ARTICLE IN PRESS Journal of Biomechanics 42 (2009) 2171–2176
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Use of a statistical model of the whole femur in a large scale, multi-model study of femoral neck fracture risk Rebecca Bryan a, Prasanth B. Nair b,a, Mark Taylor a, a b
Bioengineering Sciences Research Group, University of Southampton, Highfield, SO17 1BJ Southampton, UK Computational Engineering and Design Group, University of Southampton, Southampton, UK
a r t i c l e in fo
abstract
Article history: Accepted 17 May 2009
Interpatient variability is often overlooked in orthopaedic computational studies due to the substantial challenges involved in sourcing and generating large numbers of bone models. A statistical model of the whole femur incorporating both geometric and material property variation was developed as a potential solution to this problem. The statistical model was constructed using principal component analysis, applied to 21 individual computer tomography scans. To test the ability of the statistical model to generate realistic, unique, finite element (FE) femur models it was used as a source of 1000 femurs to drive a study on femoral neck fracture risk. The study simulated the impact of an oblique fall to the side, a scenario known to account for a large proportion of hip fractures in the elderly and have a lower fracture load than alternative loading approaches. FE model generation, application of subject specific loading and boundary conditions, FE processing and post processing of the solutions were completed automatically. The generated models were within the bounds of the training data used to create the statistical model with a high mesh quality, able to be used directly by the FE solver without remeshing. The results indicated that 28 of the 1000 femurs were at highest risk of fracture. Closer analysis revealed the percentage of cortical bone in the proximal femur to be a crucial differentiator between the failed and non-failed groups. The likely fracture location was indicated to be intertrochantic. Comparison to previous computational, clinical and experimental work revealed support for these findings. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Femur Femoral neck fracture risk Statistical model Material property Principal component analysis
1. Introduction The vast majority of orthopaedic computational studies are performed using a single bone model. The derived results are then extrapolated to try to draw conclusions for the population as a whole, overlooking the inherent and significant interpatient variability found in both bone geometry and bone quality (Prendergast, 1997; Viceconti et al., 1998; Keyak et al., 1990). With reference to the performance of orthopaedic implants, such intersubject variations have been shown to make a dramatic difference to the success of otherwise comparable joint replacement procedures (Kobayashi et al., 2000; Wong et al., 2005). In daily activity, intersubject variability has been seen to dominate intertask variability in a computational study of bone-implant micromotion driven by in vivo data from an instrumented femoral prosthesis (Pancanti et al., 2003). In reaction to this shortcoming, patient specific modelling techniques have begun to be developed. These use high level imaging modalities such as computer tomography (CT) to build computational models of the set of
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[email protected] (M. Taylor). 0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.05.038
patient or cadaveric anatomies being assessed, often then validating finite element analyses of these with experimental tests (Testi et al., 1999; Cody et al., 1999; Keyak et al., 1990; Viceconti et al., 2004; Radcliffe and Taylor, 2007). In this way it is possible to gain an understanding of whether the results seen are down to the tests being performed or the anatomy of the subject. However, a major barrier preventing multi-subject finite element studies from becoming commonplace is the task of creating multiple models from sources such as CT scans. Without robust and reliable automated model generation techniques this is a time consuming, laborious task and relies on access to high quality image data, which is often scarce (Viceconti et al., 1998; Radcliffe and Taylor, 2007). This work proposes the use of statistical modelling as a source of FE bone models to provide a potential solution to this problem. Statistical models aim to capture the variation possible within a class of shapes by analysing a set of training data. The principles of shape modelling using principal component analysis (PCA) were illustrated by Cootes and Taylor (Cootes et al., 1995). It was shown how a model could be trained on a set of possible shapes, analysed using PCA and its outputs used in two ways; firstly to investigate the main modes of variation in the training data and secondly to generate new, realistic instances of that shape. Further
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work incorporated texture, described by greylevel, into the model (Cootes and Taylor, 2001). Originally these techniques were developed within computer vision and therefore used with twodimensional images, applying them to three-dimensional shapes vastly increases the computational complexity. Any methods relying on construction through manual landmarking become highly inefficient and impractical to apply. Rueckert et al. (1999, 2003) solved the problem of matching three-dimensional shapes using free form deformation of B-splines. This technique has been applied to a variety of biomedical problems from modelling bones such as the proximal femur and humorous (Querol et al., 2006; Couteau et al., 2000; Yang et al., 2004) to tracking soft tissue changes in breast and brain MRIs (Rueckert et al., 1999, 2003). The aim of this study was to apply the statistical femur model to the problem of proximal femoral fracture, and asses its ability to produce meaningful results. Meaningful, being that the results show comparable trends to existing published investigations. A femoral neck fracture risk (FNFR) investigation was chosen for the present study as a well investigated problem from computational, experimental and clinical perspectives. The majority of FNF occur in elderly women and are the result of a fall (Lotz et al., 1991; Koval and Zuckerman, 1994), with around 250–300,000 cases reported in the US each year (Cummings and Nevitt, 1989; Cooper et al., 1992). The injury is potentially devastating for this age group, in many cases leading to reduced mobility, long term disability and reduced capacity for independent living (Marks et al., 2003). Mortality rates are significant at 15–25% within 6 months of injury, rising to 30–40% at 1 year (Cummings et al., 1985; Keene et al., 1993). Many studies, mainly based on clinical data, have investigated fracture risk in relation to femur geometry and bone quality (Theobald et al., 1998; Peacock et al., 1998; Bergot et al., 2002; Michelotti and Clark, 1999; Gnudi et al., 1999). Several computational studies, often in conjunction with experimental work, have also tried to predict fracture loads and location (Lotz et al., 1991; Keyak et al., 1997, 2001a; Cody et al., 1999; Cheng et al., 1997a; Majumder et al., 2007; Bessho et al., 2007). However, these have often been limited to investigating a single bone or at best a small set of between 15 and 20 examples. This study conducted a FNFR study using 1000 generated femurs created from a statistical model, then compared the results to
femur and fracture characteristics found by previous fracture risk studies. 2. Methods The first stage of the study was the creation and sampling of a statistical model of the whole human femur using PCA, a detailed explanation of which is available in Appendix I. The model was trained on femurs generated from CT scans of 8 female and 13 male subjects with a mean age of 68, ranging from 43 to 84 years. Each femur was extracted by semi-automated segmentation of bone with grey s level thresholding tools and manual slice-by-slice corrections using Avizo (Mercury Computer Systems, Berlin). To build the PCA model, accurate correspondence was established between each training member by morphing a high quality baseline tetrahedral mesh onto each example. The baseline femur was the median length training example, meshed to a high quality within ANSYS& ICEM CFDTM (ANSYS. Inc., Canonsburg, PA) such that a global tetrahedral element size of 3 mm was refined to 1–1.5 mm in the proximal and distal thirds of the bone. This resulted in a 615,225 element mesh, controlling computational cost while ensuring high mesh density in the regions with most clinical interest as well as geometric and material property variability. Correspondence was achieved through the development of an elastic surface matching registration scheme based on the three-dimensional generalisation of Burr’s registration algorithm proposed by Moshfeghi et al. (1994) and a mesh morphing scheme based around solving a decoupled three-dimensional Laplace equation (Robertson and Sherwin, 1999). Following registration all training examples, and subsequent generated models, were defined by the same fine tetrahedral mesh with individualised material properties and element to element correspondence. The high quality of the generated meshes allowed their direct use in FE analysis. Subject specific material properties were extracted from the original CT data using BioMesh (Andrew Hopkins, Imperial College, London), which assigned each node in the mesh a grey level value. By exploiting the proportional relationship between grey level and apparent density it was possible to use the equation defined for density–elasticity relation in the femoral neck by Morgan et al. (2003) to give each node, and hence element by averaging the values at its constituent nodes, a Young’s modulus. Each training example, described by their nodal coordinate positions and modulus value at each node, was then analysed by PCA using a correlation based approach (Jolliffe, 1986). The statistical model was then used to generate 1000 femur models, each of which was realistic and a unique combination of the interpatient variability captured from the training data. The process incorporated automated element distortion checks to guard against errors due to poor mesh quality during later FEA. As a Monte Carlo approach was adopted for this simulation it was important to ensure the model was sampled evenly. To achieve this a Sobol (1994) sequence was used which provided a quasi-random set of well dispersed sampling points over the entire multi-dimensional parameter space defined by prescribed limits. The boundaries of this space for the statistical model were established from sensitivity tests, aiming to optimise mesh quality while producing instances which showed the
LOAD
LOAD
20°
30°
Fig. 1. Illustration of loading conditions applied to each femur to simulate a fall.
ARTICLE IN PRESS R. Bryan et al. / Journal of Biomechanics 42 (2009) 2171–2176 full range of variation present in the training data. Reconstruction tests and analysis of meaningful measurements such as femur length, neck-shaft angle, anteversion and regional material modulus were used to investigate this. Inclusion of additional modes or expanding the sampling range too far led to mesh degradation and the production of femurs which exceeded the parameters of those seen in the original data. The optimum values were found to be 8 PCA eigenmodes ranging between 71:5 standard deviations of their mean influence in the training set. A loading condition was specified on the baseline femur to simulate an oblique fall backwards and to the side. This fall configuration has repeatedly been shown to be the most severe scenario, with the lowest fracture load (Lotz et al., 1991; Keyak et al., 2001b; Bessho et al., 2004). It was possible to transfer these conditions directly between each generated mesh as they consisted of an equal number of nodes, with correspondence between their relative positions. The simulation aimed to replicate the mechanical testing of Keyak et al. (1997), hence the femur was rotated so the shaft axis lay at a 303 and the neck axis in transverse plane at 203 to the horizontal (Fig. 1). The femur was fully restrained in two places; a short depth of the lowest part of the greater trochanter, replicating the PMMA cup holding the femur in the experimental test, and from the mid-shaft of the femur down. A force was equally distributed over a 3 cm diameter area of the proximal, anterior femoral head. The applied force was set at one times body weight, due to the linearity of the model any strain results produced could be scaled so the choice of load magnitude was arbitrary. As all 1000 femurs were created statistically, no subject weight was known so this information was generated as follows. Femur length, taken as the distance from the most distal point of the lateral condyle to the most proximal point of the greater trochanter, was assumed to be 26.75% of subject height (Feldesman and Fountain, 1996). This was a generic relationship, ignoring gender and race with a subsequent possible error in predicted height reported at o0:6 cm. A body mass index (BMI) distribution curve was generated from data available from the National Health and Nutritional Examination Survey 1999–2002, conducted on all age groups within the US population (McDowell, 2005). By randomly sampling a BMI value from the distribution, it was possible to calculate a subject weight in kilograms as BMI multiplied by the square of the predicted height in metres. Various metrics were devised to aid interrogation of the FE results (Fig. 2). A range of geometric parameters were automatically taken from each generated femur, based on parameters which have previously been used to analyse femoral
FHD
FND
NAL
A
ITW NSA B
C
2173
shape (Theobald et al., 1998; Michelotti and Clark, 1999). These were: neck axis length (NAL), neck-shaft angle (NSA), femoral head and neck diameters (FHD and FND), intertrochantic width (ITW), femoral shaft width (FSW, measured 3 cm below the lesser trochanter) and anteversion angle (AA). In addition, three key volumes were identified within the proximal femur to gauge bone quality and judge failure risk, these were: lower femoral head (A), femoral neck (B) and the intertrochantic region (C). To highlight those femurs which were at highest risk of failure a conservative criterion was created identifying models where any of the three proximal sections experienced 410% volume exceeding yield strain, 0.7% (Morgan and Keaveny, 2001).
3. Results By the conservative failure criteria defined in this study 28 of the 1000 femurs tested were identified as being at risk of failure. These 28 models were grouped together and their geometric and material property characteristics compared against the 972 femurs which survived the simulation. The strain distributions are clearly different, with the low risk group on average showing almost no bone exceeding 0.4% strain, where the at risk group show notable percentages above this level (Fig. 3). The strain distributions in the other regions showed a similar trend. In all, 11 geometric parameters were considered along with six bone property metrics for each of the three proximal sections. Seven metrics were indicated as significant between the two groups by an F-test analysis (Table 1). The most important of which was the percentage of cortical bone ð43000 MPaÞ in each section, especially significant in the lower femoral head where the mean cortical modulus was also highlighted. Three geometric parameters appeared to be important, neck shaft angle and to a lesser extent anteversion angle and femoral neck diameter ratio. The neck diameter ratio indicated the ovality of the neck, calculated as a ratio between neck diameters measured in the superior–inferior and anterior–posterior directions. All other metrics proved to have low significance. These included the further geometric measures detailed previously, patient parameters such as height, BMI and applied load, and interrogations of bone modulus comprising mean cortical and cancellous bone modulus. The likely origin of any fracture was identified by viewing the areas of highest strain in the 28 femurs which failed the fall simulation. The majority, 15 of 28, indicated failure in the trochanteric region with eight of these showing highest strain along the intertrochantic ridge (Fig. 4a). Four femurs highlighted the anterior subcapital region and the remaining nine had multiple regions of high strain making a specific location hard to identify (Figs. 4b, c). Most femurs showed some localised high strain around the greater trochanter restraint, but no model showed this to be the only high strain location or potential fracture lines stemming from this area.
4. Discussions
FSW
Fig. 2. Illustration of metrics taken from femur models. Main areas of interest: A—lower femoral head, B—femoral neck, C—intertrochanteric. Measures include: femoral head and neck diameters (FHD, FND), neck axis length (NAL), neck shaft angle (NSA), intertrochantic width (ITW), shaft width (FSW) and anteversion angle.
The current study was able to elegantly run a large scale, multi-bone model, finite element analysis for the first time without significant manual intervention. High mesh quality was ensured by incorporating element distortion checks, allowing direct use of the models in an FE solver without risk of failure or poor results. This allowed the whole analysis to be completely automated, requiring no manual intervention to generate 1000 FE femurs models with individual material properties, apply subject specific loads and boundary conditions, simulate a fall and post process the elemental strains produced. The entire process took approximately 12 min per femur. The FEA results were investigated to see if any geometric or material property metrics could be found to be significantly
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Fig. 3. Box plots illustrating the strain in trochanteric region by percentage volume up to 1% strain. Volumes exceeding 1% strain are summed and shown as þ1:0% strain: (a) 28 fracture risk group and (b) 972 not at risk group. The box shows the median, upper and lower quartiles and the whiskers extend to 1:5 the interquartile range, with values beyond this shown by crosses.
Table 1 Results of the most significant modulus and geometric metrics found when comparing the at risk and low risk groups. F-test
(A) Cortical vol. (%) (B) Cortical vol. (%) (C) Cortical vol. (%) Neck-shaft angle (deg) (A) Mean cort. modulus (MPa) Anteversion (deg) Femoral neck dia. ratio
o0:01 o0:01 o0:01 o0:025 o0:025 o0:1 o0:1
Not at risk
At risk
Min
Mean
Max
Min
Mean
Max
0.00 6.61 9.38 120.8 3002.25 15.05 0.86
2.48 22.86 25.34 128.7 3274.23 22.06 1.02
21.97 50.36 46.01 123.6 3864.67 28.75 1.26
0.00 6.17 8.49 121.3 3016.14 16.91 0.94
0.05 9.79 11.10 124.4 3299.91 20.45 1.02
0.51 15.79 23.98 127.8 3675.44 23.98 1.13
The minimum, maximum and mean of each group are shown. A, B and C indicate the section of the femur.
Fig. 4. Illustration of the areas suffering highest strain following fall loading: (a) intertrochantic, (b) anterior subcapital and (c) multiple regions. Areas highlighted exceed 1.5% strain.
different between the group of femurs which were classed as at risk under a fall load and those which were not. The model identified the overall percentage volume of cortical bone through the proximal femur, and the mean modulus of cortical bone in the lower femoral head as significant bone quality metrics. In terms of geometry, neck shaft angle, anteversion and the ovality of the femoral neck were seen to be important.
Previous studies have suggested femoral geometric and material features which may result in a predisposition towards femoral fracture with the exact features frequently contradicted between studies. The main feature which is agreed on is that a low bone mineral density (BMD) is a high indicating factor of risk (Cheng et al., 1997a; Gnudi et al., 1999; Bergot et al., 2002; Alonso et al., 2000; Lotz et al., 1991), and also low cortical thickness
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(although usually defined in the proximal femoral shaft) (Cheng et al., 1997a; Theobald et al., 1998; Michelotti and Clark, 1999). This was very clearly supported by the results of the model, with cortical bone percentage by far the most significant difference between the at risk and low risk groups. There was no evidence that neck axis length was an indicator of risk, agreeing with some work (Michelotti and Clark, 1999; Alonso et al., 2000) but contradicting others (Bergot et al., 2002; Theobald et al., 1998; Gnudi et al., 1999; Faulkner et al., 1993). An interesting geometric parameter which was shown as significant was neck-shaft angle. Again this parameter had been shown to have little or no influence on fracture risk by some (Bergot et al., 2002; Faulkner et al., 1993) and yet important by others (Gnudi et al., 1999; Michelotti and Clark, 1999; Alonso et al., 2000). The studies which did indicate this measurement suggest that a larger angle increases the risk, however the current study’s results show a smaller angle in the failed group. Michelotti and Clark (1999) observed that the trend of a smaller angle increasing risk was seen in studies which took measurements from three-dimensional images as opposed to two-dimensional X-ray. Suggesting that subject positioning during imaging, particularly external femoral rotation, can result in apparent changes to neck axis length and neck shaft angle, a finding supported by work on the affect of anteversion (Cheng et al., 1997b). This parameter may well be affected by the limited training set as it is known to be generally larger in women than men (Alonso et al., 2000), however, with only 21 femurs available it was not feasible to separate male and female subjects to generate gender specific models. The present study corroborates previous findings that the majority of failures under fall loading occur in the intertrochantic region (Cheng et al., 1997a; Cody et al., 1999; Keyak et al., 1997, 2001a, 2001b; Bessho et al., 2004). Keyak et al. (2001a) published some details of likely fracture locations under a fall load which were tested experimentally as well as modelled computationally. The experimental conditions applied in Keyak’s work were replicated in the current study. The fracture site was identifiable for 15 tested femurs. Although the descriptions of fracture initiation sites are a little vague, it can be seen that a similar distribution of results has been found in both Keyak’s work and this study (Table 2). There are limitations to this work. The model may suffer from the relatively small size of the training data set, 21 subjects. The data set is taken from quite a general population group and so does not incorporate factors such as osteoporosis, tumours or other pathologies which would weaken bone. Ideally separate models would be generated for different genders, ages, ethnicities and pathologies, as these are known to affect femoral geometry and bone density (Theobald et al., 1998; Peacock et al., 1998). Therefore biases in the training set could, in theory, influence the
Table 2 Table showing the percentage of femurs identified with various fracture location origins. Keyak—finite element results (%) Trochantic 60 Intertrochantic Cervical 13 Multiple – Subtrochantic 0
Keyak—experimental results (%)
Statistical model results (%)
47
29 25 14 32 0
40 – 13
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statistical result of some geometric parameters. Investigations were performed on femurs generated by the statistical model to ensure that both the geometry and material properties being produced were valid and feasible. To do this the metrics devised to analyse femoral characteristics were used to compare the variations present in the generated femurs to the training data set. This showed that realistic models were produced which were a fair representation of the training set. The finite element analysis performed on the data was relatively simple to minimise computational cost. A static load was used to simulate a fall and bone was modelled as an isotropic linear material, when in reality it has anisotropic non-linear properties. This simplification follows that of the study being replicated and was justified in a later study by Keyak (2001) where the gains in predicted and actual fracture load correlation were small in comparison to the added complexity. In addition, the linear method and the impact rather than progressive loading meant that the precise value of load applied was not crucial to the result. The load chosen, 1 bodyweight, was a realistic value for a fall and proved sufficient to highlight an ‘at risk’ group from the data set. A further simplification to this FE analysis was the lack of inclusion of muscle forces, surrounding tissues and impact surface. Again this was justified by the current work’s aim of replicating Keyak’s study, showing that the model would replicate the trends reported from this earlier work. The case study has shown the potential of this methodology to generate large numbers of models which describe the variations present in the data used to create it. The ability to characterise population wide variability potentially has useful applications in both computational-experimental analysis and clinical settings. Keyak et al. (2001a) is a good example of the type of experimental-computational work which could be enhanced by incorporating this statistical modelling technique, where relatively small number of cadaveric femurs were tested, 18, and compared to computational models. If the statistical model was used to replicate the experimental test results accurately, the model could then be extended to a wider population of femur models with some confidence. Another possible use of being able to run such large scale simulations is the ability to gain an understanding of how factors affect a population, such that parameters taken from any patient can be compared to these to see how they fit. This could give a more sophisticated indicator of risk factors than current methods such as the World Health Organisation’s arbitrary cut off, set at 2.5 standard deviation from the mean (World Health Organistation, 1994), to quantify predictions for osteoporotic hip fracture. Conflict of interest statement Rebecca Bryan and Prasanth Nair have no conflicts. Mark Taylor is a retained consultant to Finsbury Orthopaedics and DePuy International. Acknowledgements This research has been possible thanks to CT data kindly provided by DePuy International and East Sussex Hospital Trust, and funding received from Technology Strategy Board (UK). Thanks also to Andrew Hopkins for the use of material property extraction software. Appendix A. Supplementary data
Comparing the results seen by Keyak et al. (2001a) for the 15 femurs where experimentally identifiable failure locations were compared to FE predictions, with the failure locations predicted by this study using femur models generated from a statistical model.
Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jbiomech.2009.05.038.
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References Alonso, C., Curiel, M., Carranza, F., Cano, R., Perez, A., 2000. Femoral bone mineral density, neck-shaft angle and mean femoral neck width as predictors of hip fracture in men and women. Multicenter Project for Research in Osteoporosis. Osteoporos International 11 (8), 714–720. Bergot, C., Bousson, V., Meunier, A., Laval-Jeantet, M., Laredo, J., 2002. Hip fracture risk and proximal femur geometry from DXA scans. Osteoporosis International 13 (7), 542–550. Bessho, M., Ohnishi, I., Matsuyama, J., Matsumoto, T., Imai, K., Nakamura, K., 2007. Prediction of strength and strain of the proximal femur by a ct-based finite element method. Journal of Biomechanics 40 (8), 1745–1753. Bessho, M., Ohnishi, I., Okazaki, H., Sato, W., Kominami, H., Matsunaga, S., Nakamura, K., 2004. Prediction of the strength and fracture location of the femoral neck by CT-based finite-element method: a preliminary study on patients with hip fracture. Journal of Orthopaedic Science 9 (6), 545–550. Cheng, X., Lowet, G., Boonen, S., Nicholson, P., Brys, P., Nijs, J., Dequeker, J., 1997a. Assessment of the strength of proximal femur in vitro: relationship to femoral bone mineral density and femoral geometry. Bone 20 (3), 213–218. Cheng, X., Nicholson, P., Boonen, S., Brys, P., Lowet, G., Nijs, J., Dequeker, J., 1997b. Effects of anteversion on femoral bone mineral density and geometry measured by dual energy X-ray absorptiometry: a cadaver study. Bone 21 (1), 113–117. Cody, D., Gross, G.J., Hou, F., Spencer, H., Goldstein, S.P., Fyhrie, D., 1999. Femoral strength is better predicted by finite element models than QCT and DXA. Journal of Biomechanics 32 (10), 1013–1020. Cooper, C., Campion, G., Melton, L., 1992. Hip fractures in the elderly: a world-wide projection. Osteoporosis International 2 (6), 285–289. Cootes, T., Taylor, C., 2001. Statistical models of appearance for medical image analysis and computer vision. Proceedings SPIE Medical Imaging 42. Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J., 1995. Active shape models—their training and application. Computer Vision and Image Understanding 61 (1), 38–59. Couteau, B., Payan, Y., Lavalle e, S., 2000. The mesh-matching algorithm: an automatic 3D mesh generator for finite element structures. Journal of Biomechanics 33 (8), 1005–1009. Cummings, S., Kelsey, J., Nevitt, M., O’Dowd, K., 1985. Epidemiology of osteoporosis and osteoporotic fractures. Epidemiologic Reviews 7 (1), 178–208. Cummings, S., Nevitt, M., 1989. A hypothesis: the causes of hip fractures. Journal of Gerontolology 44 (4), 107–111. Faulkner, K., Cummings, S., Black, D., Palermo, L., Gluer, C., Genant, H., 1993. Simple measurement of femoral geometry predicts hip fracture: the study of osteoporotic fractures. Journal of Bone and Mineral Research 8 (10), 1211–1217. Feldesman, M., Fountain, R., 1996. Race specificity and the femur/stature ratio. American Journal of Physical Anthropology 100 (2), 207–224. Gnudi, S., Ripamonti, C., Gualtieri, G., Malavolta, N., 1999. Geometry of proximal femur in the prediction of hip fracture in osteoporotic women. British Journal of Radiology 72 (860), 729. Jolliffe, I., 1986. Principal Component Analysis. Springer, New York. Keene, G., Parker, M., Pryor, G., 1993. Mortality and morbidity after hip fractures. British Medical Journal 307 (6914), 1248. Keyak, J., 2001. Improved prediction of proximal femoral fracture load using nonlinear finite element models. Medical Engineering and Physics 23 (3), 165–173. Keyak, J., Meagher, J., Skinner, H., Mote, C., 1990. Automated 3-dimensional finite element modeling of bone—a new method. Journal of Biomedical Engineering 12 (5), 389–397. Keyak, J., Rossi, S., Jones, K., Les, C., Skinner, H., 2001a. Prediction of fracture location in the proximal femur using finite element models. Medical Engineering and Physics 23 (9), 657–664. Keyak, J., Rossi, S., Jones, K., Skinner, H., 1997. Prediction of femoral fracture load using automated finite element modeling. Journal of Biomechanics 31 (2), 125–133. Keyak, J., Skinner, H., Fleming, J., 2001b. Effect of force direction on femoral fracture load for two types of loading conditions. Journal of Orthopaedic Research 19, 539–544. Kobayashi, S., Saito, N., Horiuchi, H., Iorio, R., Takaoka, K., 2000. Poor bone quality or hip structure as risk factors affecting survival of total-hip arthroplasty. The Lancet 355 (9214), 1499–1504.
Koval, K., Zuckerman, J., 1994. Hip fractures: I. overview and evaluation and treatment of femoral-neck fractures. Journal of American Academy of Orthopaedic Surgery 2 (3), 141–149. Lotz, J., Cheal, E., Hayes, W., 1991. Fracture prediction for the proximal femur using finite element models: part i—linear analysis. Journal of Biomechanical Engineering 113, 353–360. Majumder, S., Roychowdhury, A., Pal, S., 2007. Simulation of hip fracture in sideways fall using a 3D finite element model of pelvis–femur–soft tissue complex with simplified representation of whole body. Medical Engineering and Physics 29 (10), 1167–1178. Marks, R., Allegrante, J., Ronald MacKenzie, C., Lane, J., 2003. Hip fractures among the elderly: causes consequences and control. Ageing Research Reviews 2 (1), 57–93. McDowell, M.A., Frayer, C.H.R.O.C., 2005. Anthropometric reference data for children and adults: U.S. population, 1999–2002. US Department of Health and Human Services 361. Michelotti, J., Clark, J., 1999. Femoral neck length and hip fracture risk. Journal of Bone and Mineral Research 14 (10), 1714–1720. Morgan, E., Bayraktar, H., Keaveny, T., 2003. Trabecular bone modulus–density relationships depend on anatomic site. Journal of Biomechanics 36 (7), 897–904. Morgan, E., Keaveny, T., 2001. Dependence of yield strain of human trabecular bone on anatomic site. Journal of Biomechanics 34 (5), 569–577. Moshfeghi, M., Ranganath, S., Nawyn, K., 1994. Three-dimensional elastic matching of volumes. IEEE Transactions on Image Processing 3 (2), 128–138. Pancanti, A., Bernakiewicz, M., Viceconti, M., 2003. The primary stability of a cementless stem varies between subjects as much as between activities. Journal of Biomechanics 36 (6), 777–785. Peacock, M., Liu, G., Carey, M., Ambrosius, W., Turner, C.H., Hui, S.C.C., Johnston, J., 1998. Bone mass and structure at the hip in men and women over the age of 60 years. Osteoporosis International 8 (3), 231–239. Prendergast, P.J., 1997. Finite element models in tissue mechanics and orthopaedic implant design. Clinical Biomechanics 12 (6), 343–366. ¨ P., Rueckert, D., Nolte, L., Ballester, M., 2006. Statistical finite Querol, L., Buchler, element model for bone shape and biomechanical properties. MICCAI, 405–411. Radcliffe, I., Taylor, M., 2007. Investigation into the affect of cementing techniques on load transfer in the resurfaced femoral head: a multi-femur finite element analysis. Clinical Biomechanics 22 (4), 422–430. Robertson, I., Sherwin, S., 1999. Free-surface flow simulation using hp spectral elements. Journal of Computational Physics 155 (1), 26–53. Rueckert, D., Frangi, A., Schnabel, J., 2003. Automatic construction of 3-d statistical deformation models of the brain using nonrigid registration. IEEE Transactions on Medical Imaging 22 (8), 1014–1025. Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., Hawkes, D.J., 1999. Nonrigid registration using free-form deformations: application to breast mr images. IEEE Transactions on Medical Imaging 18 (8), 712–721. Sobol, I., 1994. A Primer for the Monte Carlo Method. CRC Press, Boca Raton, FL. Testi, D., Viceconti, M., Baruffaldi, F., Cappello, A., 1999. Risk of fracture in elderly patients: a new predictive index based on bone mineral density and finite element analysis. Computer Methods and Programs in Biomedicine 60 (1), 23–33. Theobald, T.M., Cauley, J.A., Gluer, C.C., Bunker, C.H., Ukoli, F.A.M., Genant, H.K., 1998. Black-white differences in hip geometry. Osteoporosis International 8 (1), 61–67. Viceconti, M., Bellingeri, L., Cristofolini, L., Toni, A., 1998. A comparative study on different methods of automatic mesh generation of human femurs. Medical Engineering and Physics 20 (1), 1–10. Viceconti, M., Davinelli, M., Taddei, F., Cappello, A., 2004. Automatic generation of accurate subject-specific bone finite element models to be used in clinical studies. Journal of Biomechanics 37 (10), 1597–1605. Wong, A.S, New, A.M.R, Isaacs, G., Taylor, M., 2005. Effect of bone material properties on the initial stability of a cementless hip stem: a finite element study. Proceedings of the Institution of Mechanical Engineers Part H—Journal of Engineering in Medicine 219 (H4), 265–275. World Health Organisation, 1994. Assessment of fracture risk and its application to screening for postmenopausal osteoporosis: Report of who study group. World Health Organisation, Geneva, Switzerland, 843. Yang, J., Zhang, D., Frangi, A.F., Yang, J., 2004. Two-dimensional pca: a new approach to appearance-based face representation and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 26 (1), 131–137.
