Biomechanics of leg deformity treatment

At pre-school age, there is a possibility to treat severe varosity and/or valgosity of legs by orthoses. The three points force effect of the orthosis partially corrects the pathologic defect of the leg. If the orthosis is intermittently used for a long time the correction is permanent. Step by step correction of bone deformities are based on remodelling of growth epiphyses and bones that are caused by orthotic bending pre-stressing. According to Hüter-Volkmann's law, the oblique loading regulates the growth of epiphyseal plates of long bone into the direction of the pressure result and the bone remodelling process is started: it means that the bone grows at the tensile part of growth epiphyses more quickly than at pressure one and gradually eliminates the varosity and/or valgosity defect. The knowledge of stress values for starting of the bone remodelling process is principal for clinical praxis. The values of pre-stressing cannot be increased by starting the remodelling process from the ethical point of view but it can be judged on its starting according to the success of the treatment. The aim of this article is to study the bone, ligament stress state and deformations of successful treatment. Method and calculation algorithm of stress state and deformation that are necessary for the starting of the remodelling process at the knee region were verified on a group of eight patients that were fitted by orthoses with bending pre-stressing. The space models of the knee, femur and tibia were composed with the help of X-ray, CT and MRI scan. The calculation algorithm was implemented on a PC and the program can be easily applied at clinical praxis.     

Implant–bone interface healing and adaptation in resurfacing hip replacement

Hip resurfacing demonstrates good survivorship as a treatment for young patients with osteoarthritis, but occasional implant loosening failures occur. On the femoral side there is radiographic evidence suggesting that the implant stem bears load, which is thought to lead to proximal stress shielding and adaptive bone remodelling. Previous attempts aimed at reproducing clinically observed bone adaptations in response to the implant have not recreated the full set of common radiographic changes, so a modified bone adaptation algorithm was developed in an attempt to replicate more closely the effects of the prosthesis on the host bone. The algorithm features combined implant–bone interface healing and continuum bone remodelling. It was observed that remodelling simulations that accounted for progressive gap filling at the implant–bone interface predicted the closest periprosthetic bone density changes to clinical X-rays and DEXA data. This model may contribute to improved understanding of clinical failure mechanisms with traditional hip resurfacing designs and enable more detailed pre-clinical analysis of new designs.     

Implant-bone interface healing and adaptation in resurfacing hip replacement

Hip resurfacing demonstrates good survivorship as a treatment for young patients with osteoarthritis, but occasional implant loosening failures occur. On the femoral side there is radiographic evidence suggesting that the implant stem bears load, which is thought to lead to proximal stress shielding and adaptive bone remodelling. Previous attempts aimed at reproducing clinically observed bone adaptations in response to the implant have not recreated the full set of common radiographic changes, so a modified bone adaptation algorithm was developed in an attempt to replicate more closely the effects of the prosthesis on the host bone. The algorithm features combined implant-bone interface healing and continuum bone remodelling. It was observed that remodelling simulations that accounted for progressive gap filling at the implant-bone interface predicted the closest periprosthetic bone density changes to clinical X-rays and DEXA data. This model may contribute to improved understanding of clinical failure mechanisms with traditional hip resurfacing designs and enable more detailed pre-clinical analysis of new designs.     

Stress changes in the femoral head due to porous ingrowth surface replacement arthroplasty

Finite element stress analyses were conducted of the canine femoral head before and after implantation of various surface replacement-type components. The femoral head was replaced by four implant geometries; (a) shell, (b) shell with peg, (c) shell with rod, and (d) a new epiphyseal replacement design. All implants were modelled to simulate bony ingrowth along the underside of the shell and along the surfaces of the peg and rod. The results indicated that in the normal femur the forces are transferred from the articular surface through the femoral head cancellous bone to the inferior cortical shell of the femoral neck. After shell-type surface replacement, forces were transferred more distally at the rim of the shell and at the end of the peg or rod, thereby reducing the stresses in the proximal head cancellous bone. Computer simulation of bone remodelling due to proximal bone stress reduction was shown to accentuate the abnormality of the stress fields. Surface replacement with a lower modulus material created a less abnormal redistribution of bone stresses. The new epiphyseal replacement design resulted in stress distributions similar to those in the normal femoral head and minimal shear stresses at the implant/bone interface. These findings suggest that the epiphyseal replacement concept may provide better initial mechanical integrity and create a more benign milieu for adaptive bone remodelling than conventional, shell-type surface replacement components.     

Sensitivity Analysis and Optimal Shape Design for Bone-Prosthesis Interfaces in a Femoral Head Surface Replacement

A numerical optimization procedure has been applied for the shape optimal design of a femoral head surface replacement. The failure modes of the prosthesis that were considered in the formulation of the objective functions concerned the interface stress magnitude and the bone remodelling activity beneath the implant. In order to find a compromising solution between different requirements demanded by the two objective functions, a two step optimization procedure has been developed. Through step 1 the minimization of interface stress was achieved, through step 2 the minimization of bone remodelling was achieved with constraints on interface stresses. The results obtained provided an optimal design that generates limited bone remodelling activity with controlled interface stress distribution. The computational procedure was based on the application of the finite element method, linked to a mathematical programming package and a design sensitivity analysis package.     

Sensitivity Analysis and Optimal Shape Design for Bone-Prosthesis Interfaces in a Femoral Head Surface Replacement

Abstract

A numerical optimization procedure has been applied for the shape optimal design of a femoral head surface replacement. The failure modes of the prosthesis that were considered in the formulation of the objective functions concerned the interface stress magnitude and the bone remodelling activity beneath the implant. In order to find a compromising solution between different requirements demanded by the two objective functions, a two step optimization procedure has been developed. Through step I the minimization of interface stress was achieved, through step 2 the minimization of bone remodelling was achieved with constraints on interface stresses.

The results obtained provided an optimal design that generates limited bone remodelling activity with controlled interface stress distribution.

The computational procedure was based on the application of the finite element method, linked to a mathematical programming package and a design sensitivity analysis package.     

A novel mathematical model of bone remodelling cycles for trabecular bone at the cellular level

After an initial phase of growth and development, bone undergoes a continuous cycle of repair, renewal and optimisation by a process called remodelling. This paper describes a novel mathematical model of the trabecular bone remodelling cycle. It is essentially formulated to simulate a remodelling event at a fixed position in the bone, integrating bone removal by osteoclasts and formation by osteoblasts. The model is developed to construct the variation in bone thickness at a particular point during the remodelling event, derived from standard bone histomorphometric analyses. The novelties of the approach are the adoption of a predator-prey model to describe the dynamic interaction between osteoclasts and osteoblasts, using a genetic algorithm-based solution; quantitative reconstruction of the bone remodelling cycle; and the introduction of a feedback mechanism in the bone formation activity to co-regulate bone thickness. The application of the model is first demonstrated by using experimental data recorded for normal (healthy) bone remodelling to predict the temporal variation in the number of osteoblasts and osteoclasts. The simulated histomorphometric data and remodelling cycle characteristics compare well with the specified input data. Sensitivity studies then reveal how variations in the model's parameters affect its output; it is hoped that these parameters can be linked to specific biochemical factors in the future. Two sample pathological conditions, hypothyroidism and primary hyperparathyroidism, are examined to demonstrate how the model could be applied more broadly, and, for the first time, the osteoblast and osteoclast populations are predicted for these conditions. Further data are required to fully validate the model's predictive capacity, but this work shows it has potential, especially in the modelling of pathological conditions and the optimisation of the treatment of those conditions.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone–soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone–soft tissue interface, resulting in bone resorption.     

Influence of the change in stem length on the load transfer and bone remodelling for a cemented resurfaced femur

The effect of a short-stem femoral resurfacing component on load transfer and potential failure mechanisms has rarely been studied. The stem length has been reduced by approximately 50% as compared to the current long-stem design. Using 3-D FE models of natural and resurfaced femurs, the study is aimed at investigating the influence of a short-stem resurfacing component on load transfer and bone remodelling. Applied loading conditions include normal walking and stair climbing. The mechanical role of the stem along with implant–cement and stem–bone contact conditions was observed to be crucial. Shortening the stem length to half of the current length (long-stem) led to several favourable effects, even though the stress distributions in the implant and the cement were similar in both the cases. The short-stem implant led not only to a more physiological stress distribution but also to bone apposition (increase of 20–70% bone density) in the superior resurfaced head, when the stem–bone contact prevailed. This also led to a reduction in strain concentration in the cancellous bone around the femoral neck–component junction. The normalised peak strain in this region was lower for the short-stem design as compared to that of the long-stem one, thereby reducing the initial risk of neck fracture. The effect of strain shielding (50–75% reduction) was restricted to a small bone volume underlying the cement, which was approximately half of that of the long-stem design. Consequently, bone resorption was considerably less for the short-stem design. The short-stem design offers better prospects than the long-stem resurfacing component.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone-soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone-soft tissue interface, resulting in bone resorption.     

Numerical estimation of bone density and elastic constants distribution in a human mandible

In this paper, we try to predict the distribution of bone density and elastic constants in a human mandible, based on the stress level produced by mastication loads using a mathematical model of bone remodelling. These magnitudes are needed to build finite element models for the simulation of the mandible mechanical behavior. Such a model is intended for use in future studies of the stability of implant-supported dental prostheses. Various models of internal bone remodelling, both phenomenological and more recently mechanobiological, have been developed to determine the relation between bone density and the stress level that bone supports. Among the phenomenological models, there are only a few that are also able to reproduce the level of anisotropy. These latter have been successfully applied to long bones, primarily the femur. One of these models is here applied to the human mandible, whose corpus behaves as a long bone. The results of bone density distribution and level of anisotropy in different parts of the mandible have been compared with various clinical studies, with a reasonable level of agreement.     

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.     

Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement

In this work, a new model for internal anisotropic bone remodelling is applied to the study of the remodelling behaviour of the proximal femur before and after total hip replacement (THR). This model considers bone remodelling under the scope of a general damage-repair theory following the principles of continuum damage mechanics. A "damage-repair" tensor is defined in terms of the apparent density and Cowin's "fabric tensor", respectively, associated with porosity and directionality of the trabeculae. The different elements of a thermodynamically consistent damage theory are established, including resorption and apposition criteria, evolution law and rate of remodelling. All of these elements were introduced and discussed in detail in a previous paper (García, J. M., Martinez, M. A., Doblaré, M., 2001. An anisotrophic internal-external bone adaptation model based on a combination of CAO and continuum damage mechanics technologies. Computer Methods in Biomechanics and Biomedical Engineering 4(4), 355-378.), including the definition of the proposed mechanical stimulus and the qualitative properties of the model. In this paper, the fundamentals of the proposed model are briefly reviewed and the computational aspects of its implementation are discussed. This model is then applied to the analysis of the remodelling behaviour of the intact femur obtaining densities and mass principal values and directions very close to the experimental data. The second application involved the proximal femoral extremity after THR and the inclusion of an Exeter prosthesis. As a result of the simulation process, some well-known features previously detected in medical clinics were recovered, such as the stress yielding effect in the proximal part of the implant or the enlargement of the cortical layer at the distal part of the implant. With respect to the anisotropic properties, bone microstructure and local stiffness are known to tend to align with the stress principal directions. This experimental fact is mathematically proved in the framework of this remodelling model and clearly shown in the results corresponding to the intact femur. After THR the degree of anisotropy decreases tending, specifically in the proximal femur, to a more isotropic behaviour.     

Prediction of bone adaptation in the ulnar-osteotomized sheep's forelimb using an anatomical finite element model

A method for the prediction of the time-course of bone adaptation based on an alternative hypothesis of strength optimization has been previously investigated and developed by Prendergast and Taylor¹. This paper extends our work in the study of the effectiveness of this bone adaptation model in predicting similar bone remodelling to that observed in animal experiments. In particular the experimental work which has been modelled is that of Lanyon, Goodship, Pye and McFie². An anatomical finite element model of the sheep's forelimb has been generated for this purpose and is used to estimate stresses in the bone structure for the normal and osteotomized condition. The propensity for remodelling of the altered bone structure is predicted using the proposed remodelling law for the new stress field in the bone structure. The preliminary results indicate an initial bone adaptation pattern similar to that observed experimentally without the necessity to use arbitrarily different constants for the endosteal and periosteal surfaces. We therefore suggest that the remodelling law based on damage and repair gives a better predictive model of bone adaptation than previous models.     

On the role of bone damage in calcium homeostasis

Bone serves as the reservoir of some minerals including calcium. If calcium is needed anywhere in the body, it can be removed from the bone matrix by resorption and put back into the blood flow. During bone remodelling the resorbed tissue is replaced by osteoid which gets mineralized very slowly. Then, calcium homeostasis is controlled by bone remodelling, among other processes: the more intense is the remodelling activity, the lower is the mineral content of bone matrix. Bone remodelling is initiated by the presence of microstructural damage. Some experimental evidences show that the fatigue properties of bone are degraded and more microdamage is accumulated due to the external load as the mineral content increases. That damage initiates bone remodelling and the mineral content is so reduced. Therefore, this process prevents the mineral content of bone matrix to reach very high (non-physiological) values. A bone remodelling model has been used to simulate this regulatory process. In this model, damage is an initiation factor for bone remodelling and is estimated through a fatigue algorithm, depending on the macroscopic strain level. Mineral content depends on bone remodelling and mineralization rate. Finally, the bone fatigue properties are defined as dependent on the mineral content, closing the interconnection between damage and mineral content. The remodelling model was applied to a simplified example consisting of a bar under tension with an initially heterogeneous mineral distribution. Considering the fatigue properties as dependent on the mineral content, the mineral distribution tends to be homogeneous with an ash fraction within the physiological range. If such dependance is not considered and fatigue properties are assumed constant, the homogenization is not always achieved and the mineral content may rise up to high non-physiological values. Thus, the interconnection between mineral content and fatigue properties is essential for the maintenance of bone's structural integrity as well as for the calcium homeostasis.     

Bone remodelling of a proximal femur with the thrust plate prosthesis: an in vitro case

The key to the development of a successful implant is an understanding of the effect of bone remodelling on its long-term fixation. In this study, clinically observed patterns of bone remodelling have been compared with computer-based predictions for one particular design of prosthesis, the Thrust Plate Prosthesis (Centerpulse Orthopedics, Winterthur, Switzerland). Three-dimensional finite-element models were created using geometrical and bone density data obtained from CT scanning. Results from the bone remodelling simulation indicated that varying the relative rate of bone deposition/resorption and the interfacial conditions between the bone and the implant could produce the trend towards the two clinically observed patterns of remodelling.     

Bone Remodelling of a Proximal Femur with the Thrust Plate Prosthesis: An In Vitro Case

The key to the development of a successful implant is an understanding of the effect of bone remodelling on its long-term fixation. In this study, clinically observed patterns of bone remodelling have been compared with computer-based predictions for one particular design of prosthesis, the Thrust Plate Prosthesis (Centerpulse Orthopedics, Winterthur, Switzerland). Three-dimensional finite-element models were created using geometrical and bone density data obtained from CT scanning. Results from the bone remodelling simulation indicated that varying the relative rate of bone deposition/resorption and the interfacial conditions between the bone and the implant could produce the trend towards the two clinically observed patterns of remodelling.     

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.     

The role of the Wnt signalling pathway in the energy metabolism of bone remodelling

ObjectivesBone remodelling is necessary to repair old and impaired bone caused by aging and its effects. Injury in the process of bone remodelling generally leads to the development of various bone diseases. Energy metabolism plays crucial roles in bone cell formation and function, the disorder of which will disrupt the balance between bone formation and bone resorption.Materials and MethodsHere, we review the intrinsic interactions between bone remodelling and energy metabolism and the role of the Wnt signalling pathway.ResultsWe found a close interplay between metabolic pathways and bone homeostasis, demonstrating that bone plays an important role in the regulation of energy balance. We also discovered that Wnt signalling is associated with multiple biological processes regulating energy metabolism in bone cells.ConclusionsThus, targeted regulation of Wnt signalling and the recovery of the energy metabolism function of bone cells are key means for the treatment of metabolic bone diseases.

As a critical physiological process, bone remodelling is necessary to repair impaired bone caused by daily physical load and to prevent the effects of ageing. The homeostasis of bone remodelling largely depends on the balance of energy metabolism, such as glucose, glutamine, and fatty acid metabolism, and the disturbance of which will disrupt the balance between bone formation and bone resorption. Wnt signalling pathway including critical Wnt molecules (Wnt3a, Wnt7b, Wnt10b) is significant in these life processes, which links the intrinsic interactions between bone remodelling and energy metabolism, making it a promising target for the treatment of metabolic bone diseases.