Long-term study of bone remodelling after femoral stem: a comparison between dexa and finite element simulation

A hip replacement with a cemented or cementless femoral stem produces an effect on the bone called adaptive remodelling, attributable to mechanical and biological factors. The objective of all of cementless prostheses designs has been to achieve a perfect transfer of loads in order to avoid stress-shielding, which produces an osteopenia. In order to quantify this, the long term and mass-produced study with dual energy X-ray absorptiometry (DEXA) is necessary. Finite element (FE) simulation makes possible the explanation of the biomechanical changes which are produced in the femur after stem implantation. The good correlation obtained between the results of the FE simulation and the densitometric study allow, on one hand, to explain from the point of view of biomechanical performance the changes observed in bone density in the long-term, where it is clear that these are due to a different transfer of load in the implanted model compared to the healthy femur; on the other hand, it validates the simulation model, in a way that it can be used in different conditions and at different time periods, to carry out a sufficiently precise prediction of the evolution of the bone density from the biomechanical behaviour in the interaction between the prosthesis and femur.     

A finite element study relating to the rapid filling phase of the human ventricles

During the rapid diastolic filling phase at rest, the ventricles of the human heart double approximately in volume. In order to investigate whether the ventricular filling pressures measured under physiological conditions can give rise to such an extensive augmentation in ventricular volumes, a finite element model of the human right and left ventricles has been developed, taking into account the nonlinear mechanical behavior and effective compressibility of the myocardial tissue. The results were compared with the filling phase of the human left ventricle as extrapolated from measurements documented in the literature. We arrived at the conclusion that the ventricular pressures measured during the rapid filling phase cannot be the sole cause of the rise of the observed ventricular volumes. We rather advocate the assumption that further dilating mechanisms might be part of ventricular activity thus heralding a multiple function of the ventricular muscle body. A further result indicates that under normal conditions the influence of the viscoelasticity of the tissue should not be disregarded in ventricular mechanics.     

A study of the viscoelastic effect in a bone remodeling model

The present paper addresses the following question can a simple regulatory bone remodeling model predict effects of viscosity on the trabecular morphology? For that, we propose an extension of a previous bone remodeling model by taking into account the viscosity properties of the tissue. Zener’s law is used to describe the mechanical behavior of the bone and a specific law of the apparent bone density rate is proposed. Based on stability analysis, numerical simulations are then performed to investigate the viscosity role on simulations of the bone remodeling process. We show that the viscous contribution affects the evolution of the apparent bone density, by slowing down the adaptation process, which seems to be confirmed by simulations with real data obtained from rat tibia.     

深龋修复的力学模型分析

目的:模拟下颌第一磨牙Ⅰ类洞深龋,计算机分析得到修复体最佳应力分布时基底材料与修复材料厚度比例。方法 采用三维有限元法建立数值模型,利用SAP84(V4.2)程序计算并作力学分析。结果:在能护髓前提下应尽量减少次基厚度(1)银汞修复时,银汞合金厚度应大于基底厚度时应力分布最佳。(2)树脂修复时,树脂厚度与基底厚度相近,应力分布最佳。结论 根据材料弹性模量来决定基底材料与修复材料厚度比例。     

A finite element simulation scheme for biological muscular hydrostats

An explicit finite element scheme is developed for biological muscular hydrostats such as squid tentacles, octopus arms and elephant trunks. The scheme is implemented by embedding muscle fibers in finite elements. In any given element, the fiber orientation can be assigned arbitrarily and multiple muscle directions can be simulated. The mechanical stress in each muscle fiber is the sum of active and passive parts. The active stress is taken to be a function of activation state, muscle fiber shortening velocity and fiber strain; while the passive stress depends only on the strain. This scheme is tested by simulating extension of a squid tentacle during prey capture; our numerical predictions are in close correspondence with existing experimental results. It is shown that the present finite element scheme can successfully simulate more complex behaviors such as torsion of a squid tentacle and the bending behavior of octopus arms or elephant trunks.     

An Anisotropic Internal-External Bone Adaptation Model Based on a Combination of CAO and Continuum Damage Mechanics Technologies

Abstract

In this work, a complete internal-external bone-remodelling scheme is presented and implemented into a finite element code. This model uses a combination of an anisotropic internal remodelling model based on a new Continuum "Damage-Repair" theory and an external adaptation approach that follows the idea, early introduced by Mattheck et ah, to simulate the growth behaviour of biological systems, known as CAO method. This combined scheme qualitatively resembles most of the main features of the bone adaptive behaviour, like the bone mass distribution (heterogeneity and porosity), the directional internal structure (anisotropy), the alignment of the microstructure with the constitutive principal directions and these with those of the stress tensor when permanently loaded by a unique stress state (WolfFs law). It is also thermodynamically consistent, fulfilling a principle of minimum mechanical dissipation. Finally, the comparison between the predicted results and the ones obtained by different experimental tests allows us to conclude that this model is able of reproducing qualitatively the global behaviour of bone tissue when subjected to external mechanical loads.     

Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation

Computational implementation of physical and physiologically realistic constitutive models is critical for numerical simulation of soft biological tissues in a variety of biomedical applications. It is well established that the highly nonlinear and anisotropic mechanical behaviors of soft tissues are an emergent behavior of the underlying tissue microstructure. In the present study, we have implemented a structural constitutive model into a finite element framework specialized for membrane tissues. We noted that starting with a single element subjected to uniaxial tension, the non-fibrous tissue matrix must be present to prevent unrealistic tissue deformations. Flexural simulations were used to set the non-fibrous matrix modulus because fibers have little effects on tissue deformation under three-point bending. Multiple deformation modes were simulated, including strip biaxial, planar biaxial with two attachment methods, and membrane inflation. Detailed comparisons with experimental data were undertaken to insure faithful simulations of both the macro-level stress–strain insights into adaptations of the fiber architecture under stress, such as fiber reorientation and fiber recruitment. Results indicated a high degree of fidelity and demonstrated interesting microstructural adaptions to stress and the important role of the underlying tissue matrix. Moreover, we apparently resolve a discrepancy in our 1997 study (Billiar and Sacks, 1997. J. Biomech. 30 (7), 753–756) where we observed that under strip biaxial stretch the simulated fiber splay responses were not in good agreement with the experimental results, suggesting non-affine deformations may have occurred. However, by correctly accounting for the isotropic phase of the measured fiber splay, good agreement was obtained. While not the final word, these simulations suggest that affine fiber kinematics for planar collagenous tissues is a reasonable assumption at the macro level. Simulation tools such as these are imperative in the design and simulation of native and engineered tissues.     

Effects of sitting postures on risks for deep tissue injury in the residuum of a transtibial prosthetic-user: a biomechanical case study

Transtibial amputation prosthetic-users are at risk of developing deep tissue injury (DTI) while donning their prosthesis for prolonged periods; however, no study addresses the mechanical loading of the residuum during sitting with a prosthesis. We combined MRI-based 3D finite element modelling of a residuum with an injury threshold and a muscle damage law to study risks for DTI in one sitting subject in two postures: 30°-knee-flexion vs. 90°-knee-flexion. We recorded skin-socket pressures, used as model boundary conditions. During the 90°-knee-flexion simulations, major internal muscle injuries were predicted (>1000 mm³). In contrast, the 30°-knee-flexion simulations only produced minor injury ( < 14 mm³). Predicted injury rates at 90°-knee-flexion were over one order of magnitude higher than those at 30°-knee-flexion. We concluded that in this particular subject, prolonged 90°-knee-flexion sitting theoretically endangers muscle viability in the residuum. By expanding the studies to large subject groups, this research approach can support development of guidelines for DTI prevention in prosthetic-users.     

A numerical and experimental study of compliance and collapsibility of preterm lamb tracheae

Knowledge of the mechanical behaviour of immature tracheae is crucial in order to understand the effects exerted on central airways by ventilatory treatments, particularly of Total Liquid Ventilation. In this study, a combined experimental and computational approach was adopted to investigate the compliance and particularly collapsibility of preterm lamb tracheae in the range of pressure likely applied during Total Liquid Ventilation (−30 to 30 cmH₂O). Tracheal samples of preterm lambs (n=5; gestational age 120–130 days) were tested by altering transmural pressure from −30 to 30 cmH₂O. Inflation (S_i) and collapsing (S_c) compliance values were calculated in the ranges 0 to 10 cmH₂O and –10 to 0 cmH₂O, respectively. During the tests, an asymmetric behaviour of the ΔV/V₀ vs. P curves at positive and negative pressure was observed, with mean S_i=0.013 cmH₂O⁻¹ and S_c=0.053 cmH₂O⁻¹. A different deformed configuration of the sample regions was observed, depending on the posterior shape of cartilaginous ring. A three-dimensional finite-element structural model of a single tracheal ring, based on histology measurements of the tested samples was developed. The model was parameterised in order to represent rings belonging to three different tracheal regions (craniad, median, caudal) and numerical analyses replicating the collapse test conditions were performed to evaluate the ring collapsibility at pressures between 0 and −30 cmH₂O. Simulation results were compared to experimental data to verify the model's reliability. The best model predictions occurred at pressures −30 to −10 cmH₂O. In this range, a model composed of median rings best interpreted the experimental data, with a maximum error of 2.7%; a model composed of an equal combination of all rings yielded an error of 12.6%.     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

Simple finite element models for use in the design of therapeutic footwear

Therapeutic footwear is frequently prescribed in cases of rheumatoid arthritis and diabetes to relieve or redistribute high plantar pressures in the region of the metatarsal heads. Few guidelines exist as to how these interventions should be designed and what effect such interventions actually have on the plantar pressure distribution. Finite element analysis has the potential to assist in the design process by refining a given intervention or identifying an optimal intervention without having to actually build and test each condition. However, complete and detailed foot models based on medical image segmentation have proven time consuming to build and computationally expensive to solve, hindering their utility in practice. Therefore, the goal of the current work was to determine if a simplified patient-specific model could be used to assist in the design of foot orthoses to reduce the plantar pressure in the metatarsal head region. The approach is illustrated by a case study of a diabetic patient experiencing high pressures and pain over the fifth metatarsal head. The simple foot model was initially calibrated by adjusting the individual loads on the metatarsals to approximate measured peak plantar pressure distributions in the barefoot condition to within 3%. This loading was used in various shod conditions to identify an effective orthosis. Model results for metatarsal pads were considerably higher than measured values but predictions for uniform surfaces were generally within 16% of measured values. The approach enabled virtual prototyping of the orthoses, identifying the most favorable approach to redistribute the patient’s plantar pressures.     

Towards accurate numerical method for monodomain models using a realistic heart geometry

The simulation of cardiac electrophysiological waves are known to require extremely fine meshes, limiting the applicability of current numerical models to simplified geometries and ionic models. In this work, an accurate numerical method based on a time-dependent anisotropic remeshing strategy is presented for simulating three-dimensional cardiac electrophysiological waves. The proposed numerical method greatly reduces the number of elements and enhances the accuracy of the prediction of the electrical wave fronts. Illustrations of the performance and the accuracy of the proposed method are presented using a realistic heart geometry. Qualitative and quantitative results show that the proposed methodology is far superior to the uniform mesh methods commonly used in cardiac electrophysiology.     

Effect of bone fragment impact velocity on biomechanical parameters related to spinal cord injury: A finite element study

Several experimental and computational studies have investigated the effect of bone fragment impact on the spinal cord during trauma. However, the effect of the impact velocity of a fragment generated by a burst fracture on the stress and strain inside the spinal cord has not been computationally investigated, even though spinal canal occlusion and peak pressure at various impact velocities were provided in experimental studies. These stresses and strains are known factors related to clinical symptoms or injuries. In this study, a fluid-structure interaction model of the spinal cord, dura mater, and cerebrospinal fluid was developed and validated. The von-Mises stress distribution in the cord, the longitudinal strain, the cord compression and cross-sectional area at the impact center, and the obliteration of the cerebrospinal fluid layer were analyzed for three pellet sizes at impact velocities ranging from 1.5 m/s to 7.5 m/s. The results indicate that stress in the cord was substantially elevated when the initial impact velocity of the pellet exceeded a threshold of 4.5 m/s. Cord compression, reduction in cross-sectional area, and obliteration of the cerebrospinal fluid increased gradually as the velocity of the pellet increased, regardless of the size of the pellet. The present study provides insight into the mechanisms underlying spinal cord injury.     

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles

In shock-wave lithotripsy—a medical procedure to fragment kidney stones—the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.     

Mapping anisotropy of the proximal femur for enhanced image based finite element analysis

Finite element (FE) models of bone derived from quantitative computed tomography (QCT) rely on realistic material properties to accurately predict bone strength. QCT cannot resolve bone microarchitecture, therefore QCT-based FE models lack the anisotropy apparent within the underlying bone tissue. This study proposes a method for mapping femoral anisotropy using high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of human cadaver specimens. Femur HR-pQCT images were sub-divided into numerous overlapping cubic sub-volumes and the local anisotropy was quantified using a ‘direct-mechanics’ method. The resulting directionality reflected all the major stress lines visible within the trabecular lattice, and provided a realistic estimate of the alignment of Harvesian systems within the cortical compartment. QCT-based FE models of the proximal femur were constructed with isotropic and anisotropic material properties, with directionality interpolated from the map of anisotropy. Models were loaded in a sideways fall configuration and the resulting whole bone stiffness was compared to experimental stiffness and ultimate strength. Anisotropic models were consistently less stiff, but no statistically significant differences in correlation were observed between material models against experimental data. The mean difference in whole bone stiffness between model types was approximately 26%, suggesting that anisotropy can still effect considerable change in the mechanics of proximal femur models. The under prediction of whole bone stiffness in anisotropic models suggests that the orthotropic elastic constants require further investigation. The ability to map mechanical anisotropy from high-resolution images and interpolate information into clinical-resolution models will allow testing of new anisotropic material mapping strategies.     

A numerical study of the Belousov-Zhabotinskii reaction using Galerkin finite element methods

The Belousov-Zhabotinskii reaction has been modelled by Field and Noyes [5] as a pair of nonlinear parabolic equations. Previous studies of these, both theoretical and numerical, have assumed wave solutions travelling with constant velocity leading to a simplification of the mathematical model in the form of a system of ordinary differential equations. In the present study a finite element Galerkin method is used directly on the original parabolic system for a range of parameter values.     

Finite element analysis of retroacetabular osteolytic defects following total hip replacement

Periprosthetic osteolysis in the retroacetabular region with cancellous bone loss is a recognized phenomenon in the long-term follow-up of total hip replacement. The effects on load transfer in the presence of defects are less well known. A finite element model incorporating a retroacetabular defect behind a cementless component was validated against a 4th generation sawbone pelvis. Computational predictions of surface strain and von Mises stresses were closely correlated to experimental findings. The presence of a cancellous defect increased von Mises stress in the cortical bone of the medial wall of the pelvis. At a load of 600 N this was under the predicted failure stress for cortical bone. Increases in the cup size relative to the acetabulum caused increased stress in the cortical bone of the lateral wall of the pelvis, adjacent to the acetabulum. We are confident that our modeling approach can be applied to patient specific defects to predict pelvis stress with large loads and a range of activities.     

Three-dimensional finite element stress analysis of the dentate human mandible.

The biomechanical events which accompany functional loading of the human mandible are not fully understood. The techniques normally used to record them are highly invasive. Computer modelling offers a promising alternative approach in this regard, with the additional ability to predict regional stresses and strains in inaccessible locations. In this study, we built two three-dimensional finite element (FE) models of a human mandible reconstructed from tomographs of a dry dentate jaw. The first model was used for a complete mechanical characterization of physical events. It also provided comparative data for the second model, which had an increased vertical corpus depth. In both cases, boundary conditions included rigid restraints at the first right molar and endosteal cortical surfaces of the articular eminences of temporal bones. Groups of parallel multiple vectors simulated individual masticatory muscle loads. The models were solved for displacements, stresses, strains, and forces. The simulated muscle loads in the first model deformed the mandible helically upward and toward its right (working) side. The highest principal stresses occurred at the bite point, anterior aspects of the coronoid processes, symphyseal region, and right and left sides of the mandibular corpus. In general, the observed principal stresses and strains were highest on the periosteal cortical surface and alveolar bone. At the symphyseal region, maximum principal stresses and strains were highest on the lower lingual mandibular aspect, whereas minimum principal stresses and strains were highest on its upper labial side. Subcondylar principal strains and condylar forces were higher on the left (balancing or nonbiting) side than on the right mandibular side, with condylar forces more concentrated on the anteromedial aspect of the working-side condyle and on the central and lateral aspects of the left. When compared with in vivo strain data from macaques during comparable biting events, the predictive strain values from the first model were qualitatively similar. In the second model, the reduced tensile stress on the working-side, and decreased shear stress bilaterally, confirmed that lower stresses occurred on the lower mandibular border with increased jaw depth. Our results suggested that although the mandible behaved in a beam-like manner, its corpus acted more like a combination of open and closed cross sections due to the presence of tooth sockets, at least for the task modelled.(ABSTRACT TRUNCATED AT 400 WORDS)     

How plate positioning impacts the biomechanics of the open wedge tibial osteotomy; A finite element analysis

A numerical model of the medial open wedge tibial osteotomy based on the finite element method was developed. Two plate positions were tested numerically. In a configuration, (a), the plate was fixed in a medial position and (b) in an anteromedial position. The simulation took into account soft tissues preload, muscular tonus and maximal gait load.

The maximal stresses observed in the four structural elements (bone, plate, wedge, screws) of an osteotomy with plate in medial position were substantially higher (1.13–2.8 times more) than those observed in osteotomy with an anteromedial plate configuration. An important increase (1.71 times more) of the relative micromotions between the wedge and the bone was also observed. In order to avoid formation of fibrous tissue at the bone wedge interface, the osteotomy should be loaded under 18.8% (～50 kg) of the normal gait load until the osteotomy interfaces union is achieved.     

Finite element simulation of interactions between pelvic organs: Predictive model of the prostate motion in the context of radiotherapy

The setting up of predictive models of the pelvic organ motion and deformation may prove an efficient tool in the framework of prostate cancer radiotherapy, in order to deliver doses more accurately and efficiently to the clinical target volume (CTV). A finite element (FE) model of the prostate, rectum and bladder motion has been developed, investigating more specifically the influence of the rectum and bladder repletions on the gland motion. The required organ geometries are obtained after processing the computed tomography (CT) images, using specific softwares. Due to their structural characteristics, a 3D shell discretization is adopted for the rectum and the bladder, whereas a volume discretization is adopted for the prostate. As for the mechanical behavior modelling, first order Ogden hyperelastic constitutive laws for both the rectum and bladder are identified. The prostate is comparatively considered as more rigid and is accordingly modelled as an elastic tissue undergoing small strains. A FE model is then created, accounting for boundary and contact conditions, internal and applied loadings being selected as close as possible to available anatomic data.The order of magnitude of the prostate motion predicted by the FE simulations is similar to the measurements done on a deceased person, accounting for the delineation errors, with a relative error around 8%. Differences are essentially due to uncertainties in the constitutive parameters, pointing towards the need for the setting up of direct measurement of the organs mechanical behavior.