Modeling distraction osteogenesis: analysis of the distraction rate

A 4D time-lapse morphometry method to quantify bone formation and resorption during distraction osteogenesis

Distraction osteogenesis (DO) is widely utilized for treating limb length discrepancy, nonunion, bone deformities and defects. This study sought to develop a 4D time-lapse morphometry method to quantify bone formation and resorption in mouse femur during DO based on image registration of longitudinal in vivo micro-CT scans. Female C57BL/6 mice (n = 7) underwent osteotomy, followed by 5 days of latency, 10 days of distraction and 35 days of consolidation. The mice were scanned with micro-CT at Days 5, 15, 25, 35, 45, and 50. Histological sectioning and Movat Pentachrome straining were performed at Day 50. After registration of two consecutive micro-CT images of the same bone (day x and day y), the spatially- and temporally-linked sequences of formation, resorption and quiescent bones at the distraction gap were identified and bone formation and resorption rates (BFRdayx-y and BRRdayx-y) were calculated. The overall percentage error of the registration method was 2.98% ± 0.89% and there was a strong correlation between histologically-measured bone area fraction and micro-CT-determined bone volume fraction at Day 50 (r = 0.89, p < 0.05). The 4D time-lapse morphometry indicated a rapid bone formation during the first 10 days of the consolidation phase (BFRday15-25 = 0.14 ± 0.05 mm3/day), followed by callus reshaping via equivalent bone formation and resorption rates. The 4D time-lapse morphometry method developed in this study allows for a continuous quantitative monitoring of the dynamic process of bone formation and resorption following distraction, which may offer a better understanding of the mechanism for mechano-regulated bone regeneration and aid for development of new treatment strategies of DO.

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.

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.

Bone Regenerate Evaluation Methods

Since its introduction by Ilizarov, the distraction osteogenesis technique has been used to treat trauma-related conditions, infections, bone tumors, and congenital diseases, either as methods of bone transport or elongation. One of the major dilemmas for the orthopedic surgeon who performs osteogenic distraction is establishing a reproducible method of assessing the progression of the osteogenesis, enabling the early detection of regenerate failures, in order to effectively interfere during treatment, and to determine the appropriate time to remove the external fixator. Several quantitative monitoring methods to evaluate the structural recovery and biomechanical properties of the bone regenerate at different stages, as well as the bone healing process, are under study. These methods can reveal data on bone metabolism, stiffness, bone mineral content, and bone mineral density. The present review comprehensively summarizes the most recent techniques to assess bone healing during osteogenic distraction, including conventional radiography and pixel values in digital radiology, ultrasonography, bone densitometry and scintigraphy, quantitative computed tomography, biomechanical evaluation, biochemical markers, and mathematical models. We believe it is crucial to know the different methods currently available, and we understand that using several monitoring methods simultaneously can be an ideal solution, pointing to a future direction in the follow-up of osteogenic distraction.

Effect of the accordion technique on bone regeneration during distraction osteogenesis: A computational study

BACKGROUND AND OBJECTIVE

Distraction osteogenesis (DO), a bone lengthening technique, is widely employed to treat congenital and acquired limb length discrepancies and large segmental bone defects. However, a major issue of DO is the prolonged consolidation phase (10-36 months) during which patients must wear a cumbersome external fixator. Attempts have been made to accelerate the healing process of DO by an alternating distraction and compression mode (so-called "accordion" technique or AT). However, it remains unclear how varied AT parameters affect DO outcomes and what the most effective AT mode is.

METHODS

Based on an experimentally-verified mechanobiological model, we performed a parametric analysis via in silico simulation of the bone regeneration process of DO under different AT modes, including combinations of varied application times (AT began at week 1-8 of the consolidation phase), durations (AT was used continuously for 1 week, 2 weeks or 4 weeks) and rates (distraction or compression at 0.25, 0.5, 0.75, and 1 mm/12 h). The control group had no AT applied during the consolidation phase.

RESULTS

Compared with the control group (no AT), AT applied at an early consolidation stage (e.g. week 1 of the consolidation phase) significantly enhanced bone formation and reduced the overall healing time. However, the effect of AT on bone healing was dependent on its duration and rate. Specifically, a moderate rate of AT (e.g. 0.5 mm/12 h) lasting for two weeks promoted blood perfusion recovery and bone regeneration, ultimately shortening the healing time. Conversely, over-high rates (e.g. 1 mm/12 h) and longer durations (e.g. 4 weeks) of AT adversely affected bone regeneration and blood perfusion recovery, thereby delaying bone bridging.

CONCLUSIONS

These results suggest that the therapeutic effects of AT on DO are highly dependent of the AT parameters of choice. Under appropriate durations and rates, the AT applied at an early consolidation phase is beneficial for blood recovery and bone regeneration. These results may provide a basis for selecting effective AT modes to accelerate consolidation and reduce the overall treatment period of DO.

In vivo and in silico monitoring bone regeneration during distraction osteogenesis of the mouse femur

BACKGROUND AND OBJECTIVE

Distraction osteogenesis (DO) is a mechanobiological process of producing new bone by gradual and controlled distraction of the surgically separated bone segments. Mice have been increasingly used to study the role of relevant biological factors in regulating bone regeneration during DO. However, there remains a lack of in silico DO models and related mechano-regulatory tissue differentiation algorithms for mouse bone. This study sought to establish an in silico model based on in vivo experimental data to simulate the bone regeneration process during DO of the mouse femur.

METHODS

In vivo micro-CT, including time-lapse morphometry was performed to monitor the bone regeneration in the distraction gap. A 2D axisymmetric finite element model, with a geometry originating from the experimental data, was created. Bone regeneration was simulated with a fuzzy logic-based two-stage (distraction and consolidation) mechano-regulatory tissue differentiation algorithm, which was adjusted from that used for fracture healing based on our in vivo experimental data. The predictive potential of the model was further tested with varied distraction frequencies and distraction rates.

RESULTS

The computational simulations showed similar bone regeneration patterns to those observed in the micro-CT data from the experiment throughout the DO process. This consisted of rapid bone formation during the first 10 days of the consolidation phase, followed by callus reshaping via bone remodeling. In addition, the computational model predicted a faster and more robust bone healing response as the model's distraction frequency was increased, whereas higher or lower distraction rates were not conducive to healing.

CONCLUSIONS

This in silico model could be used to investigate basic mechanobiological mechanisms involved in bone regeneration or to optimize DO strategies for potential clinical applications.

Novel approach to estimate distraction forces in distraction osteogenesis and application in the human lower leg

PURPOSE

In distraction osteogenesis (DO) of long bones, new bone tissue is distracted to lengthen limbs or reconstruct bone defects. However, mechanical boundary conditions in human application such as arising forces are mainly based on limited empirical data. Our aim was the numerical determination of the callus distraction force (CDF) and the total distraction force (TDF) during DO in the tibia of adults to advance the understanding of callus tissue behavior and optimize DO procedures.

METHOD

We implemented a mathematical model based on an animal experiment to enable the calculation of forces arising while distracting callus tissue, excluding the influence of surrounding soft tissue (muscles, skin etc.). The CDF progression for the distraction period was calculated using the implemented model and varying distraction parameters (initial gap, area, step size, time interval, length). Further, we estimated the CDF based on reported forces in humans and compared the results to our model predictions. In addition, we calculated the TDF based on our CDF predictions in combination with reported resisting forces due to soft tissue presence in human cadavers. Finally, we compared the progressions to in vivo TDF measurements for validation.

RESULTS

Due to relaxation, a peak and resting CDF is observable for each distraction step. Our biomechanical results show a non-linear degressive increase of the resting and peak CDF at the beginning and a steady non-linear increase thereafter. The calculated resting and peak CDF in the tibial metaphysis ranged from 0.00075 to 0.0089 N and 0.22-2.6 N at the beginning as well as 20-25 N and 70-75 N at the end of distraction. The comparison to in vivo data showed the plausibility of our predictions and resulted in a 10-33% and 10-23% share of resting CDF in the total resting force for bone transport and elongation, respectively. Further, the percentage of peak CDF in total peak force was found to be 29-58% and 27-55% for bone transport and elongation, respectively. Moreover, our TDF predictions were valid based on the comparison to in vivo forces and resulted in a degressive increase from 6 to 125 N for the peak TDF and from 5 to 76 N for the resting TDF.

CONCLUSION

Our approach enables the estimation of forces arising due to the distraction of callus tissue in humans and results in plausible force progressions as well as absolute force values for the callus distraction force during DO. In combination with measurements of resisting forces due to the presence of soft tissue, the total distraction force in DO may also be evaluated. We thus propose the application of this method to approximate the behavior of mechanical callus properties during DO in humans as an alternative to in vivo measurements.

Time-Dependent Collagen Fibered Structure in the Early Distraction Callus: Imaging Characterization and Mathematical Modeling

Collagen is a ubiquitous protein present in regenerating bone tissues that experiences multiple biological phenomena during distraction osteogenesis until the deposition of phosphate crystals. This work combines fluorescence techniques and mathematical modeling to shed light on the mechano-structural processes behind the maturation and accommodation-to-mineralization of the callus tissue. Ovine metatarsal bone calluses were analyzed through confocal images at different stages of the early distraction osteogenesis process, quantifying the fiber orientation distribution and mean intensity as fiber density measure. Likewise, a mathematical model based on the experimental data was defined to micromechanically characterize the apparent stiffening of the tissue within the distracted callus. A reorganization of the fibers around the distraction axis and increased fiber density were found as the bone fragments were gradually separated. Given the degree of significance between the mathematical model and previous in vivo data, reorganization, densification, and bundle maturation phenomena seem to explain the apparent mechanical maturation observed in the tissue theoretically.

Enhancing the Efficiency of Distraction Osteogenesis through Rate-Varying Distraction: A Computational Study

Distraction osteogenesis (DO) is a mechanobiological process of producing new bone and overlying soft tissues through the gradual and controlled distraction of surgically separated bone segments. The process of bone regeneration during DO is largely affected by distraction parameters. In the present study, a distraction strategy with varying distraction rates (i.e., "rate-varying distraction") is proposed, with the aim of shortening the distraction time and improving the efficiency of DO. We hypothesized that faster and better healing can be achieved with rate-varying distractions, as compared with constant-rate distractions. A computational model incorporating the viscoelastic behaviors of the callus tissues and the mechano-regulatory tissue differentiation laws was developed and validated to predict the bone regeneration process during DO. The effect of rate-varying distraction on the healing outcomes (bony bridging time and bone formation) was examined. Compared to the constant low-rate distraction, a low-to-high rate-varying distraction provided a favorable mechanical environment for angiogenesis and bone tissue differentiation, throughout the distraction and consolidation phase, leading to an improved healing outcome with a shortened healing time. These results suggest that a rate-varying clinical strategy could reduce the overall treatment time of DO and decrease the risk of complications related to the external fixator.

Mechanobiology of Bone Consolidation During Distraction Osteogenesis: Bone Lengthening Vs. Bone Transport

Bone lengthening and bone transport are regeneration processes that commonly rely on distraction osteogenesis, a widely accepted surgical procedure to deal with numerous bony pathologies. Despite the extensive study in the literature of the influence of biomechanical factors, a lack of knowledge about their mechanobiological differences prevents a clinical particularization. Bone lengthening treatments were performed on sheep metatarsus by reproducing the surgical and biomechanical protocol of previous bone transport experiments. Several in vivo monitoring techniques were employed to build an exhaustive comparison: gait analysis, radiographic and CT assessment, force measures through the fixation, or mechanical characterization of the new tissue. A significant initial loss of the bearing capacity, quantified by the ground reaction forces and the limb contact time with the ground, is suffered by the bone lengthening specimens. The potential effects of this anomaly on the musculoskeletal force distribution and the evolution of the bone callus elastic modulus over time are also analyzed. Imaging techniques also seem to reveal lower bone volume in the bone lengthening callus than in the bone transport one, but an equivalent mineralization rate. The simultaneous quantification of biological and mechanical parameters provides valuable information for the daily clinical routine and numerical tools development.

Multiscale Characterisation of Cortical Bone Tissue

Multiscale analysis has become an attractive technique to predict the behaviour of materials whose microstructure strongly changes spatially or among samples, with that microstructure controlling the local constitutive behaviour. This is the case, for example, of most biological tissues—such as bone. Multiscale approaches not only allow, not only to better characterise the local behaviour, but also to predict the field-variable distributions (e.g., strains, stresses) at both scales (macro and micro) simultaneously. However, multiscale analysis usually lacks sufficient experimental feedback to demonstrate its validity. In this paper an experimental and numerical micromechanics analysis is developed with application to cortical bone. Displacement and strain fields are obtained across the microstructure by means of digital image correlation (DIC). The other mechanical variables are computed following the micromechanics theory. Special emphasis is given to the differences found in the different field variables between the micro- and macro-structures, which points out the need for this multiscale approach in cortical bone tissue. The obtained results are used to establish the basis of a multiscale methodology with application to the analysis of bone tissue mechanics at different spatial scales.

Evolution of callus tissue behavior during stable distraction osteogenesis

Multiple studies have sought to characterize the mechanical behavior of callus tissue in vivo during distraction osteogenesis. The aims of such studies are to understand the mechanobiology of distraction and elucidate the complex viscoelasticity and evolution of the tissue. The former objective has direct clinical relevance to surgical technique and process control while the latter is necessary for the calibration and validation of the predictive healing models. Such models seek to reduce the researcher's dependence on animal studies and prospectively allow improved surgical planning. To date, no study has been capable of controlling the mechanical conditions sufficiently enough to decouple the distraction process from the secondary mechanical stimulation associated with the finite stiffness of the fixation constructs employed. It is the goal of this work to understand the mechanobiology of pure distraction as well as characterize viscoelastic tissue behavior under precisely defined mechanical conditions. This is achieved using a novel lateral distraction model. The structural integrity of the bone is maintained, allowing the collection of force relaxation data due to a stepwise distraction process without the superimposed influence of secondary mechanical stimulation. The average instantaneous modulus increases from approximately 2 kPa to approximately 1100 kPa while the equilibrium modulus increases from approximately 0 kPa to 200 kPa over the distraction period.

Simulating lateral distraction osteogenesis

Distraction osteogenesis is an effective method for generating large amounts of bone in situ for treating pathologies such as large bone defects or skeletal malformations, for instance leg-length discrepancies. While an optimized distraction procedure might have the potential to reduce the rate of complications significantly, our knowledge of the underlying mechanobiological processes is still insufficient for systematic optimization of treatment parameters such as distraction rate or fixation stiffness. We present a novel numerical model of lateral distraction osteogenesis, based on a mechanically well-controlled in vivo experiment. This model extends an existing numerical model of callus healing with viscoplastic material properties for describing stress relaxation and stimuli history-dependent tissue differentiation, incorporating delay and memory effects. A reformulation of appositional growth based non-local biological stimuli in terms of spatial convolution as well as remeshing and solution-mapping procedures allow the model to cope with severe mesh distortions associated with large plastic deformations. With these enhancements, our model is capable of replicating the in vivo observations for lateral distraction osteogenesis in sheep using the same differentiation rules and the same set of parameters that successfully describes callus healing in sheep, indicating that tissue differentiation hypotheses originally developed for fracture healing scenarios might indeed be applicable to distraction as well. The response of the model to modified distraction parameters corresponds to existing studies, although the currently available data is insufficient for rigorous validation. As such, this study provides a first step towards developing models that can serve as tools for identifying both interesting research questions and, eventually, even optimizing clinical procedures once better data for calibration and validation becomes available.

In silico study of bone tissue regeneration in an idealised porous hydrogel scaffold using a mechano-regulation algorithm

Mechanical stimulation, in the form of fluid perfusion or mechanical strain, enhances osteogenic differentiation and overall bone tissue formation by mesenchymal stems cells cultured in biomaterial scaffolds for tissue engineering applications. In silico techniques can be used to predict the mechanical environment within biomaterial scaffolds, and also the relationship between bone tissue regeneration and mechanical stimulation, and thereby inform conditions for bone tissue engineering experiments. In this study, we investigated bone tissue regeneration in an idealised hydrogel scaffold using a mechano-regulation model capable of predicting tissue differentiation, and specifically compared five loading cases, based on known experimental bioreactor regimes. These models predicted that low levels of mechanical loading, i.e. compression (0.5% strain), pore pressure of 10 kPa and a combination of compression (0.5%) and pore pressure (10 kPa), could induce more osteogenic differentiation and lead to the formation of a higher bone tissue fraction. In contrast greater volumes of cartilage and fibrous tissue fractions were predicted under higher levels of mechanical loading (i.e. compression strain of 5.0% and pore pressure of 100 kPa). The findings in this study may provide important information regarding the appropriate mechanical stimulation for in vitro bone tissue engineering experiments.

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

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Histological evolution of the regenerate during bone transport: an experimental study in sheep

INTRODUCTION

Bone transport (BT) for segmentary bone defects is a well-known technique as it enables correction with new bone formation, which is similar to the previous bone. Despite the high number of experimental studies of distraction osteogenesis in bone lengthening, the types of ossification and histological changes that occur in the regenerate of the bone transport process remain controversial.

OBJECTIVE

The aim of this study is to provide the complete evolution of tissues and the types of ossification in the regenerate during the different phases of bone formation after BT until the end of the remodelling period.

METHODS

A histological study was performed using ten adult sheep that were submitted to BT. The types of ossification as well as the evolution of different tissues in the regenerate were determined using histomorphometry and inmunohistochemical studies. The evolution of trabeculae thickness, osteoblast and osteoclast densities, relationship between collagen types and changes in vascularization were also studied.

RESULTS

Ossification was primarily intramembranous, with some focus of endochondral ossification in isolated animals. The cell counts showed a progression of cellular activity from the periphery to the centre, presenting the same progression as the growth of bone trabeculae, whose trabeculae thickness was quadrupled at the end of remodelling. Inmunohistochemical studies confirmed the prevalence of type I collagen and the ratio of the Type I/Type II collagen ratio was found to be 2.48. The percentages of the vascularized areas were proximally higher than distally in all animals, but distal zone obtained higher rates than the central region.

CONCLUSIONS

Bone transport regenerate exhibits a centripetal ossification model and a mixed pattern with predominance of intramembranous over endochondral ossification. The data obtained resemble partially to those found in models of bone lengthening applied to large animals. This study provides a detailed structural characterization of the newly formed tissue, which may help to explain the development of the regenerate of bone transport in humans. It will also serve for future mechanobiological models that may aid research on the effect of loading or distractor stiffness in clinical results.

A mathematical model for cell differentiation, as an evolutionary and regulated process

We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.

Responses of distraction regenerate to high-frequency traction at a rapid rate

BACKGROUND

Continuous traction is capable of creating an optimal biological environment for bone healing which may finally compensate for the rapid distraction rate in distraction osteogenesis. This study was designed to investigate the response of distraction callus to continuous distraction at a rapid rate using a rabbit model of mandibular lengthening.

METHODS

Thirty adult New Zealand white rabbits were randomly assigned to the intermittent (1 step/d) or continuous distraction (8 steps/s) group, with 15 in each. After osteotomy, manual-driven or autodriven distractor was adapted accordingly. The distraction was activated at a rate of 3.0 mm/d for 4 days. Five rabbits in each group were killed at week 2, week 4, and week 12 of consolidation, respectively. Plain radiography, microcomputed tomography, and histology examinations were used to evaluate the bone regeneration status.

RESULTS

Plain radiographs and histologic studies demonstrated more advanced bone healing in continuous distraction group than that in intermittent distraction group at all the examined time points. Quantitative microcomputed tomography analysis showed significantly higher bone volume in continuous distraction group at week 2 (p < 0.01) and week 4 (p < 0.05) of consolidation.

CONCLUSIONS

Continuous traction by autodriven distractor could be a promising clinical alternative to shorten the treatment course of distraction osteogenesis. Further studies to test its clinical potential using large animals that have similar metabolic rate and muscular resistance with human being are necessary.

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.

[Autologous tissue engineering by means of distraction osteogenesis: Biomechanical considerations]

Tissue engineering consists in producing functional replacement tissue. Distraction osteogenesis is a tissue engineering technique that uses the mechanical environment of cells to induce tissue regeneration, without need for exogenous biochemical factors. A better understanding of the optimal mechanical conditions of distraction callus stretching may reduce the duration, discomfort, and even social impact of distraction protocols, and complications and failures. We present the current state of knowledge in this field by addressing the fundamentals of elongating bone tissue biomechanics, the influence of rhythm and rate of distraction, and that of vectors and stability. Finally, we present the innovations currently studied, which may modify our clinical protocol in the short term.

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

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

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.

Mathematical modeling in wound healing, bone regeneration and tissue engineering

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.