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Keywords:

  • bone remodelling;
  • acetabulum;
  • finite elements;
  • hip muscles

SUMMARY

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

A modelling framework using the international Physiome Project is presented for evaluating the role of muscles on acetabular stress patterns in the natural hip. The novel developments include the following: (i) an efficient method for model generation with validation; (ii) the inclusion of electromyography-estimated muscle forces from gait; and (iii) the role that muscles play in the hip stress pattern. The 3D finite element hip model includes anatomically based muscle area attachments, material properties derived from Hounsfield units and validation against an Instron compression test. The primary outcome from this study is that hip loading applied as anatomically accurate muscle forces redistributes the stress pattern and reduces peak stress throughout the pelvis and within the acetabulum compared with applying the same net hip force without muscles through the femur. Muscle forces also increased stress where large muscles have small insertion sites. This has implications for the hip where bone stress and strain are key excitation variables used to initiate bone remodelling based on the strain-based bone remodelling theory. Inclusion of muscle forces reduces the predicted sites and degree of remodelling. The secondary outcome is that the key muscles that influenced remodelling in the acetabulum were the rectus femoris, adductor magnus and iliacus.Copyright © 2013 John Wiley & Sons, Ltd.

INTRODUCTION

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

The acetabulum is the articulating region at the pelvis where forces are transmitted from the lower limb. The hip has been reported to endure 2–4 times body weight during walking and stair ascent [1] and measured up to 6 times body weight using instrumented in vivo devices [2]. When healthy, it can receive a lifetime of loading but disease, injury and a change in loading pattern can initiate a cycle of bone degeneration.

A wealth of studies in the literature focuses on artificial hip and implant intervention [3]. However, with increased focus on early intervention and non-invasive treatments, an evaluation of the bone stress in the natural hip can provide an understanding of the homeostatic state of stress provided by muscle forces. Diseases such as osteoarthritis are often initiated by deviation from this natural state. Multibody dynamics offers a robust tool for calculating whole body dynamics and muscle forces. Alternatively, finite element (FE) models allow for subject-specific geometry, articular contact and spatially varying material properties suitable for investigating joint stress and remodelling [3].

Dalstra and Huiskes combined experimental data with a finite element model and showed the major load transfer is through the cortical bone with stresses up to 50 times greater than those recorded in cancellous bone during single leg stance. The specific regions of the pelvis that bear the most load are the superior acetabular rim, the posterior column (in particular the sciatic notch) and to a lesser degree through the superior pubic ramus [1]. The thicker cortical pelvic bone supports this observation as bone grows in order to minimise strain in highly loaded zones. They also reported that the elastic modulus of pelvic trabecular bone is generally lower than that found in the femur or tibia and is not highly anisotropic. Most importantly, they showed that peak stresses reduced when hip loading was applied through muscle forces as opposed to an equivalent net hip force applied through the femur. This highlighted the role of muscles as stress distributors. More recently, Ford et al. [4] showed that large strain errors in FE Analysis (FEA) prediction occurred when muscle origin and insertions were removed. The importance of 3D anatomically based models was reported by Cilingir et al. [5] who showed that anatomically based FE models produce significantly different stress distributions to simpler 2D and 3D axisymmetric models even though the contact force may be similar. The recent work of Anderson et al. [6] found that smoothed idealised geometries underestimated contact pressures when compared with patient-specific geometries.

The aim of this study was to use an anatomically accurate validated hip modelling framework adapted from the International Union of Physiological Sciences Physiome Project to evaluate the muscle-induced stress patterns across the pelvis with an emphasis on the acetabulum. This model has spatially varying trabecular material properties derived from computed tomography (CT) and is loaded with hip-crossing muscle forces calculated from walking gait. We evaluate the degree to which muscle forces influence the stress/strain stimulus and remodelling response in the acetabulum when using the strain-based bone remodelling mechanostat approach. Although it has been reported that the hip-crossing gluteus maximus and adductor magnus muscles contribute significantly to the hip contact force through rigid body models [7], it is of interest to know how these and other muscles contribute to the stress pattern in the acetabulum using a finite element model. This has implications on interventions that upset the muscle force balance and lead to a stress change that can initiate and progress joint disease.

METHODS

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

The modelling framework used in this study integrated gait analysis data and muscle forces computed using a hybrid electromyography (EMG)-assisted method [8, 9] with an anatomically based FE model of the hip complex derived from the visible human dataset and the International Union of Physiological Sciences Physiome Project [10](Figure 1). This study was conducted in three stages.

image

Figure 1. (Left) Semi-automated geometric mesh creation of pelvic bone from computed tomography data slices; (Right) Fitting of existing femur to computed tomography data. The blue points of the femur are morphed to the red points via free-form deformation. The newly morphed surface is then re-fitted to the data.

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Muscle force computation

One healthy male subject (age: 28 years, height: 183 cm, mass: 67 kg) volunteered for this investigation and gave informed, written consent. The project was approved by the Human Research Ethics Committee at the University of Western Australia. The motion data acquired from the subject were static anatomical poses and dynamic gait trials. During all trials, the three-dimensional location of 27 retro-reflective markers placed on the subject's lower extremities, pelvis and trunk was recorded (at 250 Hz) using a 12-camera motion capture system (Vicon, Oxford, UK). During the Dynamic1 trials, ground reaction forces and EMG data were collected (2000 Hz) synchronously with marker trajectories using an in-ground force plate (AMTI, Watertown, USA), and bipolar electrodes with a telemetered EMG system (Noraxon, Scottsdale, USA), respectively. EMG data were collected by placing a pair of electrodes in the correspondence of 16 muscle groups including: hip adductors, gluteus maximus, gluteus medius, gracilis, tensor fasciae latae, lateral hamstrings, medial hamstrings, sartorius, rectus femoris, vastus medialis, vastus lateralis, gastrocnemius medialis, gastrocnemius lateralis, peroneus group, soleus and tibialis anterior.

Both ground reaction forces and marker trajectories were low-pass filtered with a fourth-order Butterworth filter. Cut-off frequencies (between 2 and 8 Hz) were determined by a trial-specific residual analysis [11]. EMGs were processed by band-pass filtering (10–450 Hz), then full-wave rectifying and low-pass filtering (6 Hz). The resulting linear envelopes were normalised with respect to the peak-processed EMG values obtained from the entire set of recorded trials [9]. The human movement data were collected from eight repeated trials of walking at a speed of 1.3 ± 0.25m/s. The gait data was used within an EMG-informed methodology for the prediction of the forces in the musculotendon units (MTUs) crossing the hip, knee and ankle joints [8, 9]. The activity of deeply located MTUs that could not be experimentally measured (iliacus and psoas MTUs) was predicted using a standard static optimization-based approach. Specifically, MTU forces were resolved by minimising the sum of squared MTU activations subject to matching the experimental joint moments at the hip. The amplitude of the experimentally available EMG linear envelopes that were recorded were adjusted (i.e. increased or decreased) to further minimise the discrepancy between experimental and predicted joint moments and account for limitations in EMG processing [8, 9]. Both static optimization and EMG amplitude adjustment were based on a simulated annealing optimization algorithm [12].

Adjusted and predicted EMG linear envelopes were then used to drive a forward dynamic EMG-driven musculoskeletal model of the human lower extremity [9, 13]. In this model, the musculoskeletal geometry of the human lower extremity was based on a previously presented rigid-body model in which the MTU kinematics was represented by lines of action with MTU-to-bone wrapping points and surfaces [14, 15]. The MTU dynamics was based on a Hill-type muscle model that included non-linear passive tendons in series to parallel non-linear active and passive fibre contractile elements [13]. The musculoskeletal model was comprised of 34 MTUs and six DOF in the lower extremity including: hip flexion-extension, hip adduction-abduction, hip internal-external rotation, knee flexion-extension, ankle plantar-dorsi flexion and ankle subtalar flexion. The proposed musculoskeletal model was scaled and then calibrated to the actual subject [9, 13]. In brief, the scaling procedure used the software opensim (The National Center for Simulation in Rehabilitation Research (NCSRR), Stanford, CA, USA) [14] to scale a generic model of the human musculoskeletal geometry to match the individual subject's anthropometry. In this process, virtual markers were created and placed on the generic musculoskeletal geometry model on the basis of the position of the experimental markers. The anthropomorphic properties of the anatomical segments and MTUs were then linearly scaled on the basis of the relative distances between experimental markers and their corresponding virtual markers. The adjusted segment and MTU properties included: anatomical segment length, width, depth, center of mass location and mass moment of inertia, as well as MTU insertion, origin and MTU-to-bone wrapping points.

The model calibration step was used to identify a set of intrinsic MTU parameters that vary non-linearly across individuals because of anatomical and physiological differences [9, 13]. These included: tendon slack length, optimal fibre length and maximum isometric force. A nominal set of parameters taken from [14, 16] was initially used in the model to predict the MTU force and the resulting joint moment as a function of EMG signals during a set of calibration trials. The initial parameter set was repeatedly refined using a simulated annealing algorithm [12] until the mismatch between predicted and experimental joint moments was minimised. The specific hip-crossing muscles modelled, which were used as input to the FE model, were the adductors (brevis, longus and magnus), biceps femoris, gluteus maximus, medius and minimus, gracilis, iliacus, psoas, rectus femoris, sartorius, semimembranosus, semitendinosus and tensor fascia late (Figure 2).

image

Figure 2. Hip musculotendon forces from electromyography-assisted gait simulation during the stance phase of the gait cycle.

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Model setup

Figure 1(left) shows the geometric model of the pelvis, which was semi-automatically constructed from CT data of a cadaveric specimen [17] and stored within the Physiome database [18]. These meshes use high-order cubic Hermite elements that are suited to contact mechanics as they allow for the surface normal to be C1 continuous across elements [19]. For the femur mesh, we used an existing model from the Physiome repository and fit this to the cadaveric CT data in two steps. Firstly, using host-mesh fitting [19], we morphed the Physiome femur to roughly match the cadaveric CT data at key anatomical points (Figure 1 right). Blue landmark points of the femur were pulled towards the target red points. Secondly, the newly morphed femur surface was refit to accurately match the complete CT dataset.

The pelvis model was previously validated using an Instron test as shown in Figure 3 [20]. Specifically, three cadaveric embalmed pelvises were each loaded with 600 N (single leg stance of a 60 kg subject) and strain gauged. Finite element models were then generated from the CT scans. Material properties for cancellous bone were obtained from the CT scans and assigned to the FE mesh using a spatially varying field embedded inside the mesh. In the acetabular region, the model showed good agreement between predicted surface strains and experimental strains with an R 2 of 0.9.

image

Figure 3. (Top) Cadaveric hip harvested; Instron compression testing within the acetabulum and equivalent finite element model predicted strains with fixed regions highlighted (posterior superior iliac spine and pubic symphysis) and (Bottom) Correlation of finite element analysis predicted strain and experimentally measured strain.

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The material properties of the model were adapted from Hounsfield units (HU) [17, 21] from CT as shown at the numerical integration points in Figure 4. The specific relationship between material property and HU is detailed in Appendix A. A ‘St Venant Kirchoff’ model [22], which is a linear elastic constitutive law that uses the large deformation Green strain tensor, was used for both bone and cartilage. A constant cortical bone stiffness of 16.7 GPa with Poisson's ratio of 0.3 [1, 23]; a spatially varying trabecular bone stiffness ranged from 200 MPa to 2.2 GPa with Poisson's ratio of 0.3 [21]; and a cartilage stiffness of 10 MPa with Poisson's ratio of 0.4 were used in the model [24]. The pelvis was fixed at the posterior superior iliac spine and the pubic symphysis, which are the attachment points for the two symmetric pelvis halves. The pelvis was loaded via a ground reaction force through the femur with muscle attachments crossing the hip. The femur was left free to resolve for an equilibrium position at each solution step.

image

Figure 4. Cortical and trabecular material properties from Hounsfield units visualised at finite element integration points.

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The muscle forces computed using the EMG-assisted method were applied to the FE model using muscle belly centroid paths. The muscle paths were identified from the visible human male dataset [25] (Figure 5) and the origin and insertion areas on bone were digitised (Figure 6) with the assistance of an orthopaedic surgeon. These points were then stored in a coordinate frame that is fixed to the meshed bone so they would remain unchanged during morphing and transformation routines. During the gait cycle the action lines of each muscle was used to direct the force onto the pelvis and femur (Figure 5). At the attachment point to the bone, the net force was distributed over the insertion/origin areas (Figure 6). The cartilage was modelled as a uniform layer of elements adjacent to the bone. The high-order cubic Hermite interpolation allowed for non-linear deformations with a single layer of elements.

image

Figure 5. Identified muscles and action paths used in the current finite element hip model.

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image

Figure 6. Muscle contact areas identified from the visible human male and orthopaedic advice. (O) indicates origin and (I) indicates insertion.

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Mechanics

The bone and cartilage contact problem was solved using the bioengineering software cmiss (Auckland Bioengineering Institute, Auckland, New Zealand) (www.cmiss.org). A series of finite elastic quasi-static simulations were computed for one cycle of gait. Although bone typically undergoes less than 10% strain (allowing a linear elasticity approximation), the hip cartilage strains are higher and finite elasticity was employed instead. The governing equations for solid mechanics used in the problem are given in Appendix B. The strain and resulting von Mises stress was computed over one gait cycle, and the average was used for this analysis. Remodelling in the hip was based on the strain-based mechanostat approach [26, 27] where strain stimulus less than 1000 μϵ lowers bone density and strain above 3000 μϵ increases bone density. Strains between these values maintain bone density (a homeostatic state). The piecewise stimulus for remodelling, ϵs, is related to the von Mises strain, ϵVM, by

  • display math(1)

For this study, we used the von Mises scalar measure for bone (cartilage was not included in the analysis). The von Mises strain accounts for all principal components and is not directionally biased.

The outputs from the simulation included the pelvic von Mises bone stress, bone remodelling stimulus pattern and the contribution of each muscle to the bone remodelling stress stimulus in the acetabulum by perturbing each muscle individually.

RESULTS

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

Inclusion of muscle forces increased stress on the anterior superior iliac spine (ASIS) but reduced stress in the iliac fossa (Figure 7). The predicted von Mises stress ranged from less than 1 MPa up to peak of 17.8 MPa. At the ASIS, muscle forces increased the mean von Mises stress from 10.7 ± 2.4 MPa to 11.5 ± 2.7 MPa (7.5% increase) and increased the peak stress from 15.6 to 17.0 MPa (9% increase). Comparing all elements within the ASIS region using a one-way ANOVA this difference was not significant at the 95 % confidence level but was significant at the 90% confidence level (P < 0.1). Within the iliac fossa, muscle forces reduced the mean von Mises stress from 11.9 ± 3.4 to 9.7 ± 2.8 MPa (18.5% decrease) and decreased the peak stress from 17.8 to 17.6 MPa (1.1% decrease). This difference was significant (P < 0.05). All computed stress means, standard deviations, peak stresses and p-values are summarised in Table 1.

image

Figure 7. Medial-anterior view of pelvis von Mises stress pattern for (left) without muscles and (right) with hip-crossing muscles. The labelled sites of key difference are highlighted showing mean value (with peak in bold red) and standard deviation of stresses in that region. The legend shows red is 18 MPa and dark blue is < 1 MPa.

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Table 1. Mean stress and standard deviation (including peak stress) for the identified pelvic regions in Figures 7-9. The p-values from a one-way ANOVA on a per element comparison identify statistically significant differences (p < 0.05) in pelvic stress with and without muscle inclusion.
RegionStress (MPa) Mean(peak) ± SD (Without muscles)Stress (MPa) Mean(peak) ± SD (With muscles)ANOVA p-value
Anterior superior iliac spine10.7(15.6) ± 2.411.5(17.0) ± 2.7p < 0.1
Iliac fossa11.9(17.8) ± 3.49.7(17.6) ± 2.8* p < 0.05
Ischium1.9(2.7) ± 0.54.5(9.0) ± 1.7* p < 0.05
Acetabular margin12.4(17.8) ± 2.910.9(14.8) ± 2.3p < 0.1
Acetabular notch6.1(7.3) ± 0.88.8(11.0) ± 1.3* p < 0.05
Acetabular fossa6.4(9.1) ± 1.35.2(7.4) ± 1.2* p < 0.05

Inclusion of muscle forces increased stress in the ischium (inferior region of the pelvis) (Figure 8). The peak value was 9 MPa, and the stress pattern more uniform than that observed on the ASIS or iliac fossa. Along the ischium, muscle forces increased the mean von Mises stress from 1.9 ± 0.5 to 4.5 ± 1.7 MPa (136.8% increase) and increased the peak stress from 2.7 to 9.0 MPa (233.3% increase). This difference was significant (p < 0.05).

image

Figure 8. Lateral-posterior (acetabulum side) view of hip von Mises stress pattern for (left) without muscles and (right) with hip-crossing muscles. The labelled sites of key difference are highlighted showing mean value (with peak in bold red) and standard deviation of stresses in that region. The legend shows red is 18 MPa and dark blue is < 1 MPa.

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An expanded view of the acetabulum (Figure 9) shows inclusion of muscle forces reduced stress on the superior ridge of the acetabulum (acetabular margin) and acetabular fossa but increased stress at the inferior ridge of the acetabulum (acetabular notch). At the acetabular margin, muscle forces decreased the stress from 12.4 ± 2.9 to 10.9 ± 2.3 MPa (12.1% decrease) and decreased the peak from 17.8 to 14.8 MPa (16.9% decrease). This was not significant at the 95 % confidence level but was significant at the 90% confidence level (p < 0.1). Within the acetabular fossa, muscle forces decreased stress from 6.4 ± 1.3 to 5.2 ± 1.2 MPa (18.8% decrease) and decreased peak stress from 9.1 to 7.4 MPa (18.7% decrease). At the acetabular notch, muscle forces increased stress from 6.1 ± 0.8 to 8.8 ± 1.3 MPa (44.2% increase) and increased peak stress from 7.3 to 11.0 MPa (50.7% increase). Changes at the acetabular notch and fossa were significant (p < 0.05).

image

Figure 9. Expanded acetabulum view of hip von Mises stress pattern for (left) without muscles and (right) with hip-crossing muscles. The labelled sites of key difference are highlighted showing mean value (with peak in bold red) and standard deviation of stresses in that region. The legend shows red is 18 MPa and dark blue is < 1 MPa.

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By using the strain-based mechanostat bone remodelling rules, Figure 10 shows the likely regions of remodelling within and surrounding the acetabulum. Firstly, when muscles are included, the region of bone that undergoes modelling (bone density increase) is reduced by 26% in the acetabulum. The modelling area decreased with the fossa. Secondly, at the inferior ridge, muscle forces increased prediction of modelling. Thirdly, the degree of remodelling (bone density decrease) increased at the superior ramus of the pubis.

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Figure 10. Expanded acetabulum view of hip mechanostat remodelling pattern for (left) no muscles and (right) with hip-crossing muscles. The sites of key difference are highlighted. Green is quiescent bone (1000–3000  μϵ), red is bone density increase ( > 3000μϵ) and dark blue is bone density decrease ( < 1000μϵ).

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The muscle forces during the stance phase of gait as computed by the EMG-assisted method (Figure 2) showed that the major contributors to the hip contact force are the gluteus medius, gluteus maximus, iliacus, rectus femoris and tensor fascia latae. Through perturbing each muscle by 10%, we computed that the major contributors to the muscle-induced stress pattern within the acetabulum (Figure 11) are the rectus femoris, adductor magnus and iliacus, which contribute 8.5%, 7.7% and 7.6% of the muscle-induced stress pattern, respectively. The next major contributors are the adductor longus and psoas muscles, which contribute 6.3% and 6.2%, respectively. The gluteus muscles, gracilis, sartorius, semimembranosus, semitendinosus and tensor fascia latae all exhibited a similar contribution of ∼ 6% to the muscle-induced von Mises stress pattern. The biceps femoris long head and adductor brevis contributed the least at 4.7% and 4.6%, respectively.

image

Figure 11. Graph of percentage contribution to acetabulum von Mises stress pattern from each hip-crossing muscle.

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DISCUSSION

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

Model predictions were consistent with previous hip studies. For example, the predicted acetabulum stress pattern during gait was observed to be primarily superior to the cup and along the ridge, consistent with previous works [1, 28, 29]. The range of stress predicted was from less than 1 MPa to a peak of 17.8 MPa, which is similar to the ranges previously reported [30, 31] from 6 to 27 MPa during physiological loading, and Tepic et al. [32] found that contact pressures within the human hip could exceed 10 MPa. Muscle forces generally lowered the peak stress throughout the pelvis and within the acetabulum, which was consistent with Dalstra and Huiskes [1]. However, muscle forces also contributed to increased regions of isolated von Mises stress at specific sites. These isolated increased regions of stress corresponded to either a strong muscle focussed on a small insertion site (in the case of the rectus femoris) or pelvis bending introduced by muscles attaching at regions that have large moment arms relative to the acetabulum centre. Interestingly, the increased peak stress observed on the inferior ridge of the acetabulum coincided with increased material stiffness observed within the trabecular bone at around 2.2 GPa in Figure 4. In general, the pelvis is a sandwich structure where most load is supported by the cortical bone, but in thin areas, the trabecular bone also bears some load. The inclusion of muscle forces may partly explain the increased material stiffness observed in the inferior acetabulum derived from the cadaveric model.

This study should be interpreted with the following limitations in mind. (i) This study only considered gait as the loading for the hip. Although this is our most common task, our hip endures a rich loading pattern from multiple activities. A better loading stimulus might account for an accumulated load over different tasks. However, this should not detract from the conclusions of this study, that muscles modify the stress pattern. (ii) The cartilage model, which transfers the load to the subchondral bone was treated as linearly elastic and included no time-dependent effects such as viscoelasticity or a biphasic fluid component. This would likely not affect the model predictions given that walking is a rapid loading task, and time-dependent models behave as incompressible elastic materials over short periods [33]. (iii) The stress patterns are partly a function of the geometric shape and may vary from subject to subject. The von Mises stress shown here is for a healthy adult pelvis, and a subject-specific model would likely show subtle variations from this. Moreover, the stress is strongly influenced by the boundary conditions. For example, the model of Phillips et al. [29] used spring boundary conditions and found additional stress across the pelvic crest that we did not predict in this model. Our model was fixed at the two symmetric points where the left and right pelvises meet, namely the posterior superior iliac spine and the pubic symphysis. We chose this to be consistent with our previous hip models and validation study. (iv) We only considered muscles that cross the hip joint and were distributed over bone insertion sites, assuming a uniform distribution. Hence, we have not accounted for two key muscles that are known to indirectly contribute to hip joint contact, the vasti and gastrocnemius, and we have not accounted for muscles that impart force non-uniformly. (v) The bone remodelling algorithm used in this study did not account for osteocyte sensor cells, microstructure or accumulative damage history. Given that information was not known for this model, we did not make additional assumptions other than knowing bone and muscle-induced strain. The presented macro-level remodelling results are part of a multiscale framework within the Physiome Project that will incorporate finer scales and more sophisticated remodelling rules as the next step. (vi) The embalming process used for our cadaveric hip does influence material properties of bone [34]. However, many other studies indicated that, although embalming does have some effect on bone mechanical properties, it may not be large enough to be detected by the common engineering method used in mechanical testing [35-38]. Therefore, we are confident that the use of an embalmed pelvis did not compromise the accuracy or validity of the current study. Moreover, unlike other studies that used only one pelvis for their validation [1, 23], we used three with consistent results.

Bone remodelling was overestimated within the acetabulum fossa when muscles were not included. This suggests that one function of muscles is to spread the load more evenly and protect against peak stress. This is consistent with previous studies that have shown that peak strains/stresses are reduced when including muscle forces, but in this model, we also show that this leads to a modified remodelling pattern within the acetabulum. Although this pattern change is not dramatically different, it does lead to a smaller remodelling zone in the fossa, decreased material stiffness on the superior acetabular rim and increased material stiffness at the inferior acetabular rim. Bones are optimised structures that increase or decrease stiffness in order to cope with everyday loads. Muscle forces play a role in distributing the load across the pelvis, and this influence also includes the acetabulum, which was shown to be statistically significant in this study. Although our model incorporated spatially varying material properties for trabecular bone, we only had a single value for cortical bone. Because most of the pelvic load is bore by the cortical bone (like a sandwich structure), the correlation with trabecular material stiffness was less clear. However, where there was very thin cortical bone on the lower acetabular rim (the acetabular notch) and the trabecular bone did bear some load, we did note a peak stress due to muscle forces, which matched the increased material stiffness from HU measurements. Future validation of this work may be possible with temporal imaging of a hip from the same subject with known history or through the use of NaF [39] tracers used as part of positron emission tomography-CT to indicate bone metabolic activity.

The major contributors to the muscle-induced stress pattern were the rectus femoris, adductor magnus and iliacus. The rectus femoris attaches at the ASIS, the adductor magnus attaches along the ischium and inferior pubis regions, while the iliacus attaches along the upper iliac crest. Therefore, each of these muscles is both large in magnitude and has a large moment arm about the acetabulum centre. This introduced pelvic bending and redistributed the stress pattern.

Finally, we evaluated the possibility of errors in the hip force direction by perturbing the force vector up to ± 10% through the femoral head in the model with no muscle forces to see if we could recreate any of the stress patterns observed in the model with muscles. As we were unable to recreate any of the distinct stress patterns, we observed that the modified stress distribution was likely attributed solely to muscles.

CONCLUSION

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

This study shows that muscle forces influence the pelvic stress distribution and remodelling stimulus using a validated hip model. Stress patterns were shown to be primarily superior to the cup and along the ridge. The stress range was 1–17.8 MPa, consistent with previous work. Muscle forces generally lowered stresses in the pelvis and distributed them more evenly. However, the acetabulum notch, ischium and fossa stress increased because of muscle forces. The ischium and fossa corresponded to regions with large moment arms relative to the acetabulum. The acetabular notch corresponded with thin cortical bone with increased trabecular stiffness. Within the acetabulum, muscle-induced stress change in the iliac fossa, ischium, acetabular notch and acetabular fossa were statistically significant (p < 0.05), whereas changes at the ASIS and acetabular margin were significant at the 90% confidence level (p < 0.1). The rectus femoris, adductor magnus and iliacus contributed most to the acetabular stress pattern, and the bone remodelling pattern in the acetabular fossa reduced when muscles were included. An important implication from this study is that muscle forces both reduce and increase pelvic stress spatially. Artificial hip designs should account for these boundary conditions. This will have implications on strain shielding that is often associated with bone loss and implant loosening.

APPENDIX

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

The HU values were obtained from CT scans and converted to density by calibrating HU number into density with the following relationship [17].

  • display math(A1)

where the density of hydroxyapatite ρphantom in our phantom was 800 mg/ml. CT H20 and CT HA are obtained from the phantom CT scans, and CT bone is from the subject's CT scan. This was then converted to modulus using the relationship from Dalstra et al. [21].

  • display math(A2)

where ρHA is HA equivalent density, while ρapp is apparent density.

APPENDIX

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

The virtual work statement for the hip and femur contact problem in the absence of body forces can be written as

  • display math(B1)

where V o is the undeformed mesh volume, and Sc is the surface in contact used to account for the interaction between the femoral head and acetabulum. δuj is a virtual displacement, and inline image is the deformation gradient tensor, which maps between the spatial (xj) and material coordinates (υβ). The Jacobian, J, is the determinant of the deformation gradient tensor, F, and fc is the frictionless contact force implemented using a ‘cross-constraints’ penalty-based method with the complete details reported in Fernandez et al. [22]. Tαβ is the second Piola-Kirchoff stress tensor,

  • display math(B2)

where p is the hydrostatic pressure arising from an incompressibility constraint that conserves cartilage volume. Eαβ is Green's strain components, and inline image is the contravariant metric tensor which transforms between the rectangular Cartesian (xk) and mesh-curvilinear coordinate system (υα).

ACKNOWLEDGEMENTS

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES

We acknowledge funding from a Wishbone trust grant awarded to V. Shim, and an Aotearoa Bioengineering Fellowship from the Robertson Foundation awarded to J. Fernandez.

REFERENCES

  1. Top of page
  2. SUMMARY
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. APPENDIX
  9. APPENDIX
  10. ACKNOWLEDGEMENTS
  11. REFERENCES
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