Local displacement and strain uncertainties in different bone types

16 Pages·2017·4.9 MB·English

by  Marco Palanca

JournalofBiomechanicsxxx(2017)xxx–xxx
ContentslistsavailableatScienceDirect
Journal of Biomechanics
journal homepage: www.elsevier.com/locate/jbiomech
www.JBiomech.com
Local displacement and strain uncertainties in different bone types by
digital volume correlation of synchrotron microtomograms
Marco Palancaa, Andrew J. Bodeyb, Mario Giorgic, Marco Vicecontid, Damien Lacroixd, Luca Cristofolinia,
Enrico Dall’Arac,⇑
aDepartmentofIndustrialEngineering,SchoolofEngineeringandArchitecture,AlmaMaterStudiorum-UniversitàdiBologna,ViaTerracini24/28,Bologna40131,Italy
bDiamondLightSource,OxfordshireOX110QX,UK
cDepartmentofOncologyandMetabolismandINSIGNEOInstituteforInSilicoMedicine,UniversityofSheffield,SirFrederickMappinBuilding,PamLiversidgeBuilding,
SheffieldS13JD,UK
dDepartmentofMechanicalEngineeringandINSIGNEOInstituteforInSilicoMedicine,UniversityofSheffield,SirFrederickMappinBuilding,PamLiversidgeBuilding,
SheffieldS13JD,UK
a r t i c l e i n f o a b s t r a c t
Articlehistory: Understandingbonemechanicsatdifferenthierarchicallevelsisfundamentaltoimprovepreclinicaland
Accepted9April2017 clinicalassessmentsofbonestrength.DigitalVolumeCorrelation(DVC)istheonlyexperimentalmea-
Availableonlinexxxx surementtechniqueusedformeasuringlocaldisplacementsandcalculatinglocalstrainswithinbones.
Todate,itscombinationwithlaboratorysourcemicro-computedtomography(LS-microCT)datatypically
Keywords: leadstohighuncertainties,whichlimititsapplication.Here,thebenefitsofsynchrotronradiationmicro-
Synchrotron computedtomography(SR-microCT)forDVCarereported.Specimensofcorticalandtrabecularbovine
microCT
boneandmurinetibiae,wereeachscannedunderzero-strainconditionswithaneffectivevoxelsizeof
Digitalvolumecorrelation
1.6lm.Inordertoconsidertheeffectofthevoxelsize,analyseswerealsoperformedondownsampled
Bone
imageswithvoxelsizeof8lm.Toevaluatedisplacementandstrainuncertainties,eachpairoftomo-
Strain
Uncertainties gramswascorrelatedusingaglobalDVCalgorithm(ShIRT-FE).Displacementrandomerrorsfororiginal
SR-microCT ranged from 0.024 to 0.226lm, depending on DVC nodal spacing. Standard deviation of
strainerrorswasbelow200microstrain(ca.1/10ofthestrainassociatedwithphysiologicalloads)for
correlationsperformedwithameasurementspatialresolutionbetterthan40lmforcorticalbovinebone
(240lmfordownsampledimages),80lmfortrabecularbovinebone(320lmfordownsampledimages)
and murine tibiae (120lm for downsampled images). This study shows that the uncertainties of
SR-microCT-based DVC, estimated from repeated scans, are lower than those obtained from
LS-microCT-basedDVConsimilarspecimensandlowenoughtomeasureaccuratelythelocaldeforma-
tionatthetissuelevel.
!2017TheAuthor(s).PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBYlicense
(http://creativecommons.org/licenses/by/4.0/).
1.Introduction 2015)invivo.CombinationofFEmodelsandmathematicalmodels
of bone remodelling (Lerebours et al., 2015) can estimate bone
Musculoskeletal pathologies, such as osteoporosis or bone changesovertime.However,firstweneedtounderstandhowwell
metastasis, are associated with alterations of bone structures at the structural FE models predict the local 3-dimensional strain
different spatial scales. Assessment of bone quality (Bouxsein, field,whichcanbe usedtoestimatethe localcell activityonthe
2003)andmineraldensityhavebecomekeytostudyingtheeffects bonestructuralunits(Levchuketal.,2014).
ofpathologiesandrelatedtreatmentsatdifferentbonehierarchical ApossiblewayofvalidatingtheFEmodelsatthetissuelevelis
levels.Subject-specificcomputedtomographybasedfiniteelement byusingdigitalvolumecorrelation(DVC)(Bayetal.,1999).DVCis
(FE)analyseshavebeenusedtoestimatebonemechanicalproper- afull-field,contactlesstechniquethatprovidesbothdisplacement
ties(Dall’Araetal.,2013;Dall’Araetal.,2012;Schileoetal.,2008) andstrainmapsinsidebonespecimensviathecomparisonof3D
andtheeffectofinterventions(Keavenyetal.,2014;Zyssetetal., imagesacquiredin,for example,theunloadedand loadedcondi-
tions(GrassiandIsaksson,2015).DVCapproachesbasedon‘labo-
ratory source’ micro-computed tomography (LS-microCT) can
Correspondingauthor. measuredisplacementsinboneswithsub-voxelaccuracyandpre-
⇑
E-mailaddress:e.dallara@sheffield.ac.uk(E.Dall’Ara).
http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
0021-9290/!2017TheAuthor(s).PublishedbyElsevierLtd.
ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
2 M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx
cision(ca.1/10–1/20oftheeffectivevoxelsize)(Chenetal.,2017; longaxescorrespondedtotherotationaxisduringdatacollection.Eachspecimen
Zaueletal.,2006).However,currentLS-microCT-basedDVCcannot wasscannedtwiceunderzero-strainconditionsandwithoutanyrepositioning.
Twocubicvolumesofinterest(VOIs),withsidelengthsof1000voxels,were
measure strain in bone with enough precision to validate the
croppedfromthemiddleofeachcorticalandtrabecularspecimen(Fig.1d,e,g,
modeloutputwithinabonestructuralunit(e.g.atrabeculaoran h)usingImageJ-v1.49(Rasband,NIH,Maryland,USA,http://imagej.nih.gov/ij/).In
osteon)(Dall’Araetal.,2014;Robertsetal.,2014).Todate,thetyp- ordertoincludebothtrabecularandcorticalbone,onecubicVOI(Fig.1f,i)was
icalmeasurementuncertaintyenabledusingDVC todiscriminate croppedfromtheproximalpartofeachmurinetibia.
InordertoallowcomparisonbetweentheresultsobtainedfromotherDVC
the pre- or post-yielding conditions in vertebra bodies scanned
approaches,theimagedatasetsusedinthepresentstudyareavailablebycontact-
with LS-microCT with a voxel size of approximately 35–40lm
ingthecorrespondingauthor(resultscanbefoundathttps://doi.org/10.15131/shef.
(Danesietal.,2016;Husseinetal.,2012;Tozzietal.,2016).Infact, data.4865300)..
as bone yields at a deformation of 7000–10,000 microstrain InordertoevaluatetheDVCerrorsonlywherebonetissueispresent,masked
(Bayraktar et al., 2004), a measurement uncertainty of approxi- images were created: after applying a Gaussian filter (r=4) to reduce high-
frequencynoise,imagesegmentationwasperformed,followedbya single-level
mately700microstraincouldbeacceptableforclassifyingregions
thresholdinthevalleybetweenthefirsttwopeaksofthegreyscalehistogram.
startingtoyieldfromthosestillintheelasticregime.Afterexten- Thethresholdwasadjustedvisuallybycomparingthesegmentedandgreyscale
sive optimisation, DVC based on LS-microCT has reached accept- images.Thesebinaryimages(0forbackground,1forbonevoxels)werethenused
able accuracyand precision,onthe orderof200microstrain,but alsotomasktheoriginalbovinetrabecularboneandmurinetibiaVOIs(Fig.1j,k).
ForeachVOIthesolidvolumefraction(solidvolume/totalvolume,SV/TV),was
onlyifastrongcompromisewithmeasurementspatialresolution
determinedastheratiobetweenthenumberofbonevoxelsandthetotalnumberof
is accepted (measurements every 500–600lm) (Dall’Ara et al.,
voxelsintheVOI,usingtheImageJplug-inBoneJ(Doubeetal.,2010).
2014;Palancaetal.,2015).Unfortunately,duetotheheterogeneity The potential benefit associated with SR-microCT could be due both to the
ofbonetissue,DVCbasedonLS-microCTcannotbeusedtoobtain signal-to-noiseratioandthevoxelsize.Inordertoevaluatetheeffectofthevoxel
accuratemeasurementsofstrainwithinthetypicalelementsizeof sizeonthestrainuncertainties,alloriginal(notmasked)VOIsweredownsampled
toavoxelsizeof8lm(byaveragingthevoxelsgrey-values)usingImageJ.Witha
microCT-basedFEmodels(ontheorderof10–20lm).
similarapproach,downsampledbinarymaskswerecreatedfromtheoriginalmasks
InordertoreducethestrainmeasurementerrorsofDVCwecan fortrabecularboneandmurinetibiaeandassigning1toanyvaluegreaterthan0.
trytoimprovetheinputimagesby,e.g.,usingsynchrotronradia-
tion microCT (SR-microCT). However, it is currently not clear if,
2.2.DVCprotocol
andtowhatextent,betterqualitytomogramswouldimprovethe
accuracyofDVCstrainmeasurements.Totheauthors’knowledge, TheadoptedDVCapproach(ShIRT-FE)wasacombinationofaglobaldeform-
theonlypublishedstudythatcharacterisedtheaccuracyofstrains able image registration algorithm (Sheffield Image Registration toolkit, ShIRT
computedwithDVCbasedonSR-microCTofbonefocusedonthe (Barber and Hose, 2005; Barber et al., 2007)) that computes the displacements
maps,andafiniteelement(FE)softwarepackageforthecalculationandvisualiza-
crackpropagationinmurinefemora(Christenetal.,2012).How-
tionofthestrains(Dall’Araetal.,2014;Palancaetal.,2015;Palancaetal.,2016;
ever,inthatstudytheprecisionofthemethodwasassessedonly Tozzietal.,2017).Briefly,agridwithselectablenodalspacing(NS)wassuperim-
on virtually moved or stretched images, which has been shown posedontheVOIsfrompairsofrepeatedscans.ShIRTcomputesthedisplacements
to underestimate the realerror inducedby image noiseand arti- atthenodesofthegridbysolvingtheregistrationequation(BarberandHose,2005;
facts (Dall’Ara et al., 2014). Therefore, the real potential of SR- Barberetal.,2007).Thegridisthenconvertedinto8-nodeshexahedralFEmesh,the
computeddisplacementsareassignedasboundaryconditions(Fig.2),theFEsoft-
microCT based DVC for bone applications is still partially unex-
warepackageisusedtodifferentiatethedisplacementfield(ANSYSMechanical
plored as the potential benefits of using high-quality tomograms APDLv.15.0,Ansys,Inc.,USA),andthesixcomponentsofstrainarecomputedat
thatallowresolvingmicro-featuressuchasosteocytelacunaeare eachnode.Asithasbeendemonstratedthatnodalspacing(NS)affectsuncertain-
notyetknown. tiesofthemethod(Dall’Araetal.,2014),aseriesofNSvalueswasused(from10
to300voxels,equivalentto16.0–480.0lm)foreverypairofrepeatedtomograms
TheaimofthisstudywastoquantifytheimprovementthatSR-
(Table1).
microCTdatacouldbringtoglobalDVCfordifferentbonetissues,
Forthebovinetrabecularboneandmurinetibiasamples,whichshowedlower
by investigating the compromise between measurement spatial SV/TVthanthebovinecorticalsamples(approximately96%forcorticalboneversus
resolutionanduncertainties. approximately26%fortrabecularboneandmurinetibia,Fig.1),twoapproaches
weretakeninordertoinvestigatetheeffectoftheinclusionofthemarrowregions
duringtheregistration:eitherthewholeVOI(‘unmasked’),oronlythepartsofthe
VOI within the mask (‘masked’) were registered. In both cases (unmasked and
2.Materialsandmethods masked)thecellsofthemeshwithallnodesoutsidethemaskwereignoredand
theerrorswereaveragedonlyintheremainingnodes(Fig.2),inordertoaccount
2.1.Specimenpreparation,tomographyandimageprocessing onlyfortheerrorswithinthebonetissue.Thesameprotocolwasappliedalsoto
thedownsampledimagesusingthedownsampledmasks.
In order to investigate the effect of microstructure on measurement errors,
three different tissue types were used (Fig. 1a–c): four 3mm in diameter and
12mminlengthcorticalbonecoresobtainedfromthediaphysisofafreshbovine 2.3.Quantificationoferrors
femur(18monthsold,killedforalimentarypurposes);three8mmindiameterand
12mminlengthtrabecularbonecoresobtainedfromthegreatertrochanterofthe The systematic error for the displacements could not be quantified, due to
samefemur;andfourpairedtibiae,whichhadbeenusedinapreviousstudy(Lu unknownnano-movementsofthemovingpartsofthescanner.Conversely,asthe
etal.,2015),obtainedfromtwo14-weekoldfemaleC57BL/6Jmice(HarlanLabora- testwasbasedonazero-straincondition,anynon-zerovaluesofstrainwerecon-
tories,Bicester,UK).Allmachiningwasperformedunderconstantwaterirrigation. sideredaserror,andbothprecisionandaccuracycouldbeestimated.Thefollowing
Thesofttissuesaroundthetibiaewerecarefullyremovedwithascalpel.Allspec- parameterswerecomputedforeachregistration:
imens were dehydrated overnight at room temperature and then embedded in
acrylicresinwithoutboneinfiltration. - Randomerrorforthedisplacement:standarddeviation(SD)ofeachcomponent
Tomography was performed at the Diamond-Manchester Imaging Beamline ofdisplacement,asin(Benoitetal.,2009;Madietal.,2013;Palancaetal.,2015;
l13-2ofDiamondLightSource,UK.Afiltered(950lmC,2mmAl,20lmNi)poly- Rouxetal.,2008);
chromatic‘pink’beam(5–35keV)ofparallelgeometrywasusedwithanundulator - Meanabsoluteerror(MAER):averageoftheaverageoftheabsolutevaluesof
gapof5mm.Thepropagationdistancewasapproximately10mm.Tomography thesixcomponentsofstrainineachnode,referredas‘‘accuracy”in(Liuand
datawereacquiredusingapco.edge5.5detector(PCOAG,Germany)coupledto Morgan,2007);
a750lm-thickCdWO4scintillator,withvisualopticsproviding4!totalmagnifica- - Standarddeviationoferror(SDER):SDoftheaverageoftheabsolutevaluesof
tion. This lead to an effective pixel size of 1.6lm and a field of view of thesixcomponentsofstrainineachnode,referredas‘‘precision”in(Liuand
4.2 3.5mm.4001projectionimageswerecollectedatequally-spacedanglesover Morgan,2007);
!
180"ofcontinuousrotation,withanexposuretimeof53ms.Thetotalscanning - Systematicerrorforeachcomponentofstrain:averageoftherespectivecom-
timewasapproximatelyfourminutes.Theprojectionimageswereflatanddark ponentofstrainontheevaluatednodes,asin(Gillardetal.,2014;Palanca
correctedpriortoreconstructionusingthetomographicreconstructionmoduleof etal.,2016);
Dawnv1.7(Ashtonetal.,2015;Bashametal.,2015),whichincorporatedringarte- - Randomerrorforeachcomponentofstrain:SDoftherespectivecomponentof
factsuppression(Titarenkoetal.,2010).Samplesweremountedsuchthattheir strainontheevaluatednodes,asin(Gillardetal.,2014;Palancaetal.,2016);
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx 3
Fig.1. Typicalspecimenforeachtissuetype.Fromtoptobottom:3-dimensional(3D)representationofatypicalspecimen;3DrepresentationoftypicalVOI;2-dimensional
(2D)cross-sectionthroughthemiddleofeachVOI;masked2Dcross-sections;solidvolumefraction(SV/TV)values(median±standarddeviation).Thesidelengthofeach
crosssectionis1000voxels,equivalentto1600lm.
The medianandstandard deviation werecomputed withineachsamplefor a NS of 10, Table2). The maximalrandomerrors,obtained atNS
sucherrors. equal to 10, were smallest for the bovine cortical sample (below
0.054voxels for z-direction, 0.088lm), followed by the ones for
the murine tibia sample (below 0.080voxels for x-direction,
3.Results 0.130lm),andlargestfortheonescomputedforbovinetrabecular
sample(below0.139voxelsforz-direction,0.226lm).Theerrors
3.1.Randomerrorforthedisplacements obtained for the displacements using the masked images were
lowerthanthosefortheunmaskedimagesforbothbovinetrabec-
The random errors of each component of the displacement, ular bone and murine tibia samples (Table 2). A trend could be
obtained using the registration based on the unmasked images observedforallbonetypes:thehighertheNS,thelowertheran-
neverexceeded0.139voxels(0.226lm;fortrabecularbonewith domerror.Nopreferentialdirectionwasobserved.
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
4 M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx
Fig.2. Workflowoftheregistrationprocedure.Tomogramswereobtainedbyscanningthespecimenstwicewithoutanyrepositioning.Fromlefttoright:agridofparticular
nodalspacing(NS,from10to300voxels)wassuperimposedonthecroppedVOIs(unmaskedormasked,incaseoftrabecularandmurinetibiae);thedisplacementswere
evaluatedateachnodebyShIRT;thegridwasconvertedtoanFEmeshandcomputeddisplacementsassignedasboundaryconditions;thecellsofthegridwithallnodes
outsidethemaskwereignoredwhenevaluatingmeasurementuncertainties.
3.2.Accuracyandprecision:averageofcomponents
Table1
As expected from the results reported in previous studies on
List of investigated nodal spacings and nominal numbers of elements and nodes
insidetheVOI.FinerstepswereusedforlowerNS(10–25voxels)andcoarsersteps bone (Benoit et al., 2009; Dall’Ara et al., 2014; Palanca et al.,
forhigherNS(50–300voxels). 2016) and on polypropylene-foam (Roux et al., 2008), the uncer-
tainties of the DVC approach (MAER and SDER) had decreasing
Nodal Nodal Nominalnumberof Nominalnumberof
spacing spacing elementsinsideVOI nodesinsideVOI trendswithrespecttoNS,foralltypesofbone(Fig.3).Foragiven
(voxels) (lm) NS,thevaluesofMAERwerelargerthanSDER.
10 16.0 1,000,000 1,030,301 Theranges(forNSof16.0–480.0lm)ofthemediansforMAER
15 24.0 314,432 328,509 andSDERforbovinecorticalbonesamplewerebetween29–2026
20 32.0 125,000 132,651 microstrain and between 8–890 microstrain, respectively. Errors
25 40.0 64,000 68,921
for this bone type were lower than those obtained for the other
50 80.0 8,000 9,261
75 120.0 2,744 3,375 types of bone (from registration based on masked or unmasked
100 160.0 1,000 1,331 images). For bovine trabecular bone the MAER ranged between
150 240.0 512 729 49–4058microstrainand41–1795microstrainforunmaskedand
200 320.0 216 343 maskedimages, respectively. For murinetibiae the MAER ranged
250 400.0 64 125
between 43–3868 microstrain and 51–1394 microstrain for
300 480.0 64 125
unmasked and masked images, respectively. Lower SDER was
found for the bovine trabecular bone (between 17–2253 micros-
Table2
Randomerrorsforthecomponentsofdisplacement(lm)foreachbonetype.
Ns Displacementrandomerrors(lm)
Bovinecortical Bovinetrabecular Bovinetrabecularmasked Murinetibiaunmasked Murinetibiamasked
unmasked
X Y Z X Y Z X Y Z X Y Z X Y Z
10 0.073 0.072 0.088 0.171 0.176 0.226 0.108 0.101 0.152 0.130 0.118 0.118 0.103 0.087 0.084
15 0.053 0.049 0.069 0.143 0.143 0.192 0.095 0.092 0.133 0.093 0.078 0.079 0.099 0.081 0.078
20 0.051 0.046 0.067 0.139 0.141 0.201 0.090 0.083 0.128 0.089 0.074 0.081 0.094 0.077 0.072
25 0.047 0.041 0.061 0.123 0.125 0.186 0.086 0.077 0.116 0.085 0.072 0.078 0.092 0.076 0.070
50 0.039 0.033 0.058 0.087 0.091 0.156 0.068 0.064 0.102 0.074 0.061 0.066 0.085 0.071 0.059
75 0.036 0.032 0.061 0.075 0.081 0.144 0.056 0.057 0.098 0.070 0.057 0.061 0.083 0.069 0.052
100 0.033 0.027 0.055 0.056 0.062 0.114 0.043 0.051 0.086 0.067 0.054 0.053 0.082 0.068 0.049
150 0.031 0.029 0.060 0.047 0.053 0.096 0.037 0.045 0.079 0.062 0.051 0.045 0.075 0.071 0.047
200 0.029 0.025 0.055 0.038 0.041 0.084 0.031 0.042 0.076 0.057 0.050 0.041 0.076 0.071 0.045
250 0.034 0.038 0.068 0.050 0.056 0.103 0.037 0.042 0.062 0.055 0.043 0.057 0.068 0.065 0.040
300 0.024 0.026 0.053 0.030 0.030 0.061 0.027 0.034 0.056 0.049 0.039 0.033 0.065 0.063 0.038
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx 5
Fig.3. MAER(top)andSDER(bottom)foreachbonetype(bovinecorticalboneinblue,bovinetrabecularboneinorangeandmurinetibiaingreen),forunmaskedand
maskedimages(solidandstripedbars,respectively)asafunctionofthenodalspacingNS.Barsrepresentthemedianvalues,whileerrorbarsrepresentthestandard
deviation.Ontheright,thepowerlawsandthecoefficientsofdetermination(R2)arereported.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderis
referredtothewebversionofthisarticle.)
train and 9–1162 microstrainfor unmaskedand masked images) resolution,downsampledimagesandLS-microCTimagesofsimilar
and for the murine tibia sample (between 14–2012 and 24–909 samples(Dall’Araetal.,2014)(Fig.4).
microstrainforunmaskedandmaskedimages).
Downsampling the images increased the median errors for all 3.3.Systematicerrorsforeachcomponentofstrain
bone types for both MAER (113–11971 microstrain for cortical
bone, 265–14650 microstrain for trabecular bone and 86–7011 The systematic errors were independent from NS, for all bone
microstrain for murine tibiae) and SDER (36–4790 microstrain types and for both registrations based on unmasked or masked
for cortical bone, 124–8985 microstrain for trabecular bone and images(Fig.Sup.1inSupplementaryMaterial).Onlyweakreduc-
19–4165microstrainformurinetibiae).ThepowerlawsforMAER tions of the systematic errors for the normal components have
andSDERshowedsimilartrendsbutdifferentamplitudefornative been observed for mouse tibiae for both unmasked and masked
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
6 M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx
Fig.4. MediansandpowerlawscomputedforMAER(top)andSDER(bottom)foreachbonetype(bovinecorticalboneinblue,bovinetrabecularboneinorangeandmurine
tibiaingreen),fornativeSR-microCTimages(solidlines),downsampledSR-microCTimages(dashedlines)andLS-microCTimagesfromDall’Araetal.(2014)(dash-dotlines).
Ontheright,thepowerlawsandthecoefficientsofdetermination(R2)arereported.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferred
tothewebversionofthisarticle.)
images.Themediansofthesystematicerrorsforthebovinecorti- trabecularbonewithunmaskedandmaskedimages,respectively;
calbonesamplerangedbetween 43and80microstrain,andwere between 17 and 197 microstrain and between 6 and 209
" " "
lowerthanthoseoftheothertwobonetypes(between 55and microstrainformurinetibiaeusingunmaskedandmaskedimages,
"
124microstrainandbetween 133and88microstrainforbovine respectively). In most cases no systematic preferential direction
"
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx 7
wasobserved.Largererrorswerefoundfornormalcomponentsin DVC. Conversely for murine tibiae the SDERs computed with
the mouse tibiae. The downsampled images confirmed the inde- unmasked or masked images were similar for NSs larger than
pendenceofthesystematicerrorsfromtheNS,butshowedhigher 10voxels (16lm). This different effect of the masking could be
values errors (between 74 and 264 microstrain for the bovine duetodifferencesinsizeandshapeofthebonefeaturesthatform
"
cortical bone, between 207 and 590 for the bovine trabecular thetwomicrostructures.
"
bone,andbetween 12and219forthemurinetibiae). This study explored the relationships between spatial resolu-
"
tionoftheDVCstrainmeasurementsandtheassociatederrorfor
3.4.Randomerrorsforeachcomponentofstrain the different bone types. Not surprisingly, the trend of the DVC
uncertaintiesfollowedapowerlawforallbonetypes,confirming
For all registrations, increasing the NS reduced the random whatwaspreviouslyfoundforLS-microCTbasedbonespecimens
errorforeachcomponentofstrain(Fig.5).Asobservedforthedis- (Dall’Ara et al., 2014; Roberts et al., 2014) or for polypropylene-
placement,bovinecorticalboneshowedthelowestrandomerrors, foam specimens (Roux et al., 2008). For NSs of 40lm or larger,
with medians ranging between 14 and 3271 microstrain. Bovine theSDERforthecorticalboneimageswerelowerthan200micros-
trabecularbonewasassociatedtorandomerrorsof32–7480and train, acceptable error when investigating deformations in the
23–3228microstrainusingunmaskedimages,andmaskedimages, physiological range. For registrations using the masked images,
respectively.Themurinetibiaeshowederrorsof23–6669and23– median SDER values lower than 200 microstrain were found for
2543 microstrain using unmasked and masked images, respec- NS larger than 80lm for the murine tibiae, or larger than
tively.Randomerrorswerelargestfortheshearstrainsinallcases 120lmforthebovinetrabecularbone.LargerNSswererequired
(approximately 1.5 times higher than for the normal strain). The toreducetheerrorassociatedtoeachcomponentofstrainbelow
sametrendwasobservedforthedownsampledimages.Here,the 200microstrain(80lmforthecorticalbone,160lmformasked
murine tibiae had the lowest random errors (57–12,051 micros- trabecularbone,and120lmformaskedmurinetibiae).Theseval-
train). The bovine cortical bone had errors between 77 and uesareacceptableformeasurementsperformedonbonestructural
18,810 microstrain and the bovine trabecular bone between 249 units,andsuggestthattheSR-microCTbasedDVCcanbeusedto
and25,185microstrain. validatecomputationalmodelsthataimtopredictlocalstrainsat
the tissue level (Chen et al., 2017; Eswaran et al., 2007; Van
Rietbergenetal.,1995;Verhulpetal.,2006).
3.5.Spatialdistributionoftheerrors
In the present study the errors were vastly lower than those
obtained processing traditional LS-microCT (voxel size of
The distribution of the apparent normal strain along the z-
10lm)images(Dall’Araetal.,2014)ofsimilarspecimensfrom
directionvariedbetweenbonetypes,andevenmorepronouncedly #
the same femur processed in this study, using the same DVC
withtheNS(Fig.6).HavingappliedtheDVCtorepeatedimagesof
approachonRepeated-Scan-Tests. Inthatstudy,SDERbelow200
the same undeformed specimens (zero-strain condition), this
microstrainwereachievedonlyforNSabove472lmfortrabecular
strainrepresentstheerrordistributionwithineachbonestructure.
bone,and536lmforcorticalbone.Thepresentstudyprovedthat
Forbovinecorticalbone,areasonablyuniformstraindistribu-
theDVC uncertaintiescouldbereduced,improvingthe measure-
tion was obtained with NS equal to 50 and 100voxels (80 and
ment spatial resolution almost fourteen times for cortical bone
160lm). Conversely, for the bovine trabecular bone and murine
and almost four times for trabecular bone. This difference could
tibiae, the bone surface and those regions with limited number
be due to the superimposition of two effects in the SR-microCT
of features within the volume (e.g. central portion of the murine
images:the smallereffective voxel sizeand thehigher signal-to-
tibia)showedlargerstrainerrors.Itmustbenotedthatfortrabec-
noiseratio.Whenthedownsampledimageswereanalysed,SDER
ularbonewithNSequalto50voxels(80lm)thepeakerrorswere
of200microstrainwereachievedwithameasurementspatialres-
inmostcasesinregionsoutsidetheboneorclosetotheborderof
olutionof176lmforthecorticalbone(fivetimescoarserthanthe
theimage.
34lmneededfortheoriginalimages),andof402lmforthetra-
becular bone (four times coarser than the 97 of the original
4.Discussion images).Theseanalysesshowedthatafinervoxelsizecanexplain
only partially the lower SDER of the DVC with SR-microCT. Such
ThepotentialofDVCforboneapplicationsisstillpartiallyunex- measurement spatial resolutions were still better than those
plored, as this approach has not been yet applied intensively to required to obtain the same SDER with LS-microCT (Dall’Ara
high-quality images. In this study measurement uncertainties of et al., 2014). The larger improvement for cortical bone is likely
aSR-microCTbasedDVCapproachwereevaluatedforthefirsttime duetothemuchhighernumberoffeatures(i.e.theosteocytelacu-
for three different types of bone by using Repeated-Scan-Tests naearoundthevascularpores)resolvablewithSR-microCTimages
(Palancaetal.,2015). forsuchmicrostructurecomparedtoLS-microCTimages.However,
InlinewithpreviousstudiesperformedonLS-microCTimages as comparisons were made between SR-microCT and LS-microCT
(Dall’Ara et al., 2014; Palanca et al., 2015; Palanca et al., 2016; imagesofsimilar(butnotidentical)specimens,furtherinvestiga-
Tozzi et al., 2017), also for DVC based on SR-microCT, the larger tionscouldhelptobetterclarifythesourcesoferrors.
the NS the lower the measurement uncertainties. This trend is Alltheabove-mentionedconsiderationswerebasedonanalyses
probablyduetothefactthatevenforhigherimagequality,thedis- of data from zero-strain tests. While a detailed analyses of DVC
placement errors were only modestly affectedby the NS (e.g. for precision under loading will need a more comprehensive future
NS 10 and 100voxels, the random error was reduced by a factor studyforestimatingtheeffectofloadingcondition,loadingdirec-
2 if the NS was increased by a factor 10, Table 1), which lead to tion and loading level for different structures, in this manuscript
increased strain errors for smallest distance between the nodes wereportsomepreliminaryresultsobtainedfromvirtuallycom-
ofthegrid. pressedcorticalspecimens(SectionS2inSupplementaryMaterial).
Forthebovinetrabecularbone,registrationsbasedonmasked To the authors’ knowledge, this is the first study where the
images showed lower errors compared to the ones obtained by displacement and strain errors of a global DVC approach based
registering unmasked images. This finding highlights how the on SR-microCT images were evaluated with Repeated-Scan-Tests
exclusion of low-contrast marrow regions, for which noise and and virtually compressed repeated images for different types of
artefacts probably dominate the registration, is beneficial for bone specimens. Another study used synchrotron images on a
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
8 M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx
Fig.5. Medianoftherandomerrorforeachbonetype(corticalboneonthetop,trabecularboneinthemiddleandmurinetibiaeonthebottom),foreachregistrationmethods
(fromunmaskedimagesontheleft,frommaskedimagesontheright),foreachcomponentofstrain,asafunctionofNS.Toimprovethereadability,errorbarsrepresenting
standarddeviationswerereportedonlyonthetopofeachhistogram.Tohelpinterpretingtheresults,arangeforthetypicalphysiologicaldeformations(1,000–2,000
microstrainYang.,etal.,2011)isindicated.Forthescopeofthisstudy,alsothetargetvalueforthemeasurementerrorisindicated(oneorderofmagnitudelower:200
microstrain).
DVCapproachandperformedapreliminaryevaluationoftheerror registration algorithm, was applied to SR-microCT images (voxel
(Christenetal.,2012)onvirtuallymovedandstretchedimagesof size of 740nm) with a NS of approximately 30lm and provided
murine femur. That DVC approach, based on demons deformable SDERofapproximately1800microstrain,morethanfourtimeslar-
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx 9
Fig.6. Distributionofz-directionnormalstrainshownforamid-heightcross-sectionforatypicalspecimenofeachbonetypeforthreenodalspacing(10,50,100).For
trabecularboneandmurinetibiaethemaskedimageswereusedforthisanalyses.AstheDVCwasappliedtorepeatedimagesofthesameundeformedspecimens,the
reportedstrainrepresentsinfacttheDVCmeasurementuncertainties.Thecross-sectionimageofthecorrespondingslicewasoverlappedtothestrainerrormap.Forevery
microstructure,thesidelengthoftheimageis1,600lm.
gerthanthatfoundformaskedmurinetibiaeinthisstudy.Thisdif- approach. While similar trends can be expected also for local
ferencemightbeduetodifferencesinmicrostructure,tomographic DVCapproaches(Leclercetal.,2012;Palancaetal.,2015)research-
resolutionand registration method. However, considering that in ers are welcome to download the images used in this study for
thatstudytheSDERwascomputedonvirtuallymovedimagesthat comparingdifferentmethods.
donotincludetheeffectofimagenoise,themethodproposedin
this study is by far the one with the highest precision (lowest
5.Conclusion
SDER)reportedintheliteraturetodateforanalysesonbonespec-
imens.ItremainstobeinvestigatedifotherDVCapproacheswould
The uncertainties associated with a global DVC approach
achievesimilar(or better)precisionif basedonthesameimages
applied to Synchrotron tomograms with small voxel size are
usedinthepresentstudy.
sufficiently low to allow reliable strain measurements at the
DespitethehighpotentialofSR-microCTbasedDVC,bonedam-
tissue-levelindifferentbonestructures.Thismethodcanbeused
age induced by X-ray synchrotron irradiation is apparently the
toevaluatelocalbonedeformationsunderloading,andtovalidate
majorlimitationforitsapplicationintime-lapsedinsitumechan-
thestrainpredictedbycomputationalmodelsatthetissue-level.
icaltests(Barthetal.,2010).Previousauthorshaveattemptedto
mechanically test bone samples within a synchrotron facility
(Christen et al., 2012; Thurneret al., 2006) but reported that the Conflictofinterest
irradiationand/orassociatedheataffectedthelocalmaterialprop-
ertiesofthetissue(Barthetal.,2010).InordertoapplythisDVC Authorshavenoconflictofinterestassociatedtothispaper.
approach to SR-microCT in situ mechanically tested and imaged
bone samples further scanning optimization (Pacureanu et al., Acknowledgments
2012)andanalysistoreducethisproblemby,forexample,reduc-
ing exposure times, supressing lower X-ray frequencies or sub- TheauthorswouldliketoacknowledgeYuanChen,AndreCas-
merging samples in aqueous buffer, would form the basis of a tro, Ana Campos-Marin, Claudia Wittkowske, Luke Boldock and
usefulmethodologicalstudy. Kazimir Wanelik for help during experiments at Diamond Light
The main limitation of this study is that the measurement Source. We acknowledge Diamond Light Source for time at the
uncertainties were investigated in a homogeneous zero-strain Diamond-Manchester Imaging Beamline I13-2, under proposal
case.Itwouldbeinterestingtofurtherstudytheevolutionoferrors MT10315. This study was partially funded by the FP7 European
within strained specimens, especially where the gradients of programMAMBO(PIEF-GA-2012-327357)andbytheEPSRCFron-
strains are highest. Moreover, the error associated to the strain tier Grant Multisim (EP/K03877X/1). Palanca acknowledges the
and displacement measurements was evaluated for a global DVC ‘MarcoPolo’travelgrantawardedbyUniversityofBologna.
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007
10 M.Palancaetal./JournalofBiomechanicsxxx(2017)xxx–xxx
AppendixA.Supplementarymaterial Fuerst, Radcliffe, H.S., Libanati, C., 2014. Femoral and vertebral strength
improvements in postmenopausal women with osteoporosis treated with
denosumab.J.BoneMiner.Res.29,158–165.
Supplementarydataassociatedwiththisarticlecanbefound,in Leclerc,H.,Perle,J.N.,Hild,F.,Roux,S.,2012.Digitalvolumecorrelation:whatare
the online version, at http://dx.doi.org/10.1016/j.jbiomech.2017. thelimitstothespatialresolution?Mech.Ind.13,361–371.
04.007. Lerebours, C., Buenzli, P.R., Scheiner, S., Pivonka, P., 2015. A multiscale
mechanobiologicalmodelofboneremodellingpredictssite-specificboneloss
in the femur during osteoporosis and mechanical disuse. Biomech. Model.
References Mechanobiol.15,1.
Levchuk,A.,Zwahlen,A.,Weigt,C.,Lambers,F.M.,Badilatti,S.D.,Schulte,F.A.,Kuhn,
G.,Muller,R.,2014.TheClinicalBiomechanicsAward2012-presentedbythe
Ashton,A.W.,Aishima,J.,Basham,M.,Chang,P.,ElKassaby,B.,Filik,J.,Gerring,M.,
EuropeanSocietyofBiomechanics:largescalesimulationsoftrabecularbone
Levik,K.,Sikharulidze,I.,Webber,M.,Wharmby,M.T.,2015.DawnSciencev1.7
adaptationtoloadingandtreatment.Clin.Biomech.29,355–362.
(DLSEdition).p.
Liu,L.,Morgan,E.F.,2007.Accuracyandprecisionofdigitalvolumecorrelationin
Barber,D.C.,Hose,D.R.,2005.Automaticsegmentationofmedicalimagesusing
quantifyingdisplacementsandstrainsintrabecularbone.J.Biomech.40,3516–
imageregistration:diagnosticandsimulationapplications.J.Med.Eng.Tech.
3520.
29,53–63.
Lu,Y.,Boudiffa,M.,Dall’Ara,E.,Bellantuono,I.,Viceconti,M.,2015.Evaluationofin-
Barber,D.C.,Oubel,E.,Frangi,A.F.,Hose,D.R.,2007.Efficientcomputationalfluid
vivomeasurementerrorsassociatedwithmicro-computedtomographyscans
dynamicsmeshgenerationbyimageregistration.Med.ImageAnal.11,648–
bymeansofthebonesurfacedistanceapproach.Med.Eng.Phys.37,1091–
662.
1097.
Barth,H.D.,Launey,M.E.,Macdowell,A.A.,Ager3rd,J.W.,Ritchie,R.O.,2010.Onthe
Madi,K.,Tozzi,G.,Zhang,Q.H.,Tong,J.,Cossey,A.,Au,A.,Hollis,D.,Hild,F.,2013.
effectofX-rayirradiationonthedeformationandfracturebehaviorofhuman
Computation of full-field displacements in a scaffold implant using digital
corticalbone.Bone46,1475–1485.
volumecorrelationandfiniteelementanalysis.Med.Eng.Phys.35,1298–1312.
Basham,M.,Filik,J.,Wharmby,M.T.,Chang,P.C.,ElKassaby,B.,Gerring,M.,Aishima,
Pacureanu, A., Langer, M., Boller, E., Tafforeau, P., Peyrin, F., 2012. Nanoscale
J.,Levik,K.,Pulford,B.C.,Sikharulidze,I.,Sneddon,D.,Webber,M.,Dhesi,S.S.,
imaging of the bone cell network with synchrotron X-ray tomography:
Maccherozzi,F.,Svensson,O.,Brockhauser,S.,Naray,G.,Ashton,A.W.,2015.
optimizationofacquisitionsetup.Med.Phys.39,2229–2238.
DataanalysisWorkbeNch(DAWN).J.SynchrotronRadiat.22,853–858.
Palanca, M., Tozzi, G., Cristofolini, L., Viceconti, M., Dall’Ara, E., 2015. 3D local
Bay,B.K.,Smith,T.S.,Fyhrie,D.P.,Saad,M.,1999.Digitalvolumecorrelation:three-
measurementsofbonestrainanddisplacement:comparisonofthreedigital
dimensionalstrainmappingusingX-raytomography.Exp.Mech.39,217–226.
volumecorrelationapproaches.J.Biomech.Eng.(ASME)137.071006-071001/
Bayraktar,H.H.,Morgan,E.F.,Niebur,G.L.,Morris,G.E.,Wong,E.K.,Keaveny,T.M.,
071006-071014.
2004. Comparison of the elastic and yield properties of human femoral
Palanca,M.,Tozzi,G.,Dall’Ara,E.,Curto,M.,Innocente,F.,Danesi,V.,Cristofolini,L.,
trabecularandcorticalbonetissue.J.Biomech.37,27–35.
2016.DigitalVolumeCorrelationcanbeusedtoestimatelocalstrainsinnatural
Benoit,A.,Guerard,S.,Gillet,B.,Guillot,G.,Hild,F.,Mitton,D.,Perie,J.N.,Roux,S.,
andaugmentedvertebrae:anorgan-levelstudy.J.Biomech.49,3882–3890.
2009.3Danalysisfrommicro-MRIduringinsitucompressiononcancellous
Roberts, B.C., Perilli, E., Reynolds, K.J., 2014. Application of the digital volume
bone.J.Biomech.42,2381–2386.
correlationtechniqueforthemeasurementofdisplacementandstrainfieldsin
Bouxsein,M.L.,2003.Bonequality:wheredowegofromhere?Osteoporos.Int.14
bone:aliteraturereview.J.Biomech.47,923–934.
(Suppl.5),S118–S127.
Roux,S.,Hild,F.,Viot,P.,Bernard,D.,2008.Three-dimensionalimagecorrelation
Chen,Y.,Dall’Ara,E.,Sales,E.,Manda,K.,Wallace,R.,Pankaj,P.,Viceconti,M.,2017.
fromX-raycomputedtomographyofsolidfoam.Compos.AAppl.Sci.Manuf.
Micro-CTbasedfiniteelementmodelsofcancellousbonepredictaccurately
39,1253–1265.
displacement once the boundary condition is well replicated: A validation
Schileo, E., Dall’ara, E., Taddei, F., Malandrino, A., Schotkamp, T., Baleani, M.,
study.J.Mech.BehaviorBiomed.Mater.65,644–651.
Viceconti, M., 2008. An accurate estimation of bone density improves the
Christen, D., Levchuk, A., Schori, S., Schneider, P., Boyd, S.K., Muller, R., 2012.
accuracyofsubject-specificfiniteelementmodels.J.Biomech.41,2483–2491.
Deformable image registration and 3D strain mapping for the quantitative
Thurner, P.J., Wyss, P., Voide, R., Stauber, M., Stampanoni, M., Sennhauser, U.,
assessmentofcorticalbonemicrodamage.J.Mech.BehaviorBiomed.Mater.8,
Müller, R., 2006. Time-lapsed investigation of three-dimensional failure and
184–193.
damage accumulation in trabecular bone using synchrotron light. Bone 39,
Dall’Ara, E., Barber, D., Viceconti, M., 2014. About the inevitable compromise
289–299.
betweenspatialresolutionandaccuracyofstrainmeasurementforbonetissue:
Titarenko,S.,Withers,P.J.,Yagola,A.,2010.Ananalyticalformulaforringartefact
a3Dzero-strainstudy.J.Biomech.47,2956–2963.
suppressioninX-raytomography.Appl.Math.Lett.23,1489–1495.
Dall’Ara, E., Luisier, B., Schmidt, R., Kainberger, F., Zysset, P., Pahr, D., 2013. A
Tozzi, G., Dall’Ara, E., Palanca, M., Curto, M., Innocente, F., Cristofolini, L., 2017.
nonlinear QCT-based finite element model validation study for the human
StrainuncertaintiesfromtwoDVCapproachesinprophylacticallyaugmented
femurtestedintwoconfigurationsinvitro.Bone52,27–38.
vertebrae:localanalysisonboneandbone-cementmicrostructures.J.Mech.
Dall’Ara, E., Pahr, D., Varga, P., Kainberger, F., Zysset, P., 2012. QCT-based finite
BehaviorBiomed.Mater.67,117–126.
elementmodelspredicthumanvertebralstrengthinvitrosignificantlybetter
Tozzi, G., Danesi, V., Palanca, M., Cristofolini, L., 2016. Elastic full-field strain
thansimulatedDEXA.Osteoporos.Int.23,563–572.
analysis and microdamage progression in the vertebral body from digital
Danesi,V.,Tozzi,G.,Cristofolini,L.,2016.Applicationofdigitalvolumecorrelation
volumecorrelation.Strain52,446–455.
tostudytheefficacyofprophylacticvertebralaugmentation.Clin.Biomech.39,
VanRietbergen,B.,Weinans,H.,Huiskes,R.,Odgaard,A.,1995.Anewmethodto
14–24.
determine trabecular bone elastic properties and loading using
Doube,M.,Klosowski,M.M.,Arganda-Carreras,I.,Cordelieres,F.,Dougherty,R.P.,
micromechanicalfinite-elementmodels.J.Biomech.28,69–81.
Jackson, J., Schmid, B., Hutchinson, J., Shefelbine, S., 2010. BoneJ: free and
Verhulp,E.,vanRietbergen,B.,Huiskes,R.,2006.Comparisonofmicro-leveland
extensibleboneimageanalysisinImageJ.Bone47,1076–1079.
continuum-levelvoxelmodelsoftheproximalfemur.J.Biomech.39,2951–
Eswaran,S.K.,Gupta,A.,Keaveny,T.M.,2007.Locationsofbonetissueathighriskof
2957.
initialfailureduringcompressiveloadingofthehumanvertebralbody.Bone41,
Zauel,R.,Yeni,Y.N.,Bay,B.K.,Dong,X.N.,Fyhrie,D.P.,2006.Comparisonofthelinear
733–739.
finiteelementpredictionofdeformationandstrainofhumancancellousbone
Gillard,F.,Boardman,R.,Mavrogordato,M.,Hollis,D.,Sinclair,I.,Pierron,F.,Browne,
to3Ddigitalvolumecorrelationmeasurements.J.Biomech.Eng.128,1–6.
M., 2014. The application of digital volume correlation (DVC) to study the
Zysset,P.,Pahr,D.,Engelke,K.,Genant,H.K.,McClung,M.R.,Kendler,D.L.,Recknor,
microstructural behaviour of trabecular bone during compression. J. Mech.
C., Kinzl, M., Schwiedrzik, J., Museyko, O., Wang, A., Libanati, C., 2015.
Behav.Biomed.Mater.29,480–499.
Comparisonofproximalfemurandvertebralbodystrengthimprovementsin
Grassi, L., Isaksson, H., 2015. Extracting accurate strain measurements in bone
theFREEDOMtrialusinganalternativefiniteelementmethodology.Bone81,
mechanics:acriticalreviewofcurrentmethods.J.Mech.Behav.Biomed.Mater.
122–130.
50,43–54.
Yang,P.F.,Bruggemann,G.P.,Rittweger,J.,2011.Whatdowecurrentlyknowfrom
Hussein,A.I.,Barbone,P.E.,Morgan,E.F.,2012.Digitalvolumecorrelationforstudy
in vivo bone strain measurements in humans? J. Musculoskelet. Neuronal
ofthemechanicsofwholebones.ProcediaIUTAM4,116–125.
Interact.11,8–20.
Keaveny,T.M.,McClung,M.R.,Genant,H.K.,Zanchetta,J.R.,Kendler,D.,Brown,J.P.,
Goemaere,S.,Recknor,C.,Brandi,M.L.,Eastell,R.,Kopperdahl,D.L.,Engelke,K.,
Pleasecitethisarticleinpressas:Palanca,M.,etal.Localdisplacementandstrainuncertaintiesindifferentbonetypesbydigitalvolumecorrelationof
synchrotronmicrotomograms.J.Biomech.(2017),http://dx.doi.org/10.1016/j.jbiomech.2017.04.007