Sensitivity of tissue differentiation and bone healing predictions to tissue properties

Comment on permeability conditions in finite element simulation of bone fracture healing

The most popular model of the bone healing considers the fracture callus as poroelastic medium. As such it requires an assumption of the callus' external permeability. In this work a systematic study of the influence of the permeability of the callus boundary on the simulated bone healing progress is performed. The results show, that these conditions starts to play significant role with the decrease of the callus size. Typically enforced impermeability inhibits the progress of healing during simulation. A remedy for this effect is imposing drainage conditions at the callus' boundary.

Micro-osteoperforation for enhancement of orthodontic movement: A mechanical analysis using the finite element method

BACKGROUND

Micro-osteoperforation is a minimally invasive technique aimed at accelerating tooth movement. The goal of this novel experimental study was to assess tooth movement and stress distribution produced by the force of orthodontic movement on the tooth structure, periodontal ligament, and maxillary bone structure, with and without micro-osteoperforation, using the finite element method.

MATERIALS AND METHODS

Cone-beam computed tomography was used to obtain a virtual model of the maxilla and simulate the extraction of right and left first premolars. Three micro-osteoperforations (1.5 x 5 mm) were made in the hemiarch on the distal and mesial surfaces of upper canines, according to the power tip geometry of the Propel device (Propel Orthodontics, Ossining, New York, USA). An isotropic model of the maxilla was fabricated according to the finite element method by insertion of mechanical properties of the tooth structures, with orthodontic force (1.5 N) simulation in the distal movement on the upper canine of a hemiarch.

RESULTS

Initial movement was larger when micro-osteoperforations were performed on the dental crown (24%) and on the periodontal ligament (29%). In addition, stress distribution was higher on the bone structure (31%) when micro-osteoperforations were used.

CONCLUSIONS

Micro-osteoperforations considerably increased the movement of both the dental crown and periodontal ligament, which highlights their importance in the improvement of orthodontic movement, as well as in stress distribution across the bone structure. Important stress absorption regions were identified within micro-osteoperforations.

Comparative analysis of mechanical conditions in bone union following first metatarsophalangeal joint arthrodesis with varied locking plate positions: A finite element analysis

BACKGROUND

First metatarsophalangeal joint arthrodesis is a typical medical treatment performed in cases of arthritis or joint deformity. The gold standard for this procedure is arthrodesis stabilisation with the dorsally positioned plate. However, according to the authors' previous studies, medially positioned plate provides greater bending stiffness. It is worth to compare the mechanical conditions for bone formation in the fracture callus for both placements of the locking plate.

METHODS

Two finite element models of the first metatarsophalangeal joint with the dorsally and medially positioned plate were defined in the Abaqus software to simulate differentiation of the fracture callus. A simplified load application, i.e. one single step per each day and the diffusion of the mesenchymal stem cells into the fracture region were assumed in an iterative hardening process. The changes of the mesenchymal stem cells into different phenotypes during the callus stiffening were governed by the octahedral shear strain and interstitial fluid velocity according to Prendergast mechanoregulation theory. Basing on the obtained results the progress of the cartilage and bone tissues formation and their distribution within the callus were compared between two models.

FINDINGS

The obtained results suggest that after 6 weeks of simulation the healing progress is in general comparable for both plates. However, earlier closing of external callus was observed for the medially positioned plate which had greater vertical bending stiffness. This process enables faster internal callus hardening and promotes symmetrical bridging.

Coupling biomechanical models of implants with biodegradation models: A case study for biodegradable mandibular bone fixation plates

In fracture fixation, biodegradable implant materials are an interesting alternative to conventional non-biodegradable materials as the latter often require a second implant removal surgery to avoid long-term complications. In this study, we present an in silico strategy to design/study biodegradable metal implants focusing on mandibular fracture fixation plates of WE43 (Mg alloy). The in silico strategy is composed of an orchestrated interaction between three separate computational models. The first model simulates the mass loss of the degradable implant based on the chemistry of Mg biodegradation. A second model estimates the loading on the jaw plate in the physiological environment, incorporating a phenomenological dynamic bone regeneration process. The third model characterizes the mechanical behavior of the jaw plate and the influence of material degradation on the mechanical behavior. A sensitivity analysis was performed on parameters related to choices regarding numerical implementation and parameter dependencies were implemented to guarantee robust and correct results. Different clinical scenarios were tested, related to the amount of screws used to fix the plate. The results showed a lower initial strength when more screw holes were left open, as well as a faster decrease over time in strength due to the increased area available for surface degradation. The obtained degradation results were found to be in accordance with previously reported data of in vivo studies with biodegradable plates. The combination of these three models allows for the design of patient-specific biodegradable fixation implants able to deliver the desired mechanical behavior tuned to the bone regeneration process.

Effect of customized abutment taper configuration on bone remodeling and peri-implant tissue around implant-supported single crown: A 3D nonlinear finite element study

PURPOSE

The optimal configuration of a customized implant abutment plays a crucial role in promoting bone remodeling and maintaining the peri-implant gingival contour. However, the biomechanical effects of abutment configuration on bone remodeling and peri-implant tissue remain unclear. This study aimed to evaluate the influence of abutment taper configurations on bone remodeling and peri-implant tissue.

MATERIALS AND METHODS

Five models with different abutment taper configurations (10°, 20°, 30°, 40°, and 50°) were analyzed using finite element analysis (FEA) to evaluate the biomechanical responses in peri-implant bone and the hydrostatic pressure in peri-implant tissue.

RESULTS

The results demonstrated that the rate of increase in bone density was similar in all models. On the other hand, the hydrostatic pressure in peri-implant gingiva revealed significantly different results. Model 10° showed the highest maximum and volume-averaged hydrostatic pressures (69.31 and 4.5 mmHg), whereas Model 30° demonstrated the lowest values (57.83 and 3.88 mmHg) with the lowest excessive pressure area. The area of excessive hydrostatic pressure decreased in all models as the degree of abutment taper increased from 10° to 30°. In contrast, Models 40° and 50° exhibited greater hydrostatic pressure concentration at the cervical region.

CONCLUSION

In conclusion, the abutment taper configuration had a slight effect on bone remodeling but exerted a significant effect on the peri-implant gingiva above the implant platform via hydrostatic pressure. Significant decreases in greatest and average hydrostatic pressures were observed in the peri-implant tissues of Model 30°. However, the results indicate that implant abutment tapering wider than 40° could result in a larger area of excessive hydrostatic pressure in peri-implant tissue, which could induce gingival recession.

Computational model of articular cartilage regeneration induced by scaffold implantation in vivo

Computational models allow to explain phenomena that cannot be observed through an animal model, such as the strain and stress states which can highly influence regeneration of the tissue. For this purpose, we have developed a simulation tool to determine the mechanical conditions provided by the polymeric scaffold. The computational model considered the articular cartilage, the subchondral bone, and the scaffold. All materials were modeled as poroelastic, and the cartilage had linear-elastic oriented collagen fibers. This model was able to explain the remodeling process that subchondral bone goes through, and how the scaffold allowed the conditions for cartilage regeneration. These results suggest that the use of scaffolds might lead the cartilaginous tissue growth in vivo by providing a better mechanical environment. Moreover, the developed computational model demonstrated to be useful as a tool prior experimental in vivo studies, by predicting the possible outcome of newly proposed treatments allowing to discard approaches that might not bring good results.

Application of finite element analysis to tissue differentiation and bone remodelling approaches and their use in design optimization of orthopaedic implants: A review

Post-operative bone growth and long-term bone adaptation around the orthopaedic implants are simulated using the mechanoregulation based tissue-differentiation and adaptive bone remodelling algorithms, respectively. The primary objective of these algorithms was to assess biomechanical feasibility and reliability of orthopaedic implants. This article aims to offer a comprehensive review of the developments in mathematical models of tissue-differentiation and bone adaptation and their applications in studies involving design optimization of orthopaedic implants over three decades. Despite the different mechanoregulatory models developed, existing literature confirm that none of the models can be highly regarded or completely disregarded over each other. Not much development in mathematical formulations has been observed from the current state of knowledge due to the lack of in vivo studies involving clinically relevant animal models, which further retarded the development of such models to use in translational research at a fast pace. Future investigations involving artificial intelligence (AI), soft-computing techniques and combined tissue-differentiation and bone-adaptation studies involving animal subjects for model verification are needed to formulate more sophisticated mathematical models to enhance the accuracy of pre-clinical testing of orthopaedic implants.

Biomechanical duality of fracture healing captured using virtual mechanical testing and validated in ovine bones

Bone fractures commonly repair by forming a bridging structure called callus, which begins as soft tissue and gradually ossifies to restore rigidity to the bone. Virtual mechanical testing is a promising technique for image-based assessment of structural bone healing in both preclinical and clinical settings, but its accuracy depends on the validity of the material model used to assign tissue mechanical properties. The goal of this study was to develop a constitutive model for callus that captures the heterogeneity and biomechanical duality of the callus, which contains both soft tissue and woven bone. To achieve this, a large-scale optimization analysis was performed on 2363 variations of 3D finite element models derived from computed tomography (CT) scans of 33 osteotomized sheep under normal and delayed healing conditions. A piecewise material model was identified that produced high absolute agreement between virtual and physical tests by differentiating between soft and hard callus based on radiodensity. The results showed that the structural integrity of a healing long bone is conferred by an internal architecture of mineralized hard callus that is supported by interstitial soft tissue. These findings suggest that with appropriate material modeling, virtual mechanical testing is a reliable surrogate for physical biomechanical testing.

The effect of the degradation pattern of biodegradable bone plates on the healing process using a biphasic mechano-regulation theory

Bone plates are used to treat bone fractures by stabilizing the fracture site and allowing treatments to take place. Mechanical properties of the applied bone plate determine the stability of the fracture site and affect the endochondral ossification process and the healing performance. In recent years, biodegradable bone plates have been used in demand for the elimination of a second surgery to remove the plate. The degradation of these plates into the body environment is commonly accompanied by alterations in the mechanical properties of the bone plate and a shift in the healing performance of the bone. In the present study, the effects of using biodegradable plates with various elastic moduli and degradation patterns, including linear and nonlinear, on the healing process are investigated. A three-dimensional finite element model of the radius bone along with a mechano-regulation theory was used to study the healing performance. Two mechanical stimuli of octahedral shear strain and interstitial fluid flow are considered as the propelling factors of healing. The results of this study indicated that increasing the bone plate's initial elastic modulus accelerates the healing process. However, by increasing the initial Young's modulus of the plate more than 100 GPa, no noticeable alteration is observed. The degradation time period of the plate was seen to be directly related to the speed of the healing process. It is shown, however, that by increasing the degradation time period to more than 8 weeks, the healing performance remains almost unchanged. The results of this work showed that the application of plates with a high enough initial elastic modulus and degradation period can prevent the healing process from decelerating.

PREDICTION OF THE TREND OF BONE FRACTURE HEALING BASED ON THE RESULTS OF THE EARLY STAGES SIMULATIONS: A FINITE ELEMENT STUDY

To date, several studies have implied the importance of early stage mechanical stability in the bone fracture healing process. This study aimed at finding a correlation between the predicted different tissue phenotypes in the early stages of healing and the ultimate healing outcome. For this purpose, the process of fracture healing was numerically simulated employing an axisymmetric bi-phasic finite element (FE) model for three initial gap sizes of 1, 3 and 6[Formula: see text]mm and four initial interfragmentary strains (IFS) of 7%, 11%, 15% and 19%. The model was validated with experimental and other numerical studies from the literature. Results of this study showed that the amount of cartilage and fibrous tissue observed in the early stage after fracture can be used to qualitatively assess the outcome of complete bone healing process. Greater amount of cartilage in early stage of healing process yielded faster callus maturation, and delayed maturation of callus was predicted in the case of high fibrous tissue production. Results of this study can be used to provide an estimation of the performance of different fixation systems by considering the amounts of cartilage and fibrous tissues observed in the early stage of healing.

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.

Understanding how reduced loading affects Achilles tendon mechanical properties using a fibre-reinforced poro-visco-hyper-elastic model

Understanding tendon mechanobiology is important for gaining insight into the development of tendon pathology and subsequent repair processes. The aim of this study was to investigate how experimentally observed mechanobiological adaptation of rat Achilles tendons translate to changes in constitutive mechanical properties and biomechanical behavior. In addition, we assessed the ability of the model to simulate tendon creep and stress-relaxation. A three dimensional finite element framework of rat Achilles tendon was implemented with a fibre-reinforced poro-visco-hyper-elastic constitutive model. Stress-relaxation and creep data from Achilles tendons of Sprague Dawley rats that had been subjected to both daily loading and a period of reduced loading were used to determine the constitutive properties of the tendons. Our results showed that the constitutive model captures creep and stress-relaxation data from rat Achilles tendons for both loaded and unloaded tendons with good accuracy (normalized root mean square error between model and experimental data were 0.010-0.027). Only when the model parameters were fitted to data from both mechanical tests simultaneously, were we able to also capture similar increase in elastic energy (increased stiffness) and decreased viscoelasticity in response to unloading, as was reported experimentally. Our study is the first to show that experimentally observed mechanobiological changes in tendon biomechanics, such as stiffness and viscoelasticity, can be designated to mechanical quantities in a constitutive model. Further investigation in this direction has potential to discriminate tissue components responsible for specific biomechanical response, and enable targeted treatment strategies for tendon health.

Influence of experimental conditions on visco-hyperelastic properties of skeletal muscle tissue using a Box-Behnken design

The Mechanical characterization of skeletal muscles is strongly dependent on numerous experimental design factors. Nevertheless, significant knowledge gaps remain on the characterization of muscle mechanics and a large number of experiments should be implemented to test the influence of a large number of factors. In this study, we propose a design of experiment method (DOE) to study the parameter sensitivity while minimizing the number of tests. A Box-Behnken design was then implemented to study the influence of strain rate, preconditioning and preloading conditions on visco-hyperelastic mechanical parameters of two rat forearm muscles. The results show that the strain rate affects the visco-hyperelastic parameters for both muscles. These results are consistent with previous work demonstrating that stiffness and viscoelastic contributions increase with strain rate. Thus, DOE has been shown to be a valid method to determine the effect of the experimental conditions on the mechanical behaviour of biological tissues such as skeletal muscle. This method considerably reduces the number of experiments. Indeed, the presented study using 3 parameters at 3 levels would have required at least 54 tests per muscle against 14 for the proposed DOE method.

Biophysical regulation of osteotomy healing: An animal study

BACKGROUND

Osteotomies have been performed for centuries yet there remains a remarkable lack of consensus on optimal methods for cutting bone. There is universal agreement, however, that preserving cell viability is critical.

PURPOSE

To identify mechanobiological parameters influencing bone formation after osteotomy site preparation.

MATERIALS AND METHODS

A murine maxillary osteotomy model was used to evaluate healing. Computational modeling characterized stress and strain distributions in the osteotomy, as well as the magnitude and distribution of heat generated by drilling. The impact of osteocyte death and bone composition were assessed using molecular and cellular assays.

RESULTS

The phases of osteotomy healing in mice align closely with results in large animals; in addition, molecular analyses extended our understanding of osteoprogenitor cell proliferation, differentiation, and mineralization. Computational analyses provided insights into temperature changes caused by drilling and the mechanobiological state in the healing osteotomies, while concomitant cellular assays correlate drill speed with osteocyte apoptosis and bone resorption. Even when drilling was controlled, trabeculated, spongy (Type III) bone healed faster than densely lamellar (Type I) bone because of the abundance of Wnt responsive osteoprogenitor cells in the former.

CONCLUSIONS

These data provide a mechanobiological framework for evaluating tools and technologies designed to improve osteotomy site preparation.

Bone fracture healing in mechanobiological modeling: A review of principles and methods

Bone fracture is a very common body injury. The healing process is physiologically complex, involving both biological and mechanical aspects. Following a fracture, cell migration, cell/tissue differentiation, tissue synthesis, and cytokine and growth factor release occur, regulated by the mechanical environment. Over the past decade, bone healing simulation and modeling has been employed to understand its details and mechanisms, to investigate specific clinical questions, and to design healing strategies. The goal of this effort is to review the history and the most recent work in bone healing simulations with an emphasis on both biological and mechanical properties. Therefore, we provide a brief review of the biology of bone fracture repair, followed by an outline of the key growth factors and mechanical factors influencing it. We then compare different methodologies of bone healing simulation, including conceptual modeling (qualitative modeling of bone healing to understand the general mechanisms), biological modeling (considering only the biological factors and processes), and mechanobiological modeling (considering both biological aspects and mechanical environment). Finally we evaluate different components and clinical applications of bone healing simulation such as mechanical stimuli, phases of bone healing, and angiogenesis.

Micromotion-induced peri-prosthetic fluid flow around a cementless femoral stem

Micromotion-induced interstitial fluid flow at the bone-implant interface has been proposed to play an important role in aseptic loosening of cementless implants. High fluid velocities are thought to promote aseptic loosening through activation of osteoclasts, shear stress induced control of mesenchymal stem cells differentiation, or transport of molecules. In this study, our objectives were to characterize and quantify micromotion-induced fluid flow around a cementless femoral stem using finite element modeling. With a 2D model of the bone-implant interface and full-factorial design, we first evaluated the relative influence of material properties, and bone-implant micromotion and gap on fluid velocity. Transverse sections around a femoral stem were built from computed tomography images, while boundary conditions were obtained from experimental measurements on the same femur. In a second step, a 3D model was built from the same data-set to estimate the shear stress experienced by cells hosted in the peri-implant tissues. The full-factorial design analysis showed that local micromotion had the most influence on peak fluid velocity at the interface. Remarkable variations in fluid velocity were observed in the macrostructures at the surface of the implant in the 2D transverse sections of the stem. The 3D model predicted peak fluid velocities extending up to 2.2 mm/s in the granulation tissue and to 3.9 mm/s in the trabecular bone. Peak shear stresses on the cells hosted in these tissues ranged from 0.1 to 12.5 Pa. These results offer insight into mechanical stimuli encountered at the bone-implant interface.

Influence of Implant Surface Texture Design on Peri-Acetabular Bone Ingrowth: A Mechanobiology Based Finite Element Analysis

The fixation of uncemented acetabular components largely depends on the amount of bone ingrowth, which is influenced by the design of the implant surface texture. The objective of this numerical study is to evaluate the effect of these implant texture design factors on bone ingrowth around an acetabular component. The novelty of this study lies in comparative finite element (FE) analysis of 3D microscale models of the implant-bone interface, considering patient-specific mechanical environment, host bone material property and implant-bone relative displacement, in combination with sequential mechanoregulatory algorithm and design of experiment (DOE) based statistical framework. Results indicated that the bone ingrowth process was inhibited due to an increase in interbead spacing from 200 μm to 600 μm and bead diameter from 1000 μm to 1500 μm and a reduction in bead height from 900 μm to 600 μm. Bead height, a main effect, was found to have a predominant influence on bone ingrowth. Among the interaction effects, the combination of bead height and bead diameter was found to have a pronounced influence on bone ingrowth process. A combination of low interbead spacing (P = 200 μm), low bead diameter (D = 1000 μm), and high bead height (H = 900 μm) facilitated peri-acetabular bone ingrowth and an increase in average Young's modulus of newly formed tissue layer. Hence, such a surface texture design seemed to provide improved fixation of the acetabular component.

A Computational Efficient Method to Assess the Sensitivity of Finite-Element Models: An Illustration With the Hemipelvis

Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.

Mechanical microenvironments and protein expression associated with formation of different skeletal tissues during bone healing

Uncovering the mechanisms of the sensitivity of bone healing to mechanical factors is critical for understanding the basic biology and mechanobiology of the skeleton, as well as for enhancing clinical treatment of bone injuries. This study refined an experimental method of measuring the strain microenvironment at the site of a bone injury during bone healing. This method used a rat model in which a well-controlled bending motion was applied to an osteotomy to induce the formation of pseudarthrosis that is composed of a range of skeletal tissues, including woven bone, cartilage, fibrocartilage, fibrous tissue, and clot tissue. The goal of this study was to identify both the features of the strain microenvironment associated with formation of these different tissues and the expression of proteins frequently implicated in sensing and transducing mechanical cues. By pairing the strain measurements with histological analyses that identified the regions in which each tissue type formed, we found that formation of the different tissue types occurs in distinct strain microenvironments and that the type of tissue formed is correlated most strongly to the local magnitudes of extensional and shear strains. Weaker correlations were found for dilatation. Immunohistochemical analyses of focal adhesion kinase and rho family proteins RhoA and CDC42 revealed differences within the cartilaginous tissues in the calluses from the pseudarthrosis model as compared to fracture calluses undergoing normal endochondral bone repair. These findings suggest the involvement of these proteins in the way by which mechanical stimuli modulate the process of cartilage formation during bone healing.

In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2

The healing of bone defects is a challenge for both tissue engineering and modern orthopaedics. This problem has been addressed through the study of scaffold constructs combined with mechanoregulatory theories, disregarding the influence of chemical factors and their respective delivery devices. Of the chemical factors involved in the bone healing process, bone morphogenetic protein-2 (BMP-2) has been identified as one of the most powerful osteoinductive proteins. The aim of this work is to develop and validate a mechano-chemical regulatory model to study the effect of BMP-2 on the healing of large bone defects in silico. We first collected a range of quantitative experimental data from the literature concerning the effects of BMP-2 on cellular activity, specifically proliferation, migration, differentiation, maturation and extracellular matrix production. These data were then used to define a model governed by mechano-chemical stimuli to simulate the healing of large bone defects under the following conditions: natural healing, an empty hydrogel implanted in the defect and a hydrogel soaked with BMP-2 implanted in the defect. For the latter condition, successful defect healing was predicted, in agreement with previous in vivo experiments. Further in vivo comparisons showed the potential of the model, which accurately predicted bone tissue formation during healing, bone tissue distribution across the defect and the quantity of bone inside the defect. The proposed mechano-chemical model also estimated the effect of BMP-2 on cells and the evolution of healing in large bone defects. This novel in silico tool provides valuable insight for bone tissue regeneration strategies.

Strain energy density gradients in bone marrow predict osteoblast and osteoclast activity: a finite element study

Huiskes et al. hypothesized that mechanical strains sensed by osteocytes residing in trabecular bone dictate the magnitude of load-induced bone formation. More recently, the mechanical environment in bone marrow has also been implicated in bone׳s response to mechanical stimulation. In this study, we hypothesize that trabecular load-induced bone formation can be predicted by mechanical signals derived from an integrative µFE model, incorporating a description of both the bone and marrow phase. Using the mouse tail loading model in combination with in vivo micro-computed tomography (µCT) we tracked load induced changes in the sixth caudal vertebrae of C57BL/6 mice to quantify the amount of newly mineralized and eroded bone volumes. To identify the mechanical signals responsible for adaptation, local morphometric changes were compared to micro-finite element (µFE) models of vertebrae prior to loading. The mechanical parameters calculated were strain energy density (SED) on trabeculae at bone forming and resorbing surfaces, SED in the marrow at the boundary between bone forming and resorbing surfaces, along with SED in the trabecular bone and marrow volumes. The gradients of each parameter were also calculated. Simple regression analysis showed mean SED gradients in the trabecular bone matrix to significantly correlate with newly mineralized and eroded bone volumes R(2)=0.57 and 0.41, respectively, p<0.001). Nevertheless, SED gradients in the marrow were shown to be the best predictor of osteoblastic and osteoclastic activity (R(2)=0.83 and 0.60, respectively, p<0.001). These data suggest that the mechanical environment of the bone marrow plays a significant role in determining osteoblast and osteoclast activity.

Physical and biological characterization of ferromagnetic fiber networks: effect of fibrin deposition on short-term in vitro responses of human osteoblasts

Ferromagnetic fiber networks have the potential to deform in vivo imparting therapeutic levels of strain on in-growing periprosthetic bone tissue. 444 Ferritic stainless steel provides a suitable material for this application due to its ability to support cultures of human osteoblasts (HObs) without eliciting undue inflammatory responses from monocytes in vitro. In the present article, a 444 fiber network, containing 17 vol% fibers, has been investigated. The network architecture was obtained by applying a skeletonization algorithm to three-dimensional tomographic reconstructions of the fiber networks. Elastic properties were measured using low-frequency vibration testing, providing globally averaged properties as opposed to mechanical methods that yield only local properties. The optimal region for transduction of strain to cells lies between the ferromagnetic fibers. However, cell attachment, at early time points, occurs primarily on fiber surfaces. Deposition of fibrin, a fibrous protein involved in acute inflammatory responses, can facilitate cell attachment within this optimal region at early time points. The current work compared physiological (3 and 5 g·L(-1)) and supraphysiological fibrinogen concentrations (10 g·L(-1)), using static in vitro seeding of HObs, to determine the effect of fibrin deposition on cell responses during the first week of cell culture. Early cell attachment within the interfiber spaces was observed in all fibrin-containing samples, supported by fibrin nanofibers. Fibrin deposition influenced the seeding, metabolic activity, and early stage differentiation of HObs cultured in the fibrin-containing fiber networks in a concentration-dependant manner. While initial cell attachment for networks with fibrin deposited from low physiological concentrations was similar to control samples without fibrin deposition, significantly higher HObs attached onto high physiological and supraphysiological concentrations. Despite higher cell numbers with supraphysiological concentrations, cell metabolic activities were similar for all fibrinogen concentrations. Further, cells cultured on supraphysiological concentrations exhibited lower cell differentiation as measured by alkaline phosphatase activity at early time points. Overall, the current study suggests that physiological fibrinogen concentrations would be more suitable than supraphysiological concentrations for supporting early cell activity in porous implant coatings.

Mechanical regulation of bone regeneration: theories, models, and experiments

How mechanical forces influence the regeneration of bone remains an open question. Their effect has been demonstrated experimentally, which has allowed mathematical theories of mechanically driven tissue differentiation to be developed. Many simulations driven by these theories have been presented, however, validation of these models has remained difficult due to the number of independent parameters considered. An overview of these theories and models is presented along with a review of experimental studies and the factors they consider. Finally limitations of current experimental data and how this influences modeling are discussed and potential solutions are proposed.

Improved fracture risk assessment based on nonlinear micro-finite element simulations from HRpQCT images at the distal radius

More accurate techniques to estimate fracture risk could help reduce the burden of fractures in postmenopausal women. Although micro-finite element (µFE) simulations allow a direct assessment of bone mechanical performance, in this first clinical study we investigated whether the additional information obtained using geometrically and materially nonlinear µFE simulations allows a better discrimination between fracture cases and controls. We used patient data and high-resolution peripheral quantitative computed tomography (HRpQCT) measurements from our previous clinical study on fracture risk, which compared 100 postmenopausal women with a distal forearm fracture to 105 controls. Analyzing these data with the nonlinear µFE simulations, the odds ratio (OR) for the factor-of-risk (yield load divided by the expected fall load) was marginally higher (1.99; 95% confidence interval [CI], 1.41-2.77) than for the factor-of-risk computed from linear µFE (1.89; 95% CI, 1.37-2.69). The yield load and the energy absorbed up to the yield point as computed from nonlinear µFE were highly correlated with the initial stiffness (R(2)  = 0.97 and 0.94, respectively) and could therefore be derived from linear simulations with little loss in precision. However, yield deformation was not related to any other measurement performed and was itself a good predictor of fracture risk (OR, 1.89; 95% CI, 1.39-2.63). Moreover, a combined risk score integrating information on relative bone strength (yield load-based factor-of-risk), bone ductility (yield deformation), and the structural integrity of the bone under critical loads (cortical plastic volume) improved the separation of cases and controls by one-third (OR, 2.66; 95% CI, 1.84-4.02). We therefore conclude that nonlinear µFE simulations provide important additional information on the risk of distal forearm fractures not accessible from linear µFE nor from other techniques assessing bone microstructure, density, or mass.

Using Design of Experiments Methods for Assessing Peak Contact Pressure to Material Properties of Soft Tissue in Human Knee

Contact pressure in the knee joint is a key element in the mechanisms of knee pain and osteoarthritis. Assessing the contact pressure in tibiofemoral joint is a challenging mechanical problem due to uncertainty in material properties. In this study, a sensitivity analysis of tibiofemoral peak contact pressure to the material properties of the soft tissue was carried out through fractional factorial and Box-Behnken designs. The cartilage was modeled as linear elastic material, and in addition to its elastic modulus, interaction effects of soft tissue material properties were added compared to previous research. The results indicated that elastic modulus of the cartilage is the most effective factor. Interaction effects of axial/radial modulus with elastic modulus of cartilage, circumferential and axial/radial moduli of meniscus were other influential factors. Furthermore this study showed how design of experiment methods can help designers to reduce the number of finite element analyses and to better interpret the results.

Prediction of fracture healing under axial loading, shear loading and bending is possible using distortional and dilatational strains as determining mechanical stimuli

Numerical models of secondary fracture healing are based on mechanoregulatory algorithms that use distortional strain alone or in combination with either dilatational strain or fluid velocity as determining stimuli for tissue differentiation and development. Comparison of these algorithms has previously suggested that healing processes under torsional rotational loading can only be properly simulated by considering fluid velocity and deviatoric strain as the regulatory stimuli. We hypothesize that sufficient calibration on uncertain input parameters will enhance our existing model, which uses distortional and dilatational strains as determining stimuli, to properly simulate fracture healing under various loading conditions including also torsional rotation. Therefore, we minimized the difference between numerically simulated and experimentally measured courses of interfragmentary movements of two axial compressive cases and two shear load cases (torsional and translational) by varying several input parameter values within their predefined bounds. The calibrated model was then qualitatively evaluated on the ability to predict physiological changes of spatial and temporal tissue distributions, based on respective in vivo data. Finally, we corroborated the model on five additional axial compressive and one asymmetrical bending load case. We conclude that our model, using distortional and dilatational strains as determining stimuli, is able to simulate fracture-healing processes not only under axial compression and torsional rotation but also under translational shear and asymmetrical bending loading conditions.

A review of the combination of experimental measurements and fibril-reinforced modeling for investigation of articular cartilage and chondrocyte response to loading

The function of articular cartilage depends on its structure and composition, sensitively impaired in disease (e.g. osteoarthritis, OA). Responses of chondrocytes to tissue loading are modulated by the structure. Altered cell responses as an effect of OA may regulate cartilage mechanotransduction and cell biosynthesis. To be able to evaluate cell responses and factors affecting the onset and progression of OA, local tissue and cell stresses and strains in cartilage need to be characterized. This is extremely challenging with the presently available experimental techniques and therefore computational modeling is required. Modern models of articular cartilage are inhomogeneous and anisotropic, and they include many aspects of the real tissue structure and composition. In this paper, we provide an overview of the computational applications that have been developed for modeling the mechanics of articular cartilage at the tissue and cellular level. We concentrate on the use of fibril-reinforced models of cartilage. Furthermore, we introduce practical considerations for modeling applications, including also experimental tests that can be combined with the modeling approach. At the end, we discuss the prospects for patient-specific models when aiming to use finite element modeling analysis and evaluation of articular cartilage function, cellular responses, failure points, OA progression, and rehabilitation.

The emergence of mechanoregulated endochondral ossification in evolution

The differentiation of skeletal tissue phenotypes is partly regulated by mechanical forces. This mechanoregulatory aspect of tissue differentiation has been the subject of many experimental and computational investigations. However, little is known about what factors promoted the emergence of mechanoregulated tissue differentiation in evolution, even though mechanoregulated tissue differentiation, for example during development or healing of adult bone, is crucial for vertebrate phylogeny. In this paper, we use a computational framework to test the hypothesis that the emergence of mechanosensitive genes that trigger endochondral ossification in evolution will stabilise in the population and create a variable mechanoregulated response, if the endochondral ossification process enhances fitness for survival. The model combines an evolutionary algorithm that considers genetic change with a mechanoregulated fracture healing model in which the fitness of animals in a population is determined by their ability to heal their bones. The simulations show that, with the emergence of mechanosensitive genes through evolution enabling skeletal cells to modulate their synthetic activities, novel differentiation pathways such as endochondral ossification could have emerged, which when favoured by natural selection is maintained in a population. Furthermore, the model predicts that evolutionary forces do not lead to a single optimal mechanoregulated response but that the capacity of endochondral ossification exists with variability in a population. The simulations correspond with many existing findings about the mechanosensitivity of skeletal tissues in current animal populations, therefore indicating that this kind of multi-level models could be used in future population based simulations of tissue differentiation.

Nell-1 protein promotes bone formation in a sheep spinal fusion model

Bone morphogenetic proteins (BMPs) are widely used as bone graft substitutes in spinal fusion, but are associated with numerous adverse effects. The growth factor Nel-like molecule-1 (Nell-1) is mechanistically distinct from BMPs and can minimize complications associated with BMP therapies. This study evaluates the efficacy of Nell-1 combined with demineralized bone matrix (DBM) as a novel bone graft material for interbody spine fusion using sheep, a phylogenetically advanced animal with biomechanical similarities to human spine. Nell-1+sheep DBM or Nell-1+heat-inactivated DBM (inDBM) (to determine the osteogenic effect of residual growth factors in DBM) were implanted in surgical sites as follows: (1) DBM only (control) (n=8); (2) DBM+0.3 mg/mL Nell-1 (n=8); (3) DBM+0.6 mg/mL Nell-1 (n=8); (4) inDBM only (control) (n=4); (5) inDBM+0.3 mg/mL Nell-1 (n=4); (6) inDBM+0.6 mg/mL Nell-1 (n=4). Fusion was assessed by computed tomography, microcomputed tomography, and histology. One hundred percent fusion was achieved by 3 months in the DBM+0.6 mg/mL Nell-1 group and by 4 months in the inDBM+0.6 mg/mL Nell-1 group; bone volume and mineral density were increased by 58% and 47%, respectively. These fusion rates are comparable to published reports on BMP-2 or autograft bone efficacy in sheep. Nell-1 is an independently potent osteogenic molecule that is efficacious and easily applied when combined with DBM.

Variability observed in mechano-regulated in vivo tissue differentiation can be explained by variation in cell mechano-sensitivity

Computational simulations of tissue differentiation have been able to capture the main aspects of tissue formation/regeneration observed in animal experiments-except for the considerable degree of variability reported. Understanding and modelling the source of this variability is crucial if computational tools are to be developed for clinical applications. The objective of this study was to test the hypothesis that differences in cell mechano-sensitivity between individuals can explain the variability of tissue differentiation patterns observed experimentally. Simulations of an experiment of tissue differentiation in a mechanically loaded bone chamber were performed. Finite element analysis was used to determine the biophysical environment, and a lattice-modelling approach was used to simulate cell activity. Differences in cell mechano-sensitivity among individuals were modelled as differences in cell activity rates, with the activation of cell activities regulated by the mechanical environment. Predictions of the tissue distribution in the chambers produced the two different classes of results found experimentally: (i) chambers with a layer of bone across the chamber covered by a layer of cartilage on top and (ii) chambers with almost no bone, mainly fibrous tissue and small islands of cartilage. This indicates that the differing cellular response to the mechanical environment (i.e., subject-specific mechano-sensitivity) could be a reason for the different outcomes found when implants (or tissue engineered constructs) are used in a population.

Fabrication of a biodegradable calcium polyphosphate/polyvinyl-urethane carbonate composite for high load bearing osteosynthesis applications

The formation of biodegradable implants for use in osteosynthesis has been a major goal of biomaterials research for the past 2-3 decades. Self-reinforced polylactide systems represent the most significant success of this research to date, however, with elastic constants up to 12-15 GPa at best, they fail to provide the initial stiffness required of devices for stabilizing fractures of major load-bearing bones. Our research has investigated the use of calcium polyphosphate (CPP), an inorganic polymer in combination with polyvinyl-urethane carbonate (PVUC) organic polymers for such applications. Initial studies indicated that composite samples formed as interpenetrating phase composites (IPC) exhibited suitable as-made strength and stiffness, however, they displayed a rapid loss of properties when exposed to in vitro aging. An investigation to determine the mechanism of this accelerated in vitro degradation for the IPCs as well as to identify possible design changes to overcome this drawback was undertaken using a model IPC system. It was found that strong interfacial strength and minimal swelling of the PVUC are very important for obtaining and maintaining appropriate mechanical properties in vitro.

Computational evaluation of the compositional factors in fracture healing affecting ultrasound axial transmission measurements

This work aimed at computationally evaluating the compositional factors in fracture healing affecting ultrasound axial transmission (UAT), using four numerical daily-changing healing models, representing more realistic clinical conditions. Using two-dimensional (2-D) simulations, a 1-MHz source and a receiver were positioned parallel to the bone surface to detect the first arriving signal (FAS). The time-of-flight of the FAS (TOF(FAS)) was found to be sensitive only to superficial modifications in the propagation path. It was also shown that callus mature bone better explained alone the variation in TOF(FAS) (R(2) >or= 0.70, p < 0.001). Better TOF(FAS) predictions are obtained when using the callus composition inside cortical fracture gap (R(2) = 0.98, p < 0.01). Callus composition could not well explain the changes in energy attenuation. These results suggest that UAT may be an important clinical tool for fracture healing assessment, identifying callus degree of mineralization and possible consolidation delays and nonunions.

Influence of the fixation stability on the healing time--a numerical study of a patient-specific fracture healing process

BACKGROUND

The healing outcome of long bone fractures is strongly influenced by the interfragmentary movement of the bone fragments. This depends on the fixation stability, the optimum value of which is still not known. The aim of this study was to simulate a patient-specific human healing process using a numerical algorithm and to retrospectively analyse the influence of the fixation stability on the healing time.

METHODS

The healing simulation was processed as an initial value problem. This was iteratively solved based on two mechanical (invariants of the strain tensor, calculated through a finite element analysis) and five biological state variables (local tissue composition and blood perfusion) using a previously published fuzzy logic algorithm. For validation purposes, the calculated interfragmentary movement was compared to in vivo measurements of this patient. By changing clinically adjustable parameters of the fixation device, the influence of the fixation stability on the healing time was analysed.

FINDING

The time course showed good agreement of the interfragmentary movement compared with the in vivo measurements. The predicted healing time was strongly influenced by the fixation stability, i.e. by changing the parameters of the fixation device, it was possible to significantly reduce the healing time.

INTERPRETATION

The time to heal could be greatly reduced by modification of the fixator design, i.e. increasing the fixation stiffness. When using external fixation devices, this could be achieved by decreasing the free bending length of the pins, using a stiff fixation body and a stiff connection between the pins and the body.

In silico design of treatment strategies in wound healing and bone fracture healing

Wound and bone fracture healing are natural repair processes initiated by trauma. Over the last decade, many mathematical models have been established to investigate the healing processes in silico, in addition to ongoing experimental work. In recent days, the focus of the mathematical models has shifted from simulation of the healing process towards simulation of the impaired healing process and the in silico design of treatment strategies. This review describes the most important causes of failure of the wound and bone fracture healing processes and the experimental models and methods used to investigate and treat these impaired healing cases. Furthermore, the mathematical models that are described address these impaired healing cases and investigate various therapeutic scenarios in silico. Examples are provided to illustrate the potential of these in silico experiments. Finally, limitations of the models and the need for and ability of these models to capture patient specificity and variability are discussed.

Cytoskeleton reorganization of spreading cells on micro-patterned islands: a functional model

Predictive numerical models of cellular response to biophysical cues have emerged as a useful quantitative tool for cell biology research. Cellular experiments in silico can augment in vitro and in vivo investigations by filling gaps in what is possible to achieve through 'wet work'. Biophysics-based numerical models can be used to verify the plausibility of mechanisms regulating tissue homeostasis derived from experiments. They can also be used to explore potential targets for therapeutic intervention. In this perspective article we introduce a single cell model developed towards the design of novel biomaterials to elicit a regenerative cellular response for the repair of diseased tissues. The model is governed by basic mechanisms of cell spreading (lamellipodial and filopodial extension, formation of cell-matrix adhesions, actin reinforcement) and is developed in the context of cellular interaction with functionalized substrates that present defined points of potential adhesion. To provide adequate context, we first review the biophysical underpinnings of the model as well as reviewing existing cell spreading models. We then present preliminary benchmarking of the model against published experiments of cell spreading on micro-patterned substrates. Initial results indicate that our mechanistic model may represent a potentially useful approach in a better understanding of cell interactions with the extracellular matrix.

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.