Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.     

Bone Load Estimation for the Proximal Femur Using Single Energy Quantitative CT Data

A density-based load estimation method was applied to determine femoral load patterns. Two-dimensional finite element models were constructed using single energy quantitative computed tomography (QCT) data from two femora. Basic load cases included parabolic pressure joint loads and constant tractions on the greater trochanter. An optimization procedure adjusted magnitudes of the basic load cases, such that the applied mechanical stimulus approached the ideal stimulus throughout each model. Dominant estimated load directions were generally consistent with published experimental data for gait. Other estimated loads suggested that loads at extreme joint orientations may be important to maintenance of bone structure. Remodeling simulations with the estimated loads produced density distributions qualitatively similar to the QCT data sets. Average nodal density errors between QCT data and predictions were 0.24 g/cm(3) and 0.28 g/cm(3). The results indicate that density-based load estimation could improve understanding of loading patterns on bones.     

Bone Load Estimation for the Proximal Femur Using Single Energy Quantitative CT Data

A density-based load estimation method was applied to determine femoral load patterns. Two-dimensional finite element models were constructed using single energy quantitative computed tomography (QCT) data from two femora. basic load cases included parabolic pressure joint loads and constant tractions on the greater trochanter. An optimization procedure adjusted magnitudes of the basic load cases, such that the applied mechanical stimulus approached the ideal stimulus throughout each model. Dominant estimated load directions were generally consistent with published experimental data for gait. Other estimated loads suggested that loads at extreme joint orientations may be important to maintenance of bone structure. Remodeling simulations with the estimated loads produced density distributions qualitatively similar to the QCT data sets. Average nodal density errors between QCT data and predictions were 0·24 g/cm³ and 0·28 g/cm³. The results indicate that density-based load estimation could improve understanding of loading patterns on bones.     

A contact algorithm for density-based load estimation

An algorithm, which includes contact interactions within a joint, has been developed to estimate the dominant loading patterns in joints based on the density distribution of bone. The algorithm is applied to the proximal femur of a chimpanzee, gorilla and grizzly bear and is compared to the results obtained in a companion paper that uses a non-contact (linear) version of the density-based load estimation method. Results from the contact algorithm are consistent with those from the linear method. While the contact algorithm is substantially more complex than the linear method, it has some added benefits. First, since contact between the two interacting surfaces is incorporated into the load estimation method, the pressure distributions selected by the method are more likely indicative of those found in vivo. Thus, the pressure distributions predicted by the algorithm are more consistent with the in vivo loads that were responsible for producing the given distribution of bone density. Additionally, the relative positions of the interacting bones are known for each pressure distribution selected by the algorithm. This should allow the pressure distributions to be related to specific types of activities. The ultimate goal is to develop a technique that can predict dominant joint loading patterns and relate these loading patterns to specific types of locomotion and/or activities.     

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.     

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.     

Mechanical significance of femoral head trabecular bone structure in Loris and Galago evaluated using micromechanical finite element models

Work on the interspecific and intraspecific variation of trabecular bone in the proximal femur of primates demonstrates important architectural variation between animals with different locomotor behaviors. This variation is thought to be related to the processes of bone adaptation whereby bone structure is optimized to the mechanical environment. Micromechanical finite element models were created for the proximal femur of the leaping Galago senegalensis and the climbing and quadrupedal Loris tardigradus by converting bone voxels from high-resolution X-ray computed tomography scans of the femoral head to eight-noded brick elements. The resulting models had approximately 1.8 million elements each. Loading conditions representing takeoff phase of a leap and more generalized load orientations were applied to the models, and the models were solved using the iterative "row-by-row" matrix-vector multiplication algorithm. The principal strain and Von Mises stress results for the leaping model were similar for both species at each load orientation. Similar hip joint reaction forces in the range of 4.9 x to 12 x body weight were calculated for both species under each loading condition, but the hip reaction values estimated for Loris were higher than predicted based on locomotor behavior. These results suggest that functional adaptation to hip joint loading may not fully explain the differences in femoral head trabecular bone structure in Galago and Loris. The finite element method represents a unique and useful tool for analyzing the functional adaptation of trabecular bone in a diversity of animals and for reconstructing locomotor behavior in extinct taxa.     

Effect of boundary conditions,impact loading and hydraulic stiffening on femoral fracture strength

Patient specific quantitative CT (QCT) imaging data together with the finite element (FE) method may provide an accurate prediction of a patient's femoral strength and fracture risk. Although numerous FE models investigating femoral fracture strength have been published, there is little consent on the effect of boundary conditions, dynamic loading and hydraulic strengthening due to intra-medullary pressure on the predicted fracture strength. We developed a QCT-derived FE model of a proximal femur that included node-specific modulus assigned based on the local bone density. The effect of three commonly used boundary conditions published in literature were investigated by comparing the resulting strain field due to an applied fracture load. The models were also augmented with viscoelastic material properties and subject to a realistic impact load profile to determine the effect of dynamic loads on the strain field. Finally, the effect of hydraulic strengthening was investigated by including node specific permeability and performing a coupled pore diffusion and stress analysis of the FE model. Results showed that all boundary conditions yield the same strain field patterns, but peak strains were 22% lower and fracture load was 18% higher when loaded at the greater trochanter than when loaded at the femoral head. Comparison of the dynamic models showed that material viscoelasticity was important, but inertial effects (vibration and shock) were not. Finally, pore pressure changes did not cause significant hydraulic strengthening of bone under fall impact loading.     

An application of principal component analysis for lower body kinematics between loaded and unloaded walking

Load carriage is a very common daily activity at home and in the workplace. Generally, the load is in the form of an external load carried by an individual, it could also be the excessive body mass carried by an overweight individual. To quantify the effects of carrying extra weight, whether in the form of an external load or excess body mass, motion capture data were generated for a diverse subject set. This consisted of twenty-three subjects generating one hundred fifteen trials for each loading condition. This study applied principal component analysis (PCA) to motion capture data in order to analyze the lower body gait patterns for four loading conditions: normal weight unloaded, normal weight loaded, overweight unloaded and overweight loaded.PCA has been shown to be a powerful tool for analyzing complex gait data. In this analysis, it is shown that in order to quantify the effects of external loads and/or for both normal weight and overweight subjects, the first principal component (PC1) is needed. For the work in this paper, PCs were generated from lower body joint angle data. The PC1 of the hip angle and PC1 of the ankle angle are shown to be an indicator of external load and BMI effects on temporal gait data.     

Influence of physical activity on the regulation of bone density

Using a mathematical model which relates bone density to daily stress histories, the influence of physical activities on the apparent density of the calcaneal cancellous bone was investigated. Assuming that the mechanical bone maintenance stimulus is constant for all bone tissue, bone apparent density was calculated by a linear superposition of the mechanical stimulus provided by different daily physical activities. An empirical weighting factor, m, accounted for possible differences in the relative importance of load magnitude and number of cycles in each activity. By considering hypothetical variations in body weight and occupational activity levels, the range of probable m values was established. The model was then applied to the results of two previous running studies in which calcaneal density was measured to obtain an estimate of the stress exponent parameter, m. The results indicate that stress magnitudes (or joint forces) have a greater influence on bone mass than the number of loading cycles. We demonstrate that by carefully considering the magnitudes of imposed skeletal forces and the number of loading cycles, it may be possible to design exercise programs to achieve predictable changes in bone mass.     

Comparison of in vivo measured loads in knee,hip and spinal implants during level walking

Walking is a task that we seek to understand because it is the most relevant human locomotion. Walking causes complex loading patterns and high load magnitudes within the human body. This work summarizes partially published load data collected in earlier in vivo measurement studies on 9 patients with telemeterized knee endoprostheses, 10 with hip endoprostheses and 5 with vertebral body replacements. Moreover, for the 19 endoprosthesis patients, additional simultaneously measured and previously unreported ground reaction forces are presented.The ground reaction force and the implant forces in the knee and hip exhibited a double peak during each step. The maxima of the ground reaction forces ranged from 100% to 126% bodyweight. In comparison, the greatest implant forces in the hip (249% bodyweight) and knee (271% bodyweight) were much greater. The mean peak force measured in the vertebral body replacement was 39% bodyweight and occurred at different time points of the stance phase.We concluded that walking leads to high load magnitudes in the knee and hip, whereas the forces in the vertebral body replacement remained relatively low. This indicates that the first peak force was greater in the hip than in the knee joint while this was reversed for the second peak force. The forces in the spinal implant were considerably lower than in the knee and hip joints.     

Bone density spatial patterns in the distal radius reflect habitual hand postures adopted by quadrupedal primates

Primates adopt diverse hand postures during terrestrial and above-branch quadrupedal locomotion--knuckle-walking, digitigrady, and palmigrady--that incorporate varying degrees of wrist dorsiflexion (i.e., extension). Although relationships between hand postures, wrist joint range of motion, and the external properties of wrist bones (e.g., surface morphology) have been examined, the relationship between hand postures and the internal properties of wrist bones (e.g., bone density) remains largely unexplored. Because articular joint surfaces transmit mechanical loads between conjoining limb bones, measures of density (e.g., magnitudes and patterns) in the subchondral cortical plate of bone of the distal radius can be used to evaluate load regimes experienced by the wrist joint in different hand postures. We assessed apparent (i.e. optical) density patterns in several extant catarrhine primate taxa partitioned into different hand posture groups: knuckle-walking apes, digitigrade monkeys, and palmigrade monkeys. Computed tomography osteoabsorptiometry (CT-OAM) was used to construct maximum intensity projection (MIP) maps of apparent densities. High apparent density areas were characterized relative to a dorsal-volar reference plane and compared across hand posture groups. All groups had large percentage areas of high apparent density in the dorsal region of the distal radial articular surface. Only knuckle-walking apes, however, had a large percentage area of high apparent density in the volar region of the distal radial articular surface. These patterns are consistent with radiocarpal articulations in specific hand postures as evidenced by available radiographic data and suggest that the different habitual hand postures adopted by monkeys and African apes during quadrupedal locomotion have different stereotypic loading patterns. This has implications for understanding the functional morphology and evolution of knuckle-walking and digitigrade hand postures in primates.     

Hip contact forces and gait patterns from routine activities.

In vivo loads acting at the hip joint have so far only been measured in few patients and without detailed documentation of gait data. Such information is required to test and improve wear, strength and fixation stability of hip implants. Measurements of hip contact forces with instrumented implants and synchronous analyses of gait patterns and ground reaction forces were performed in four patients during the most frequent activities of daily living. From the individual data sets an average was calculated. The paper focuses on the loading of the femoral implant component but complete data are additionally stored on an associated compact disc. It contains complete gait and hip contact force data as well as calculated muscle activities during walking and stair climbing and the frequencies of daily activities observed in hip patients. The mechanical loading and function of the hip joint and proximal femur is thereby completely documented. The average patient loaded his hip joint with 238% BW (percent of body weight) when walking at about 4 km/h and with slightly less when standing on one leg. This is below the levels previously reported for two other patients (Bergmann et al., Clinical Biomechanics 26 (1993) 969-990). When climbing upstairs the joint contact force is 251% BW which is less than 260% BW when going downstairs. Inwards torsion of the implant is probably critical for the stem fixation. On average it is 23% larger when going upstairs than during normal level walking. The inter- and intra-individual variations during stair climbing are large and the highest torque values are 83% larger than during normal walking. Because the hip joint loading during all other common activities of most hip patients are comparably small (except during stumbling), implants should mainly be tested with loading conditions that mimic walking and stair climbing.     

Subject-specific modeling of the scapula bone tissue adaptation

Adaptation of the scapula bone tissue to mechanical loading is simulated in the current study using a subject-specific three-dimensional finite element model of an intact cadaveric scapula. The loads experienced by the scapula during different types of movements are determined using a subject-specific large-scale musculoskeletal model of the shoulder joint. The obtained density distributions are compared with the CT-measured density distribution of the same scapula. Furthermore, it is assumed that the CT-measured density distribution can be estimated as a weighted linear combination of the density distributions calculated for different loads experienced during daily life. An optimization algorithm is used to determine the weighting factors of fourteen different loads such that the difference between the weighted linear combination of the calculated density distributions and the CT-measured density is minimal. It is shown that the weighted linear combination of the calculated densities matches the CT-measured density distribution better than every one of the density distributions calculated for individual movements. The weighting factors of nine out of fourteen loads were estimated to be zero or very close to zero. The five loads that had larger weighting factors were associated with either one of the following categories: (1) small-load small-angle abduction or flexion movements that occur frequently during our daily lives or (2) large-load large-angle abduction or flexion movements that occur infrequently during our daily lives.     

Relationships between femoral fracture loads for two load configurations

Studies of proximal femoral strength usually involve one of two types of loading conditions, loading similar to joint loading during single-limb stance or loading simulating impact from a fall. When interpreting the results of studies involving only one of these load configurations, the question arises as to their applicability to the other configuration. In addition, it is desirable to know whether, for an individual bone, fracture load for one load configuration is indicative of fracture load for the other configuration. In this study, the relationship between proximal femoral fracture loads for single-limb stance loading and loading simulating impact from a type of fall was determined from mechanical testing of 17 matched pairs of human proximal femora. Fracture loads for these two configurations were found to be linearly related (r = 0.901, p < 0.001). However, the correlation between fracture loads is not notably stronger than correlations currently available between fracture load and measures of bone density and geometry. In addition, the regression results indicate that 81% of the variance in fracture load for one loading condition is accounted for by fracture load for the other loading condition. Thus, 19% of the variance remains unexplained, indicating that the results of studies involving only one load configuration are not necessarily indicative of those that would be found for another configuration.     

In vitro modeling of human tibial strains during exercise in micro-gravity

Prolonged exposure to micro-gravity causes substantial bone loss (Leblanc et al., Journal of Bone Mineral Research 11 (1996) S323) and treadmill exercise under gravity replacement loads (GRLs) has been advocated as a countermeasure. To date, the magnitudes of GRLs employed for locomotion in space have been substantially less than the loads imposed in the earthbound 1G environment, which may account for the poor performance of locomotion as an intervention. The success of future treadmill interventions will likely require GRLs of greater magnitude. It is widely held that mechanical tissue strain is an important intermediary signal in the transduction pathway linking the external loading environment to bone maintenance and functional adaptation; yet, to our knowledge, no data exist linking alterations in external skeletal loading to alterations in bone strain. In this preliminary study, we used unique cadaver simulations of micro-gravity locomotion to determine relationships between localized tibial bone strains and external loading as a means to better predict the efficacy of future exercise interventions proposed for bone maintenance on orbit. Bone strain magnitudes in the distal tibia were found to be linearly related to ground reaction force magnitude (R(2)>0.7). Strain distributions indicated that the primary mode of tibial loading was in bending, with little variation in the neutral axis over the stance phase of gait. The greatest strains, as well as the greatest strain sensitivity to altered external loading, occurred within the anterior crest and posterior aspect of the tibia, the sites furthest removed from the neutral axis of bending. We established a technique for estimating local strain magnitudes from external loads, and equations for predicting strain during simulated micro-gravity walking are presented.     

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.     

Musculo-skeletal loading conditions at the hip during walking and stair climbing.

Musculo-skeletal loading plays an important role in the primary stability of joint replacements and in the biological processes involved in fracture healing. However, current knowledge of musculo-skeletal loading is still limited. In the past, a number of musculo-skeletal models have been developed to estimate loading conditions at the hip. So far, a cycle-to-cycle validation of predicted musculo-skeletal loading by in vivo measurements has not been possible. The aim of this study was to determine the musculo-skeletal loading conditions during walking and climbing stairs for a number of patients and compare these findings to in vivo data.Following total hip arthroplasty, four patients underwent gait analysis during walking and stair climbing. An instrumented femoral prosthesis enabled simultaneous measurement of in vivo hip contact forces. On the basis of CT and X-ray data, individual musculo-skeletal models of the lower extremity were developed for each patient. Muscle and joint contact forces were calculated using an optimization algorithm. The calculated peak hip contact forces both over- and under-estimated the measured forces. They differed by a mean of 12% during walking and 14% during stair climbing.For the first time, a cycle-to-cycle validation of predicted musculo-skeletal loading was possible for walking and climbing stairs in several patients. In all cases, the comparison of in vivo measured and calculated hip contact forces showed good agreement.Thus, the authors consider the presented approach as a useful means to determine valid conditions for the analysis of prosthesis loading, bone modeling or remodeling processes around implants and fracture stability following internal fixation.     

Density-based load estimation using two-dimensional finite element models: a parametric study

A parametric investigation was conducted to determine the effects on the load estimation method of varying: (1) the thickness of back-plates used in the two-dimensional finite element models of long bones, (2) the number of columns of nodes in the outer medial and lateral sections of the diaphysis to which the back-plate multipoint constraints are applied and (3) the region of bone used in the optimization procedure of the density-based load estimation technique. The study is performed using two-dimensional finite element models of the proximal femora of a chimpanzee, gorilla, lion and grizzly bear. It is shown that the density-based load estimation can be made more efficient and accurate by restricting the stimulus optimization region to the metaphysis/epiphysis. In addition, a simple method, based on the variation of diaphyseal cortical thickness, is developed for assigning the thickness to the back-plate. It is also shown that the number of columns of nodes used as multipoint constraints does not have a significant effect on the method.     

Density-based load estimation using two-dimensional finite element models: a parametric study

A parametric investigation was conducted to determine the effects on the load estimation method of varying: (1) the thickness of back-plates used in the two-dimensional finite element models of long bones, (2) the number of columns of nodes in the outer medial and lateral sections of the diaphysis to which the back-plate multipoint constraints are applied and (3) the region of bone used in the optimization procedure of the density-based load estimation technique. The study is performed using two-dimensional finite element models of the proximal femora of a chimpanzee, gorilla, lion and grizzly bear. It is shown that the density-based load estimation can be made more efficient and accurate by restricting the stimulus optimization region to the metaphysis/epiphysis. In addition, a simple method, based on the variation of diaphyseal cortical thickness, is developed for assigning the thickness to the back-plate. It is also shown that the number of columns of nodes used as multipoint constraints does not have a significant effect on the method.