Tissue differentiation and bone regeneration in an osteotomized mandible: a computational analysis of the latency period

Mechanoresponsive regulation of tissue regeneration during distraction osteogenesis

Distraction osteogenesis is widely used for bone tissue engineering. Mechanical stimulation plays a central role in the massive tissue regeneration observed during distraction osteogenesis. Although distraction osteogenesis has been a boon for patients with bone defects, we still have limited knowledge about the intrinsic mechanotransduction that converts physical forces into biochemical signals capable of inducing cell behavior changes and new tissue formation. In this review, we summarize the findings for mechanoresponsive factors, including cells, genes, and signaling pathways, during the distraction osteogenesis different phases. These elements function for coupling of osteogenesis and angiogenesis via the Integrin-FAK, TGF-β/BMP, Wnt/β-catenin, Hippo, MAPK, PI3K/Akt, and HIF-1α signaling pathways in a mechanoresponsive niche. The available evidence further suggests the existence of a balance between the epithelial-mesenchymal transition and mesenchymal-epithelial transition under hypoxic stress. We also briefly summarize the current in silico simulation algorithms and propose several future research directions that may advance understanding of distraction osteogenesis in the era of bioinformation, particularly the integration of artificial intelligence models with reliable single-cell RNA sequencing datasets. The objective of this review is to utilize established knowledge to further optimize existing distraction protocols and to identify potential therapeutic targets.

Influence of bite force and implant elastic modulus on mandibular reconstruction with particulate-cancellous bone marrow grafts healing: An in silico investigation

This study aims to investigate tissue differentiation during mandibular reconstruction with particulate cancellous bone marrow (PCBM) graft healing using biphasic mechanoregulation theory under four bite force magnitudes and four implant elastic moduli to examine its implications on healing rate, implant stress distribution, new bone elastic modulus, mandible equivalent stiffness, and load-sharing progression. The finite element model of a half Canis lupus mandible, symmetrical about the midsagittal plane, with two marginal defects filled by PCBM graft and stabilized by porous implants, was simulated for 12 weeks. Eight different scenarios, which consist of four bite force magnitudes and four implant elastic moduli, were tested. It was found that the tissue differentiation pattern corroborates the experimental findings, where the new bone propagates from the superior side and the buccal and lingual sides in contact with the native bone, starting from the outer regions and progressing inward. Faster healing and quicker development of bone graft elastic modulus and mandible equivalent stiffness were observed in the variants with lower bite force magnitude and or larger implant elastic modulus. A load-sharing condition was found as the healing progressed, with M3 (Ti6Al4V) being better than M4 (stainless steel), indicating the higher stress shielding potentials of M4 in the long term. This study has implications for a better understanding of mandibular reconstruction mechanobiology and demonstrated a novel in silico framework that can be used for post-operative planning, failure prevention, and implant design in a better way.

A mechano-regulation model to design and optimize the surface microgeometry of titanium textured devices for biomedical applications

In a technological context where, thanks to the additive manufacturing techniques, even sophisticated geometries as well as surfaces with specific micrometric features can be realized, we propose a mechano-regulation algorithm to determine the optimal microgeometric parameters of the surface of textured titanium devices for biomedical applications. A poroelastic finite element model was developed including a portion of bone, a portion of a textured titanium device and a layer of granulation tissue separating the bone from the device and occupying the space between them. The algorithm, implemented in the Matlab environment, determines the optimal values of the root mean square and the correlation length that the device surface must possess to maximize bone formation in the gap between the bone and the device. For low levels of compression load acting on the bone, the algorithm predicts low values of root mean square and high values of correlation length. Conversely, high levels of load require high values of root mean square and low values of correlation length. The optimal microgeometrical parameters were determined for various thickness values of the granulation tissue layer. Interestingly, the predictions of the proposed computational model are consistent with the experimental results reported in the literature. The proposed algorithm shows promise as a valuable tool for addressing the demands of precision medicine. In this approach, the device or prosthesis is no longer designed solely based on statistical averages but is tailored to each patient's unique anthropometric characteristics, as well as considerations related to their metabolism, sex, age, and more.

Computational models of bone fracture healing and applications: a review

Fracture healing is a very complex physiological process involving multiple events at different temporal and spatial scales, such as cell migration and tissue differentiation, in which mechanical stimuli and biochemical factors assume key roles. With the continuous improvement of computer technology in recent years, computer models have provided excellent solutions for studying the complex process of bone healing. These models not only provide profound insights into the mechanisms of fracture healing, but also have important implications for clinical treatment strategies. In this review, we first provide an overview of research in the field of computational models of fracture healing based on CiteSpace software, followed by a summary of recent advances, and a discussion of the limitations of these models and future directions for improvement. Finally, we provide a systematic summary of the application of computational models of fracture healing in three areas: bone tissue engineering, fixator optimization and clinical treatment strategies. The application of computational models of bone healing in clinical treatment is immature, but an inevitable trend, and as these models become more refined, their role in guiding clinical treatment will become more prominent.

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.

In silico modelling of long bone healing involving osteoconduction and mechanical stimulation

A lot of evidence has shown the importance of stimulating cell mechanically during bone repair. In this study, we modeled the challenging fracture healing of a large bone defect in tibial diaphysis. To fill the fracture gap, we considered the implantation of a porous osteoconductive biomaterial made of poly-lactic acid wrapped by a hydrogel membrane mimicking osteogenic properties of the periosteum. We identified the optimal loading case that best promotes the formation and differentiation into bone tissue. Our results support the idea that a patient's rehabilitation program should be adapted to reproduce optimal mechanical stimulations.

Time-dependent in silico modelling of orthognathic surgery to support the design of biodegradable bone plates

Orthognathic surgery is performed to realign the jaws of a patient through several osteotomies. The state-of-the-art bone plates used to maintain the bone fragments in place are made of titanium. The presence of these non-degradable plates can have unwanted side effects on the long term (e.g. higher infection risk) if they are not removed. Using a biodegradable material such as magnesium may be a possible solution to this problem. However, biodegradation leads to a decrease of mechanical strength, therefore a time-dependent computational approach can help to evaluate the performance of such plates. In the present work, a computational framework has been developed to include biodegradation and bone healing algorithms in a finite element model. It includes bone plates and the mandible, which are submitted to masticatory loads during the early healing period (two months following the surgery). Two different bone plate designs with different stiffnesses have been tested. The stiff design exhibited good mechanical stability, with maximum Von Mises stress being less than 40% of the yield strength throughout the simulation. The flexible design shows high stresses when the bone healing has not started in the fracture gaps, indicating possible failure of the plate. However, this design leads to a higher bone healing quality after two months, as more cartilage is formed due to higher strains exerted in fracture gaps. We therefore conclude that in silico modelling can support tuning of the design parameters to ensure mechanical stability and while promoting bone healing.

Elastic Modulus of Woven Bone: Correlation with Evolution of Porosity and X-ray Greyscale

The woven bone created during the healing of bone regeneration processes is characterized as being extremely inhomogeneous and having a variable stiffness that increases with time. Therefore, it is important to study how the mechanical properties of woven bone are dependent on its microarchitecture and especially on its porosity and mineral content. The porosity and the x-ray greyscale of specimens taken from bone transport studies in sheep were assessed by means of ex vivo imaging. Our study demonstrates that the porosity of the woven bone in the distraction area diminishes during the healing process from 73.3% 35 days after surgery to 31.9% 525 days after surgery. In addition, the woven bone's porosity is negatively correlated with its Young's modulus. The x-ray greyscale, was measured as an indicator of the level of mineralization of the woven bone. Greyscale index has been demonstrated to be inversely proportional to porosity and to increase to up to 60-80% of the level in cortical bone. The results of this study may contribute to the development of micromechanical models of woven bone and improvements in in silico modelling.

Three-dimensional evaluation of mandibular midline distraction: A systematic review

OBJECTIVE

To provide a literature overview on mandibular midline distraction (MMD) using three-dimensional (3D) imaging analysis techniques. Regarding different distractor types, the focus was on changes in position and/or morphology of the mandibular condyle and temporomandibular joint (TMJ), skeletal effects, dental effects, soft tissue effects, and biomechanical and masticatory effects, specifically on the mandible and TMJ.

METHODS

Studies up to March 27 2017 were included, in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement guidelines, using Embase, Medline OvidSP, Web-of-science, Scopus, Cochrane, and Google Scholar.

RESULTS

Thirty-one full-text papers were assessed for eligibility and 15 met the inclusion criteria: prospective (2), retrospective (2), case-report (1) and computational analysis (10). All included studies were graded low (level 4-5) for quality of evidence, using the Oxford Centre for Evidence-Based Medicine criteria.

CONCLUSION

There is a limited number of studies available, with low levels of evidence and small sample sizes. Bone-borne distraction seems preferable when taking skeletal effects into account. Tooth-borne distraction leads to significant dental tipping. Hybrid distractors combined with parasymphyseal step osteotomy seem to be the most stable under functional masticatory loads. The effects of chewing appeared to be marginal during the latency period. No permanent TMJ symptoms were reported, and little is known about soft tissue effects.

SYSTEMATIC REVIEW REGISTRATION

International Prospective Register of Systematic Reviews, PROSPERO CRD42014010010.

Geometry Design Optimization of Functionally Graded Scaffolds for Bone Tissue Engineering: A Mechanobiological Approach

Functionally Graded Scaffolds (FGSs) are porous biomaterials where porosity changes in space with a specific gradient. In spite of their wide use in bone tissue engineering, possible models that relate the scaffold gradient to the mechanical and biological requirements for the regeneration of the bony tissue are currently missing. In this study we attempt to bridge the gap by developing a mechanobiology-based optimization algorithm aimed to determine the optimal graded porosity distribution in FGSs. The algorithm combines the parametric finite element model of a FGS, a computational mechano-regulation model and a numerical optimization routine. For assigned boundary and loading conditions, the algorithm builds iteratively different scaffold geometry configurations with different porosity distributions until the best microstructure geometry is reached, i.e. the geometry that allows the amount of bone formation to be maximized. We tested different porosity distribution laws, loading conditions and scaffold Young’s modulus values. For each combination of these variables, the explicit equation of the porosity distribution law–i.e the law that describes the pore dimensions in function of the spatial coordinates–was determined that allows the highest amounts of bone to be generated. The results show that the loading conditions affect significantly the optimal porosity distribution. For a pure compression loading, it was found that the pore dimensions are almost constant throughout the entire scaffold and using a FGS allows the formation of amounts of bone slightly larger than those obtainable with a homogeneous porosity scaffold. For a pure shear loading, instead, FGSs allow to significantly increase the bone formation compared to a homogeneous porosity scaffolds. Although experimental data is still necessary to properly relate the mechanical/biological environment to the scaffold microstructure, this model represents an important step towards optimizing geometry of functionally graded scaffolds based on mechanobiological criteria.

A Mechanobiology-based Algorithm to Optimize the Microstructure Geometry of Bone Tissue Scaffolds

Complexity of scaffold geometries and biological mechanisms involved in the bone generation process make the design of scaffolds a quite challenging task. The most common approaches utilized in bone tissue engineering require costly protocols and time-consuming experiments. In this study we present an algorithm that, combining parametric finite element models of scaffolds with numerical optimization methods and a computational mechano-regulation model, is able to predict the optimal scaffold microstructure. The scaffold geometrical parameters are perturbed until the best geometry that allows the largest amounts of bone to be generated, is reached. We study the effects of the following factors: (1) the shape of the pores; (2) their spatial distribution; (3) the number of pores per unit area. The optimal dimensions of the pores have been determined for different values of scaffold Young's modulus and compression loading acting on the scaffold upper surface. Pores with rectangular section were predicted to lead to the formation of larger amounts of bone compared to square section pores; similarly, elliptic pores were predicted to allow the generation of greater amounts of bone compared to circular pores. The number of pores per unit area appears to have rather negligible effects on the bone regeneration process. Finally, the algorithm predicts that for increasing loads, increasing values of the scaffold Young's modulus are preferable. The results shown in the article represent a proof-of-principle demonstration of the possibility to optimize the scaffold microstructure geometry based on mechanobiological criteria.

The remodeling of alveolar bone supporting the mandibular first molar with different levels of periodontal attachment

The objective of this study was to investigate alveolar bone remodeling of the mandibular first molar with differing levels of periodontal attachment under mastication loading. Three-dimensional finite element models of the mandibular first molar with differing levels of periodontal attachment were established. The stress distributions and bone density changes were analyzed under mastication loading to simulate the remodeling process of mandibular bone based on the theory of strain energy density. The results showed that the alveolar buccal, lingual ridges and root apex areas experienced higher stresses. The stresses and densities of the alveolar bone increased proportionally to increased mastication loading. Decrease in alveolar bone density under extreme loading indicated bone resorption. The remodeling rate was continual with gradual loading. Periodontal ligament support marginally decreased with an increased remodeling rate under extreme loading. Changes in alveolar bone density can reflect the remodeling process of periodontal tissue under mastication loading. The relationship between the change in density and mastication loading during remodeling can provide useful indicators into clinical treatment and diagnosis of the periodontal disease.

Role of mathematical modeling in bone fracture healing

Bone fracture healing is a complex physiological process commonly described by a four-phase model consisting of an inflammatory phase, two repair phases with soft callus formation followed by hard callus formation, and a remodeling phase, or more recently by an anabolic/catabolic model. Data from humans and animal models have demonstrated crucial environmental conditions for optimal fracture healing, including the mechanical environment, blood supply and availability of mesenchymal stem cells. Fracture healing spans multiple length and time scales, making it difficult to know precisely which factors and/or phases to manipulate in order to obtain optimal fracture-repair outcomes. Deformations resulting from physiological loading or fracture fixation at the organ scale are sensed at the cellular scale by cells inside the fracture callus. These deformations together with autocrine and paracrine signals determine cellular differentiation, proliferation and migration. The local repair activities lead to new bone formation and stabilization of the fracture. Although experimental data are available at different spatial and temporal scales, it is not clear how these data can be linked to provide a holistic view of fracture healing. Mathematical modeling is a powerful tool to quantify conceptual models and to establish the missing links between experimental data obtained at different scales. The objective of this review is to introduce mathematical modeling to readers who are not familiar with this methodology and to demonstrate that once validated, such models can be used for hypothesis testing and to assist in clinical treatment as will be shown for the example of atrophic nonunions.

Substrate stiffness and oxygen as regulators of stem cell differentiation during skeletal tissue regeneration: a mechanobiological model

Extrinsic mechanical signals have been implicated as key regulators of mesenchymal stem cell (MSC) differentiation. It has been possible to test different hypotheses for mechano-regulated MSC differentiation by attempting to simulate regenerative events such as bone fracture repair, where repeatable spatial and temporal patterns of tissue differentiation occur. More recently, in vitro studies have identified other environmental cues such as substrate stiffness and oxygen tension as key regulators of MSC differentiation; however it remains unclear if and how such cues determine stem cell fate in vivo. As part of this study, a computational model was developed to test the hypothesis that substrate stiffness and oxygen tension regulate stem cell differentiation during fracture healing. Rather than assuming mechanical signals act directly on stem cells to determine their differentiation pathway, it is postulated that they act indirectly to regulate angiogenesis and hence partially determine the local oxygen environment within a regenerating tissue. Chondrogenesis of MSCs was hypothesized to occur in low oxygen regions, while in well vascularised regions of the regenerating tissue a soft local substrate was hypothesised to facilitate adipogenesis while a stiff substrate facilitated osteogenesis. Predictions from the model were compared to both experimental data and to predictions of a well established computational mechanobiological model where tissue differentiation is assumed to be regulated directly by the local mechanical environment. The model predicted all the major events of fracture repair, including cartilaginous bridging, endosteal and periosteal bony bridging and bone remodelling. It therefore provides support for the hypothesis that substrate stiffness and oxygen play a key role in regulating MSC fate during regenerative events such as fracture healing.

EFFECTS OF AGING ON THE LATENCY PERIOD IN MANDIBULAR DISTRACTION OSTEOGENESIS: A COMPUTATIONAL MECHANOBIOLOGICAL ANALYSIS

Mandibular symphyseal distraction osteogenesis is a clinical procedure utilized in orthodontics for solving problems of dental overcrowding on the mandibular arch. A critical issue is to evaluate the optimal duration of the latency period between the osteotomy and the first aperture of distraction device. In fact, the latency period should change with the patient's age. To this end, a computational mechanobiological model has been developed in order to find optimal durations of latency period for young, adult, and elder patients. The model is implemented in a finite element framework simulating the process of tissue differentiation in the bone callus formed after osteotomy. The biophysical stimulus regulating the tissue differentiation process is hypothesized to be a function of the octahedral shear strain and interstitial fluid flow velocity. The resulting spatial distribution of stiffness properties in the callus region is analyzed in order to assess the risk of premature bone union of osteotomy edges. The three-dimensional (3D) finite element model (FEM) of human mandible is reconstructed from computed tomography (CT) scans and also includes a tooth-borne device. Under unilateral occlusion, the mandible is submitted to full mastication loading or to mastication forces reduced by 70%. The results show that optimal durations of the latency period for preventing premature bone union are about 5–6 days for the young patient, 7–8 days for the adult patient, and 9–10 days for the elder patient. These durations seem rather insensitive to the magnitude of mastication forces. Finally, distraction force values predicted by the present mechanobiological model are in good agreement with data reported in the literature.

Influence of high-frequency cyclical stimulation on the bone fracture-healing process: mathematical and experimental models

Mechanical stimulation affects the evolution of healthy and fractured bone. However, the effect of applying cyclical mechanical stimuli on bone healing has not yet been fully clarified. The aim of the present study was to determine the influence of a high-frequency and low-magnitude cyclical displacement of the fractured fragments on the bone-healing process. This subject is studied experimentally and computationally for a sheep long bone. On the one hand, the mathematical computational study indicates that mechanical stimulation at high frequencies can stimulate and accelerate the process of chondrogenesis and endochondral ossification and consequently the bony union of the fracture. This is probably achieved by the interstitial fluid flow, which can move nutrients and waste from one place to another in the callus. This movement of fluid modifies the mechanical stimulus on the cells attached to the extracellular matrix. On the other hand, the experimental study was carried out using two sheep groups. In the first group, static fixators were implanted, while, in the second one, identical devices were used, but with an additional vibrator. This vibrator allowed a cyclic displacement with low magnitude and high frequency (LMHF) to be applied to the fractured zone every day; the frequency of stimulation was chosen from mechano-biological model predictions. Analysing the results obtained for the control and stimulated groups, we observed improvements in the bone-healing process in the stimulated group. Therefore, in this study, we show the potential of computer mechano-biological models to guide and define better mechanical conditions for experiments in order to improve bone fracture healing. In fact, both experimental and computational studies indicated improvements in the healing process in the LMHF mechanically stimulated fractures. In both studies, these improvements could be associated with the promotion of endochondral ossification and an increase in the rate of cell proliferation and tissue synthesis.

Simulation of fracture healing in the tibia: mechanoregulation of cell activity using a lattice modeling approach

In this study, a three-dimensional (3D) computational simulation of bone regeneration was performed in a human tibia under realistic muscle loading. The simulation was achieved using a discrete lattice modeling approach combined with a mechanoregulation algorithm to describe the cellular processes involved in the healing process-namely proliferation, migration, apoptosis, and differentiation of cells. The main phases of fracture healing were predicted by the simulation, including the bone resorption phase, and there was a qualitative agreement between the temporal changes in interfragmentary strain and bending stiffness by comparison to experimental data and clinical results. Bone healing was simulated beyond the reparative phase by modeling the transition of woven bone into lamellar bone. Because the simulation has been shown to work with realistic anatomical 3D geometry and muscle loading, it demonstrates the potential of simulation tools for patient-specific pre-operative treatment planning.

A mechano-regulation model of fracture repair in vertebral bodies

In this study a multi-scale mechano-regulation model was developed in order to investigate the mechanobiology of trabecular fracture healing in vertebral bodies. A macro-scale finite element model of the spinal segment L3-L4-L5, including a mild wedge fracture in the body of the L4 vertebra, was used to determine the boundary conditions acting on a micro-scale finite element model simulating a portion of fractured trabecular bone. The micro-scale model, in turn, was utilized to predict the local patterns of tissue differentiation within the fracture gap and then how the equivalent mechanical properties of the macro-scale model change with time. The patterns of tissue differentiation predicted by the model appeared consistent with those observed in vivo. Bone formation occurred primarily through endochondral ossification. New woven bone was predicted to occupy the majority of the space within the fracture site approximately 7-8 weeks after the fracture event. Remodeling of cancellous bone architecture was then predicted, with complete new trabeculae forming due to bridging of the microcallus between the remnant trabeculae.

An interspecies computational study on limb lengthening

Distraction osteogenesis is a surgical technique that produces large volumes of new bone by gradually separating two osteotomized bone segments. A previously proposed mechanical-based model that includes the effect of pre-traction stresses (stress level in the gap tissue before each distraction step) during limb lengthening is used here. In the present work, the spatial and temporal patterns of tissue distribution during distraction osteogenesis in different species (sheep, rabbit) and in the human are compared numerically to predict experimental results. Interspecies differential characteristics such as size, distraction protocol, and rate of distraction, among others, are chosen according to experiments. Tissue distributions and reaction forces are then analysed as indicators of the healing pattern. The results obtained are in agreement with experimental findings regarding both tissue distribution and reaction forces. The ability of the model to qualitatively predict the two animal models and the human healing pattern in distraction osteogenesis indicates its potential in understanding the influence of mechanics in this complex process.

Finite element method (FEM), mechanobiology and biomimetic scaffolds in bone tissue engineering

Techniques of bone reconstructive surgery are largely based on conventional, non-cell-based therapies that rely on the use of durable materials from outside the patient's body. In contrast to conventional materials, bone tissue engineering is an interdisciplinary field that applies the principles of engineering and life sciences towards the development of biological substitutes that restore, maintain, or improve bone tissue function. Bone tissue engineering has led to great expectations for clinical surgery or various diseases that cannot be solved with traditional devices. For example, critical-sized defects in bone, whether induced by primary tumor resection, trauma, or selective surgery have in many cases presented insurmountable challenges to the current gold standard treatment for bone repair. The primary purpose of bone tissue engineering is to apply engineering principles to incite and promote the natural healing process of bone which does not occur in critical-sized defects. The total market for bone tissue regeneration and repair was valued at $1.1 billion in 2007 and is projected to increase to nearly $1.6 billion by 2014.Usually, temporary biomimetic scaffolds are utilized for accommodating cell growth and bone tissue genesis. The scaffold has to promote biological processes such as the production of extra-cellular matrix and vascularisation, furthermore the scaffold has to withstand the mechanical loads acting on it and to transfer them to the natural tissues located in the vicinity. The design of a scaffold for the guided regeneration of a bony tissue requires a multidisciplinary approach. Finite element method and mechanobiology can be used in an integrated approach to find the optimal parameters governing bone scaffold performance.In this paper, a review of the studies that through a combined use of finite element method and mechano-regulation algorithms described the possible patterns of tissue differentiation in biomimetic scaffolds for bone tissue engineering is given. Firstly, the generalities of the finite element method of structural analysis are outlined; second, the issues related to the generation of a finite element model of a given anatomical site or of a bone scaffold are discussed; thirdly, the principles on which mechanobiology is based, the principal theories as well as the main applications of mechano-regulation models in bone tissue engineering are described; finally, the limitations of the mechanobiological models and the future perspectives are indicated.

Analysis of the performance of different orthodontic devices for mandibular symphyseal distraction osteogenesis

The aim of this study was to investigate the performance of different orthodontic devices for mandibular symphyseal distraction osteogenesis (MSDO). Two performance parameters were analysed, the first of which concerned the stability guaranteed by a distractor in the fracture gap under mastication loads and the second the level of reliability with which a distractor transfers a given expansion to the mandibular bone, inasmuch as the more reliable the device the smaller the difference between the degree of expansion provided to the device and the displacement achieved on the mandibular arch. Hence, a non-linear finite element (FE) model of a human mandible with different devices (tooth-borne, bone-borne, and hybrid) was constructed and then utilized to assess the structural behaviour of the mandibular bone under distraction and mastication loads. An ad hoc algorithm was developed to simulate progressive expansion of the devices; a distraction protocol comprising a 10 day latency period and a 6 day distraction period was hypothesized. The first hypothetical expansion given to the device was 2 mm, and the five subsequent expansions were 1 mm. The results showed that the hybrid device was the most stable appliance under mastication loads, followed by the tooth- and bone-borne devices. However, parasitic rotations of the mandibular arms caused by mastication might counteract the benefits of distraction. The tooth-borne device was found to have the highest reliability in transferring expansion to the mandibular bone. For this device, mandibular expansion was less than the nominal aperture of the distractor by no more than 15 per cent. Lower values of reliability were achieved with the bone-borne device. As the values of the aperture of the appliances increased, the stability guaranteed in the fracture gap increased while the reliability in transferring expansion to the mandibular arch decreased.

Estimation of the retainer height biomechanical contribution in posterior resin-bonded fixed partial dentures: a structural-thermal coupled finite element analysis

This study determines the RBFPD (resin-bonded fixed partial dentures) biomechanical aspects to retainer height using structural-thermal coupled finite element (FE) analysis under normal (37°C) and high (51°C) oral temperatures. Three RBFPD FE models with different retainer heights (100, 75, and 50% of the distance from 2 mm above the CE (cementum-enamel) junction to the occlusal surface) were created using image processing, contour stacking, and mapping mesh procedures. After FE model validation, the maximum first principal and von Mises stresses in the remaining tooth (σ(T)) and prosthesis (σ(P)), were recorded for all models under structural-thermal coupled analyses. The simulation results showed that the σ(T) and σ(p) values decreased with greater retainer height as a result of the increasing prosthesis stiffness and maximizing bonding area between the enamel and retainer at normal oral temperature (37°C). However, no significant stress differences were found according to the retainer height varying dimensions at high (51°C) temperatures. The RBFPD retainer height biomechanical response is dominated by the structural analysis result (at 37°C) and it is recommended that the prosthesis retainer have as great a height as possible to decrease the stress values.

The role of mechanical signals in regulating chondrogenesis and osteogenesis of mesenchymal stem cells

It is becoming increasingly clear that mesenchymal stem cell (MSC) differentiation is regulated by mechanical signals. Mechanical forces generated intrinsically within the cell in response to its extracellular environment, and extrinsic mechanical signals imposed upon the cell by the extracellular environment, play a central role in determining MSC fate. This article reviews chondrogenesis and osteogenesis during skeletogenesis, and then considers the role of mechanics in regulating limb development and regenerative events such as fracture repair. However, observing skeletal changes under altered loading conditions can only partially explain the role of mechanics in controlling MSC differentiation. Increasingly, understanding how epigenetic factors, such as the mechanical environment, regulate stem cell fate is undertaken using tightly controlled in vitro models. Factors such as bioengineered surfaces, substrates, and bioreactor systems are used to control the mechanical forces imposed upon, and generated within, MSCs. From these studies, a clearer picture of how osteogenesis and chondrogenesis of MSCs is regulated by mechanical signals is beginning to emerge. Understanding the response of MSCs to such regulatory factors is a key step towards understanding their role in development, disease and regeneration.

Corroboration of mechanobiological simulations of tissue differentiation in an in vivo bone chamber using a lattice-modeling approach

It is well established that the mechanical environment modulates tissue differentiation, and a number of mechanoregulatory theories for describing the process have been proposed. In this study, simulations of an in vivo bone chamber experiment were performed that allowed direct comparison with experimental data. A mechanoregulation theory for mesenchymal stem cell differentiation based on a combination of fluid flow and shear strain (computed using finite element analysis) was implemented to predict tissue differentiation inside mechanically controlled bone chambers inserted into rat tibae. To simulate cell activity, a lattice approach with stochastic cell migration, proliferation, and selected differentiation was adopted; because of its stochastic nature, each run of the simulation gave a somewhat different result. Simulations predicted the load-dependency of the tissue differentiation inside the chamber and a qualitative agreement with histological data; however, the full variability found between specimens in the experiment could not be predicted by the mechanoregulation algorithm. This result raises the question whether tissue differentiation predictions can be linked to genetic variability in animal populations.

Computer-aided design and finite-element modelling of biomaterial scaffolds for bone tissue engineering

Scaffold biomaterials for tissue engineering can be produced in many different ways depending on the applications and the materials used. Most research into new biomaterials is based on an experimental trial-and-error approach that limits the possibility of making many variations to a single material and studying its interaction with its surroundings. Instead, computer simulation applied to tissue engineering can offer a more exhaustive approach to test and screen out biomaterials. In this paper, a review of the current approach in biomaterials designed through computer-aided design (CAD) and through finite-element modelling is given. First we review the approach used in tissue engineering in the development of scaffolds and the interactions existing between biomaterials, cells and mechanical stimuli. Then, scaffold fabrication through CAD is presented and characterization of existing scaffolds through computed images is reviewed. Several case studies of finite-element studies in tissue engineering show the usefulness of computer simulations in determining the mechanical environment of cells when seeded into a scaffold and the proper design of the geometry and stiffness of the scaffold. This creates a need for more advanced studies that include aspects of mechanobiology in tissue engineering in order to be able to predict over time the growth and differentiation of tissues within scaffolds. Finally, current perspectives indicate that more efforts need to be put into the development of such advanced studies, with the removal of technical limitations such as computer power and the inclusion of more accurate biological and genetic processes into the developed algorithms.

Sensitivity of tissue differentiation and bone healing predictions to tissue properties

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

Simulation of tissue differentiation in a scaffold as a function of porosity, Young's modulus and dissolution rate: Application of mechanobiological models in tissue engineering

Numerous experimental studies have attempted to determine the optimal properties for a scaffold for use in bone tissue engineering but, as yet, no computational or theoretical approach has been developed that suggests how best to combine the various design parameters, e.g. scaffold porosity, Young's modulus, and dissolution rate. Previous research has shown that bone regeneration during fracture healing and osteochondral defect repair can be simulated using mechanoregulation algorithms based on computing strain and/or fluid flow in the regenerating tissue. In this paper a fully three-dimensional approach is used for computer simulation of tissue differentiation and bone regeneration in a regular scaffold as a function of porosity, Young's modulus, and dissolution rate--and this is done under both low and high loading conditions. The mechanoregulation algorithm employed determines tissue differentiation both in terms of the prevailing biophysical stimulus and number of precursor cells, where cell number is computed based on a three-dimensional random-walk approach. The simulations predict that all three design variables have a critical effect on the amount of bone regenerated, but not in an intuitive way: in a low load environment, a higher porosity and higher stiffness but a medium dissolution rate gives the greatest amount of bone whereas in a high load environment the dissolution rate should be lower otherwise the scaffold will collapse--at lower initial porosities however, higher dissolution rates can be sustained. Besides showing that scaffolds may be optimised to suit the site-specific loading requirements, the results open up a new approach for computational simulations in tissue engineering.