A finite element based method to determine the properties of planar soft tissue.

A finite element based method to determine the incremental elastic material properties of planar membranes was developed and evaluated. The method is applicable to tissues that exhibit inhomogeneity, geometric and material nonlinearity, and anisotropy. Markers are placed on the tissue to form a four-node quadrilateral element. The specimen is loaded to an initial reference state, then three incremental loading sets are applied and the nodal displacements recorded. One of these loadings must include shear. These data are used to solve an over-determined system of equations for the tangent stiffness matrix. The method was first verified using analytical data. Next, data obtained from a latex rubber sheet were used to evaluate experimental procedures. Finally, experiments conducted on preconditioned rat skin revealed nonlinear orthotropic behavior. The vector norm comparing the applied and calculated nodal force vectors was used to evaluate the accuracy of the solutions.     

Computed tomography-based joint locations affect calculation of joint moments during gait when compared to scaling approaches

Hip joint moments are an important parameter in the biomechanical evaluation of orthopaedic surgery. Joint moments are generally calculated using scaled generic musculoskeletal models. However, due to anatomical variability or pathology, such models may differ from the patient's anatomy, calling into question the accuracy of the resulting joint moments. This study aimed to quantify the potential joint moment errors caused by geometrical inaccuracies in scaled models, during gait, for eight test subjects. For comparison, a semi-automatic computed tomography (CT)-based workflow was introduced to create models with subject-specific joint locations and inertial parameters. 3D surface models of the femora and hemipelves were created by segmentation and the hip joint centres and knee axes were located in these models. The scaled models systematically located the hip joint centre (HJC) up to 33.6 mm too inferiorly. As a consequence, significant and substantial peak hip extension and abduction moment differences were recorded, with, respectively, up to 23.1% and 15.8% higher values in the image-based models. These findings reaffirm the importance of accurate HJC estimation, which may be achieved using CT- or radiography-based subject-specific modelling. However, obesity-related gait analysis marker placement errors may have influenced these results and more research is needed to overcome these artefacts.     

Geometric and mechanical properties of human cervical spine ligaments

This study characterized the geometry and mechanical properties of the cervical ligaments from C2-T1 levels. The lengths and cross-sectional areas of the anterior longitudinal ligament, posterior longitudinal ligament, joint capsules, ligamentum flavum, and interspinous ligament were determined from eight human cadavers using cryomicrotomy images. The geometry was defined based on spinal anatomy and its potential use in complex mathematical models. The biomechanical force-deflection, stiffness, energy, stress, and strain data were obtained from 25 cadavers using in situ axial tensile tests. Data were grouped into middle (C2-C5) and lower (C5-T1) cervical levels. Both the geometric length and area of cross section, and the biomechanical properties including the stiffness, stress, strain, energy, and Young's modulus, were presented for each of the five ligaments. In both groups, joint capsules and ligamentum flavum exhibited the highest cross-sectional area (p < 0.005), while the longitudinal ligaments had the highest length measurements. Although not reaching statistical significance, for all ligaments, cross-sectional areas were higher in the C5-T1 than in the C2-C5 group; and lengths were higher in the C2-C5 than in the C5-T1 group with the exception of the flavum (Table 1 in the main text). Force-deflection characteristics (plots) are provided for all ligaments in both groups. Failure strains were higher for the ligaments of the posterior (interspinous ligament, joint capsules, and ligamentum flavum) than the anterior complex (anterior and posterior longitudinal ligaments) in both groups. In contrast, the failure stress and Young's modulus were higher for the anterior and posterior longitudinal ligaments compared to the ligaments of the posterior complex in the two groups. However, similar tendencies in the structural responses (stiffness, energy) were not found in both groups. Researchers attempting to incorporate these data into stress-analysis models can choose the specific parameter(s) based on the complexity of the model used to study the biomechanical behavior of the human cervical spine.     

Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb

Characterisation of hip joint contact forces is essential for the definition of hip joint prosthesis design requirements. In vivo hip joint contact force measurements have been made using instrumented hip joint prostheses. However, to allow determination of the range of values of joint contact force and their directions relative to anatomical structures in a range of subject groups sufficient to form an agreed data base it is necessary to adopt a different approach without the use of an implanted transducer. The use of mathematical models of the lower limb to examine the forces in soft tissues and at the joints has provided valuable insight into internal loading conditions. Several authors have proposed mathematical musculo-skeletal models. However, there have been only limited attempts at validation of these models. It is possible to use the results of in vivo force measurements from instrumented prostheses to validate the results calculated using the mathematical models. In this study two subjects with instrumented hip joint prostheses were studied. Forces at the hip joints were calculated using a three-dimensional model of the leg. Walking at slow, normal and fast speeds (0.97-2.01m/s), weight transfer from two to one leg and back again, and sit to stand were studied. Direct comparisons were made between the 'gold standard' measured hip joint contact forces and the calculated forces. There was general agreement between the calculated and measured forces in both pattern and magnitude. There were, however, discrepancies. Reasons for these differences in results are discussed and possible model developments suggested.     

Bi-directional mechanical properties of the posterior region of the glenohumeral capsule

The objective of this study was to determine the mechanical properties of the posterior region of the glenohumeral capsule in the directions perpendicular (transverse) and parallel (longitudinal) to the longitudinal axis of the posterior band of the inferior glenohumeral ligament. A punch was used to excise one transverse and one longitudinal tissue sample from the posterior capsule of 11 cadaveric shoulders. All tissue samples exhibited the typical nonlinear behavior reported for ligaments and tendons. Significant differences (p < 0.05) were detected between the transverse and longitudinal tissue samples for ultimate stress (1.5+/-1.4 and 4.9+/-2.9 MPa, respectively) and tangent modulus (10.3+/-6.6 and 31.5+/-12.7 MPa, respectively). No significant differences (p > 0.05) were observed between the ultimate strain (transverse: 22.3+/-12.5%, longitudinal: 22.8+/-11.1%) and strain energy density (transverse: 27.2+/-52.8 MPa, longitudinal: 67.5+/-88.2 MPa) of the transverse and longitudinal tissue samples. The ratio of the longitudinal to transverse moduli (4.8+/-4.2) was similar to that found for the axillary pouch (3.3+/-2.8) in a previous study. Thus, both the axillary pouch and the posterior capsule function to stabilize the joint multi-axially. Future analytical models of the glenohumeral joint should consider the properties of the posterior capsule in its transverse and longitudinal directions to fully describe the behavior of the glenohumeral capsule. These models will be clinically important by providing a more accurate representation of the intact capsule as well as simulated capsular injuries and surgical repair procedures.     

Flexural and torsional stiffness in multi-jointed biological beams

Flexibility, the ability to deform in response to loads, is a common property of biological beams. This paper investigates the mechanical behavior of multi-jointed beams, which are characterized by a linear series of morphologically similar joints. Flexural stiffness and torsional stiffness were measured in two structurally distinct beams, crinoid arms (Echinodermata, Comatulida) and crustacean antennae (Arthropoda, Decapoda). Morphological data from these beams were used to determine the relative contributions of beam diameter and joint density (number of joints per millimeter of beam length) to the flexural and torsional stiffness of these two structures. As predicted by beam theory, beam diameter influenced stiffness in both crinoid arms and crustacean antennae. In crinoid arms, increases in joint density were associated with decreases in stiffness, but joint density had no significant influence on stiffness in crustacean antennae. In both crinoid arms and crustacean antennae, the magnitudes of flexural and torsional stiffness, as well as the ratio of these two variables, were similar to previously reported values for non-jointed biological beams. These results suggest that the structural design of a biological beam is not a limiting factor determining its mechanical properties.     

Leg stiffness adjustment for a range of hopping frequencies in humans

The purpose of the present study was to determine how humans adjust leg stiffness over a range of hopping frequencies. Ten male subjects performed in place hopping on two legs, at three frequencies (1.5, 2.2, and 3.0 Hz). Leg stiffness, joint stiffness and touchdown joint angles were calculated from kinetic and/or kinematics data. Electromyographic activity (EMG) was recorded from six leg muscles. Leg stiffness increased with an increase in hopping frequency. Hip and knee stiffnesses were significantly greater at 3.0 Hz than at 1.5 Hz. There was no significant difference in ankle stiffness among the three hopping frequencies. Although there were significant differences in EMG activity among the three hopping frequencies, the largest was the 1.5 Hz, followed by the 2.2 Hz and then 3.0 Hz. The subjects landed with a straighter leg (both hip and knee were extended more) with increased hopping frequency. These results suggest that over the range of hopping frequencies we evaluated, humans adjust leg stiffness by altering hip and knee stiffness. This is accomplished by extending the touchdown joint angles rather than by altering neural activity.     

A patient-specific computer tomography-based finite element methodology to calculate the six dimensional stiffness matrix of human vertebral bodies

In most finite element (FE) studies of vertebral bodies, axial compression is the loading mode of choice to investigate structural properties, but this might not adequately reflect the various loads to which the spine is subjected during daily activities or the increased fracture risk associated with shearing or bending loads. This work aims at proposing a patient-specific computer tomography (CT)-based methodology, using the currently most advanced, clinically applicable finite element approach to perform a structural investigation of the vertebral body by calculation of its full six dimensional (6D) stiffness matrix. FE models were created from voxel images after smoothing of the peripheral voxels and extrusion of a cortical shell, with material laws describing heterogeneous, anisotropic elasticity for trabecular bone, isotropic elasticity for the cortex based on experimental data. Validated against experimental axial stiffness, these models were loaded in the six canonical modes and their 6D stiffness matrix calculated. Results show that, on average, the major vertebral rigidities correlated well or excellently with the axial rigidity but that weaker correlations were observed for the minor coupling rigidities and for the image-based density measurements. This suggests that axial rigidity is representative of the overall stiffness of the vertebral body and that finite element analysis brings more insight in vertebral fragility than densitometric approaches. Finally, this extended patient-specific FE methodology provides a more complete quantification of structural properties for clinical studies at the spine.     

Assessment of the functional method of hip joint center location subject to reduced range of hip motion

Motion analysis of the lower extremities usually requires determination of the location of the hip joint center. The results of several recent studies have suggested that kinematic and kinetic variables calculated from motion analysis data are highly sensitive to errors in hip joint center location. "Functional" methods in which the location of the hip joint center is determined from the relative motion of the thigh and pelvis, rather than from the locations of bony landmarks, are promising but may be ineffective when motion is limited. The aims of the present study were to determine whether the accuracy of the functional method is compromised in young and elderly subjects when limitations on hip motion are imposed and to investigate the possibility of locating the hip joint center using data collected during commonly studied motions (walking, sit-to-stand, stair ascent, stair descent) rather than using data from an ad hoc trial in which varied hip motions are performed. The results of the study suggested that functional methods would result in worst-case hip joint center location errors of 26mm (comparable to the average errors previously reported for joint center location based on bony landmarks) when available hip motion is substantially limited. Much larger errors ( approximately 70mm worst-case), however, resulted when hip joint centers were located from data collected during commonly performed motions, perhaps because these motions are, for the most part, restricted to the sagittal plane. It appears that the functional method can be successfully implemented when range of motion is limited but still requires collection of a special motion trial in which hip motion in both the sagittal and frontal planes is recorded.     

Leg and Joint Stiffness in Children with Spastic Diplegic Cerebral Palsy during Level Walking

Individual joint deviations are often identified in the analysis of cerebral palsy (CP) gait. However, knowledge is limited as to how these deviations affect the control of the locomotor system as a whole when striving to meet the demands of walking. The current study aimed to bridge the gap by describing the control of the locomotor system in children with diplegic CP in terms of their leg stiffness, both skeletal and muscular components, and associated joint stiffness during gait. Twelve children with spastic diplegia CP and 12 healthy controls walked at a self-selected pace in a gait laboratory while their kinematic and forceplate data were measured and analyzed during loading response, mid-stance, terminal stance and pre-swing. For calculating the leg stiffness, each of the lower limbs was modeled as a non-linear spring, connecting the hip joint center and the corresponding center of pressure, with varying stiffness that was calculated as the slope (gradient) of the axial force vs. the deformation curve. The leg stiffness was further decomposed into skeletal and muscular components considering the alignment of the lower limb. The ankle, knee and hip of the limb were modeled as revolute joints with torsional springs whose stiffness was calculated as the slope of the moment vs. the angle curve of the joint. Independent t-tests were performed for between-group comparisons of all the variables. The CP group significantly decreased the leg stiffness but increased the joint stiffness during stance phase, except during terminal stance where the leg stiffness was increased. They appeared to rely more on muscular contributions to achieve the required leg stiffness, increasing the muscular demands in maintaining the body posture against collapse. Leg stiffness plays a critical role in modulating the kinematics and kinetics of the locomotor system during gait in the diplegic CP.     

Robust optimization of total joint replacements incorporating environmental variables.

Direct search techniques for the optimal design of biomechanical devices are computationally intensive requiring many iterations before converging to a global solution. This, along with the incorporation of environmental variables such as multiple loading conditions and bone properties, makes direct search techniques infeasible. In this study, we introduced new methods that are based on the statistical design and analysis of computer experiments to account efficiently for environmental variables. Using data collected at a relatively small set of training sites, the method employs a computationally inexpensive predictor of the structural response that is statistically motivated. By using this predictor in place of the simulator (e.g., finite element model), a sufficient number of iterations can be performed to facilitate the optimization of the complex system. The applicability of these methods was demonstrated through the design of a femoral component for total hip arthroplasty incorporating variations in joint force orientation and cancellous bone properties. Beams on elastic foundation (BOEF) finite element models were developed to simulate the structural response. These simple models were chosen for their short computation time. This allowed us to represent the actual structural response surface by an exhaustive enumeration of the design and environmental variable space, and provided a means by which to validate the statistical predictor. We were able to predict the structural response and the optimal design accurately using only 16 runs of the computer code. The general trends predicted by the BOEF models were in agreement with previous three-dimensional finite element computer simulations, and experimental and clinical results, which demonstrated that the important features of intramedullary fixation systems were captured. These results indicate that the statistically based optimization methods are appropriate for optimization studies using computationally demanding models.     

Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error ～0.5 mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.     

Fracture prediction for the proximal femur using finite element models: Part I--Linear analysis.

Over 90 percent of the more than 250,000 hip fractures that occur annually in the United States are the result of falls from standing height. Despite this, the stresses associated with femoral fracture from a fall have not been investigated previously. Our objectives were to use three-dimensional finite element models of the proximal femur (with geometries and material properties based directly on quantitative computed tomography) to compare predicted stress distributions for one-legged stance and for a fall to the lateral greater trochanter. We also wished to test the correspondence between model predictions and in vitro strain gage data and failure loads for cadaveric femora subjected to these loading conditions. An additional goal was to use the model predictions to compare the sensitivity of several imaging sites in the proximal femur which are used for the in vivo prediction of hip fracture risk. In this first of two parts, linear finite element models of two unpaired human cadaveric femora were generated. In Part II, the models were extended to include nonlinear material properties for the cortical and trabecular bone. While there was poor correspondence between strain gage data and model predictions, there was excellent agreement between the in vitro failure data and the linear model, especially using a von Mises effective strain failure criterion. Both the onset of structural yielding (within 22 and 4 percent) and the load at fracture (within 8 and 5 percent) were predicted accurately for the two femora tested. For the simulation of one-legged stance, the peak stresses occurred in the primary compressive trabeculae of the subcapital region.(ABSTRACT TRUNCATED AT 250 WORDS)     

The effect of three-dimensional postural change on shear elastic modulus of the iliotibial band

To understand and treat iliotibial band (ITB) syndrome, caused by excessive compression between the ITB and lateral femoral condyle, it is important to identify factors contributing to an increase in ITB stiffness. The purpose of this study was to clarify the factors that contribute to an increase in ITB stiffness by examining the relationship between three-dimensional postural changes and ITB stiffness. Fourteen healthy individuals performed one-leg standing under 7 conditions (including normal one-leg standing as a control condition) in which the pelvic position was changed in three planes. The shear elastic modulus in the ITB was measured using shear-wave elastography, as a measure of ITB stiffness. The three-dimensional joint angles and external joint moments in the hip and knee joints were also measured to confirm the changes in joint angles and external load. Compared to the normal one-leg standing condition, ITB stiffness was significantly increased in the pelvic posterior tilted position (i.e. hip extension), contralateral pelvic dropped position (i.e. hip adduction), and contralateral pelvic posterior rotated position (i.e. hip external rotation). The findings suggest that interventions to reduce hip extension, adduction, and external rotation might be useful if these excessive positional changes are detected in patients with ITB syndrome.     

Pressure during compaction of morsellised bone gives an increase in stiffness: an in vitro study

Morsellised bone impaction is used in joint prosthesis revision surgery to repair structural damage to the periarticular bone stock. The initial stiffness of the impacted bone is crucial for the survival of the revised hip joint. Impaction of morsellised bone in a femoral canal can cause fractures that may induce implant loosening in both femur and acetabulum. Alternative techniques to increase stiffness can therefore be of major interest. In this study we analyse whether applying a constant pressure during impaction can increase the stiffness of the morsellised bone. We constructed bone pellets by impaction with and without applying a constant pressure. The constrained stiffness and coefficient of secondary strain were determined by unidirectional load testing after construction of the pellets. A significant increase in constrained stiffness (P < 0.001) from 3.9 to 5.5 MPa and a decrease in the coefficient of secondary strain (P < 0.001) from 1.1 to 0.5 were found.     

Micro-mechanical modeling of the cement-bone interface: the effect of friction, morphology and material properties on the micromechanical response

In order to gain insight into the micro-mechanical behavior of the cement-bone interface, the effect of parametric variations of frictional, morphological and material properties on the mechanical response of the cement-bone interface were analyzed using a finite element approach. Finite element models of a cement-bone interface specimen were created from micro-computed tomography data of a physical specimen that was sectioned from an in vitro cemented total hip arthroplasty. In five models the friction coefficient was varied (mu=0.0; 0.3; 0.7; 1.0 and 3.0), while in one model an ideally bonded interface was assumed. In two models cement interface gaps and an optimal cement penetration were simulated. Finally, the effect of bone cement stiffness variations was simulated (2.0 and 2.5 GPa, relative to the default 3.0 GPa). All models were loaded for a cycle of fully reversible tension-compression. From the simulated stress-displacement curves the interface deformation, stiffness and hysteresis were calculated. The results indicate that in the current model the mechanical properties of the cement-bone interface were caused by frictional phenomena at the shape-closed interlock rather than by adhesive properties of the cement. Our findings furthermore show that in our model maximizing cement penetration improved the micromechanical response of the cement-bone interface stiffness, while interface gaps had a detrimental effect. Relative to the frictional and morphological variations, variations in the cement stiffness had only a modest effect on the micro-mechanical behavior of the cement-bone interface. The current study provides information that may help to better understand the load-transfer mechanisms taking place at the cement-bone interface.     

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

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

Comparison of viscoelastic, structural, and material properties of double-looped anterior cruciate ligament grafts made from bovine digital extensor and human hamstring tendons

Due to ready availability, decreased cost, and freedom from transmissible diseases in humans such as hepatitis and AIDS, it would be advantageous to use tendon grafts from farm animals as a substitute for human tendon grafts in in vitro experiments aimed at improving the outcome of anterior cruciate ligament (ACL) reconstructive surgery. Thus the objective of this study was to determine whether an anterior cruciate ligament (ACL) graft composed of two loops of bovine common digital extensor tendon has the same viscoelastic, structural, and material properties as a graft composed of a double loop of semitendinosus and gracilis tendons from humans. To satisfy this objective, grafts were constructed from each tissue source. The cross-sectional area was measured using an area micrometer, and each graft was then pulled using a materials testing system while submerged in a saline bath. Using two groups of tendon grafts (n = 10), viscoelastic tests were conducted over a three-day period during which a constant displacement load relaxation test was followed by a constant amplitude, cyclic load creep test (first day), a constant load creep test (second day), and an incremental cyclic load creep test (third day). Load-to-failure tests were performed on two different groups of grafts (n = 8). When the viscoelastic behavior was compared, there were no significant differences in the rate of load decay or the final load (relaxation test) and rates of displacement increase or final displacements (creep tests) (p > 0.115). To compare both the structural and material properties in the toe region (i.e., < 250 N) of the load-elongation curve, the tangent stiffness and modulus functions were computed from parameters used in an exponential model fit to the load (stress)-elongation (strain) data. Although one of the two parameters in the functions was different statistically, this difference translated into a difference of only 0.03 mm in displacement at 250 N of load. In the linear region (i.e., 50-75 percent of ultimate load) of the load-elongation curve, the linear stiffness of the two graft types compared closely (444 N/mm for bovine and 418 N/mm for human) (p = 0.341). At failure, the ultimate loads (2901 N and 2914 N for bovine and human, respectively) and the ultimate stresses (71.8 MPa and 65.6 MPa for bovine and human, respectively) were not significantly different (p > 0.261). The theoretical effect of any differences in properties between these two grafts on the results of two types of in vitro experiments (i.e., effect of surgical variables on knee laxity and structural properties of fixation devices) are discussed. Despite some statistical differences in the properties evaluated, these differences do not translate into important effects on the dependent variables of interest in the experiments. Thus the bovine tendon graft can be substituted for the human tendon graft in both types of experiments.     

Impacted bone stiffness measured during construction of morsellised bone samples

Impacted morsellised bone is widely used for filling bone deficiencies during revision of total hip arthroplasties. However, the physical properties and mechanical behaviour of this bone material are still not well understood. In this study we recorded the increase of stiffness in pellets of morsellised bone during their construction. The construction of bone pellets was measured stroke-by-stroke to ascertain optimal stiffness. We have derived an impact-constrained module of elasticity, which represents the dynamic resistance in the granulated bone mass to impaction. Drop level of the impaction slap hammer increases constrained bone stiffness during impaction and load. However, increasing the number of impaction strokes at the highest drop level does not improve stiffness properties; no significant increase in stiffness was achieved after five strokes on each layer of morsellised bone.     

Evaluating a suitable level of model complexity for finite element analysis of the intact acetabulum

To enable large-scale multi-factorial finite element (FE) studies, the FE models used must be as computationally efficient as is feasible, while maintaining a suitable level of definition. The present study seeks to find an optimum level of model complexity for use in such large-scale studies by investigating which model attributes are most influential over the chosen model outputs of principal stress and strain in the intact acetabulum. A multi-factorial sensitivity study was carried out using 128 FE models, representing combinations of the following variables: bone stiffness distribution, imposed muscle loading, boundary condition location, hip joint contact conditions and patient's bone anatomy. The relative sensitivity of each input factor was analysed, and it was concluded that the optimum level of model definition must include CT-dependent trabecular bone properties and a sliding interface at the hip joint. It was found that it was not essential to describe the ligamentous sacroiliac and pubic symphysis joints; these could be rigidly fixed in space; and for the normal walking load case, muscle forces may be neglected. It was also concluded that a variety of bone anatomies should be included in a multi-factorial analysis if results are to be inferred for a wider population.