increased, reaching a peak of 1.8 times the baseline level on postoperative day 9. Osteocalcin mRNA expression was dramatically downregulated shortly after osteotomy and remained low during the early phases of fracture repair. Osteocalcin expression trended slowly upward as healing continued, reaching peak expression by day 37 (1.7 times the control level). In contrast, collagen type IalphaI mRNA expression was acutely downregulated shortly after osteotomy, peaked on postoperative days 5, and then decreased at later time points. Histologic samples from animals killed 3 days after osteotomy demonstrated TGF-beta1 protein localized to inflammatory cells and extracellular matrix within the fracture gap, periosteum, and peripheral soft tissues. On postoperative day 7, TGF-beta1 staining was predominantly localized to the osteotomized bone edges, periosteum, surrounding soft tissues, and residual inflammatory cells. By postoperative day 37, complete bony healing was observed, and TGF-beta1 staining was localized to the newly formed bone matrix and areas of remodeling. On postoperative day 3, Tbeta-RII immunostaining localized to inflammatory cells within the fracture gap, periosteal cells, and surrounding soft tissues. By day 7, Tbeta-RII staining localized to osteoblasts of the fracture gap but was most intense within osteoblasts and mesenchymal cells of the osteotomized bone edges. On postoperative day 37, Tbeta-RII protein was seen in osteocytes, osteoblasts, and the newly formed periosteum in the remodeling bone. These observations agree with those of previous in vivo studies of endochondral bone formation, growth, and healing. In addition, these results implicate TGF-beta1 biological activity in the regulation of osteoblast migration, differentiation, and proliferation during mandibular fracture repair. Furthermore, comparison of these data with gene expression during mandibular distraction osteogenesis may provide useful insights into the treatment of poorly healing fractures because distraction osteogenesis has been shown to be effective in the management of these difficult clinical cases.     

Nonlinear elastic analysis of blood vessels

Based on the theory of Green and Adkins [9], a strain energy function is proposed to describe the nonlinear mechanical behavior of arteries. The arterial tissue is assumed to be a nonlinear elastic, incompressible material with local triclinicity and transverse isotropy. Although the arterial tissue shows viscous phenomena, experimental results have indicated that viscosity is only a second-order effect as compared to the nonlinear elasticity of the tissue. The advantage of the formulation presented herein is that it is relatively simple and results in an accurate stress-strain relation that can be used readily for the study of wave propagations in the blood vessels. For nonlinear finite strain elasticity of the order two, ten elastic constants are needed to describe the material nonlinearity of the arterial tissue. Based on the orthogonal, transverse isotropies and the incompressibility conditions, ten constraint equations may be established and the elastic constants can be uniquely determined by correlating with the experimental results. An example of calculating these elastic constants is made by using the experimental data of Patel, et al. [14-17] for the intercoastal arteries in living dogs. The predicted mechanical behavior of canine arteries is quite satisfactory as compared to the experimental data except when the longitudinal and the circumferential stretches exceed 1.60. However, such a strain magnitude may not be expected in in-vivo arteries because of the constraints of peripheral connecting tissues. Otherwise, the strain energy function including higher order strain terms should be used.(ABSTRACT TRUNCATED AT 250 WORDS)     

Geometric mouse variation: Implications to the axial ulnar loading protocol and animal specific calibration

Large variations in axial ulnar load strain calibration results suggest that animal-specific calibrations may be necessary. However, the optimal set of geometric measures for performing an animal-specific calibration are not known, potentially as a result of confounding effects associated with experimentally introduced variation. The purpose of this study was to characterize the inherent variability of ulnar geometric measures known to influence periosteal midshaft strain during axial ulnar exogenous loading, and to further quantify the relationship between the variance of those geometric measures and periosteal strain during axial loading. Thirty-nine right mouse forelimbs were scanned with microCT. Seven geometric measures that influence periosteal strain resulting from a combined axial and bending loading were computed and used to estimate animal-specific strains on the periosteal midshaft. Animal specific strains were estimated using a theoretical model based on the generalized flexure formula. The predicted mean and standard deviation of the simulated midshaft strain gauge measurement resulting from the inter-animal geometric differences was −985±148 με/N. The complete beam bending term associated with bending about the I_min axis accounted for 89% of the variance and reduced the residual RMSE to 50.4 με. Eccentricity associated with the axial loading contributed a substantial portion of variation to the computed strain suggesting that calibration procedures to account for animal differences should incorporate that variable. The method developed in this study provides a relatively simple procedure for computing animal-specific strains using microCT scan data, without the need of a load/strain calibration study or computationally intensive finite element models.     

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.     

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.     

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.     

Cortical remodeling data are affected by sampling location

It has been argued that techniques for estimating adult ageat-death from cortical histology are deleteriously affected by sampling location. This study uses nine complete femoral midshaft cross-sections to test the effect of sampling site on measurement of a standard histological variable, percent remodeled bone. Circumferential periosteal fields from four anatomically defined locations (anterior, posterior, medial, lateral) and four mechanically defined locations (maximum and minimum moments of area) were evaluated. Locations deviating from the periosteal surface toward the endosteal surface were also compared. Significant differences were found for both location and field placement. The anatomical axes exhibited greater variability than the mechanical axes, in particular the anterior location, a standard sampling site for age-at-death estimation techniques. More endosteal fields tended to show elevated levels of percent remodeled bone. This study demonstrates that circumferential and radial sampling locations are important considerations in deriving and applying predictive equations based on cortical remodeling. © 1995 Wiley-Liss, Inc.     

Inflammatory phase of bone healing initiates the regenerative healing cascade

Bone healing commences with an inflammatory reaction which initiates the regenerative healing process leading in the end to reconstitution of bone. An unbalanced immune reaction during this early bone healing phase is hypothesized to disturb the healing cascade in a way that delays bone healing and jeopardizes the successful healing outcome. The immune cell composition and expression pattern of angiogenic factors were investigated in a sheep bone osteotomy model and compared to a mechanically-induced impaired/delayed bone healing group. In the impaired/delayed healing group, significantly higher T cell percentages were present in the bone hematoma and the bone marrow adjacent to the osteotomy gap when compared to the normal healing group. This was mirrored in the higher cytotoxic T cell percentage detected under delayed bone healing conditions indicating longer pro-inflammatory processes. The highly activated periosteum adjourning the osteotomy gap showed lower expression of hematopoietic stem cell markers and angiogenic factors such as heme oxygenase and vascular endothelial growth factor. This indicates a deferred revascularization of the injured area due to ongoing pro-inflammatory processes in the delayed healing group. Results from this study suggest that there are unfavorable immune cells and factors participating in the initial healing phase. In conclusion, identifying beneficial aspects may lead to promising therapeutical approaches that might benefit further by eliminating the unfavorable factors.     

Correlations between indentation modulus and mineral density in bone-fracture calluses

The mechanical properties of a healing bone fracture depend not only on the geometry of the fracture callus but also on the material properties of the callus tissues. Despite the biomechanical importance of callus tissues in restoring mechanical integrity to the injured bone, little is known about the material properties of these tissues and whether these properties can be estimated non-invasively. This study used nanoindentation to quantify the spatial variations in indentation modulus throughout the fracture callus and correlated the measurements of modulus with measurements of tissue mineral density (TMD) obtained from images from micro-computed tomography (μCT). Fracture calluses were harvested from rats 24 days following creation of a full-thickness, transverse osteotomy in the femoral mid-diaphysis. Calluses were imaged using μCT, and the average TMD and the median grayvalue (X-ray attenuation) of five, pre-defined volumes of interest (VOIs) in each callus were computed. Nanoindentation was then performed at multiple, regularly spaced locations across 150 μm-thick, sagittal sections of the calluses. The indentation modulus ranged from 0.51 to 1680 MPa throughout the callus, with the highest moduli in the center of the fracture gap and the lowest in the periphery of the gap (P < 0.05). TMD was also highest in the center of the gap (P < 0.05). An increasing trend in both modulus and TMD was observed in the regions of the callus adjacent to the periosteal surfaces of the cortex. While no correlation was found between the average indentation modulus in a given VOI and the median grayvalue of that VOI, the average indentation modulus and the average TMD were positively correlated (R = 0.70, P < 0.05). Together, these findings establish the spatial heterogeneity in the mechanical behavior of tissues in fracture calluses and indicate that the indentation modulus of these tissues can be estimated by non-invasive measurements of tissue mineralization.     

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

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

Anisotropic mechanical properties of ovine femoral periosteum and the effects of cryopreservation

The mechanical properties of periosteum are not well characterized. An understanding of these properties is critical to predict the environment of pluripotent and osteochondroprogenitor cells that reside within the periosteum and that have been shown recently to exhibit a remarkably rapid capacity to generate bone de novo. Furthermore, the effects of cryopreservation on periosteal mechanical properties are currently unknown. We hypothesized that the periosteum is pre-stressed in situ and that the periosteum exhibits anisotropic material properties, e.g. the elastic modulus of the periosteum depends significantly on the direction of loading. We measured the change in area, axial length, and circumferential length of anterior, posterior, medial, and lateral fresh periosteal samples removed from underlying bone (t=0-16 h) as well as the average strain in axially and circumferentially oriented anterior periosteal samples subjected to tensile strain (0.004 mm/s) until failure. The elastic modulus was calculated from the resulting stress-strain curves. Tensile testing was repeated with axially aligned samples that had been slowly cryopreserved for comparison to fresh samples. Periosteal samples from all aspects shrank 44-54%, 33-47%, and 9-19% in area, axial length, and circumferential length, respectively. At any given time, the periosteum shrank significantly more in the axial direction than the circumferential direction. Tensile testing showed that the periosteum is highly anisotropic. When loaded axially, a compliant toe region of the stress-strain curve (1.93±0.14 MPa) is followed by a stiffer region until failure (25.67±6.87 MPa). When loaded circumferentially, no toe region is observable and the periosteum remained compliant until failure (4.41±1.21 MPa). Cryopreservation had no significant effect on the elastic modulus of the periosteum. As the periosteum serves as the bounding envelope of the femur, anisotropy in periosteal properties may play a key role in modulating bone growth, healing and adaptation, in health, disease, and trauma.