Numerical simulation of tissue differentiation around loaded titanium implants in a bone chamber

Peri-implant cell differentiation in delayed and immediately-loaded dental implant: A mechanobiological simulation

OBJECTIVE

This study aimed to investigate the effect of immediate versus delayed dental implant placement strategies on cell differentiation in a dental callus.

DESIGN

The implant was placed in the mandible with two nearby teeth using an idealized two-dimensional finite element model. Eight weeks after surgery, the mechanobiological modeling of healing was used to estimate cell differentiation. It was assumed that the callus was initially filled by mesenchymal cells. The model then transformed mechanical stimuli received by the callus from loadings in terms of distortional and dilatational strains into predictions of the cellular phenotypes, including fibroblasts, chondrocytes, and osteoblasts, or whether they would remain unchanged or die.

RESULTS

The results demonstrated that delayed loading led to greater bone formation than immediate loading. Osteoblast colonies were observed in the base of threads in the immediately-loaded implant, whereas the delayed loading caused distant bone formation from the surrounding bone side towards the implant. The osteoblasts were differentiated from both intramembranous and endochondral mechanisms of ossification. After eight weeks, approximately 61 % of the callus was ossified in the delayed placement model compared to 35 % in the immediate placement model, resulting in a greater amount of fibrocartilaginous tissue on the bone side of the callus.

CONCLUSIONS

Immediate and delayed loading models generated different results. In the delayed strategy, bone cells were supplied appropriately during the first few weeks following surgery, whereas the immediate loading caused fibrocartilaginous tissue differentiation. In the form of distant osseointegration, the secondary stability of the dental implant was higher and faster due to the delayed placement.

Bone tissue growth in ultrasonically stimulated bioinspired scaffolds

We develop computational models of bone growth in ultrasonically stimulated porous tissue scaffolds with uniform square pores and a bioinspired structure. While bone growth in the bioinspired scaffolds is slower, it produces amounts of bone comparable to the square pore scaffold, making the bioinspired structure ideal for enhancing bone growth with better structural integrity. Controlling the initial mesenchymal stem cell distribution in the scaffolds also affects the growth rate and total bone formation, which could be further useful for controlling bone growth in the scaffold based on an individual's physiology.

Gradient scaffolds for osteochondral tissue engineering and regeneration

The tissue engineering approach for repairing osteochondral (OC) defects involves the fabrication of a biological tissue scaffold that mimics the physiological properties of natural OC tissue (e.g., the gradient transition between the cartilage surface and the subchondral bone). The OC tissue scaffolds described in many research studies exhibit a discrete gradient (e.g., a biphasic or tri/multiphasic structure) or a continuous gradient to mimic OC tissue attributes such as biochemical composition, structure, and mechanical properties. One advantage of a continuous gradient scaffold over biphasic or tri/multiphasic tissue scaffolds is that it more closely mimics natural OC tissue since there is no distinct interface between each layer. Although research studies to this point have yielded good results related to OC regeneration with tissue scaffolds, differences between engineered scaffolds and natural OC tissue remain; due to these differences, current clinical therapies to repair OC defects with engineered scaffolds have not been successful. This paper provides an overview of both discrete and continuous gradient OC tissue scaffolds in terms of cell type, scaffold material, microscale structure, mechanical properties, fabrication methods, and scaffold stimuli. Fabrication of gradient scaffolds with three-dimensional (3D) printing is given special emphasis due to its ability to accurately control scaffold pore geometry. Moreover, the application of computational modeling in OC tissue engineering is considered; for example, efforts to optimize the scaffold structure, mechanical properties, and physical stimuli generated within the scaffold-bioreactor system to predict tissue regeneration are considered. Finally, challenges associated with the repair of OC defects and recommendations for future directions in OC tissue regeneration are proposed.

Morse taper performance: A finite element analysis study

OBJECTIVES

To evaluate and compare the magnitude and distribution of stresses generated on implants, abutments and first molar metal-ceramic crowns using finite element analysis.

METHODS

Preliminary three-dimensional models were created using the computer-aided design software SolidWorks. Stress and strain values were observed for two distinct virtual models: model 1 - Morse taper and solid abutment; model 2 - Morse taper and abutment with screw. A load (250 N) was applied to a single point of the occlusal surface at 15° to the implant long axis. Von Mises stresses were recorded for both groups at four main points: 1) abutment-retaining screws; 2) abutment neck; 3) cervical bone area; 4) implant neck.

RESULTS AND CONCLUSION

Model 1 showed a higher stress value (1477.5 MPa) at the abutment-retaining screw area than the stresses found in model 2 (1091.1 MPa for the same area). The cervical bone strain values did not exceed 105 µm for either model.

Three-dimensional computational model simulating the fracture healing process with both biphasic poroelastic finite element analysis and fuzzy logic control

A dynamic model regulated by both biphasic poroelastic finite element analysis and fuzzy logic control was established. Fuzzy logic control was an easy and comprehensive way to simulate the tissue differentiation process, and it is convenient for researchers and medical experts to communicate with one another to change the fuzzy logic rules and improve the simulation of the tissue differentiation process. In this study, a three-dimensional fracture healing model with two different interfragmentary movements (case A: 0.25 mm and case B: 1.25 mm) was analysed with the new set-up computational model. As the healing process proceeded, both simulated interfragmentary movements predicted a decrease and the time that the decrease started for case B was later than that for case A. Compared with experimental results, both cases corresponded with experimental data well. The newly established dynamic model can simulate the healing process under different mechanical environments and has the potential to extend to the multiscale healing model, which is essential for reducing the animal experiments and helping to characterise the complex dynamic interaction between tissue differentiations within the callus region.

Mechanobiological modelling of tendons: Review and future opportunities

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.

Finite element analysis of the effect of medullary contact on fracture healing and remodeling in the intramedullary interlocking nail-fixed tibia fracture

Intramedullary interlocking nail is an effective treatment for tibial diaphyseal fracture. The contact between medullary rod and diaphyseal cortex is able to enhance fracture stability. However, how and to what degree the contact affects fracture healing and subsequent bone remodeling is still unclear. To investigate this, fracture healing and remodeling algorithms were combined, improved, and used to simulate the healing and remodeling processes in a transverse tibial diaphyseal fracture fixed with an intramedullary interlocking nail device. Two different diaphyseal fracture statuses, three different initial loading levels, and two nail materials were considered. The results showed that the medullary contact could significantly enhance the fixation stability; the strain reduction was up to 80% in the initial granulation callus. However, low initial loading level was found to be a more potential risk factor for the insufficient loading-induced nonunion other than medullary contact and stiffer nail material. Furthermore, the stabilizing effect of medullary contact diminished when stiff bone tissue formed in the callus; thus, the remodeling in the long-term was not affected by medullary contact. Copyright © 2016 John Wiley & Sons, Ltd.

In silico bone mechanobiology: modeling a multifaceted biological system

Mechanobiology, the study of the influence of mechanical loads on biological processes through signaling to cells, is fundamental to the inherent ability of bone tissue to adapt its structure in response to mechanical stimulation. The immense contribution of computational modeling to the nascent field of bone mechanobiology is indisputable, having aided in the interpretation of experimental findings and identified new avenues of inquiry. Indeed, advances in computational modeling have spurred the development of this field, shedding new light on problems ranging from the mechanical response to loading by individual cells to tissue differentiation during events such as fracture healing. To date, in silico bone mechanobiology has generally taken a reductive approach in attempting to answer discrete biological research questions, with research in the field broadly separated into two streams: (1) mechanoregulation algorithms for predicting mechanobiological changes to bone tissue and (2) models investigating cell mechanobiology. Future models will likely take advantage of advances in computational power and techniques, allowing multiscale and multiphysics modeling to tie the many separate but related biological responses to loading together as part of a larger systems biology approach to shed further light on bone mechanobiology. Finally, although the ever‐increasing complexity of computational mechanobiology models will inevitably move the field toward patient‐specific models in the clinic, the determination of the context in which they can be used safely for clinical purpose will still require an extensive combination of computational and experimental techniques applied to in vitro and in vivo applications. WIREs Syst Biol Med 2016, 8:485–505. doi: 10.1002/wsbm.1356

For further resources related to this article, please visit the WIREs website.

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.

Occlusal overload and bone/implant loss

AIM

The aim of this search was to assess the biological consequences that overload might have on already osseointegrated oral implants through a systematic screening of the scientific literature.

METHOD

Detailed searches through PUBMED, OVID, EMBASE and LILACS databases were made. Articles published up to December 2011 and those reported on the clinical, radiographic and/or histological outcome of oral implants subjected to so-called overload were considered eligible for inclusion. Identified studies were assessed by one non-blinded reviewer according to well-defined inclusion and exclusion criteria. When doubt arose, the co-authors were counselled until final agreement was obtained. The PICO questions formulated was:"what is the effect of overload vs. no overload on bone/implant loss in clinically stable implants?"

RESULTS

The database searches as well as additional hand searching, resulted in 726 potentially relevant titles. Eventually, 16 clinical and 25 animal studies were considered relevant to the topic. After inclusion/exclusion criteria assessment, all clinical studies and all but three animal studies and one systematic review were considered at high risk of bias and excluded. The included animal studies did not reveal an association between overload and peri-implant bone loss in the absence of peri-implant inflammation, whereas in its presence, overload seemed to aggravate the peri-implant tissue breakdown.

CONCLUSIONS

The effect of implant overload on bone/implant loss in clinically well-integrated implants is poorly reported and provides little unbiased evidence to support a cause-and-effect relationship. The PICO question remained unanswered. At the animal level, "overload", mimicked by supra-occlusal contacts acting in an uninflamed peri-implant environment, did not negatively affect osseointegration and even was anabolic. In contrast, supra-occlusal contacts in the presence of inflammation significantly increased the plaque-induced bone resorption.

Biomechanical determinants of the stability of dental implants: influence of the bone-implant interface properties

Dental implants are now widely used for the replacement of missing teeth in fully or partially edentulous patients and for cranial reconstructions. However, risks of failure, which may have dramatic consequences, are still experienced and remain difficult to anticipate. The stability of biomaterials inserted in bone tissue depends on multiscale phenomena of biomechanical (bone-implant interlocking) and of biological (mechanotransduction) natures. The objective of this review is to provide an overview of the biomechanical behavior of the bone-dental implant interface as a function of its environment by considering in silico, ex vivo and in vivo studies including animal models as well as clinical studies. The biomechanical determinants of osseointegration phenomena are related to bone remodeling in the vicinity of the implants (adaptation of the bone structure to accommodate the presence of a biomaterial). Aspects related to the description of the interface and to its space-time multiscale nature will first be reviewed. Then, the various approaches used in the literature to measure implant stability and the bone-implant interface properties in vitro and in vivo will be described. Quantitative ultrasound methods are promising because they are cheap, non invasive and because of their lower spatial resolution around the implant compared to other biomechanical approaches.

Evaluating of bone healing around porous coated titanium implant and potential systematic bias on the traditional sampling method

INTRODUCTION

The mechanical properties of bone can largely be explained by bone density and the anisotropic orientation of the trabecular bone. The type of trabecular structure plays an important role in determining the mechanical properties of cancellous bone. Gap-healing and implant fixation could be affected by the various quality and quantity of bone in the local environment. Thus, implant fixation in one part might differ from the other part of the implant. This study aimed to investigate the influence of the sampling method on data evaluation.

MATERIAL AND METHODS

Titanium alloy implants (Biomet Inc.) of 10mm in length and 6mm in diameter were inserted bilaterally into the proximal humerus of 8 skeletally mature sheep. Thus two implants with a concentric gap of 2mm were implanted in each sheep. The gap was filled with allograft. Standardised surgical procedure was used. At sacrifice, 6 weeks after surgery, both proximal humeri were harvested. The specimens were randomized to superficial or profound groups. In the superficial group, mechanical testing or histological analysis was carried out on the superficial part of the implant. In the profound group, the mechanical testing or histological analysis was performed on the profound part of the implant.

RESULT

The mechanical fixation, bone volume and bone ongrowth showed no statistically significant differences. Mechanical test demonstrated a slight tendency to increased strength and failure energy were observed in the superficial group. Histomorphomety revealed bone ongrowth was slightly increased and volume fraction was decreased in the profound group.

CONCLUSION

Histological analysis and mechanical testing can be applied to the superficial or profound part of the implant.

Interface micromotions increase with less-conforming cementless glenoid components

BACKGROUND

The optimal degree of conformity between the glenoid and humeral components in total shoulder arthroplasty for best performance and durability is still a matter of debate. The main aim of this study is to evaluate the influence of joint conformity on the bone-implant interface micromotions in a cementless glenoid implant.

MATERIALS AND METHODS

Polyethylene inlays with different degrees of conformity (radial mismatch of 0, 2, 4, and 6 mm) were mounted on a cementless metal back and then implanted in a bone substitute. These glenoid components were loaded by a prosthetic humeral head during a force-controlled experiment. Normal-to-interface micromotions and bone substitute deformations were measured at different points of the interface. Rim displacement and humeral head translation were also measured. A finite element (FE) model of the experiments was implemented to estimate the normal- and tangent-to-interface micromotions in the entire bone-implant interface.

RESULTS

All measured variables increased with less-conforming PE inlays. Normal-to-interface micromotions were significantly larger (P < .05) when the radial mismatch was 6 mm compared with the fully conforming inlay. The FE model was in agreement and complemented the experimental results. FE model-predicted interface micromotions were already significantly larger when the radial mismatch was equal to 4 mm.

DISCUSSION

In a force-controlled experiment with a cementless glenoid component, a non-conforming PE inlay allows larger interface micromotions than a conforming inlay, reaching a magnitude that may hamper local bone ingrowth in this type of component. This is mainly because of the larger humeral head translation that boosts the effects of the so-called rocking-horse phenomenon.

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.

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.

In silico biology of bone modelling and remodelling: regeneration

Bone regeneration is the process whereby bone is able to (scarlessly) repair itself from trauma, such as fractures or implant placement. Despite extensive experimental research, many of the mechanisms involved still remain to be elucidated. Over the last decade, many mathematical models have been established to investigate the regeneration process in silico. The first models considered only the influence of the mechanical environment as a regulator of the healing process. These models were followed by the development of bioregulatory models where mechanics was neglected and regeneration was regulated only by biological stimuli such as growth factors. The most recent mathematical models couple the influences of both biological and mechanical stimuli. Examples are given to illustrate the added value of mathematical regeneration research, specifically in the in silico design of treatment strategies for non-unions. Drawbacks of the current continuum-type models, together with possible solutions in extending the models towards other time and length scales are discussed. Finally, the demands for dedicated and more quantitative experimental research are presented.

Influence of implant connection type on the biomechanical environment of immediately placed implants - CT-based nonlinear, three-dimensional finite element analysis

PURPOSE

The purpose of the present study was to evaluate the biomechanical environment of immediately placed implants, before and after osseointegration, by comparing three different implant-abutment connection types.

MATERIALS AND METHODS

A computer tomography-based finite element model of an upper central incisor extraction socket was constructed containing implants with either external hex, internal hex, or Morse-taper connection. Frictional contact elements were used in the bone, implant, abutment, and abutment screw interfaces in the immediately placed simulations. In osseointegrated simulations, the repair of bone alveolar defect and a glued bone-to-implant interface were assumed. By analysis of variance, the influence was assessed of connection type, clinical situation, and loading magnitude on the peak equivalent strain in the bone, peak von Mises stress in the abutment screw, bone-to-implant relative displacement, and abutment gap.

RESULTS

The loading magnitudes had a significant contribution, regardless of the assessed variable. However, the critical clinical situation of an immediately placed implant itself was the main factor affecting the peak equivalent strain in the bone and bone-to-implant displacement. The largest influence of the connection type in this protocol was seen on the peak equivalent stress in the abutment screw. On the other hand, a higher influence of the various connection types on bone stress/strain could be noted in osseointegrated simulations.

CONCLUSIONS

The implant-abutment connection design did not significantly influence the biomechanical environment of immediately placed implants. Avoiding implant overloading and ensuring a sufficient initial intraosseous stability are the most relevant parameters for the promotion of a safe biomechanical environment in this protocol.

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.

Identification of mechanosensitive genes during embryonic bone formation

Although it is known that mechanical forces are needed for normal bone development, the current understanding of how biophysical stimuli are interpreted by and integrated with genetic regulatory mechanisms is limited. Mechanical forces are thought to be mediated in cells by “mechanosensitive” genes, but it is a challenge to demonstrate that the genetic regulation of the biological system is dependant on particular mechanical forces in vivo. We propose a new means of selecting candidate mechanosensitive genes by comparing in vivo gene expression patterns with patterns of biophysical stimuli, computed using finite element analysis. In this study, finite element analyses of the avian embryonic limb were performed using anatomically realistic rudiment and muscle morphologies, and patterns of biophysical stimuli were compared with the expression patterns of four candidate mechanosensitive genes integral to bone development. The expression patterns of two genes, Collagen X (ColX) and Indian hedgehog (Ihh), were shown to colocalise with biophysical stimuli induced by embryonic muscle contractions, identifying them as potentially being involved in the mechanoregulation of bone formation. An altered mechanical environment was induced in the embryonic chick, where a neuromuscular blocking agent was administered in ovo to modify skeletal muscle contractions. Finite element analyses predicted dramatic changes in levels and patterns of biophysical stimuli, and a number of immobilised specimens exhibited differences in ColX and Ihh expression. The results obtained indicate that computationally derived patterns of biophysical stimuli can be used to inform a directed search for genes that may play a mechanoregulatory role in particular in vivo events or processes. Furthermore, the experimental data demonstrate that ColX and Ihh are involved in mechanoregulatory pathways and may be key mediators in translating information from the mechanical environment to the molecular regulation of bone formation in the embryo.

While mechanical forces are known to be critical to adult bone maintenance and repair, the importance of mechanobiology in embryonic bone formation is less widely accepted. The influence of mechanical forces on cells is thought to be mediated by “mechanosensitive genes,” genes which respond to mechanical stimulation. In this research, we examined the situation in the developing embryo. Using finite element analysis, we simulated the biophysical stimuli in the developing bone resulting from spontaneous muscle contractions, incorporating detailed morphology of the developing chick limb. We compared patterns of stimuli with expression patterns of a number of genes involved in bone formation and demonstrated a clear colocalisation in the case of two genes (Ihh and ColX). We then altered the mechanical environment of the growing chick embryo by blocking muscle contractions and demonstrated changes in the magnitudes and patterns of biophysical stimuli and in the expression patterns of both Ihh and ColX. We have demonstrated the value of combining computational techniques with in vivo gene expression analysis to identify genes that may play a mechanoregulatory role and have identified genes that respond to mechanical stimulation during bone formation in vivo.

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.

Angiogenesis in bone fracture healing: a bioregulatory model

The process of fracture healing involves the action and interaction of many cells, regulated by biochemical and mechanical signals. Vital to a successful healing process is the restoration of a good vascular network. In this paper, a continuous mathematical model is presented that describes the different fracture healing stages and their response to biochemical stimuli only (a bioregulatory model); mechanoregulatory effects are excluded here. The model consists of a system of nonlinear partial differential equations describing the spatiotemporal evolution of concentrations and densities of the cell types, extracellular matrix types and growth factors indispensable to the healing process. The model starts after the inflammation phase, when the fracture callus has already been formed. Cell migration is described using not only haptokinetic, but also chemotactic and haptotactic influences. Cell differentiation is controlled by the presence of growth factors and sufficient vascularisation. Matrix synthesis and growth factor production are controlled by the local cell and matrix densities and by the local growth factor concentrations. Numerical simulations of the system, using parameter values based on experimental data obtained from literature, are presented. The simulation results are corroborated by comparison with experimental data from a standardised rodent fracture model. The results of sensitivity analyses on the parameter values as well as on the boundary and initial conditions are discussed. Numerical simulations of compromised healing situations showed that the establishment of a vascular network in response to angiogenic growth factors is a key factor in the healing process. Furthermore, a correct description of cell migration is also shown to be essential to the prediction of realistic spatiotemporal tissue distribution patterns in the fracture callus. The mathematical framework presented in this paper can be an important tool in furthering the understanding of the mechanisms causing compromised healing and can be applied in the design of future fracture healing experiments.

Application of mechanoregulatory models to simulate peri-implant tissue formation in an in vivo bone chamber

Several mechanoregulatory tissue differentiation models have been proposed over the last decade. Corroboration of these models by comparison with experimental data is necessary to determine their predictive power. So far, models have been applied with various success rates to different experimental set-ups investigating mainly secondary fracture healing. In this study, the mechanoregulatory models are applied to simulate the implant osseointegration process in a repeated sampling in vivo bone chamber, placed in a rabbit tibia. This bone chamber provides a mechanically isolated environment to study tissue differentiation around titanium implants loaded in a controlled manner. For the purpose of this study, bone formation around loaded cylindrical and screw-shaped implants was investigated. Histologically, no differences were found between the two implant geometries for the global amount of bone formation in the entire chamber. However, a significantly larger amount of bone-to-implant contact was observed for the screw-shaped implant compared to the cylindrical implant. In the simulations, a larger amount of bone was also predicted to be in contact with the screw-shaped implant. However, other experimental observations could not be predicted. The simulation results showed a distribution of cartilage, fibrous tissue and (im)mature bone, depending on the mechanoregulatory model that was applied. In reality, no cartilage was observed. Adaptations to the differentiation models did not lead to a better correlation between experimentally observed and numerically predicted tissue distribution patterns. The hypothesis that the existing mechanoregulatory models were able to predict the patterns of tissue formation in the in vivo bone chamber could not be fully sustained.

Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation

Computational models have shown that biophysical stimuli can be correlated with observed patterns of tissue differentiation, and simulations have been performed that predict the time course of tissue differentiation in, for example, long bone fracture healing. Some simulations have used a diffusion model to simulate the migration and proliferation of cells with the differentiating tissue. However, despite the convenience of the diffusion model, diffusion is not the mechanism of cell dispersal: cells disperse by crawling or proliferation, or are transported in a moving fluid. In this paper, a random-walk model (i.e., a stochastic model), with and without a preferred direction, is studied as an approach to simulate cell proliferation/migration in differentiating tissues and it is compared with the diffusion model. A simulation of tissue differentiation of gap tissue in a two-dimensional model of a bone/implant interface was performed to demonstrate the differences between diffusion vs. random walk with a preferred direction. Results of diffusion and random-walk models are similar with respect to the change in the stiffness of the gap tissue but rather different results are obtained regarding tissue patterning in the differentiating tissues; the diffusion approach predicted continuous patterns of tissue differentiation whereas the random-walk model showed a more discontinuous pattern-histological results are not available that can unequivocally establish which is most similar to experimental observation. Comparing isotropic to anisotropic random walk (preferred direction of proliferation and cell migration), a more rapid reduction of the relative displacement between implant and bone is predicted. In conclusion, we have shown how random-walk models of cell dispersal and proliferation can be implemented, and shown where differences between them exist. Further study of the random-walk model is warranted, given the importance of cell seeding and cell dispersal/proliferation in many mechanobiological problems.

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

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

Prediction of the optimal mechanical properties for a scaffold used in osteochondral defect repair

The optimal mechanical properties of a scaffold to promote cartilage generation in osteochondral defects in vivo are not known. During normal daily activities cartilage is subjected to large cyclic loads that not only facilitate nutrient transport and waste removal through the dense tissue but also act as a stimulus to the chondrocytes. In contrast, cartilage tissue is commonly engineered in vitro in a static culture; hence, in many cases, the properties of scaffolds have been tailored to suit this in vitro environment. In this study, a mechanoregulation algorithm for tissue differentiation was used to determine the influence of scaffold material properties on chondrogenesis in a finite element model of an osteochondral defect. It is predicted that increasing the stiffness of the scaffold increases the amount of cartilage formation and reduces the amount of fibrous tissue formation in the defect, but this only holds true up to a certain threshold stiffness above which the amount of cartilage formed is reduced. Reducing the permeability of the scaffold was also predicted to be beneficial. Considering a nonhomogeneous scaffold, an optimal design was determined by parametrically varying the mechanical properties of the scaffold through its depth. The Young's modulus reduced nonlinearly from the superficial region through the depth of the scaffold, while the permeability of the scaffold was lowest in the superficial region. As tissue engineering moves from a science toward a product, engineering design becomes more relevant, and predictive models such as that presented here can provide a scientific basis for design choices.

Corroboration of mechanoregulatory algorithms for tissue differentiation during fracture healing: Comparison with in vivo results

Several mechanoregulation algorithms proposed to control tissue differentiation during bone healing have been shown to accurately predict temporal and spatial tissue distributions during normal fracture healing. As these algorithms are different in nature and biophysical parameters, it raises the question of which reflects the actual mechanobiological processes the best. The aim of this study was to resolve this issue by corroborating the mechanoregulatory algorithms with more extensive in vivo bone healing data from animal experiments. A poroelastic three-dimensional finite element model of an ovine tibia with a 2.4 mm gap and external callus was used to simulate the course of tissue differentiation during fracture healing in an adaptive model. The mechanical conditions applied were similar to those used experimentally, with axial compression or torsional rotation as two distinct cases. Histological data at 4 and 8 weeks, and weekly radiographs, were used for comparison. By applying new mechanical conditions, torsional rotation, the predictions of the algorithms were distinguished successfully. In torsion, the algorithms regulated by strain and hydrostatic pressure failed to predict healing and bone formation as seen in experimental data. The algorithm regulated by deviatoric strain and fluid velocity predicted bridging and healing in torsion, as observed in vivo. The predictions of the algorithm regulated by deviatoric strain alone did not agree with in vivo data. None of the algorithms predicted patterns of healing entirely similar to those observed experimentally for both loading modes. However, patterns predicted by the algorithm based on deviatoric strain and fluid velocity was closest to experimental results. It was the only algorithm able to predict healing with torsional loading as seen in vivo.

Bone ingrowth simulation for a concept glenoid component design

Glenoid component loosening is the major problem of total shoulder arthroplasty. It is possible that uncemented component may be able to achieve superior fixation relative to cemented component. One option for uncemented glenoid is to use porous tantalum backing. Bone ingrowth into the porous backing requires a degree of stability to be achieved directly post-operatively. This paper investigates the feasibility of bone ingrowth with respect to the influence of primary fixation, elastic properties of the backing and friction at the bone prosthesis interface. Finite element models of three glenoid components with different primary fixation configurations are created. Bone ingrowth into the porous backing is modelled based on the magnitude of the relative interface micromotions and mechanoregulation of the mesenchymal stem cells that migrated via the bonded part of the interface. Primary fixation had the most influence on bone ingrowth. The simulation showed that its major role was not to firmly interlock the prosthesis, but rather provide such a distribution of load, that would result in reduction of the peak interface micromotions. Should primary fixation be provided, friction has a secondary importance with respect to bone ingrowth while the influence of stiffness was counter intuitive: a less stiff backing material inhibits bone ingrowth by higher interface micromotions and stimulation of fibrous tissue formation within the backing.