Assessment of Hip Fracture Risk Using Cross-Section Strain Energy Determined by QCT-Based ...

15 Pages·2015·1.99 MB·English

Hindawi Publishing Corporation
BioMed Research International
Volume 2015, Article ID 413839, 15 pages
http://dx.doi.org/10.1155/2015/413839
Research Article
Assessment of Hip Fracture Risk Using Cross-Section Strain
Energy Determined by QCT-Based Finite Element Modeling
HosseinKheirollahi1andYunhuaLuo1,2
1DepartmentofMechanicalEngineering,FacultyofEngineering,UniversityofManitoba,Winnipeg,MB,CanadaR3T5V6
2DepartmentofAnatomy,SouthernMedicalUniversity,Guangzhou510515,China
CorrespondenceshouldbeaddressedtoYunhuaLuo;[email protected]
Received24April2015;Revised28June2015;Accepted29June2015
AcademicEditor:KengoYamamoto
Copyright©2015H.KheirollahiandY.Luo.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttribution
License,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperly
cited.
Accurateassessmentofhipfractureriskisveryimportanttopreventhipfractureandtomonitortheeffectofatreatment.Asubject-
specificQCT-basedfiniteelementmodelwasconstructedtoassesshipfractureriskatthecriticallocationsoffemurduringthe
single-legstanceandthesidewaysfall.Theaimofthisstudywastoimprovethepredictionofhipfractureriskbyintroducinga
novelfailurecriteriontomoreaccuratelydescribebonefailuremechanism.Hipfractureriskindexwasdefinedusingcross-section
strainenergy,whichisabletointegrateinformationofstresses,strains,andmaterialpropertiesaffectingbonefailure.Itwasfound
thatthefemoralneckandtheintertrochantericregionhavehigherfractureriskthanotherpartsofthefemur,probablyowingtothe
largercontentofcancellousboneintheseregions.Thestudyresultsalsosuggestedthatwomenaremorepronetohipfracturethan
men.Thefindingsinthisstudyhaveagoodagreementwiththoseclinicalobservationsreportedintheliterature.Theproposedhip
fractureriskindexbasedonstrainenergyhasthepotentialofmoreaccurateassessmentofhipfracturerisk.However,experimental
validationshouldbeconductedbeforeitsclinicalapplications.
1.Introduction Statistical models and bone mineral density (BMD)
capturedby Dual-EnergyX-rayAbsorptiometry(DXA)are
Twoofthemajordeterminantsofproximalfemurfractures used for in vivo osteoporotic fracture risk assessment [4,
among the elderly are osteoporosis and sideways fall. The 5]. However, their accuracy in assessment of fractures is
most common serious injury associated with the fall of an limited;mostosteoporoticfracturesactuallyoccurwithBMD
elderly person is hip fracture. Furthermore, hip fracture is measurementsthatareabovetheconventionalosteoporotic
associatedwithanupto20%chanceofdeath,a25%chance threshold [6]. Fracture Risk Assessment Tool (FRAX) is a
oflongterminstitutionalization,andlessthana50%chance tooltoevaluateanindividual’sfractureprobabilityinthenext
offullrecovery[1].Thetotalnumberofhipfracturesinmen 10years,adoptedbytheWHOin2008[7].FRAXdoesnot
andwomenin1990wasestimatedtobe338,000and917,000, takeintoaccountfall-inducedimpactforcethatiscritically
respectively,overtheworld[2].Assumingnochangeinthe important in the hip fracture risk assessment [8, 9]. The
age-andsex-specificincidence,thenumberofhipfractures main limitations of the FRAX include the following: it is a
isestimatedtoapproximatelydoubleto2.6millionbytheyear statisticalmodelandfractureriskisnotconsistentwithin10
2025and4.5millionbytheyear2050overtheworld[2].By yearswithsomeofthetreatmentresults[10].Hipstructure
theincreasingtrendinhipfracturesbecauseoftheagingof analysis (HSA) program is now commercially available and
thepopulation,theworldwideannualcostsofhipfracturesin isusedto automaticallyassess thegeometricandstructural
theyear2050havebeenestimatedtobe$131.5billion[3].So, parametersofthefemur.WhereasHSAisbasedonabeam
hipfractureriskshouldbeassessedinindividualswhoareat model,thedeformationofboneisoversimplified,especially
ariskforanosteoporotichipfracturetoprovideproperplans in the femoral neck and the intertrochanteric region where
topreventfutureprobablefractures. osteoporotic femoral fractures most often occur; therefore
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CT-scans Applying loading/boundary Computing strain energy over
conditions the critical cross-sections
Image processing
and segmentation
Finite element analysis Computing the maximum
allowable strain energy over
Constructing the critical cross-sections
3D model Finding the critical
cross-sections
Computing fracture risk
Measuring neck-
index (FRI) of the critical
shaft angle Finite element cross-sections
analysis
Generating finite
element mesh Fracture risk index
calculation
Assigning material
properties
Finite element model
construction
Figure1:Theproposedmethodologyforcalculatinghipfractureriskindexusingthestrainenergycriterion.
thedeformationistoocomplicatedtobedescribedasabeam riskindex(FRI)overaregionofinterest(ROI)basedonthe
model[11]. strainenergycriteriontheoreticallyshouldbemoreaccurate
Finite element models constructed from quantitative forassessinghipfracturerisk.Tothebestofourknowledge,
computed tomography (QCT) are very helpful in assessing there are currently no published studies that use the strain
hip fracture risk, as they are based on well-established energy criterion for the hip fracture risk assessment. The
biomechanical principles and theories. In QCT-based finite objective of this study is to improve the hip fracture risk
element modeling, choosing a proper failure criterion is assessmentprocedurepreviouslydevelopedbyLuoetal.[11]
very important to accurate assessment of hip fracture risk. byintroducingthestrainenergycriterion.
CommonlyusedbonefailurecriteriaincludevonMisesstress
and strain criteria [12–15], maximum principle stress and 2.MaterialsandMethods
straincriteria[16–19],maximumshearstresscriterion[20],
and maximum distortion energy criterion [20]. The femur The proposed methodology for assessment of hip fracture
consists of inhomogeneous (porous) cancellous bone and risk in the critical regions of femur using the strain energy
nearly homogenous cortical bone, and their failure mech- criteriondeterminedfromQCT-basedfiniteelementmodel
anisms are different due to their different microstructure. isshowninFigure1.Theprocedureisexplainedindetailin
Failure mechanism of the cancellous bone is mostly in the thefollowing.
formofspicule(trabecula)buckling,andthefailureofdenser
cancellousboneandthecorticalboneismostlycharacterized
2.1.QCT-BasedFiniteElementModel
bylocalcracking[21,22].Corticalandcancellousbonehave
differentproperties.Corticalboneisusuallymorebrittle[23], 2.1.1. QCT-Scan of Femur. The purpose of this study is to
while cancellous bone is more ductile. The current failure accurately assess hip fracture risk, so, a 3D finite element
criteria are not convenient in describing their properties. model of subject’s femur is required to achieve it. The 3D
Therefore,thetotalstrainenergy,whichintegratesallinfor- model can be constructed from the subject’s femur QCT
mation of stress, strain, and material properties, is a better images. QCT slices are produced using multiple scanners
option[21].Mirzaeietal.[21,24]predictedfailurestrength withasetofproperacquisitionandreconstructionparame-
and failure patterns of human proximal femur and human ters(Figure2(a)).Slicethicknessof1mmiscommonlyused.
vertebraeusingthestrainenergycriterionwithaQCT-based ThescannedQCTimagesarestoredintheformatofDigital
FE model. Their predictions of the failure loads and failure ImagingandCommunicationsinMedicine(DICOM),which
locations were in a good agreement with the experimental canbeusedfortheconstructionofa3DFEmodel.Aproper
findings.Thestrainenergycriterioniswidelyusedinfracture segmentationisdonetoseparatethefemurforconstructing
analysisofengineeringmaterials.Itisusuallyusedincrack the3Dmodel.EachvoxelintheQCT-scanhasanintensity
problems [25–27], composite laminates [28, 29], and bone (or grey scale) that is expressed as Hounsfield Unit (HU),
cementanalysis[30].Therefore,computationofhipfracture whichiscorrelatedtobonedensity[31,32].Thresholdvalue
BioMedResearchInternational 3
Table1:Statisticalinformationofthe60clinicalcases.
Gender Age(years) Height(cm) Bodyweight(kg) BMI(kg/m2)
Range 50–82 149–174.7 51.7–110.9 21.01–43.36
Female
Average 65 163.92 77.58 28.81
Range 50–78 163.4–193.2 61.5–126.6 18.83–40.96
Male
Average 64.71 175.74 86.22 27.9
(a) (b) (c) (d) (e) (f)
Figure2:QCT-basedfiniteelementmodeling:(a)QCT-scanofthesubject’sfemur;(b)3DmodelgeneratedfromtheQCTimages;(c)3D
finiteelementmodel;(d)distributionofelasticitymodulus;(e)single-legstanceconfiguration;and(f)sidewaysfallconfiguration.
forthecancellousboneisfrom100HUto200HUandforthe solution, meaning that the number of elements is different
corticalboneisbetween200HUand2000HU.QCTimages fromcasetocase.
of60clinicalcases(30femalesand30males)wereacquired
fromtheWinnipegHealthScienceCentreinananonymous 2.1.3.AssignmentofMaterialProperties. Toconstructamore
wayunderahumanresearchethicsapproval.Thesubjectsare faithful FE model, bone material properties are considered
in the age scope from 50 to 82 years (average of 65 years). inhomogeneousand isotropicin thisstudy. Informationon
StatisticalinformationoftheclinicalcasesislistedinTable1. the inhomogeneous isotropic mechanical properties of the
bonecanbederivedfromtheCTdatausingamathematical
2.1.2. Generation of Finite Element Mesh. In the first step, relationship between the CT numbers and the mechanical
the geometrical model of the femur is generated from properties of bone. The following empirical equation was
clinical QCT images using Mimics (Materialise, Leuven, usedtodetermineboneashdensity(𝜌 )fromHUnumber
ash
Belgium).QCTimages(inDICOMformat)areimportedto [33,34]:
Mimics for segmentation (Figure2(a)) and construction of
𝜌 =0.04162+0.000854HU (g/cm3). (1)
3D geometric model of the femur (Figure2(b)). With the ash
3D geometric model, a FE mesh is generated using the 3-
Equations (2) and (3), derived by Keller [35], were,
matic module in Mimics (Figure2(c)). The 4-node linear
respectively, used to assign Young’s modulus (𝐸) and yield
tetrahedral element SOLID72 in ANSYS was used in this
study. To investigate model convergence, FE models with stress(𝜎𝑌)accordingtotheboneashdensity:
different maximum element edge lengths were created. For 𝐸=10500𝜌2.29 (MPa) (2)
eachFEmodel,displacementwascalculatedunderthesame ash
leodagdeinlegngatnhdthbaotupnroddaruycecdocnodnitvieorngse.dThfineitmeealxeimmeunmtsoelluemtioennst 𝜎𝑌 =116𝜌a2s.h03 (MPa). (3)
wasobtainedandusedinalltherestofFEsimulations.The A constant Poisson’s ratio (] = 0.4) was considered as
number of elements for each case is assigned based on the suggested in the literature [13, 36, 37]. To assign material
maximumelementedgelengththatprovidedconvergedFE properties, elements are grouped into a number of discrete
4 BioMedResearchInternational
material bins using Mimics (Materialise, Leuven, Belgium),
toapproximatelyrepresentthecontinuousdistributionofthe A
inhomogeneous bone mechanical properties. To determine B
the maximum number of material bins, convergence study
was performed. Models with different material bins were A
createdforconvergencestudy.ForeachFEmodel,displace-
mentwascalculatedunderthesameloadingandboundary
B
conditions. The maximum number of material bins that
generated converged finite element solutions was obtained. 5cm
Figure2(d)showstheisotropicinhomogeneousdistribution
ofmaterialproperties. C C
2.2.FiniteElementAnalysisUsingANSYS. Thefiniteelement
model of femur with the assigned material properties was
outputfromMimicsandthenimportedtoANSYSforfinite
elementanalysis.Forapreciseassessmentofhipfracturerisk
duringthesingle-legstanceandthesidewaysfall,loadingand
boundaryconditionssimulatingthesingle-legstanceandthe
sideways fall configurations are required in the FE model.
Figure3:Threecriticalcross-sectionsoffemur:thesmallestfemoral
Tosimulatethesingle-legstanceconfiguration,2.5timesthe
neckcross-section(A-A),theintertrochantericcross-section(B-B),
patient’sbodyweightwasappliedasadistributedloadonthe
andthesubtrochantericcross-section(C-C).
femoralheadindirectionoffemoralshaftaxis[38]andfemur
wasfixedatthedistalend[13,39];seeFigure2(e).Consider
𝐹 =2.5𝑤 (N), (4) betweenthefemoralneckaxisandthefemoralshaftaxis.This
Stance
angletraditionallyismeasuredonconventionalradiography
where 𝑤 is the subject’s body weight in Newton (N). To images, or using 2D images projected from CT/MRI data.
simulatesidewaysfall,thedistalendoffemurwascompletely In spite of their popularity, these methods are based on
fixedandthesurfaceoffemoralheadwasfixedintheloading oversimplification of the real 3D anatomy and may lead
direction(Figure2(f))[40,41].Theimpactforceduringthe to large errors due to the inaccuracies in selection of the
sidewaysfallactingonthegreatertrochanterperpendicularly measurement plane [44–46]. In this study, the neck-shaft
(Figure2(f))isgivenby[38,42]: angle was measured using a 3D measurement technique
based on fitting functions. In this technique, the shapes
ℎ 1/2
𝐹 =8.25𝑤( ) (N), (5) of particular parts of the femur are approximated using
Impact 170 geometricentitiessuchascircle,cylinder,andsphere,which
are well fitted to the actual anatomy, and the geometrical
where ℎ is the height of the subject in centimeter (cm). relationshipsbetweentheseentitiesareobtainedtoestimate
Loadingandboundaryconditionsonthegreatertrochanter, theneck-shaftangle.
thefemoralhead,andthedistalendoffemurwereappliedto First, a sphere was fitted to the femoral head, to obtain
agroupofnodesusingAPDLcodes(Figures2(e)and2(f)). the position of the joint’s centre of rotation, which is also
AfterimportingtheQCT-basedFEmodelandapplyingthe thefemoralheadcentre.Then,thefemoralneckaxisandthe
loadingandboundaryconditions,finiteelementanalysiswas femoral shaft axis are identified by applying the “fit ruled
performedandfiniteelementsolutionswereobtained.Inall surface direction” function on the femoral neck and shaft.
the analysis, the nodal displacements, stresses, and strains Allfittingfunctionswereappliedusingthe3-maticmodule
wereobtainedforeachsubject. in Mimics. The neck-shaft angle was also measured by 3-
maticmoduleofMimics(Figure4).Withthefemoralneck-
2.3.DetectionoftheThreeCriticalCross-SectionsontheFemur. shaftangle,theintertrochantericcross-sectionandthesmall-
Hipfracturesusuallyoccuratoneoftheanatomicallocations: est femoral neck cross-section were found using in-house
thefemoralneck,theintertrochanter,andthesubtrochanter computer codes. The smallest femoral neck cross-section is
asillustratedinFigure3.Accordingtoclinicalobservations, chosenasthecross-sectionwiththesmallestareaintheneck
49percentofhipfracturesareintertrochanteric,37percent regionandtheintertrochantericcross-sectionischosenasthe
are at femoral neck, and 14 percent are subtrochanteric cross-sectionthathasthelargestareaintheintertrochanteric
[43].Therefore,thesmallestfemoralneckcross-section(SFN region[47].ByusingAPDLcodes,perpendicularplaneson
CS), the intertrochanteric cross-section (IntT CS), and the thefemoralneckaxisweredeterminedandthenareasofthe
subtrochantericcross-section(SubTCS)arethethreecritical cross-sectionswerecalculated.Theplaneswiththesmallest
cross-sectionsoffemurthatusuallyhavethehighestfracture andthelargestareaswerechosen,respectively,asthesmallest
risk (Figure3). To determine the smallest femoral neck femoral neck cross-section and the intertrochanteric cross-
cross-section and the intertrochanteric cross-section, neck- section.Thesubtrochantericcross-sectionisconsideredfive
shaft angle is needed. The neck-shaft angle is the angle centimetersbelowthelessertrochanter[48](Figure3).
BioMedResearchInternational 5
and 𝑛 is the number of integration points over the triangle
element.Thestrainenergydensityatanintegrationpoint(𝑖)
wasdeterminedfromthefiniteelementsolutionsobtainedby
theQCT-basedFEmodel;thatis,
𝑈̂ = 1{𝜎}𝑇{𝜀}, (8)
118.51∘ 𝑖 2
118.51∘
where {𝜎} = [𝐷]{𝜀} and {𝜀} = [𝐵]{𝑑}. The strain energy
densityateachintegrationpointcanbeexpressedbythefinite
elementsolutionsas
𝑈̂ = 1{𝑑}𝑇[𝐵]𝑇[𝐷] [𝐵] {𝑑} , (9)
𝑖 𝑒 𝑒 𝑒 𝑒 𝑒
2
where{𝑑}isthedisplacementvectorconsistingofdisplace-
ments at the nodes of Element 𝑒; matrix [𝐵] consists of the
derivativesofshapefunctionsoftheelement;and[𝐷]isthe
materialpropertymatrix.Consider
Figure4:Neck-shaftanglemeasuredbythefittingfunctionsinthe 𝐸
[𝐷] =
3-maticmoduleofMimics. 𝑒 (1+])(1−2])
1−] ] ] 0 0 0
2.4.HipFractureRiskIndexDefinitionUsingtheStrainEnergy [ ]
[ ] 1−] ] 0 0 0 ]
Criterion. Based on the previous discussion of the bone [ ]
[ ]
failure mechanism and microstructure, the strain energy [[ ] ] 1−] 0 0 0 ]] (10)
criterion is theoretically more favourable for hip fracture ⋅[[ 1 ]],
risk assessment. The strain energy at the three critical [ 0 0 0 −] 0 0 ]
[ 2 ]
ccoromssp-usetecdtiounssinogfifne-mhuorusiendduecveedlobpyedthMeAapTpLlAieBd fcoordceess awnads [[[ 0 0 0 0 1 −] 0 ]]]
[ 2 ]
the data extracted by APDL codes from the obtained finite 1
0 0 0 0 0 −]
elementsolutions.Theplaneboundariesofthethreecritical [ 2 ]
cross-sections,extractedfromthefiniteelementmesh,were
where Poisson’s ratio is constant (] = 0.4) and Young’s
imported to MATALB to generate a 2D mesh for calcu-
modulusisafunctionofthebonedensityasgivenin(2).For
lating the cross-section strain energy. Figure5 shows the
eachintegrationpoint,itsYoung’smodulusisdeterminedby
generated triangle elements over the smallest femoral neck
thebonedensityatthepoint.
cross-section, the intertrochanteric cross-section, and the
The maximum allowable strain energy over a critical
subtrochantericcross-section.
cross-section of the femur was also computed from the
The strain energy at the three critical cross-sections
obtained finite element solutions using in-house MATLAB
inducedbytheappliedforcesisthesumofstrainenergyin
codes. The maximum allowable strain energy (or the yield
allthetriangleelements;thatis,
strainenergy)overacriticalcross-sectionisobtainedas
𝑚
𝑚
𝑈=∑𝑈𝑒, (6) 𝑈𝑌 =∑𝑈𝑌𝑒, (11)
𝑖=1
𝑖=1
where 𝑈𝑒 is the strain energy in Element 𝑒 induced by where 𝑈𝑒 is the yield strain energy in Element 𝑒 and 𝑚 is
the applied forces and 𝑚 is the number of triangle ele- 𝑌
the number of triangle elements over the concerned cross-
ments created over the concerned cross-section. Gaussian
section. The Gaussian integration method was also used
integration method was used to calculate the strain energy
to calculate the maximum allowable strain energy in each
in elements. Integration points in each triangle element
triangleelement.Themaximumallowablestrainenergythat
were determined using in-house MATLAB codes. By using atriangleelement(𝑒)cansustainisgivenby
Gaussianintegrationmethod,thestrainenergyofElement𝑒
𝑛
inducedbytheappliedforcesiscalculatedas 𝑈𝑌𝑒 =∬ 𝑈̂𝑌𝑒 𝑑𝐴≈∑𝑊𝑖|𝐽|𝑈̂𝑌𝑖, (12)
𝑛 𝑖=1
𝑈𝑒 =∬ 𝑈̂𝑒𝑑𝐴≈∑𝑖=1𝑊𝑖|𝐽|𝑈̂𝑖, (7) where𝑈̂𝑌𝑒 istheyieldstrainenergydensityinElement𝑒;𝑛is
where 𝑈̂𝑒 is the strain energy density of Element 𝑒; 𝑈̂𝑖 is ethneernguymdbenersiotyfainttiengtreagtriaotniopnopinotisn;ta𝑖nadnd𝑈̂𝑌is𝑖cisaltchuelaytieedldasstrain
the strain energy density at the integration point 𝑖 of in
Element𝑒;𝑊𝑖istheweightattheintegrationpoint;|𝐽|isthe 𝑈̂ = 1𝜎 𝜀 = 𝜎𝑌2𝑖, (13)
determinantoftheJacobeanmatrixofthetriangleelement; 𝑌𝑖 2 𝑌𝑖 𝑌𝑖 2𝐸𝑖
6 BioMedResearchInternational
(a) (b) (c)
Figure5:Generatedtriangleelementsover(a)thesmallestfemoralneckcross-section,(b)theintertrochantericcross-section,and(c)the
subtrochantericcross-section.
0.4 0.24
0.23
0.3 m)
m
nt ( 0.22 RI
0.2 me F
e
c
a
pl 0.21
0.1 Dis
0.2
12 10 8 6 4 2 0
0
50 40 30 20 10 0 Maximum element edge length (mm)
Maximum element edge length of 3D FE model (mm) Figure7:ConvergenceofFRI.
Figure6:Convergenceoffiniteelementsolutionswithelementsize.
neck cross-section was monitored under the same loading
where𝜎𝑌𝑖and𝐸𝑖are,respectively,theyieldstressandYoung’s and boundary conditions. Data on the displacement were
compared among the FE models with different material
modulusattheintegrationpoint.Bothofthemarefunction
bins. The results of the convergence study showed that the
ofbonedensity,asgivenin(2)and(3).
Hip fracture risk index (𝜂) at a critical cross-section is displacement did not change significantly with the number
ofmaterialbinslargerthan50.Therefore,intheassignment
definedas
of material properties for all the cases, 50 discrete material
𝑈 binswereconsidered.
𝜂= ,
(14)
𝑈
𝑌
3.1.3.ElementSizeinCalculatingCross-SectionStrainEnergy.
where𝑈and𝑈𝑌are,respectively,obtainedfrom(6)and(11). Convergence study was also performed to determine the
elementsizeusedinintegratingcross-sectionstrainenergy,
3.Results asitaffectsthecalculatedfractureriskindex(FRI).TheFRI
attheconcernedcross-sectionwascalculatedwithdifferent
3.1.ConvergenceStudies maximum element edge lengths. The results are plotted in
Figure7. The FRI did not change significantly with the
3.1.1. Element Size in Femur Finite Element Analysis. The maximumelementedgelengthsmallerthan5mm.Therefore,
convergence of finite element solutions in a representative the maximum element edge length was set to 5mm in
case is shown in Figure6. The convergence study showed calculatingcross-sectionstrainenergy.
that the finite element displacements converged with the
maximumelementedgelengthsmallerthan8mm.Therefore,
3.1.4.TheNumberofIntegrationPointsinCalculatingCross-
inconstructionoftherestoffemurFEmodels,themaximum
SectionStrainEnergy. Theeffectofthenumberofintegration
elementedgelengthwassetto8mm.
points on the calculated FRI was investigated. FRI at the
smallest femoral neck cross-section was computed for 5
3.1.2.AssignmentofInhomogeneousMaterialProperties. For clinicalcaseswithdifferentnumberofintegrationpoints.The
convergencestudyinassigningtheinhomogeneousmaterial relativeerrorsbetweenFRIsobtainedwith3and7integration
properties,3DfemurFEmodelswithdifferentmaterialbins pointsareshowninTable2.Asitcanbeseen,theerrorsare
were created. For each FE model with different material not significant. Therefore, the 3-point integration rule was
bins, the maximum displacement at the smallest femoral usedinthisstudytoreducecomputationaltime.
BioMedResearchInternational 7
60 Single-leg stance 160 Sideways fall
140
50
120
Pa) 40 Pa)
M M 100
Mises stress ( 30 Mises stress ( 6800
n 20 n
o o
v v 40
10
20
0 0
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Clinical cases (right femurs) Clinical cases (right femurs)
60 Single-leg stance 80 Sideways fall
70
50
60
a) a)
MP 40 MP
50
es stress ( 30 es stress ( 40
Mis Mis 30
n 20 n
o o
v v 20
10
10
0 0
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Clinical cases (left femurs) Clinical cases (left femurs)
SFN CS SFN CS
IntT CS IntT CS
SubT CS SubT CS
Figure8:ThemaximumvonMisesstress(Mpa)atthesmallestfemoralneckcross-section(SFNCS),theintertrochantericcross-section
(IntTCS),andthesubtrochantericcross-section(SubTCS)ofrightandleftfemursof10clinicalcasesduringthesingle-legstanceandthe
sidewaysfall.
Table 2: Femoral neck FRI obtained with different number of stressandstrainatthethreecriticalcross-sectionsoffemur
integrationpoints. during both the single-leg stance and the sideways fall are
shown in Figures 8 and 9. It can be observed that, during
Case FRI Relativeerror
thesidewaysfall,thefemoralneckandtheintertrochanteric
number 3integrationpoints 7integrationpoints (%) region received higher stresses than the subtrochanteric
1 0.239 0.2416 1.07 region(Table4).Butduringthesingle-legstance,thepatterns
2 0.6898 0.6975 1.1 in the stresses are different (Table3); first, the differences
betweenthestressesoverthethreeregionsaremuchsmaller;
3 0.2966 0.2976 0.33
forsomecases,thestressesatthesubtrochantericregionare
4 0.8885 0.899 1.16
higherthanthoseintheothertworegions(Figure8).Strains
5 1.1482 1.1701 1.87
in the three regions have similar patterns during both the
single-legstanceandthesidewaysfall(Tables5and6).
3.2. Stress and Strain Patterns at the Three Critical Cross- 3.3. Comparison of Hip Fracture Risk at the Three Critical
Sections. For the 10 clinical cases (5 females and 5 males, Cross-Sections. For the 60 clinical cases (30 females and 30
totally 20 right and left femurs), the maximum von Mises males), hip fracture risk indices based on the strain energy
8 BioMedResearchInternational
Table3:AveragemaximumvonMisesstress(MPa)atthesmallestfemoralneckcross-section(SFNCS),theintertrochantericcross-section
(IntTCS),andthesubtrochantericcross-section(SubTCS)ofrightandleftfemursof10clinicalcasesduringthesingle-legstance.
MaximumvonMisesstress(MPa)
Rightfemurs Leftfemurs
SFNCS IntTCS SubTCS SFNCS IntTCS SubTCS
Range 21.7–49.96 22.23–45.37 26.93–52.47 19.56–52.38 23.55–47.8 27.09–43.04
Average 33.63 32.97 37.89 32.93 32.41 35.84
Table4:AveragemaximumvonMisesstress(MPa)atthesmallestfemoralneckcross-section(SFNCS),theintertrochantericcross-section
(IntTCS),andthesubtrochantericcross-section(SubTCS)ofrightandleftfemursof10clinicalcasesduringthesidewaysfall.
MaximumvonMisesstress(MPa)
Rightfemurs Leftfemurs
SFNCS IntTCS SubTCS SFNCS IntTCS SubTCS
Range 26.69–148.53 21.57–74.3 9.8–70.63 22.78–69.97 16.2–60.3 6.73–33.2
Average 57.22 40.74 27.08 46.52 33.48 18.66
Single-leg stance Sideways fall
2.00E−02 1.60E−01
1.60E−02
1.20E−01
n n
ai 1.20E−02 ai
Mises str Mises str 8.00E−02
n 8.00E−03 n
o o
v v
4.00E−02
4.00E−03
0.00E+00 0.00E+00
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Clinical cases (right femurs) Clinical cases (right femurs)
2.00E−02 2.50E−01
Single-leg stance Sideways fall
1.60E−02 2.00E−01
n n
Mises strai 81..0200EE−−0032 Mises strai 11..0500EE−−0011
n n
o o
v v
4.00E−03 5.00E−02
0.00E+00 0.00E+00
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Clinical cases (left femurs) Clinical cases (left femurs)
SFN CS SFN CS
IntT CS IntT CS
SubT CS SubT CS
Figure9:ThemaximumvonMisesstrainatthesmallestfemoralneckcross-section(SFNCS),theintertrochantericcross-section(IntTCS),
andthesubtrochantericcross-section(SubTCS)ofrightandleftfemursof10clinicalcasesduringthesingle-legstanceandthesidewaysfall.
BioMedResearchInternational 9
Table5:AveragemaximumvonMisesstrainatthesmallestfemoral 0.25 Single-leg stance
neck cross-section (SFN CS), the intertrochanteric cross-section
(IntTCS),andthesubtrochantericcross-section(SubTCS)ofright 0.2
andleftfemursof10clinicalcasesduringthesingle-legstance.
0.15
Range Average RI
F
Rightfemurs 0.1
SFNCS 3.54𝐸−03–1.46𝐸−02 9.15𝐸−03
0.05
IntTCS 5.89𝐸−03–1.74𝐸−02 1.08𝐸−02
Maximum SubTCS 2.3𝐸−03–4.75𝐸−03 3.32𝐸−03 0
vonMises 135791357913579135791357913579
Leftfemurs 1111122222333334444455555
strain SFNCS 5.25𝐸−03–1.55𝐸−02 9.55𝐸−03 Clinical cases
IntTCS 5.49𝐸−03–1.87𝐸−02 1.05𝐸−02 SFN CS
SubTCS 2.14𝐸−03–4.34𝐸−03 3.11𝐸−03 IntT CS
SubT CS
Figure10:Fractureriskindexinsingle-legstanceconfiguration.
Table6:AveragemaximumvonMisesstrainatthesmallestfemoral
neck cross-section (SFN CS), the intertrochanteric cross-section
(IntTCS),andthesubtrochantericcross-section(SubTCS)ofright 3.5 Sideways fall
andleftfemursof10clinicalcasesduringthesidewaysfall. 3
Range Average 2.5
Rightfemurs 2
SFNCS 1.67𝐸−02–1.04𝐸−01 5.29𝐸−02 FRI 1.5
IntTCS 4.34𝐸−02–1.50𝐸−01 9.80𝐸−02
1
Maximum SubTCS 12𝐸−03–6.38𝐸−03 2.44𝐸−03
vonMises 0.5
Leftfemurs
strain
SFNCS 1.67𝐸−02–7.43𝐸−02 4.26𝐸−02 0
135791357913579135791357913579
IntTCS 3.35𝐸−02–1.91𝐸−01 9.37𝐸−02 1111122222333334444455555
Clinical case
SubTCS 5.08𝐸−04–3.31𝐸−03 1.74𝐸−03
SFN CS
IntT CS
SubT CS
criterion were calculated for the smallest femoral neck, the Figure11:Fractureriskindexinsidewaysfallconfiguration.
intertrochanteric, and the subtrochanteric cross-section of
femurduringthesingle-legstanceandthesidewaysfall.The
calculatedfractureriskindicesareshowninFigures10and
3.4. Comparison of Hip Fracture Risk in Women and Men.
11.
In this study, hip fracture risk for the 30 females and 30
AsshowninTables7,8,9,and10andFigures12and13,
maleswasassessed.Theaveragehipfractureriskoffemales
theaverageFRIatthesmallestfemoralneckwashigherthan
was generally higher than that of males. As it can be seen
thoseattheintertrochantericandthesubtrochantericcross-
from Tables 11–13 and Figures 15 and 16, the average FRI at
sectionduringboththesingle-legstanceandsidewaysfall.
thesmallestfemoralneckcross-section,theintertrochanteric
For the single-leg stance, FRIs for all cases at the three
critical cross-sections are much lower than one (FRI ≪ 1), cross-section, and the subtrochanteric cross-section of the
30 females is higher than that of the 30 males for both the
indicatingthatthepossibilityofhipfractureincidenceinthe
single-leg stance and the sideways fall. Figure17 shows the
single-legstancewaslow.Forthesidewaysfall,FRIsof8right
numberofpossiblehipfracturesinwomenandmenduring
femursand7leftfemursatthesmallestfemoralneckcross-
thesidewaysfallforthestudiedcases.
section and FRIs of 7 right femurs and 5 left femurs at the
intertrochantericcross-sectionwerehigherthanone(FRI>
1), meaning that there is possibility for fracture occurring 4.Discussion
in these regions; but the FRIs at the subtrochanteric cross-
section in all cases were much lower than one (FRI ≪ 1), Hipfracturemayoccuranywherefromthearticularcartilage
indicating that there is lower possibility of fracture in this ofthehipjointtothefemurshaft[48].Notonlythelocation
region. Figure14 shows the number of possible fractures at of the fracture types but also the etiology differs. It was
thethreecriticalcross-sectionsoffemurduringthesideways reportedthatwomenwiththeintertrochantericfracturehave
fall,thatis,thecasesthathaveFRIlargerthanone(FRI>1) significantly lower BMD than those with the femoral neck
atoneofthethreecriticalcross-sections. fracture[49–51].Ontheotherhand,thefemoralneckfracture
10 BioMedResearchInternational
Table7:AverageFRIatthethreecriticalcross-sectionsof60rightfemursduringthesingle-legstance.
FRI
Smallestfemoralneckcross-section Intertrochantericcross-section Subtrochantericcross-section
Range 0.0261–0.2124 0.0099–0.143 0.0058–0.0363
Average 0.0752 0.0351 0.0155
Table8:AverageFRIatthethreecriticalcross-sectionsof60leftfemursduringthesingle-legstance.
FRI
Smallestfemoralneckcross-section Intertrochantericcross-section Subtrochantericcross-section
Range 0.023–0.1936 0.0095–0.1078 0.0037–0.0337
Average 0.0681 0.0329 0.0142
Table9:AverageFRIatthethreecriticalcross-sectionsof60rightfemursduringthesidewaysfall.
FRI
Smallestfemoralneckcross-section Intertrochantericcross-section Subtrochantericcross-section
Range 0.1725–3.0448 0.1226–1.534 0.0004–0.0812
Average 0.6944 0.5245 0.0091
Table10:AverageFRIatthethreecriticalcross-sectionsof60leftfemursduringthesidewaysfall.
FRI
Smallestfemoralneckcross-section Intertrochantericcross-section Subtrochantericcross-section
Range 0.1599–1.8301 0.116–1.5493 0.0004–0.0585
Average 0.6395 0.4864 0.0083
0.08 Single-leg stance 0.8
Sideways fall
0.07 0.7
0.06 0.6
FRI 0.05 RI 0.5
age 0.04 ge F 0.4
Aver 0.03 Avera 0.3
0.02
0.2
0.01
0.1
0
Left femurs Right femurs 0
Left femurs Right femurs
SFN CS
IntT CS
SubT CS SFN CS
IntT CS
Figure12:AverageFRIatthesmallestfemoralneckcross-section SubT CS
(SFN CS), the intertrochanteric cross-section (IntT CS), and the
subtrochantericcross-section(SubTCS)of60rightfemursand60 Figure13:AverageFRIatthesmallestfemoralneckcross-section
leftfemursduringthesingle-legstance. (SFN CS), the intertrochanteric cross-section (IntT CS), and the
subtrochantericcross-section(SubTCS)of60rightfemursand60
leftfemursduringthesidewaysfall.
maynotbemainlyattributedtolowBMDbutmayberelated
to external causes such as sideways fall [52]. Femoral neck theotherhand,aretypicallytheresultofhighenergyimpacts
and intertrochanteric fractures are often the result of falls suchasmotorvehicleaccidentsandfallsfromaheight[53].
fromstandingheightandimpactontothegreatertrochanter, The selection of bone failure criterionis challenging. In
particularlyfortheelderly.Thesubtrochantericfractures,on literatures, stress and strain based failure criteria such as