Bone remodelling algorithms incorporating both strain and microdamage stimuli

Biomechanical theories to predict bone remodelling have used either mechanical strain or microdamage as the stimulus driving cellular responses. Even though experimental data have implicated both stimuli in bone cell regulation, a mechano-regulatory system incorporating both stimuli has not yet been proposed. In this paper, we test the hypothesis that bone remodelling may be regulated by signals due to both strain and microdamage. Four mechano-regulation algorithms are studied where the stimulus is: strain, damage, combined strain/damage, and either strain or damage with damage-adaptive remodelling prioritised when damage is above a critical level. Each algorithm is implemented with both bone lining cell (surface) sensors and osteocyte cell (internal) sensors. Each algorithm is applied to prediction of a bone multicellular unit (BMU) remodelling on the surface of a bone trabecula. It is predicted that a regulatory system capable of responding to changes in either strain or microdamage but which prioritises removal of damaged bone when damage is above a critical level, is the only one that provides a plausible prediction of BMU behaviour. A mechanism for this may be that, below a certain damage threshold, osteocyte processes can sense changes in strain and fluid flow but above the threshold damage interferes with the signalling mechanism, or causes osteocyte apoptosis so that a remodelling response occurs to remove the dead osteocytes.     

Relation between subject-specific hip joint loading, stress distribution in the proximal femur and bone mineral density changes after total hip replacement

In the prediction of bone remodelling processes after total hip replacement (THR), modelling of the subject-specific geometry is now state-of-the-art. In this study, we demonstrate that inclusion of subject-specific loading conditions drastically influences the calculated stress distribution, and hence influences the correlation between calculated stress distributions and changes in bone mineral density (BMD) after THR.For two patients who received cementless THR, personalized finite element (FE) models of the proximal femur were generated representing the pre- and post-operative geometry. FE analyses were performed by imposing subject-specific three-dimensional hip joint contact forces as well as muscle forces calculated based on gait analysis data. Average values of the von Mises stress were calculated for relevant zones of the proximal femur. Subsequently, the load cases were interchanged and the effect on the stress distribution was evaluated. Finally, the subject-specific stress distribution was correlated to the changes in BMD at 3 and 6 months after THR.We found subject-specific differences in the stress distribution induced by specific loading conditions, as interchanging of the loading also interchanged the patterns of the stress distribution. The correlation between the calculated stress distribution and the changes in BMD were affected by the two-dimensional nature of the BMD measurement.Our results confirm the hypothesis that inclusion of subject-specific hip contact forces and muscle forces drastically influences the stress distribution in the proximal femur. In addition to patient-specific geometry, inclusion of patient-specific loading is, therefore, essential to obtain accurate input for the analysis of stress distribution after THR.     

Extracellular NO signalling from a mechanically stimulated osteocyte

Bone remodelling is a dynamic process that requires the coordinated interaction of osteocytes, osteoblasts, and osteoclasts, collaborating in basic multicellular units (BMUs). Communication between these cells can be by extracellular soluble molecules as well as directly propagating intercellular signalling molecules. Key to the understanding of bone remodelling is osteocyte mechanosensing and chemical signalling to the surrounding cells, since osteocytes are believed to be the mechanosensors of bone, responding to mechanical stresses. Nitric oxide (NO) is an important parameter to study osteocyte activation following mechanical loading. It is a small short-lived molecule, which makes its real-time, quantitative monitoring difficult. However, recently we demonstrated that DAR-4M AM chromophore can be used for real-time quantitative monitoring of intracellular NO production in individual cells following mechanical loading. Here we studied if a single mechanically stimulated osteocyte communicates with, and thus activates its surrounding cells via extracellular soluble factors. We monitored quantitatively intracellular NO production in the stimulated osteocyte and in its surrounding osteocytes, which were not interconnected. Mechanical stimulation by microneedle of a single-MLO-Y4 osteocyte-like cell upregulated the average intracellular NO production by 94% in the stimulated cell, and by 31-150% in the surrounding osteocytes. In conclusion, a single osteocyte can disseminate a mechanical stimulus to its surrounding osteocytes via extracellular soluble signalling factors. This reinforces the putative mechanosensory role of osteocytes, and demonstrates a possible mechanism by which a single mechanically stimulated osteocyte can communicate with other cells in a BMU, which might help to better understand the intricacies of intercellular interactions in BMUs and thus bone remodelling.     

Phenotypic characterization of osteoarthritic osteocytes from the sclerotic zones: a possible pathological role in subchondral bone sclerosis

Subchondral bone sclerosis is a well-recognised manifestation of osteoarthritis (OA). The osteocyte cell network is now considered to be central to the regulation of bone homeostasis; however, it is not known whether the integrity of the osteocyte cell network is altered in OA patients. The aim of this study was to investigate OA osteocyte phenotypic changes and its potential role in OA subchondral bone pathogenesis. The morphological and phenotypic changes of osteocytes in OA samples were investigated by micro-CT, SEM, histology, immunohistochemistry, TRAP staining, apoptosis assay and real-time PCR studies. We demonstrated that in OA subchondral bone, the osteocyte morphology was altered showing rough and rounded cell body with fewer and disorganized dendrites compared with the osteocytes in control samples. OA osteocyte also showed dysregulated expression of osteocyte markers, apoptosis, and degradative enzymes, indicating that the phenotypical changes in OA osteocytes were accompanied with OA subchondral bone remodelling (increased osteoblast and osteoclast activity) and increased bone volume with altered mineral content. Significant alteration of osteocytes identified in OA samples indicates a potential regulatory role of osteocytes in subchondral bone remodelling and mineral metabolism during OA pathogenesis.     

Tensile trabeculae--myth or reality?

Understanding of the functional role of the trabecular bone is very important for the analysis and computer-aided simulations of bone remodelling processes. The aspired wide clinical applications remain a remote future despite a great number of developed up-to-date approaches and theories and collected data on both material properties of the trabecular bone and its reaction to various stimuli. It is widely accepted that the mechanical loading plays the major role for the structure of the cancellous bone. The in vivo loading conditions of the cancellous bone are not known. Hence, for the computer-aided analysis and modelling of the trabecular bone specimens, simplified loading conditions are used. Also for the analysis of the cancellous bone as a part of a whole bone simplified loading conditions are assumed based on previous research without questioning its accuracy or relevance to the real in vivo conditions. In particular, the bending loading of the bone, which originates from the well-known observations made more than a century ago that have evolved in the trajectorial theory or "tensile trabeculae tradition", is often assumed to reflect the physiological loading conditions of bones. Some studies show that the bending or tensile-compressive orthogonal loading conditions for the cancellous bone may lead to plausible results. However, some other research works suggest that the presence of the tensile trabecular structures (particularly in the proximal femur) is doubtful and the bending loading conditions in bone should be treated with caution. Moreover, the loading conditions with compensated (or minimised) bending also produce results that correlate with the material distribution in the bone. The purpose of this review is to analyse some of the data and ideas available in the literature and to discuss the question of the major factors that define the shape and structure of the trabecular bone during the process of functional adaptation.     

Strain-derived canalicular fluid flow regulates osteoclast activity in a remodelling osteon--a proposal

The concept of bone remodelling by basic multicellular units is well established, but how the resorbing osteoclasts find their way through the pre-existing bone matrix remains unexplained. The alignment of secondary osteons along the dominant loading direction suggests that remodelling is guided by mechanical strain. This means that adaptation (Wolff's Law) takes place throughout life at each remodelling cycle. We propose that alignment during remodelling occurs as a result of different canalicular flow patterns around cutting cone and reversal zone during loading. Low canalicular flow around the tip of the cutting cone is proposed to reduce NO production by local osteocytes thereby causing their apoptosis. In turn, osteocyte apoptosis could be the mechanism that attracts osteoclasts, leading to further excavation of bone in the direction of loading. At the transition between cutting cone and reversal zone, however, enhanced canalicular flow will stimulate osteocytes to increase NO production, which induces osteoclast retraction and detachment from the bone surface. Together, this leads to a treadmill of attaching and detaching osteoclasts in the tip and the periphery of the cutting cone, respectively, and the digging of a tunnel in the direction of loading.     

Simulation of bone remodelling in orthodontic treatment

Orthodontic treatments not only displace irregular teeth but also induce responses in surrounding bone tissues. Bone remodelling is regarded as the regulatory mechanism triggered by mechanical loading. This study was aimed at investigating the effect of orthodontic loading on both tooth movement and neighbouring bone density distribution. A set of computational algorithms incorporating both external and internal remodelling mechanisms was implemented into a patient-specific 3D finite element (FE) model to investigate and analyse orthodontic treatment under four typical modes of orthodontic loading. The consequence of orthodontic treatment was reproduced numerically by using this FE-based technique. The results indicated that the diverse modes of orthodontic loading would result in different magnitudes of tooth movement and particular morphology of bone density distribution. It is illuminated that the newly developed algorithms may replicate the clinical situation more closely compared with the previous proposed method.     

Influence of mastication and edentulism on mandibular bone density

The aim of this study was to demonstrate that external loading due to daily activities, including mastication, speech and involuntary open–close cycles of the jaw contributes to the internal architecture of the mandible. A bone remodelling algorithm that regulates the bone density as a function of stress and loading cycles is incorporated into finite element analysis. A three-dimensional computational model is constructed on the basis of computerised tomography (CT) images of a human mandible. Masticatory muscle activation involved during clenching is modelled by static analysis using linear optimisation. Other loading conditions are approximated by imposing mandibular flexure. The simulations predict that mandibular bone density distribution results in a tubular structure similar to what is observed in the CT images. Such bone architecture is known to provide the bone optimum strength to resist bending and torsion during mastication while reducing the bone mass. The remodelling algorithm is used to simulate the influence of edentulism on mandibular bone loss. It is shown that depending on the location and number of missing teeth, up to one-third of the mandibular bone mass can be lost due to lack of adequate mechanical stimulation.     

Decreased pericellular matrix production and selection for enhanced cell membrane repair may impair osteocyte responses to mechanical loading in the aging skeleton

Transient plasma membrane disruptions (PMD) occur in osteocytes with in vitro and in vivo loading, initiating mechanotransduction. The goal here was to determine whether osteocyte PMD formation or repair is affected by aging. Osteocytes from old (24 months) mice developed fewer PMD (?76% females, ?54% males) from fluid shear than young (3 months) mice, and old mice developed fewer osteocyte PMD (?51%) during treadmill running. This was due at least in part to decreased pericellular matrix production, as studies revealed that pericellular matrix is integral to formation of osteocyte PMD, and aged osteocytes produced less pericellular matrix (?55%). Surprisingly, osteocyte PMD repair rate was faster (+25% females, +26% males) in osteocytes from old mice, and calcium wave propagation to adjacent nonwounded osteocytes was blunted, consistent with impaired mechanotransduction downstream of PMD in osteocytes with fast PMD repair in previous studies. Inducing PMD via fluid flow in young osteocytes in the presence of oxidative stress decreased postwounding cell survival and promoted accelerated PMD repair in surviving cells, suggesting selective loss of slower‐repairing osteocytes. Therefore, as oxidative stress increases during aging, slower‐repairing osteocytes may be unable to successfully repair PMD, leading to slower‐repairing osteocyte death in favor of faster‐repairing osteocyte survival. Since PMD are an important initiator of mechanotransduction, age‐related decreases in pericellular matrix and loss of slower‐repairing osteocytes may impair the ability of bone to properly respond to mechanical loading with bone formation. These data suggest that PMD formation and repair mechanisms represent new targets for improving bone mechanosensitivity with aging.     

Bone morphology allows estimation of loading history in a murine model of bone adaptation

Bone adapts its morphology (density/micro- architecture) in response to the local loading conditions in such a way that a uniform tissue loading is achieved (‘Wolff’s law’). This paradigm has been used as a basis for bone remodeling simulations to predict the formation and adaptation of trabecular bone. However, in order to predict bone architectural changes in patients, the physiological external loading conditions, to which the bone was adapted, need to be determined. In the present study, we developed a novel bone loading estimation method to predict such external loading conditions by calculating the loading history that produces the most uniform bone tissue loading. We applied this method to murine caudal vertebrae of two groups that were in vivo loaded by either 0 or 8 N, respectively. Plausible load cases were sequentially applied to micro-finite element models of the mice vertebrae, and scaling factors were calculated for each load case to derive the most uniform tissue strain-energy density when all scaled load cases are applied simultaneously. The bone loading estimation method was able to predict the difference in loading history of the two groups and the correct load magnitude for the loaded group. This result suggests that the bone loading history can be estimated from its morphology and that such a method could be useful for predicting the loading history for bone remodeling studies or at sites where measurements are difficult, as in bone in vivo or fossil bones.     

Adaptive diffuse domain approach for calculating mechanically induced deformation of trabecular bone

Remodelling of trabecular bone is essentially affected by the mechanical load of the trabeculae. Mathematical modelling and simulation of the remodelling process have to include time-consuming calculations of the displacement field within the complex trabecular structure under loading. We present an adaptive diffuse domain approach for calculating the elastic bone deformation based on micro computer tomogram data of real trabecular bone structures and compared it with a conventional voxel-based finite element method. In addition to allowing for higher computational efficiency, the adaptive approach is characterised by a very smooth representation of the bone surface, which suggests that this approach would be suitable as a basis for future simulations of bone resorption and formation processes within the trabecular structure.     

Orbital and maxillofacial computer aided surgery: patient-specific finite element models to predict surgical outcomes

This paper addresses an important issue raised for the clinical relevance of Computer-Assisted Surgical applications, namely the methodology used to automatically build patient-specific finite element (FE) models of anatomical structures. From this perspective, a method is proposed, based on a technique called the mesh-matching method, followed by a process that corrects mesh irregularities. The mesh-matching algorithm generates patient-specific volume meshes from an existing generic model. The mesh regularization process is based on the Jacobian matrix transform related to the FE reference element and the current element.This method for generating patient-specific FE models is first applied to computer-assisted maxillofacial surgery, and more precisely, to the FE elastic modelling of patient facial soft tissues. For each patient, the planned bone osteotomies (mandible, maxilla, chin) are used as boundary conditions to deform the FE face model, in order to predict the aesthetic outcome of the surgery. Seven FE patient-specific models were successfully generated by our method. For one patient, the prediction of the FE model is qualitatively compared with the patient's post-operative appearance, measured from a computer tomography scan. Then, our methodology is applied to computer-assisted orbital surgery. It is, therefore, evaluated for the generation of 11 patient-specific FE poroelastic models of the orbital soft tissues. These models are used to predict the consequences of the surgical decompression of the orbit. More precisely, an average law is extrapolated from the simulations carried out for each patient model. This law links the size of the osteotomy (i.e. the surgical gesture) and the backward displacement of the eyeball (the consequence of the surgical gesture).     

Influence of interface condition and implant design on bone remodelling and failure risk for the resurfaced femoral head

Resurfacing of the femur has experienced a revival, particularly in younger and more active patients. The implant is generally cemented onto the reamed trabecular bone and theoretical remodelling for this configuration, as well as uncemented variations, has been studied with relation to component positioning for the most common designs. The purpose of this study was to investigate the influence of different interface conditions, for alternative interior implant geometries, on bone strains in comparison to the native femur, and its consequent remodelling. A cylindrical interior geometry, two conical geometries and a spherical cortex-preserving design were compared with a standard implant (ASR, DePuy International, Ltd., UK), which has a 3° cone. Cemented as well as uncemented line to line and press-fit conditions were modelled for each geometry. A patient-specific finite element model of the proximal femur was used with simulated walking loads. Strain energy density was compared between the reference and resurfaced femur, and input into a remodelling algorithm to predict density changes post-operatively. The common cemented designs (cylindrical, slightly conical) had strain shielding in the superior femoral head (>35% reduction) as well as strain concentrations (strain>5%) in the neck regions near the implant rim. The cortex-preserving (spherical) and strongly conical designs showed less strain shielding. In contrast to the cemented implants, line to line implants showed a density decrease at the centre of the femoral head, while all press-fit versions showed a density increase (>100%) relative to the native femur, which suggests that uncemented press-fit implants could limit bone resorption.     

Fluid flow in the osteocyte mechanical environment: a fluid–structure interaction approach

Osteocytes are believed to be the primary sensor of mechanical stimuli in bone, which orchestrate osteoblasts and osteoclasts to adapt bone structure and composition to meet physiological loading demands. Experimental studies to quantify the mechanical environment surrounding bone cells are challenging, and as such, computational and theoretical approaches have modelled either the solid or fluid environment of osteocytes to predict how these cells are stimulated in vivo. Osteocytes are an elastic cellular structure that deforms in response to the external fluid flow imposed by mechanical loading. This represents a most challenging multi-physics problem in which fluid and solid domains interact, and as such, no previous study has accounted for this complex behaviour. The objective of this study is to employ fluid–structure interaction (FSI) modelling to investigate the complex mechanical environment of osteocytes in vivo. Fluorescent staining of osteocytes was performed in order to visualise their native environment and develop geometrically accurate models of the osteocyte in vivo. By simulating loading levels representative of vigorous physiological activity ( $3,000\,\upmu \upvarepsilon $ compression and 300 Pa pressure gradient), we predict average interstitial fluid velocities $(\sim 60.5\,\upmu \text{ m/s })$ and average maximum shear stresses $(\sim 11\, \text{ Pa })$ surrounding osteocytes in vivo. Interestingly, these values occur in the canaliculi around the osteocyte cell processes and are within the range of stimuli known to stimulate osteogenic responses by osteoblastic cells in vitro. Significantly our results suggest that the greatest mechanical stimulation of the osteocyte occurs in the cell processes, which, cell culture studies have indicated, is the most mechanosensitive area of the cell. These are the first computational FSI models to simulate the complex multi-physics mechanical environment of osteocyte in vivo and provide a deeper understanding of bone mechanobiology.     

Mechanical compression and hydrostatic pressure induce reversible changes in actin cytoskeletal organisation in chondrocytes in agarose

In numerous cell types, the cytoskeleton has been widely implicated in mechanotransduction pathways involving stretch-activated ion channels, integrins and deformation of intracellular organelles. Studies have also demonstrated that the cytoskeleton can undergo remodelling in response to mechanical stimuli such as tensile strain or fluid flow. In articular chondrocytes, the mechanotransduction pathways are complex, inter-related and as yet, poorly understood. Furthermore, little is known of how the chondrocyte cytoskeleton responds to physiological mechanical loading. This study utilises the well-characterised chondrocyte-agarose model and an established confocal image-analysis technique to demonstrate that both static and cyclic, compressive strain and hydrostatic pressure all induce remodelling of actin microfilaments. This remodelling was characterised by a change from a uniform to a more punctate distribution of cortical actin around the cell periphery. For some loading regimes, this remodelling was reversed over a subsequent 1h unloaded period. This reversible remodelling of actin cytoskeleton may therefore represent a mechanism through which the chondrocyte alters its mechanical properties and mechanosensitivity in response to physiological mechanical loading.     

The response of bone to mechanical loading and disuse: fundamental principles and influences on osteoblast/osteocyte homeostasis

Bone’s response to increased or reduced loading/disuse is a feature of many clinical circumstances, and our daily life, as habitual activities change. However, there are several misconceptions regarding what constitutes loading or disuse and why the skeleton gains or loses bone. The main purpose of this article is to discuss the fundamentals of the need for bone to experience the effects of loading and disuse, why bone loss due to disuse occurs, and how it is the target of skeletal physiology which drives pathological bone loss in conditions that may not be seen as being primarily due to disuse. Fundamentally, if we accept that hypertrophy of bone in response to increased loading is a desirable occurrence, then disuse is not a pathological process, but simply the corollary of adaptation to increased loads. If adaptive processes occur to increase bone mass in response to increased load, then the loss of bone in disuse is the only way that adaptation can fully tune the skeleton to prevailing functional demands when loading is reduced. The mechanisms by which loading and disuse cause bone formation or resorption are the same, although the direction of any changes is different. The osteocyte and osteoblast are the key cells involved in sensing and communicating the need for changes in mass or architecture as a result of changes in experienced loading. However, as those cells are affected by numerous other influences, the responses of bone to loading or disuse are not simple, and alter under different circumstances. Understanding the principles of disuse and loading and the mechanisms underlying them therefore represents an important feature of bone physiology and the search for targets for anabolic therapies for skeletal pathology.     

The effect of muscle loading on the simulation of bone remodelling in the proximal femur

A large number of finite element analyses of the proximal femur rely on a simplified set of muscle and joint contact loads to represent the boundary conditions of the model. In the context of bone remodelling analysis around hip implants, muscle loading affects directly the spatial distribution of the remodelling signal. In the present study we performed a sensitivity analysis on the effect of different muscle loading configurations on the outcome of the bone remodelling simulation. An anatomical model of the femur with the implanted stem in place was constructed using the CT data of the Visible Human Project dataset of the National Institute of Health. The model was loaded with three muscle force configurations with increasing level of complexity. A strain adaptive remodelling rule was employed to simulate the post-operative bone changes around the implant stem and the results of the simulation were assessed quantitatively in terms of the bone mineral content changes in 18 periprosthetic regions of interest. The results showed considerable differences in the amount of bone loss predicted between the three cases. The simplified models generally predicted more pronounced bone loss. Although the overall remodelling patterns observed were similar, the bone conserving effect of additional muscle forces in the vicinity of their areas of attachment was clear. The results of this study suggest that the loading configuration of the FE model does play an important role in the outcome of the remodelling simulation.     

Determination of dynamically adapting anisotropic material properties of bone under cyclic loading

Because bone tissue adapts to loading conditions, finite element simulations of remodelling bone require a precise prediction of dynamically changing anisotropic elastic parameters. We present a phenomenological theory that refers to the tissue in terms of the tendency of the structure to align with principal stress directions. We describe the material parameters of remodelling bone. This work follows findings by the same research group and independently by Danilov (1971) in the field of plasticity, where the dependencies of the components of the stiffness tensor in terms of time are based on Hill's anisotropy. We modify such an approach in this novel theory that addresses bone tissue that can regenerate. The computational assumption of the theory is that bone trabeculae have the tendency to orient along one of the principal stress directions but during remodelling the principal stresses change continuously and the resulting orientation of the trabeculae can differ from the principal stress direction at any given time. The novelty of this work consists in the limited number of parameters needed to compute the twenty-one anisotropic material parameters at any given location in the bone tissue. In addition to the theory, we present here two cases of simplified geometry, loading and boundary conditions to show the effect of (1) time on the material properties; and (2) change of loading conditions on the anisotropic parameters. The long term goal is to experimentally verify that the predictions generated by theory provide a reliable simulation of cancellous bone properties.     

Numerical simulation of the remodelling process of trabecular architecture around dental implants

Dental implants may alter the mechanical environment in the jawbone, thereby causing remodelling and adaptation of the surrounding trabecular bone tissues. To improve the efficacy of dental implant systems, it is necessary to consider the effect of bone remodelling on the performance of the prosthetic systems. In this study, finite element simulations were implemented to predict the evolution of microarchitecture around four implant systems using a previously developed model that combines both adaptive and microdamage-based mechano-sensory mechanisms in bone remodelling process. Changes in the trabecular architecture around dental implants were mainly focused. The simulation results indicate that the orientational and ladder-like architecture around the implants predicted herein is in good agreement with those observed in animal experiments and clinical observations. The proposed algorithms were shown to be effective in simulating the remodelling process of trabecular architecture around dental implant systems. In addition, the architectural features around four typical dental implant systems in alveolar bone were evaluated comparatively.