Principles of determination and verification of muscle forces in the human musculoskeletal system: Muscle forces to minimise bending stress

While there are a growing number of increasingly complex methodologies available to model geometry and material properties of bones, these models still cannot accurately describe physical behaviour of the skeletal system unless the boundary conditions, especially muscular loading, are correct. Available in vivo measurements of muscle forces are mostly highly invasive and offer no practical way to validate the outcome of any computational model that predicts muscle forces. However, muscle forces can be verified indirectly using the fundamental property of living tissue to functional adaptation and finite element (FE) analysis. Even though the mechanisms of the functional adaptation are not fully understood, its result is clearly seen in the shape and inner structure of bones. The FE method provides a precise tool for analysis of the stress/strain distribution in the bone under given loading conditions. The present work sets principles for the determination of the muscle forces on the basis of the widely accepted view that biological systems are optimized light-weight structures with minimised amount of unloaded/underloaded material and hence evenly distributed loading throughout the structure. Bending loading of bones is avoided/compensated in bones under physiological loading. Thus, bending minimisation provides the basis for the determination of the musculoskeletal system loading. As a result of our approach, the muscle forces for a human femur during normal gait and sitting down (peak hip joint force) are obtained such that the bone is loaded predominantly in compression and the stress distribution in proximal and diaphyseal femur corresponds to the material distribution in bone.     

Scaling of form and function in the xenarthran femur: a 100-fold increase in body mass is mitigated by repositioning of the third trochanter

How animals cope with increases in body size is a key issue in biology. Here, we consider scaling of xenarthrans, particularly how femoral form and function varies to accommodate the size range between the 3 kg armadillo and its giant relative the 300 kg glyptodont. It has already been noted that femoral morphology differs between these animals and suggested that this reflects a novel adaptation to size increase in glyptodont. We test this idea by applying a finite element analysis of coronal plane forces to femoral models of these animals, simulating the stance phase in the hind limb; where the femur is subject to bending owing to longitudinal compressive as well as abduction loads on the greater trochanter. We use these models to examine the hypothesis that muscles attaching on the third trochanter (T3) can reduce this bending in the loaded femur and that the T3 forces are more effective at reducing bending in glyptodont where the T3 is situated at the level of the knee. The analysis uses traditional finite element methods to produce strain maps and examine strains at 200 points on the femur. The coordinates of these points before and after loading are also used to carry out geometric morphometric (GM) analyses of the gross deformation of the model in different loading scenarios. The results show that longitudinal compressive and abductor muscle loading increases bending in the coronal plane, and that loads applied to the T3 reduce that bending. In the glyptodont model, the T3 loads are more effective and can more readily compensate for the bending owing to longitudinal and abductor loads. This study also demonstrates the usefulness of GM methods in interpreting the results of finite element analyses.     

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.     

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone’s material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur’s volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.     

Correlation of muscle function and bone strain in the hindlimb of the river cooter turtle (Pseudemys concinna)

During terrestrial locomotion, limb muscles must generate mechanical work and stabilize joints against the ground reaction force. These demands can require high force production that imposes substantial loads on limb bones. To better understand how muscle contractile function influences patterns of bone loading in terrestrial locomotion, and refine force platform equilibrium models used to estimate limb bone safety factors, we correlated in vivo recordings of femoral strain with muscle activation and strain in a major propulsive hindlimb muscle, flexor tibialis internus (FTI), of a species with a published model of hindlimb force production (river cooter turtles, Pseudemys concinna). Electromyography (EMG) recordings indicate FTI activity prior to footfall that continues through approximately 50% of the stance phase. Large EMG bursts occur just after footfall when the muscle has reached its maximum length and is beginning to actively shorten, concurrent with increasing compressive strain on the anterior femur. The FTI muscle shortens through 35% of stance, with mean fascicle shortening strains reaching 14.0 ± 5.4% resting length (L₀). At the time of peak compressive strains on the femur, the muscle fascicles remain active, but fascicles typically lengthen until mid‐stance as the knee extends. Influenced by the activity of the dorsal knee extensor femorotibialis, the FTI muscle continues to passively lengthen simultaneously with knee extension and a shift to tensile axial strain on the anterior femur at approximately 40% of stance. The near coincidence in timing of peak compressive bone strain and peak muscle shortening (5.4 ± 4.1% stance) indicates a close correlation between the action of the hip extensor/knee flexor, FTI, and femoral loading in the cooter hindlimb. In the context of equilibrium models of limb bone loading, these results may help explain differences in safety factor estimates observed between previous force platform and in vivo strain analyses in cooters. J. Morphol. 274:1060–1069, 2013. © 2013 Wiley Periodicals, Inc.     

LISS钢板治疗股骨远端骨折有限元建模及分析

目的建立LISS-DF治疗股骨远端骨折近端螺钉不同单双皮质固定的三维有限元模型,并进行初步生物力学分析。方法提取CT图片相关数据,利用自行编写程序生成命令流文件,建立完整股骨以及16个不同LISS-DF治疗股骨远端AO分型33-A3型骨折的实体模型（钢板和股骨不接触、螺钉分别固定于钢板和股骨）,进行网格划分。分析不同载荷作用下完整股骨和LISS钢板近端螺钉全双皮质固定治疗骨折的模型受力状况。结果建立了相关的有限元模型。不同载荷作用下,LISS钢板近端螺钉全双皮质固定模型和完整股骨的应力集中均位于股骨颈内侧和股骨干外侧中下1/3处。相同载荷作用下,LISS钢板近端螺钉全双皮质固定模型的股骨颈部最大等效应力值略减小,股骨干最大等效应力值明显减小。结论研究建立的三维有限元模型,为应用LISS治疗股骨骨折的生物力学分析提供了良好的实验平台和基础。从生物力学角度而言,LISS-DF近端螺钉全双皮质固定为治疗股骨远端复杂骨折的有效方法。     

Internal forces and moments in the femur of the rat during gait

The rat is of increasing importance for experimental studies on fracture healing. The healing outcome of long bone fractures is strongly influenced by mechanical factors, such as the interfragmentary movement. This movement depends on the stability of the fracture fixation and the musculoskeletal loads. However, little is known about these loads in rats.The musculoskeletal loads during gait were estimated using an inverse-dynamic musculoskeletal model of the right hindlimb of the rat. This model was based on a micro-CT scan of the lower extremities and an anatomical study using 15 rat cadavers. Kinematics were reconstructed from X-ray movies, taken simultaneously from two perpendicular directions during a gait cycle. The ground reaction forces were taken from the literature. The muscle forces were calculated using an optimization procedure.The internal forces and moments varied over the gait cycle and along the femoral axis. The greatest internal force (up to 7 times bodyweight) acted in the longitudinal direction. The greatest internal moment (up to 13.8 bodyweight times millimeter) acted in the sagittal plane of the femur. The validity of the model was corroborated by comparing the estimated strains caused by the calculated loads on the surface of the femoral mid-shaft with those from the literature.Knowledge of the internal loads in the femur of the rat allows adjustment of the biomechanical properties of fixation devices in fracture healing studies to the desired interfragmentary movement.     

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.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

Bone density, breaking force and leg muscle mass as functions of weight in bipedal rats

Femur density, femur breaking force and muscle weight on the hind limbs of normal and bipedal rats have been measured. The bipeds had more muscle on the hindlimbs than controls. Increasing muscle mass was associated with increasing femur density and breaking force. It is concluded that weight bearing influences bone density and breaking force through muscle mass.     

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.     

Compression or tension? The stress distribution in the proximal femur

Background  

Questions regarding the distribution of stress in the proximal human femur have never been adequately resolved. Traditionally, by considering the femur in isolation, it has been believed that the effect of body weight on the projecting neck and head places the superior aspect of the neck in tension. A minority view has proposed that this region is in compression because of muscular forces pulling the femur into the pelvis. Little has been done to study stress distributions in the proximal femur. We hypothesise that under physiological loading the majority of the proximal femur is in compression and that the internal trabecular structure functions as an arch, transferring compressive stresses to the femoral shaft.     

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.     

A method of quantification of stress shielding in the proximal femur using hierarchical computational modeling

Stress shielding is a biomechanical phenomenon causing adaptive changes in bone strength and stiffness around metallic implants, which potentially lead to implant loosening. Accordingly, there is a need for standard, objective engineering measures of the “stress shielding” performances of an implant that can be employed in the process of computer-aided implant design. To provide and test such measures, we developed hierarchical computational models of adaptation of the trabecular microarchitecture at different sites in the proximal femur, in response to insertion of orthopaedic screws and in response to hypothetical reductions in hip joint and gluteal muscle forces. By identifying similar bone adaptation outcomes from the two scenarios, we were able to quantify the stress shielding caused by screws in terms of analogous hypothetical reductions in hip joint and gluteal muscle forces. Specifically, we developed planar lattice models of trabecular microstructures at five regions of interest (ROI) in the proximal femur. The homeostatic and abnormal loading conditions for the lattices were determined from a finite element model of the femur at the continuum scale and fed to an iterative algorithm simulating the adaptation of each lattice to these loads. When screws were inserted to the femur model, maximal simulated bone loss (17% decrease in apparent density, 10% decrease in thickness of trabeculae) was at the greater trochanter and this effect was equivalent to the effect of 50% reduction in gluteal force and normal hip joint force. We conclude that stress shielding performances can be quantified for different screw designs using model-predicted hypothetical musculoskeletal load fractions that would cause a similar pattern and extent of bone loss to that caused by the implants.     

A method of quantification of stress shielding in the proximal femur using hierarchical computational modeling

Stress shielding is a biomechanical phenomenon causing adaptive changes in bone strength and stiffness around metallic implants, which potentially lead to implant loosening. Accordingly, there is a need for standard, objective engineering measures of the "stress shielding" performances of an implant that can be employed in the process of computer-aided implant design. To provide and test such measures, we developed hierarchical computational models of adaptation of the trabecular microarchitecture at different sites in the proximal femur, in response to insertion of orthopaedic screws and in response to hypothetical reductions in hip joint and gluteal muscle forces. By identifying similar bone adaptation outcomes from the two scenarios, we were able to quantify the stress shielding caused by screws in terms of analogous hypothetical reductions in hip joint and gluteal muscle forces. Specifically, we developed planar lattice models of trabecular microstructures at five regions of interest (ROI) in the proximal femur. The homeostatic and abnormal loading conditions for the lattices were determined from a finite element model of the femur at the continuum scale and fed to an iterative algorithm simulating the adaptation of each lattice to these loads. When screws were inserted to the femur model, maximal simulated bone loss (17% decrease in apparent density, 10% decrease in thickness of trabeculae) was at the greater trochanter and this effect was equivalent to the effect of 50% reduction in gluteal force and normal hip joint force. We conclude that stress shielding performances can be quantified for different screw designs using model-predicted hypothetical musculoskeletal load fractions that would cause a similar pattern and extent of bone loss to that caused by the implants.     

Numerical simulation of load-induced bone structural remodelling using stress-limit criterion

A simple and efficient numerical method for predicting the remodelling of adaptive materials and structures under applied loading was presented and implemented within a finite element framework. The model uses the trajectorial architecture theory of optimisation to predict the remodelling of material microstructure and structural organisation under mechanical loading. We used the proposed model to calculate the density distribution of proximal femur in the frontal plane. The loading considered was the hip joint contact forces and muscular forces at the attachment sites of the muscles to the bone. These forces were estimated from a separate finite element calculation using a heterogeneous three-dimensional model of the proximal femur. The density distributions obtained by this procedure has a qualitative similarity with in vivo observations. Solutions displayed the characteristic high-density channels that are evident in the Dual X-ray Absorptiometry scan. There is also evidence of the intramedullary canal, as well as low-density regions in the femoral neck. Several parametric studies were carried out to highlight the advantages of the proposed method, which includes fast convergence and low-computational cost. The potential applications of the proposed method in predicting bone structural remodelling in cancer are also briefly discussed.     

Virtual trial to evaluate the robustness of cementless femoral stems to patient and surgical variation

Primary stability is essential for the success of cementless femoral stems. In this study, patient specific finite element (FE) models were used to assess changes in primary stability due to variability in patient anatomy, bone properties and stem alignment for two commonly used cementless femoral stems, Corail® and Summit® (DePuy Synthes, Warsaw, USA). Computed-tomography images of the femur were obtained for 8 males and 8 females. An automated algorithm was used to determine the stem position and size which minimized the endo-cortical space, and then span the plausible surgical envelope of implant positions constrained by the endo-cortical boundary. A total of 1952 models were generated and ran, each with a unique alignment scenario. Peak hip contact and muscle forces for stair climbing were scaled to the donor’s body weight and applied to the model. The primary stability was assessed by comparing the implant micromotion and peri-prosthetic strains to thresholds (150 μm and 7000 µε, respectively) above which fibrous tissue differentiation and bone damage are expected to prevail. Despite the wide range of implant positions included, FE prediction were mostly below the thresholds (medians: Corail®: 20–74 µm and 1150–2884 µε, Summit®: 25–111 µm and 860–3010 µε), but sensitivity of micromotion and interfacial strains varied across femora, with the majority being sensitive (p < 0.0029) to average bone mineral density, cranio-caudal angle, post-implantation anteversion angle and lateral offset of the femur. The results confirm the relationship between implant position and primary stability was highly dependent on the patient and the stem design used.     

Bone adaptation to altered loading after spinal cord injury: a study of bone and muscle strength

Bone loss from the paralysed limbs after spinal cord injury (SCI) is well documented. Under physiological conditions, bones are adapted to forces which mainly emerge from muscle pull. After spinal cord injury (SCI), muscles can no longer contract voluntarily and are merely activated during spasms. Based on the Ashworth scale, previous research has suggested that these spasms may mitigate bone losses. We therefore wished to assess muscle forces after SCI with a more direct measure and compare it to measures of bone strength. We hypothesized that the bones in SCI patients would be in relation to the loss of muscle forces. Six male patients with SCI 6.4 (SD 4.3) years earlier and 6 age-matched, able-bodied control subjects were investigated. Bone scans from the right knee were obtained by pQCT. The knee extensor muscles were electrically stimulated via the femoral nerve, isometric knee extension torque was measured and patellar tendon force was estimated. Tendon force upon electrical stimulation in the SCI group was 75% lower than in the control subjects (p<0.01). Volumetric bone mineral density of the patella and of the proximal tibia epiphysis were 50% lower in the SCI group than in the control subjects (p<0.01). Cortical area was lower by 43% in the SCI patients at the proximal tibia metaphysis, and by 33% at the distal femur metaphysis. No group differences were found in volumetric cortical density. Close curvilinear relationships were found between stress and volumetric density for the tibia epiphysis (r(2)=0.90) and for the patella (r(2)=0.91). A weaker correlation with the tendon force was found for the cortical area of the proximal tibia metaphysis (r(2)=0.63), and none for the distal femur metaphysis. These data suggest that, under steady state conditions after SCI, epiphyseal bones are well adapted to the muscular forces. For the metaphysis of the long bones, such an adaptation appears to be less evident. The reason for this remains unclear.