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.     

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.     

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.     

Stress analysis and failure prediction in the proximal femur before and after total hip replacement

An investigation was performed to determine the effects of the presence of two lengths of proximal Müller prosthesis on predicted failure loads, as compared to those for an intact femur. Three-dimensional stresses in a bone/cement/prosthesis system were determined using finite element methods, with both isotropic and transversely isotropic material properties used for the diaphyseal cortex. Significant increases in prosthesis stem stresses were found when the transversely isotropic material properties were employed in the diaphyseal cortex. This leads to the conclusion that accurate anisotropic material properties for bone are essential for precise stress determination and optimum design in prosthetic implants. Failure loads were also predicted for vertical compression and axial torque, similar to available experimental conditions, and were within the range of the experimental failure data found in the literature. The technique developed herein can be used to systematically assess existing as well as future implant designs, taking into account the complex three-dimensional interaction effects of the overall bone/cement/prosthesis system.     

Plausibility and parameter sensitivity of micro-finite element-based joint load prediction at the proximal femur

A micro-finite element-based method to estimate the bone loading history based on bone architecture was recently presented in the literature. However, a thorough investigation of the parameter sensitivity and plausibility of this method to predict joint loads is still missing. The goals of this study were (1) to analyse the parameter sensitivity of the joint load predictions at one proximal femur and (2) to assess the plausibility of the results by comparing load predictions of ten proximal femora to in vivo hip joint forces measured with instrumented prostheses (available from www.orthoload.com). Joint loads were predicted by optimally scaling the magnitude of four unit loads (inclined \(-20^{\circ }\) to \(100^{\circ }\) with respect to the vertical axis) applied to micro-finite element models created from high-resolution computed tomography scans (\(30.3~\upmu \)m voxel size). Parameter sensitivity analysis was performed by varying a total of nine parameters and showed that predictions of the peak load directions (range 10\(^{\circ }\)–\(30^{\circ }\)) are more robust than the predicted peak load magnitudes (range 2344.8–4689.5 N). Comparing the results of all ten femora with the in vivo loading data of ten subjects showed that peak loads are plausible both in terms of the load direction (in vivo: \(18.2\pm 2.0^{\circ }\), predicted: \(20.0^{\circ }\)) and magnitude (in vivo: \(2707.6\pm 443.3~\hbox {N}\), predicted: \(3372.2\pm 597.9~\hbox {N}\)). Overall, this study suggests that micro-finite element-based joint load predictions are both plausible and robust in terms of the predicted peak load direction, but predicted load magnitudes should be interpreted with caution.     

Densitometric, morphometric and mechanical distributions in the human proximal femur

With the prevalent use of DXA-measured BMD to assess pathologic hip fractures and its recently reported lack of reliability to predict fracture or account for efficacy of anti-resorptive therapy, it is reasonable to assess whether variations in the primary and secondary tensile and compressive trabecular microstructure can account for variations in proximal femur strength in comparison to DXA-measured BMD. To that end, microstructural and densitometric measures of trabecular bone specimens, from discrete sites within the proximal femur, were correlated with their mechanical properties. We hypothesize that accounting for regional variations in trabecular microstructure will improve predictions of proximal femur strength and stiffness compared to bone density measured by DXA. Forty-seven samples (seven donors) from seven distinct sites of human proximal femur underwent DXA and muCT imaging and mechanical testing. The results revealed significant variations in BMC, morphometric indices and mechanical properties within the proximal femur. This work has demonstrated that the mechanical performance of each sub-region is highly dependent on the corresponding trabecular microstructure. BMD measured by DXA at standard regions of interest cannot resolve the variations in trabecular density and microstructure that govern the mechanical behavior of the proximal femur. This work suggests that a quantitative Singh index that uses high resolution QCT to monitor the trabecular microstructure at specific sub-regions of the proximal femur may allow better predictions of hip fracture risk in individual patients and an improved assessment of changing bone structure in response to pharmacological interventions.     

Osteoporosis,falls, and age in fracture of the proximal femur.

The relative importance of osteoporosis and risk of falling in causing hip fracture is not known. Femoral neck bone mass was measured in 708 elderly people, all of whom had fallen and injured a hip. Below 75 years of age there was a steep increase in relative risk of fracture with reduced bone mass, measured by Singh grade. Above that age the increase in risk was small, and neuromuscular responses which protect the skeleton against trauma may be more important than bone mass.     

Trabecular bone ontogeny in the human proximal femur

Ontogenetic changes in the human femur associated with the acquisition of bipedal locomotion, especially the development of the bicondylar angle, have been well documented. The purpose of this study is to quantify changes in the three-dimensional structure of trabecular bone in the human proximal femur in relation to changing functional and external loading patterns with age. High-resolution X-ray computed tomography scan data were collected for 15 juvenile femoral specimens ranging in age from prenatal to approximately nine years of age. Serial slices were collected for the entire proximal femur of each individual with voxel resolutions ranging from 0.017 to 0.046 mm depending on the size of the specimen. Spherical volumes of interest were defined within the proximal femur, and the bone volume fraction, trabecular thickness, trabecular number, and fabric anisotropy were calculated in three dimensions. Bone volume fraction, trabecular number, and degree of anisotropy decrease between the age of 6 months and 12 months, with the lowest values for these parameters occurring in individuals near 12 months of age. By age 2-3 years, the bone volume, thickness, and degree of anisotropy increase slightly, and regions in the femoral neck become more anisotropic corresponding to the thickening of the inferior cortical bone of the neck. These results suggest that trabecular structure in the proximal femur reflects the shift in external loading patterns associated with the initiation of unassisted walking in infants.     

Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state

Two-dimensional simulation of trabecular surface remodeling was conducted for a human proximal femur to investigate the structural change of cancellous bone toward a uniform stress state. Considering that a local mechanical stimulus plays an important role in cellular activities in bone remodeling, local stress nonuniformity was assumed to drive trabecular structural change to seek a uniform stress state. A large-scale pixel-based finite element model was used to simulate structural changes of individual trabeculae over the entire bone. As a result, the initial structure of trabeculae changed from isotropic to anisotropic due to trabecular microstructural changes caused by surface remodeling according to the mechanical environment in the proximal femur. Under a single-loading condition, it was shown that the apparent structural property evaluated by fabric ellipses corresponded to the apparent stress state in cancellous bone. As is observed in the actual bone, a distributed trabecular structure was obtained under a multiple-loading condition. Through these studies, it was concluded that trabecular surface remodeling toward a local uniform stress state at the trabecular level could naturally bring about functional adaptation phenomenon at the apparent tissue level. The proposed simulation model would be capable of providing insight into the hierarchical mechanism of trabecular surface remodeling at the microstructural level up to the apparent tissue level.     

Mechanical properties of metaphyseal bone in the proximal femur

We used a three-point bending test to investigate the structural behavior of 123 rectangular flat plate specimens harvested from the metaphyseal shell of the cervical and intertrochanteric regions of five fresh/frozen human proximal femora. For comparison purposes, 36 specimens of similar geometry were also fabricated from bone of the femoral diaphysis. All specimens were oriented in either the local longitudinal or transverse directions. The mean longitudinal elastic modulus was 9650 +/- 2410 (SD) MPa and demonstrated a 24% decrease from that measured for the diaphysis (12500 +/- 2140 MPa) using the same testing technique. However, the transverse elastic moduli did not differ significantly between the proximal (5470 +/- 1720 MPa) and diaphyseal (5990 +/- 1520 MPa) specimens. The globally averaged values for the ultimate tensile strengths of the metaphyseal shell were 101 +/- 26 MPa in the longitudinal and 50 +/- 12 MPa in the transverse directions. These compared with diaphyseal values of 128 +/- 16 MPa and 47 +/- 12 MPa, respectively. While these differences were largely due to the reduced density of the proximal specimens, a slight decrease in transverse anisotropy for the proximal specimens was also noted by comparing the ratio of longitudinal to transverse moduli (1.76) and tensile strength (2.02) to the diaphyseal values (2.09 and 2.71, respectively). Use of these data should lead to improved performance of analytical models for the proximal femur, and thus help focus increased attention on the structural contribution of trabecular bone to the strength and rigidity of the proximal femur.     

Elastic moduli, yield stress, and ultimate stress of cancellous bone in the canine proximal femur

Elastic moduli, yield stress and ultimate compressive stress were determined for cancellous bone from the femoral head and neck regions of the canine femur. Unconfined compression tests were performed on 5 mm cubic samples which were cut from two femurs. Elastic moduli were measured in three orthogonal directions, and the yield stress and ultimate stress were measured along the proximal-distal axis. The results from this investigation support previous assumptions that the mechanical behavior of canine cancellous bone is qualitatively similar to human cancellous bone. The canine cancellous bone was observed to be anisotropic in elastic modulus. For two thirds of the cubic specimens tested, the elastic modulus was largest in the load-bearing, proximal-distal direction. A linear relationship between yield stress and elastic modulus was observed for canine bone, as is typical of human bone. A similar linear relationship between ultimate stress and elastic modulus was observed. Thus, for canine bone as well as for human bone, failure appears to be governed by a strain level which is position independent. The yield strain of 0.0259 and ultimate strain of 0.0288 for canine bone were both less than the yield strain of 0.0395 reported for human bone.     

Physical activity,muscle strength,and calcium intake in fracture of the proximal femur in Britain.

Regular exercise and high calcium intake possibly help to preserve bone mass. Little is known, however, about their role in preventing hip fracture. The physical activity and calcium intake of 300 elderly men and women with hip fractures were compared with those of 600 controls matched for age and sex. In both sexes increased daily activity, including standing, walking, climbing stairs, carrying, housework, and gardening protected against fracture. This was independent of other known risk factors, including body mass, cigarette smoking, and alcohol consumption. Strength of grip correlated with activity and was inversely related to the risk of fracture. Calcium intake was not related to the risk of fracture in women. Men with daily calcium intakes above 1g had lower risks. These findings point to the importance of elderly people in Britain maintaining physical activity in their day to day lives.     

Trabecular structure compared to stress trajectories in the proximal femur and the calcaneus

The theory that the trabecular structure within bones follows the principal stress trajectories, is investigated by two-dimensional finite element models of increasing complexity. This is done for the proximal femur of the human and for the calcaneus of the horse. In both cases, a simple model with well-chosen loading and boundary conditions gives good agreement between the observed trabecular structure and the calculated stress trajectories. It is shown that this stress trajectory theory has a mechanically founded explanation.     

Comparison of micro-level and continuum-level voxel models of the proximal femur

Continuum-level finite element (FE) models became standard computational tools for the evaluation of bone mechanical behavior from in vivo computed tomography scans. Such scans do not account for the anisotropy of the bone. Instead, local mechanical properties in the continuum-level FE models are assumed isotropic and are derived from bone density, using statistical relationships. Micro-FE models, on the other hand, incorporate the anisotropic structure in detail. This study aimed to quantify the effects of assumed isotropy, by comparing continuum-level voxel models of a healthy and a severely osteoporotic proximal femur with recently analyzed micro-FE models of the same bones. The micro-model element size was coarsened to generate continuum FE models with two different element sizes (0.64 and 3.04 mm) and two different density–modulus relationships found in the literature for wet and ash density. All FE models were subjected to the same boundary conditions that simulated a fall to the side, and the stress and strain distributions, model stiffness and yield load were compared. The results indicated that the stress and strain distributions could be reproduced well with the continuum models. The smallest differences between the continuum-level model and micro-level model predictions of the stiffness and yield load were obtained with the coarsest element size. Better results were obtained for both continuum-element sizes when isotropic moduli were based on ash density rather than wet density.     

Size and shape variation in the proximal femur of Australopithecus africanus

Aside from use as estimates of body mass dimorphism and fore to hind limb joint size comparisons, postcranial elements have not often contributed to assessments of variation in Australopithecus africanus. Meanwhile, cranial, facial, and dental size variation is interpreted to be high or moderately high. Further, the cranial base and face express patterns of structural (shape) variation, which are interpreted by some as evidence for the presence of multiple species. Here, the proximal femur is used to consider postcranial size and shape variation in A. africanus. Original fossils from Makapansgat and Sterkfontein, and samples from Homo, Pan, Gorilla, and Pongo were measured. Size variation was assessed by comparing the A. africanus coefficient of variation to bootstrapped distributions of coefficient of variation samples for each taxon. Shape variation was assessed from isometrically adjusted shape variables. First, the A. africanus standard deviation of log transformed shape variables was compared to bootstrapped distributions of logged standard deviations in each taxon. Second, shape variable based Euclidean distances between fossil pairs were compared to pairwise Euclidean distance distributions in each reference taxon. The degree of size variation in the A. africanus proximal femur is consistent with that of a single species, and is most comparable to Homo and Pan, lower than A. afarensis, and lower than some estimates of cranial and dental variation. Some, but not all, shape variables show more variation in A. africanus than in extant taxa. The degree of shape difference between some fossils exceeds the majority of pairwise differences in the reference taxa. Proximal femoral shape, but not size, variation is consistent with high estimates of A. africanus cranial variation.     

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.     

Concept and development of an orthotropic FE model of the proximal femur

PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).     

Numerical investigations on the strain-adaptive bone remodelling in the periprosthetic femur: Influence of the boundary conditions

Background  

There are several numerical investigations on bone remodelling after total hip arthroplasty (THA) on the basis of the finite element analysis (FEA). For such computations certain boundary conditions have to be defined. The authors chose a maximum of three static load situations, usually taken from the gait cycle because this is the most frequent dynamic activity of a patient after THA.     

Aging changes in the medullary cavity of the proximal femur in American Blacks and Whites.

This study explores changes with age in the medullary cavity in an area of the femur which is becoming of increasing clinical interest. It is based on measurements of medial-lateral and posterior-anterior radiographs of the proximal one-third of the right femur, below the greater trochanter. The study population consisted of 257 individuals from the Terry collection in the Smithsonian Institution and included Blacks and Whites, males and females, aged 20 to 90 years. Medullary cavity and external diameters were measured at 11 levels, beginning with a line drawn perpendicular to the linea aspera at the level of the inferior border of the greater trochanter. To correct for size differences, the interval between levels was set at one-fourth the individual femoral head diameter. The data were subjected to regression analysis and analysis of variance. Anterior-posterior medullary diameter is more highly correlated with age than medial-lateral diameter. Females show the greatest relative increase with age in both dimensions, especially at subtrochanteric levels, and they tend to have relatively larger medullary cavities than males at all ages. White males have relatively larger medullary diameters than Black males. Younger White females have relatively larger medullary cavities than Black females, but the latter reach parity with White females in middle age and show a greater overall percentage of medullary expansion.