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Journal of Biomechanics 42 (2009) 2171–2176

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Journal of Biomechanics

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Use of a statistical model of the whole femur in a large scale, multi-modelstudy of femoral neck fracture risk

Rebecca Bryan a, Prasanth B. Nair b,a, Mark Taylor a,�

a Bioengineering Sciences Research Group, University of Southampton, Highfield, SO17 1BJ Southampton, UKb Computational Engineering and Design Group, University of Southampton, Southampton, UK

a r t i c l e i n f o

Article history:

Accepted 17 May 2009Interpatient 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

Keywords:

Femur

Femoral neck fracture risk

Statistical model

Material property

Principal component analysis

90/$ - see front matter & 2009 Elsevier Ltd. A

016/j.jbiomech.2009.05.038

esponding author. Tel.: +44 2380 597660; fax

ail address: M.Taylor@soton.ac.uk (M. Taylor)

a b s t r a c t

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.

1. Introduction

The vast majority of orthopaedic computational studies areperformed using a single bone model. The derived results are thenextrapolated to try to draw conclusions for the population as awhole, overlooking the inherent and significant interpatientvariability 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, suchintersubject variations have been shown to make a dramaticdifference to the success of otherwise comparable joint replace-ment procedures (Kobayashi et al., 2000; Wong et al., 2005). Indaily activity, intersubject variability has been seen to dominateintertask variability in a computational study of bone-implantmicromotion driven by in vivo data from an instrumented femoralprosthesis (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 computertomography (CT) to build computational models of the set of

ll rights reserved.

: +44 2380 593016.

.

patient or cadaveric anatomies being assessed, often thenvalidating finite element analyses of these with experimentaltests (Testi et al., 1999; Cody et al., 1999; Keyak et al., 1990;Viceconti et al., 2004; Radcliffe and Taylor, 2007). In this way it ispossible to gain an understanding of whether the results seen aredown to the tests being performed or the anatomy of the subject.However, a major barrier preventing multi-subject finite elementstudies from becoming commonplace is the task of creatingmultiple models from sources such as CT scans. Without robustand reliable automated model generation techniques this is a timeconsuming, laborious task and relies on access to high qualityimage data, which is often scarce (Viceconti et al., 1998; Radcliffeand Taylor, 2007). This work proposes the use of statisticalmodelling as a source of FE bone models to provide a potentialsolution to this problem.

Statistical models aim to capture the variation possible withina class of shapes by analysing a set of training data. The principlesof shape modelling using principal component analysis (PCA)were illustrated by Cootes and Taylor (Cootes et al., 1995). It wasshown how a model could be trained on a set of possible shapes,analysed using PCA and its outputs used in two ways; firstly toinvestigate the main modes of variation in the training data andsecondly to generate new, realistic instances of that shape. Further

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R. Bryan et al. / Journal of Biomechanics 42 (2009) 2171–21762172

work incorporated texture, described by greylevel, into the model(Cootes and Taylor, 2001). Originally these techniques weredeveloped within computer vision and therefore used with two-dimensional images, applying them to three-dimensional shapesvastly increases the computational complexity. Any methodsrelying on construction through manual landmarking becomehighly inefficient and impractical to apply. Rueckert et al. (1999,2003) solved the problem of matching three-dimensional shapesusing free form deformation of B-splines. This technique has beenapplied to a variety of biomedical problems from modelling bonessuch as the proximal femur and humorous (Querol et al., 2006;Couteau et al., 2000; Yang et al., 2004) to tracking soft tissuechanges in breast and brain MRIs (Rueckert et al., 1999, 2003).

The aim of this study was to apply the statistical femur modelto the problem of proximal femoral fracture, and asses its abilityto produce meaningful results. Meaningful, being that the resultsshow comparable trends to existing published investigations. Afemoral neck fracture risk (FNFR) investigation was chosen for thepresent study as a well investigated problem from computational,experimental and clinical perspectives. The majority of FNF occurin elderly women and are the result of a fall (Lotz et al., 1991;Koval and Zuckerman, 1994), with around 250–300,000 casesreported in the US each year (Cummings and Nevitt, 1989; Cooperet al., 1992). The injury is potentially devastating for this agegroup, in many cases leading to reduced mobility, long termdisability and reduced capacity for independent living (Marks etal., 2003). Mortality rates are significant at 15–25% within 6months of injury, rising to 30–40% at 1 year (Cummings et al.,1985; Keene et al., 1993). Many studies, mainly based on clinicaldata, have investigated fracture risk in relation to femur geometryand 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 experi-mental 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 singlebone or at best a small set of between 15 and 20 examples. Thisstudy conducted a FNFR study using 1000 generated femurscreated from a statistical model, then compared the results to

LOAD

20°

LOAD

Fig. 1. Illustration of loading conditions ap

femur and fracture characteristics found by previous fracture riskstudies.

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

level thresholding tools and manual slice-by-slice corrections using Avizos

(Mercury Computer Systems, Berlin). To build the PCA model, accurate correspon-

dence 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

30°

plied to each femur to simulate a fall.

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R. Bryan et al. / Journal of Biomechanics 42 (2009) 2171–2176 2173

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

NSA

NAL

FHD

FND

ITW

FSW

A

B

C

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.

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 ofthe 1000 femurs tested were identified as being at risk of failure.These 28 models were grouped together and their geometric andmaterial property characteristics compared against the 972femurs which survived the simulation. The strain distributionsare clearly different, with the low risk group on average showingalmost no bone exceeding 0.4% strain, where the at risk groupshow notable percentages above this level (Fig. 3). The straindistributions in the other regions showed a similar trend.

In all, 11 geometric parameters were considered along with sixbone property metrics for each of the three proximal sections.Seven metrics were indicated as significant between the twogroups by an F-test analysis (Table 1). The most important ofwhich was the percentage of cortical bone ð43000 MPaÞ in eachsection, especially significant in the lower femoral head where themean cortical modulus was also highlighted. Three geometricparameters appeared to be important, neck shaft angle and to alesser 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 thesuperior–inferior and anterior–posterior directions. All othermetrics proved to have low significance. These included thefurther geometric measures detailed previously, patientparameters such as height, BMI and applied load, andinterrogations of bone modulus comprising mean cortical andcancellous bone modulus.

The likely origin of any fracture was identified by viewing theareas of highest strain in the 28 femurs which failed the fallsimulation. The majority, 15 of 28, indicated failure in thetrochanteric region with eight of these showing highest strainalong the intertrochantic ridge (Fig. 4a). Four femurs highlightedthe anterior subcapital region and the remaining nine hadmultiple regions of high strain making a specific location hardto identify (Figs. 4b, c). Most femurs showed some localised highstrain around the greater trochanter restraint, but no modelshowed this to be the only high strain location or potentialfracture lines stemming from this area.

4. Discussions

The current study was able to elegantly run a large scale,multi-bone model, finite element analysis for the first timewithout significant manual intervention. High mesh quality wasensured by incorporating element distortion checks, allowingdirect use of the models in an FE solver without risk of failure orpoor results. This allowed the whole analysis to be completelyautomated, requiring no manual intervention to generate 1000 FEfemurs models with individual material properties, apply subjectspecific loads and boundary conditions, simulate a fall and postprocess the elemental strains produced. The entire process tookapproximately 12 min per femur.

The FEA results were investigated to see if any geometric ormaterial 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 1Results of the most significant modulus and geometric metrics found when comparing the at risk and low risk groups.

F-test Not at risk At risk

Min Mean Max Min Mean Max

(A) Cortical vol. (%) o0:01 0.00 2.48 21.97 0.00 0.05 0.51

(B) Cortical vol. (%) o0:01 6.61 22.86 50.36 6.17 9.79 15.79

(C) Cortical vol. (%) o0:01 9.38 25.34 46.01 8.49 11.10 23.98

Neck-shaft angle (deg) o0:025 120.8 128.7 123.6 121.3 124.4 127.8

(A) Mean cort. modulus (MPa) o0:025 3002.25 3274.23 3864.67 3016.14 3299.91 3675.44

Anteversion (deg) o0:1 15.05 22.06 28.75 16.91 20.45 23.98

Femoral neck dia. ratio o0:1 0.86 1.02 1.26 0.94 1.02 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.

R. Bryan et al. / Journal of Biomechanics 42 (2009) 2171–21762174

different between the group of femurs which were classed as atrisk under a fall load and those which were not. The modelidentified the overall percentage volume of cortical bone throughthe proximal femur, and the mean modulus of cortical bone in thelower femoral head as significant bone quality metrics. In terms ofgeometry, neck shaft angle, anteversion and the ovality of thefemoral neck were seen to be important.

Previous studies have suggested femoral geometric andmaterial features which may result in a predisposition towardsfemoral fracture with the exact features frequently contradictedbetween studies. The main feature which is agreed on is that a lowbone mineral density (BMD) is a high indicating factor of risk(Cheng et al., 1997a; Gnudi et al., 1999; Bergot et al., 2002; Alonsoet al., 2000; Lotz et al., 1991), and also low cortical thickness

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(although usually defined in the proximal femoral shaft) (Chenget al., 1997a; Theobald et al., 1998; Michelotti and Clark, 1999).This was very clearly supported by the results of the model, withcortical bone percentage by far the most significant differencebetween the at risk and low risk groups. There was no evidencethat neck axis length was an indicator of risk, agreeing with somework (Michelotti and Clark, 1999; Alonso et al., 2000) butcontradicting others (Bergot et al., 2002; Theobald et al., 1998;Gnudi et al., 1999; Faulkner et al., 1993).

An interesting geometric parameter which was shown assignificant was neck-shaft angle. Again this parameter had beenshown to have little or no influence on fracture risk by some(Bergot et al., 2002; Faulkner et al., 1993) and yet important byothers (Gnudi et al., 1999; Michelotti and Clark, 1999; Alonsoet al., 2000). The studies which did indicate this measurementsuggest that a larger angle increases the risk, however the currentstudy’s results show a smaller angle in the failed group. Michelottiand Clark (1999) observed that the trend of a smaller angleincreasing risk was seen in studies which took measurementsfrom three-dimensional images as opposed to two-dimensionalX-ray. Suggesting that subject positioning during imaging,particularly external femoral rotation, can result in apparentchanges to neck axis length and neck shaft angle, a findingsupported by work on the affect of anteversion (Cheng et al.,1997b). This parameter may well be affected by the limitedtraining set as it is known to be generally larger in women thanmen (Alonso et al., 2000), however, with only 21 femurs availableit was not feasible to separate male and female subjects togenerate gender specific models.

The present study corroborates previous findings that themajority of failures under fall loading occur in the intertrochanticregion (Cheng et al., 1997a; Cody et al., 1999; Keyak et al., 1997,2001a, 2001b; Bessho et al., 2004). Keyak et al. (2001a) publishedsome details of likely fracture locations under a fall load whichwere tested experimentally as well as modelled computationally.The experimental conditions applied in Keyak’s work werereplicated in the current study. The fracture site was identifiablefor 15 tested femurs. Although the descriptions of fractureinitiation sites are a little vague, it can be seen that a similardistribution of results has been found in both Keyak’s work andthis study (Table 2).

There are limitations to this work. The model may suffer fromthe relatively small size of the training data set, 21 subjects. Thedata set is taken from quite a general population group and sodoes not incorporate factors such as osteoporosis, tumours orother pathologies which would weaken bone. Ideally separatemodels would be generated for different genders, ages, ethnicitiesand pathologies, as these are known to affect femoral geometryand bone density (Theobald et al., 1998; Peacock et al., 1998).Therefore biases in the training set could, in theory, influence the

Table 2Table showing the percentage of femurs identified with various fracture location

origins.

Keyak—finite

element results (%)

Keyak—experimental

results (%)

Statistical model

results (%)

Trochantic 60 47 29

Intertrochantic 25

Cervical 13 40 14

Multiple – – 32

Subtrochantic 0 13 0

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.

statistical result of some geometric parameters. Investigationswere performed on femurs generated by the statistical model toensure that both the geometry and material properties beingproduced were valid and feasible. To do this the metrics devised toanalyse femoral characteristics were used to compare thevariations present in the generated femurs to the training dataset. This showed that realistic models were produced which werea fair representation of the training set.

The finite element analysis performed on the data wasrelatively simple to minimise computational cost. A static loadwas used to simulate a fall and bone was modelled as an isotropiclinear material, when in reality it has anisotropic non-linearproperties. This simplification follows that of the study beingreplicated and was justified in a later study by Keyak (2001)where the gains in predicted and actual fracture load correlationwere small in comparison to the added complexity. In addition,the linear method and the impact rather than progressive loadingmeant that the precise value of load applied was not crucial to theresult. The load chosen, 1� bodyweight, was a realistic value for afall and proved sufficient to highlight an ‘at risk’ group from thedata set. A further simplification to this FE analysis was the lack ofinclusion of muscle forces, surrounding tissues and impactsurface. Again this was justified by the current work’s aim ofreplicating Keyak’s study, showing that the model would replicatethe trends reported from this earlier work.

The case study has shown the potential of this methodology togenerate large numbers of models which describe the variationspresent in the data used to create it. The ability to characterisepopulation wide variability potentially has useful applications inboth computational-experimental analysis and clinical settings.Keyak et al. (2001a) is a good example of the type ofexperimental-computational work which could be enhanced byincorporating this statistical modelling technique, whererelatively small number of cadaveric femurs were tested, 18, andcompared to computational models. If the statistical model wasused to replicate the experimental test results accurately, themodel could then be extended to a wider population of femurmodels with some confidence. Another possible use of being ableto run such large scale simulations is the ability to gain anunderstanding of how factors affect a population, such thatparameters taken from any patient can be compared to these tosee how they fit. This could give a more sophisticated indicator ofrisk factors than current methods such as the World HealthOrganisation’s arbitrary cut off, set at 2.5 standard deviation fromthe mean (World Health Organistation, 1994), to quantifypredictions for osteoporotic hip fracture.

Conflict of interest statement

Rebecca Bryan and Prasanth Nair have no conflicts. Mark Tayloris a retained consultant to Finsbury Orthopaedics and DePuyInternational.

Acknowledgements

This research has been possible thanks to CT data kindlyprovided 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 propertyextraction software.

Appendix A. Supplementary data

Supplementary data associated with this article can be foundin the online version at doi:10.1016/j.jbiomech.2009.05.038.

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