Modeling of dynamic fracture and damage in two-dimensional trabecular bone microstructures using the cohesive finite element method

Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Micro-finite-element models have been used to investigate the elastic and yield properties of trabecular bone but have only seen limited application in modeling the microstructure dependent fracture of trabecular bone. In this research, dynamic fracture in two-dimensional (2D) micrographs of ovine (sheep) trabecular bone is modeled using the cohesive finite element method. For this purpose, the bone tissue is modeled as an orthotropic material with the cohesive parameters calculated from the experimental fracture properties of the human cortical bone. Crack propagation analyses are carried out in two different 2D orthogonal sections cut from a three-dimensional 8 mm diameter cylindrical trabecular bone sample. The two sections differ in microstructural features such as area fraction (ratio of the 2D space occupied by bone tissue to the total 2D space), mean trabecula thickness, and connectivity. Analyses focus on understanding the effect of the rate of loading as well as on how the rate variation interacts with the microstructural features to cause anisotropy in microdamage accumulation and in the fracture resistance. Results are analyzed in terms of the dependence of fracture energy dissipation on the microstructural features as well as in terms of the changes in damage and stresses associated with the bone architecture variation. Besides the obvious dependence of the fracture behavior on the rate of loading, it is found that the microstructure strongly influences the fracture properties. The orthogonal section with lesser area fraction, low connectivity, and higher mean trabecula thickness is more resistant to fracture than the section with high area fraction, high connectivity, and lower mean trabecula thickness. In addition, it is found that the trabecular architecture leads to inhomogeneous distribution of damage, irrespective of the symmetry in the applied loading with the fracture of the entire bone section rapidly progressing to bone fragmentation once the accumulated damage in any trabeculae reaches a critical limit.     

Quantitative,structural, and image-based mechanical analysis of nonunion fracture repaired by genetically engineered mesenchymal stem cells

Stem cell-mediated gene therapy for fracture repair, utilizes genetically engineered mesenchymal stem cells (MSCs) for the induction of bone growth and is considered a promising approach in skeletal tissue regeneration. Previous studies have shown that murine nonunion fractures can be repaired by implanting MSCs over-expressing recombinant human bone morphogenetic protein-2 (rhBMP-2). Nanoindentation studies of bone tissue induced by MSCs in a radius fracture site indicated similar elastic modulus compared to intact murine bone, eight weeks post-treatment. In the present study we sought to investigate temporal changes in microarchitecture and biomechanical properties of repaired murine radius bones, following the implantation of MSCs. High-resolution micro-computed tomography (micro-CT) was performed 10 and 35 weeks post MSC implantation, followed by micro-finite element (micro-FE) analysis. The results have shown that the regenerated bone tissue remodels over time, as indicated by a significant decrease in bone volume, total volume, and connectivity density combined with an increase in mineral density. In addition, the axial stiffness of limbs repaired with MSCs was 2–1.5 times higher compared to the contralateral intact limbs, at 10 and 35 weeks post-treatment. These results could be attributed to the fusion that occurred in between the ulna and radius bones. In conclusion, although MSCs induce bone formation, which exceeds the fracture site, significant remodeling of the repair callus occurs over time. In addition, limbs treated with an MSC graft demonstrated superior biomechanical properties, which could indicate the clinical benefit of future MSC application in nonunion fracture repair.     

Cryopreservation of human teeth for future organization of a tooth bank--a preliminary study

This study was aimed at evaluating whether cryopreserved teeth can be used for future transplantation by examining the viability and differentiation capability of periodontal ligament (PDL) cells and measuring the hardness of dental hard tissue. Fifty-four teeth were divided into two groups, control and frozen teeth. A MTT assay and a TUNEL assay were performed for the examination of the viability and apoptotic death of PDL cells. Immunohistochemical staining for alkaline phosphatase was performed to observe whether the differentiation capability of PDL cells was maintained by the freezing and thawing procedure. Hardness was measured to detect whether dental hard tissue was affected by the freezing conditions. The MTT and TUNEL assays showed no significant difference in the viability of PDL cells between the two groups. The differentiation capability of PDL cells was maintained in frozen teeth as evidenced by alkaline phosphatase staining. The hardness of frozen teeth was not changed, but a longitudinal fracture was found in 25% of the frozen group. The viability and differentiation capability of PDL cells were maintained in a frozen environment; however, it is thought that a new cryopreservation method preventing fracture of dental hard tissue should be developed for clinical application.     

Characterization of Mechanical and Biological Properties of 3-D Scaffolds Reinforced with Zinc Oxide for Bone Tissue Engineering

A scaffold for bone tissue engineering should have highly interconnected porous structure, appropriate mechanical and biological properties. In this work, we fabricated well-interconnected porous β-tricalcium phosphate (β-TCP) scaffolds via selective laser sintering (SLS). We found that the mechanical and biological properties of the scaffolds were improved by doping of zinc oxide (ZnO). Our data showed that the fracture toughness increased from 1.09 to 1.40 MPam^1/2, and the compressive strength increased from 3.01 to 17.89 MPa when the content of ZnO increased from 0 to 2.5 wt%. It is hypothesized that the increase of ZnO would lead to a reduction in grain size and an increase in density of the strut. However, the fracture toughness and compressive strength decreased with further increasing of ZnO content, which may be due to the sharp increase in grain size. The biocompatibility of the scaffolds was investigated by analyzing the adhesion and the morphology of human osteoblast-like MG-63 cells cultured on the surfaces of the scaffolds. The scaffolds exhibited better and better ability to support cell attachment and proliferation when the content of ZnO increased from 0 to 2.5 wt%. Moreover, a bone like apatite layer formed on the surfaces of the scaffolds after incubation in simulated body fluid (SBF), indicating an ability of osteoinduction and osteoconduction. In summary, interconnected porous β-TCP scaffolds doped with ZnO were successfully fabricated and revealed good mechanical and biological properties, which may be used for bone repair and replacement potentially.     

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.     

A fabric-dependent fracture criterion for bone.

A fracture criterion for bone tissue is proposed. Bone material is considered to be anisotropic and its properties are described by invoking the concept of directional variation of porosity. The fracture criterion is expressed as a scalar-valued function of the stress tensor and it incorporates an orientation-dependent distribution of compressive/tensile strength. The proposed mathematical framework is applied to a numerical analysis of fracture in the proximal femur due to a fall from standing height. The risk of fracture is assessed in the context of two different porosity distributions, simulating a healthy and an osteoporotic bone.     

Changes in the Electric Field at an Injury Site During Healing Under Electrical Stimulation

Changes in the electrical properties of tissue during healing should affect the electric field and current density distributions produced by applied electric or magnetic fields. The electric field produced at a fracture site by surface electrodes is found using a finite-difference method, implemented with a commerically-available spread-sheet program on a microcomputer. The method is first validated by application to a two-layer cylinder. The model considered is the healing of a tibia fracture in an irregularly-shaped, anisotropic model of the human calf. Variations of the three components of the electric field throughout the calf due to the healing are examined. Significant changes are found at the fracture site and in its vicinity. Similar results should be observed with other forms of electromagnetic stimulation.     

A numerical approach to the biomechanical analysis of bone fracture healing

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

Expression of various growth factors for cell proliferation and cytodifferentiation during fracture repair of bone

We examined immunohistochemically the fracture repair process in rat tibial bone using antibodies to PCNA, BMP2, TGF-beta 1,-2,-3, TGF-beta R1,-R2, bFGF, bFGFR, PDGF, VEGF, and S-100. The peak level of cell proliferation as revealed by PCNA labelling appeared first in primitive mesenchymal cells and inflammatory cells at the fracture edges and neighboring periosteum at 2-days after fracture, followed by the peaks of periosteal primitive fibroblasts and chondroblasts, which appeared at fracture edges at 3- and 4-days after fracture, respectively. BMP2 was weakly positive in primitive mesenchymal cells, osteoblasts and chondroblasts. At 3-days post-fracture, periosteal osteoblasts produced osteoid tissue and callus with marrow spaces lined by osteoblasts and osteoclasts, and all primitive mesenchymal cells and osteoblasts were positive for TGF-beta 1,-2,-3, and TGF-beta R1,-R2. They were also positive for vascular growth factors bFGF, FGFR and PDGF, but negative for VEGF, and the peak of PCNA labelling of vascular endothelial cells in the marrow space was delayed to 4-days after fracture. Chondroblasts at fracture edges produced hypertrophic chondrocytes at 5-days after fracture and they were positive for TGF-beta 1,-2,-3, and TGF-beta R1,-R2. Primitive chondroblasts were positive for vascular growth factors VEGF as well as bFGF, FGFR, and the peak of PCNA labelling of vascular endothelial cells in the cartilage was at 5-days after fracture. Hypertrophic chondrocytes were also positive for these growth factors but negative for bFGF and bFGFR. S-100 protein-induced calcification was only positive on chondroblasts and hypertrophic chondrocytes. At 7-days after fracture, bone began to be formed from the cartilage at fracture edges, by a process similar to bone formation in the growth plate. Enchondral ossification established a bridge between both fracture edges and periosteal membranous ossification encompassed the fracture site like a sheath at 14 day after fracture. Our study of fracture repair of bone indicates that this process is complex and occurs through various steps involving various growth factors.     

A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity

Phenomenological computational models of tissue regeneration and bone healing have been only partially successful in predicting experimental observations. This may be a result of simplistic modeling of cellular activity. Furthermore, phenomenological models are limited when considering the effects of combined physical and biological interventions. In this study, a new model of cell and tissue differentiation, using a more mechanistic approach, is presented and applied to fracture repair. The model directly couples cellular mechanisms to mechanical stimulation during bone healing and is based on the belief that the cells act as transducers during tissue regeneration. In the model, the cells within the matrix proliferate, differentiate, migrate, and produce extracellular matrix, all at cell-phenotype specific rates, based on the mechanical stimulation they experience. The model is assembled from coupled partial differentiation equations, which are solved using a newly developed finite element formulation. The evolution of four cell types, i.e. mesenchymal stem cells, fibroblasts, chondrocytes and osteoblasts, and the production of extracellular matrices of fibrous tissue, cartilage and bone are calculated. The material properties of the tissues are iteratively updated based on actual amounts of extracellular matrix in material elements at progressive time points. A two-dimensional finite element model of a long bone osteotomy was used to evaluate the model's potential. The additional value of the presented model and the importance of including cell-phenotype specific activities when modeling tissue differentiation and bone healing, were demonstrated by comparing the predictions with phenomenological models. The model's capacity was established by showing that it can correctly predict several aspects of bone healing, including cell and tissue distributions during normal fracture healing. Furthermore, it was able to predict experimentally established alterations due to excessive mechanical stimulation, periosteal stripping and impaired effects of cartilage remodeling.     

Structural and nanoindentation studies of stem cell-based tissue-engineered bone

Stem cell-based gene therapy and tissue engineering have been shown to be an efficient method for the regeneration of critical-sized bone defects. Despite being an area of active research over the last decade, no knowledge of the intrinsic ultrastructural and nanomechanical properties of such bone tissue exists. In this study, we report the nanomechanical properties of engineered bone tissue derived from genetically modified mesenchymal stem cells (MSCs) overexpressing the rhBMP2 gene, grown in vivo in the thigh muscle of immunocompetent mice for 4 weeks, compared to femoral bone adjacent to the transplantation site. The two types of bone had similar mineral contents (61 and 65 wt% for engineered and femoral bone, respectively), overall microstructures showing lacunae and canaliculi (both measured by back-scattered electron microscopy), chemical compositions (measured by energy dispersive X-ray analysis), and nanoscale topographical morphologies (measured by tapping-mode atomic force microscopy imaging or TMAFM). Nanoindentation experiments revealed that the small length scale mechanical properties were statistically different with the femoral bone (indented parallel to the bone long axis) being stiffer and harder (apparent elastic modulus, E approximately 27.3+/-10.5 GPa and hardness, H approximately 1.0+/-0.7G Pa) than the genetically engineered bone (E approximately 19.8+/-5.6 GPa, H approximately 0.9+/-0.4G Pa). TMAFM imaging showed clear residual indents characteristic of viscoelastic plastic deformation for both types of bone. However, fine differences in the residual indent area (smaller for the engineered bone), pile up (smaller for the engineered bone), and fracture mechanisms (microcracks for the engineered bone) were observed with the genetically engineered bone behaving more brittle than the femoral control.     

Bone regeneration and stem cells

This invited review covers research areas of central importance for orthopaedic and maxillofacial bone tissue repair, including normal fracture healing and healing problems, biomaterial scaffolds for tissue engineering, mesenchymal and foetal stem cells, effects of sex steroids on mesenchymal stem cells, use of platelet-rich plasma for tissue repair, osteogenesis and its molecular markers. A variety of cells in addition to stem cells, as well as advances in materials science to meet specific requirements for bone and soft tissue regeneration by addition of bioactive molecules, are discussed.     

Insertion/deletion polymorphism in the 3′ untranslated region of COL1A2 disrupts its interaction with microRNA-382 and leads to decreased susceptibility to osteoporotic fracture

A growing body of evidence has proved that the expression of COL1A2 is associated with a reduced risk of osteoporotic fracture. One single-nucleotide polymorphism (rs3917) located within the 3′-untranslated region of COL1A2 may “alter” binding site of miR-382 and thereby associated with the risk of osteoporotic fracture. Bioinformatic analysis, luciferase reporter assay, site-directed mutagenesis, Western blot and real-time PCR were performed in this study. In this study, we validated COL1A2 as a target of miR-382 in osteoblast. In addition, bone tissue samples were genotyped as wild-type rs3917, heterozygous rs3917, and homozygous rs3917. The expression of miR-382 was comparable between the genotype groups, whereas the expression of COL1A2 mRNA and protein was much higher in heterozygous rs3917 and homozygous rs3917 than the wild-type rs3917 group. Furthermore, we transfected the wild-type rs3917 and heterozygous rs3917 cells with miR-382 mimics or inhibitors and found that the transfection with miR-382 mimics significantly increased the level of the miR-382 in the cells of both genotypes, and the introduction of miR-382 inhibitors substantially suppressed the level of miR-382 in both cells. In wild-type rs3917 cells, transfection of miR-382 mimics and COL1A2 small interfering RNA (siRNA) similarly and substantially downregulated the expression of COL1A2, while in heterozygous rs3917 cells, only COL1A2 siRNA notably reduced the expression of COL1A2, whereas introduction of miR-382 mimics left expression of COL1A2 intact. The findings showed rs3917 polymorphism interfered with the interaction between COL1A2 mRNA and miR-382, and minor allele is associated with a reduced risk of osteoporotic fracture.     

Mineral and matrix contributions to rigidity in fracture healing

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

Failure properties of vena cava tissue due to deep penetration during filter insertion

In this work, we use an in-vitro mechanical test to explore the resistance of biaxially stretched vena cava tissue against deep perforation and a methodology which integrates experimental and numerical modeling to identify constitutive fracture properties of the vena cava. Six sheep vena cava were harvested just after killing, and cyclic uniaxial tension tests in longitudinal and circumferential directions and biaxial deep penetration tests were performed. After that, we use a nonlinear finite element model to simulate in vitro penetration of the cava tissue in order to fit the fracture properties under penetration of the vena cava by defining a cohesive fracture zone. An iterative process was developed in order to fit the fracture properties of the vena cava using the previously obtained experimental results. The proposed solutions were obtained with fracture energy of 0.22 or 0.33 N/mm. In comparison with the experimental data, the simulation using \(\delta _{0}=0.01\,\hbox {mm}\), \(\delta _{r}=0.35\,\hbox {mm}\), and \(K=220\, \hbox {N}/\hbox {mm}^{3}\) parameters (\(F_{\hbox {max}}=0.92\)) is in good agreement with results from penetration experiments of cava tissue. It is noticeable that the parameter estimation process of the fracture behavior is more accurate than the estimation process of the elastic behavior for the toe region of the curve.     

Histochemical and biochemical studies on the localization and activity of lysosomal enzymes in fracture callus

Summary Quantitative biochemical studies on the activities of four lysosomal hydrolases during different stages of fracture healing in the rat were performed, and the results obtained were integrated with those of histochemical observations relating to changes in the localization of acid phosphatase in the same tissue.The findings showed presence of all the four lysosomal enzymes assayed in the callus; during early callus formation the enzyme activities calculated on a DNA basis increased up to about 12 days after the fracture. The enzyme activities appeared to be roughly reflected histochemically by the acid phosphatase staining. The increasing activity during early callus formation seemed to depend on the presence of numerous macrophage-like cells in the tissue containing many large lysosomes. A decrease in enzyme activity was found after day 12. Comparison with the histochemical and ultrastructural findings suggested that this decrease was due to a reduction in the number of macrophage-like cells and a concomitant increase in osteogenic cells with a lower enzyme content.     

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

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

Fabrication of a biomimetic spinal cord tissue construct with heterogenous mechanical properties using intrascaffold cell assembly

In tissue engineering studies, scaffolds play a very important role in offering both physical and chemical cues for cell growth and tissue regeneration. However, in some cases, tissue regeneration requires scaffolds with high mechanical properties (e.g., bone and cartilage), while cells need a soft mechanical microenvironment. In this study, to mimic the heterogenous mechanical properties of a spinal cord tissue, a biomimetic rat tissue construct is fabricated. A collagen-coated poly(lactic-co-glycolic acid) scaffold is manufactured using thermally induced phase separation casting. Primary rat neural cells (P01 Wistar rat cortex) with soft hydrogels are later printed within the scaffold using an image-guided intrascaffold cell assembly technique. The scaffolds have unidirectional microporous structure with parallel axial macrochannels (260 ± 4 µm in diameter). Scaffolds showed mechanical properties similar to rat spine (ultimate tensile strength: 0.085 MPa, Young's modulus [stretch]: 0.31 MPa). The bioink composed of gelatin/alginate/fibrinogen is precisely printed into the macrochannels and showed mechanical properties suitable for neural cells (Young's modulus [compressive]: 3.814 kPa). Scaffold interface, cell viability, and immunostaining analyses show uniform distribution of stable, healthy, and elongated neural cells and neurites over 14 culture days in vitro. The results demonstrated that this method can serve as a valuable tool to aid manufacturing of tissue constructs requiring heterogenous mechanical properties for complex cell and/or biomolecule assembly.