A Method to Determine Cortical Bone Thickness of Human Femur and Tibia Using Clinical CT Scans. Wenjing Du, Jinhuan Zhang, Jingwen Hu

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1 A Method to Determie Cortical Boe Thickess of Huma Femur ad Tibia Usig Cliical CT Scas Wejig Du, Jihua Zhag, Jigwe Hu Abstract Femur ad tibia fractures, are commoly see i motor vehicle crashes. Cortical boe thickess is a importat cotributor to boe stregth ad stress strai distributio i impacts. Curret fiite elemet lower extremity models typically focus o three huma sizes (i.e. small female, midsize male, ad large male), ad do ot cosider the variatio i tical boe thickess amog the whole populatio. Cliical computed tomography (CT) has bee used to determie the tical boe thickess distributio, but the covetioal global thresholdig method ofte fails to offer accurate thickess estimatio i thi tex areas. I this study, a ew local thresholdig method was developed to determie tical boe thickess usig cliical CT scas ad statistical models of tical boe thickess for huma femur ad tibia were also established with respect to sex, age, stature ad body mass idex (BMI). It was foud that the average thickess error of the ewly proposed local thresholdig method was less tha 0.1 mm. I thi tex areas, the proposed method provided more accurate results tha the global thresholdig method. Statistical aalysis suggested that age ad BMI sigificatly affect the tical boe thickess for both femur ad tibia. Keywords tical boe thickess, femur, tibia, parametric modellig I. INTRODUCTION The icreasig use ad improvemet of occupat restrait systems have reduced fatality ad severe ijury rates i motor vehicle crashes (MVCs), but the protectio of the lower extremity (LE) was ot improved as much as that of the head ad chest [1]. LE ijuries still accout for 36% of all AIS2+ ijuries sustaied by frot seat occupats i all frotal crashes [2]. Eve though LE ijuries are usually ot fatal, they ca lead to costly rehabilitatio ad disability, which is a heavy burde for the family ad commuity. Femur ad tibia fractures are commoly see i MVCs ad tical boes are believed to have a domiat effect o boe stregth, as they serve as a damage tolerat structural framework [3]. Agig ca cause chages i the shape, size, ad tical thickess of boes ad thus lead to icreased icidece of boe fractures [4]. Other factors such as stature ad body mass idex (BMI), ca also affect boe morphology [5 9]. Fiite elemet (FE) models are powerful ad effective tools to assess huma impact resposes i MVCs ad reproduce boe fractures. Multiple FE femur ad tibia models have bee developed previously. Refereces [10 12] reported detailed LE models usig the geometry extracted from CT ad/or magetic resoace imagig (MRI) data. However, their models could ot reflect the variatio i tical boe thickess amog the populatio, ad a method to estimate the tical boe thickess from CT scas was ot reported. Referece [8] did a comprehesive job o the developmet of parametric femur FE models, ad the populatio variatio i tical boe thickess was cosidered. They used a fixed global thresholdig method similar to [13] to segmet the tical boe from cliical CT scas, ad the thickess was determied based o the distace betwee the outer ad ier tical surfaces alog the ormal directio. However, the estimated tical thickess values were sesitive to the specified threshold, ad may itroduce sigificat errors i thi tex areas. I the field of medical image process, several tex thickess estimatio techiques based o cliical CT scas have bee proposed, such as the 50% relative threshold method [14 15]. This method cosidered boe desity, which was usually deoted by HU values i CT images. The threshold was set halfway from the soft tissue HU values to the tex HU values ad from the tex HU values to the trabecular HU values. It was effective if tex was thick eough i which case the true tical boe desity equaled to the maximum value of the desity profile (expressed i HU values) alog a lie, but it became ureliable i thi tex areas ad teded to overestimate tex thickess. Refereces [16 17] did a extesive research o femoral tical boe Wejig Du is a PhD cadidate, ad Jihua Zhag is a Professor i the State Key Laboratory of Vehicle Safety ad Eergy at Tsighua Uiversity i Beijig, Chia. Jigwe Hu is a Research Associate Professor at the Uiversity of Michiga Trasportatio Research Istitute, A Arbor, MI, USA (phoe: , jwhu@umich.edu)

2 thickess measuremet from cliical CT data based o the model derived from [14] usig a model fittig method. This techique cosidered the imagig system s poit spread fuctio (PSF) ad required kowledge of the desity (expressed i HU values) of the true tical boe, which was assumed to be a costat value for a give subject. The boe desity may vary from locatio to locatio, thus assumig the tical boe desity as costat at all measurig vertices/poits seemed problematic, ad the model fittig process might ot coverge. Nevertheless, this was a decet techique of great accuracy. Referece [18 19] the proposed a model based approach without profile fittig but still shared the assumptio of a costat tex desity i [16 17]. Boe material cotet (BMC, i.e. boe mass) was calculated with three parameters measured i the profile with the help of the 50% relative threshold method. Sice there were o model fittig iteratios, computatio efficiecy was cosiderably improved. I this study, a local thresholdig method was developed to quatify the thickess i tex areas of the femur ad tibia without model fittig process or assumptio of costat tex desity. Ispired by the 50% relative threshold method, o each local HU value profile, a ratio (ot 50%) was employed to defie a local threshold that distiguished tex from soft tissue ad trabecular boes. This ratio idicated a relative tex desity compared to the most dese part (where CT value was the highest) without the eed to assume a specific tex desity value. Ulike the groud truth obtaied from high resolutio micro CT scas i studies [16 17], the proposed method was validated agaist measuremets from a post huma mortem huma subject (PMHS). Results were compared with the covetioal global thresholdig method to show validity of this method. FE meshes of a baselie model were morphed ad fitted to the geometry surfaces recostructed from 95 cliical CT scas ad the tical boe thickess at each ode was computed usig the proposed method. Parametric femur ad tibia thickess models were developed to address the effect of sex, age, stature ad BMI o tical boe thickess distributio. II. METHODS Several parametric FE models [5 9,20] of differet huma body parts have bee developed usig a Radial Basis Fuctio (RBF) based method ad the whole process is summarised ad illustrated i Fig. 1. These models should iclude geometry shape ad size models ad thickess models. However, previous thickess models [8] did ot address the tical boe thickess well. As a key step of the process, the tical boe thickess ca be estimated usig the proposed local thresholdig method i this study. Fig. 1. Whole process of developig parametric models, takig femur as a example. Boe Geometry Extractio, Morphig ad Fittig Techiques Cliical computed tomography (CT) scas were obtaied from multiple hospitals i Chia through a protocol approved by a istitutioal review board at Tsighua Uiversity (Beijig, Chia). All scas i this study were CT agiography scas which covered a etire lower extremity (LE) from pelvis to foot. The CT scas had slice thickess ragig from to 1.25 mm with pixels o every slice of image. Pixel size varied from

3 0.623 mm to mm. I total, 95 CT scas from 59 male ad 36 female patiets were collected. Fig. 2 shows that the age rage was years, ad BMI kg/m 2. No sigificat relatio betwee age ad BMI was foud. Fig. 2. Subject characteristics distributio. All CT scas were processed i Mimics (versio 19.0, Materialise NV, Belgium). First, a global Housfield Uit (HU) threshold value was set to be 210 to segmet ad recostruct femurs ad tibias i three dimesios, ad a series of editig procedures were applied to esure the boe exteral surfaces were smooth ad water tight. The boe exteral surfaces were the exported to Rhioceros 3D (versio 5.0, Robert McNeel & Associates, Seattle, WA) to idetify homogeous ladmarks o the boe exteral surfaces of all patiets. A total of 23 ladmarks at the distal ad proximal eds for femur ad 16 for tibia were idetified. These ladmarks were either aatomic ladmarks or ca be easily distiguished. I the diaphysis regio, cetroid poits of each slice were calculated, which formed the aatomic axes for femur ad tibia. This was doe by averagig the coordiates of all pixels o each slice whose HU values were above the threshold i Mimics. Eleve poits were evely distributed o the axes ad treated as additioal ladmarks. Istead of puttig ladmarks o the diaphysis surface, usig cetroid poits ca effectively help avoid poor mesh quality i the ext few steps. Femur ad tibia meshes from a mid size male huma FE model were used as the template meshes. Followig the same protocol metioed above, homogeous ladmarks were also idetified o the template mesh. I this study, a ladmark based mesh morphig techique based o a RBF was implemeted to morph the template meshes to the boe geometry for each subject. The morphed meshes were the projected to subject geometry surfaces usig a customized MATLAB fuctio. It should be oted that the subject geometry surfaces were ot ecessarily the exterior edge of boe tex. Nodes o these surfaces offered thickess measurig positios ad helped oriet the ormal directio alog which thickess was estimated. Cortical Boe Thickess Estimatio Whe the template meshes were morphed ad fitted to the geometry of each subject, tical boe thickess at all the template odes were calculated. Two methods, global thresholdig ad local thresholdig, were used to estimate the tical boe thickess as show i Fig. 3 ad Fig. 4. Take femur as a example, a HU value versus poit locatio profile was obtaied first for each desigated ode O o the subject geometry surface. A 16 millimetre lie MN that wet through ode O was draw alog the surface ormal directio, which was log eough to cover the possible thickest tex. The start poit M of the lie was 3 millimetres away outside the template surface. Alog the lie, 161 evely distributed poits were sampled with 0.1 millimetre iterval. For each sampled poit, its HU value was iterpolated usig a distace weighted average value of its eight closest voxels with o zero HU values from CT images acdig to Equatio (1). HU 8 HU i1 est 8 where HU is the HU value estimated for a give poit o MN, est HU v, is the HU value of the i st closest voxel i ad d v, is the Euclidea distace from the i st closest voxel to the give poit. i The HU value versus poit locatio profile was the smoothed usig a thi plate splie iterpolatio. Poit i v, i d d v, i v, i (1)

4 locatio was defied as the Euclidea distace from each sampled poit to poit M. Without loss of geerality, all the profiles were from the boe exterior to the iterior. The global thresholdig method used i this study was similar to [8,13]. A fixed HU threshold value, HU, was applied to all HU value locatio profiles. Values above the threshold were cosidered tical boe; while values below the threshold were cosidered o tical boe. The distace betwee the two poits (D ad E i Fig. 3) where the HU values were equal or above the threshold was defied as tical boe thickess. Fig. 3. Cortical boe thickess estimatio based o the global thresholdig method. Fig. 4. Cortical boe thickess estimatio based o the local thresholdig method. This study proposed a ew local thresholdig method as illustrated i Fig. 4, i which the HU value threshold for each poit was dyamically determied. O the profile, poit A was defied as the first maxima poit while HU was its respodig HU value. A two millimetre lie MX was defied i the soft tissue area outside the A boe structure with relatively low HU values. I the boe area, HU values typically raged from 200 to 3,000 [21]. The derivative of the HU value locatio curve (DHU curve) was calculated, ad the DHU from M to X (soft tissue backgroud) should have a average close to zero with a small deviatio. To locate a poit o DHU whose value was sigificatly larger tha the soft tissue backgroud, a threshold of DHU was defied i Equatio (2). DHU threshold (2) D HU D HU where D HU is the mea value of DHU MX, ad first poit to reach the threshold curve as poit B o the DHU curve. Fially, the tical boe threshold, was defied i Equatio (3), D HU is the respodig stadard deviatio. Poit B is the DHU o the DHU curve ad poit C is the respodig poit o the HU threshold HU, for this specific HU profile threshold HU threshold ( HU HU ) K HU (3) A C C where HU ad A coefficiet that required calibratio through experimet. HU are the HU values at poits A ad C, respectively. C K is a key coefficiet amed tex

5 I this study, tical boe was idetified solely based o HU profiles without ay iformatio of tex boe mieral desity (BMD). K ad the local HU threshold defied a relative desity relatioship betwee the tical boe ad the surroudig soft tissue backgroud. We assumed that K was a costat i Equatio (3), ad its value was determied by relatig the estimatio to tical thickess measuremets i PMHS, described i the ext sectio. Cortical Boe Thickess Measuremet The left femur of a PMHS was used to measure tical boe thickess. The uembalmed PMHS was CT scaed ad kept froze. The femur was put i room temperature to thaw 12 hours prior to the experimet. Five cuttig plaes were defied i the femur shaft ad three more i the femur head, eck ad epicodyle, respectively, as show i Fig. 5a. The cuttig was completed followig the order from A to H usig a electric saw. After each cut, the femur samples were fixed to a clamp o the table ad the cross sectio was leveled before two photos were take from the distal ad proximal sides with a agle ruler (Fig. 5b ad Fig. 6). I additio, a 3D laser scaer was used to obtai the exteral surface of each cut femur sample. The scaed exteral surface was traslated ad rotated to match the CT image based o aatomic ladmarks (red roud solid dots) as show i Fig. 5a. At least three o colliear poits o each cuttig plae from the exteral surface were required to defie a plae for re orietig the cross sectio from the CT sca. I this way, the cuttig plaes i the real femur ca match the CT images. Poits where tical boe thickess was measured were marked i the photos ad CT images. Vertex ormal vectors at all measured poits were estimated usig a method described i [22]. I the photos, a caliper was used to measure the distace betwee the measurig poit ad the boudary where tical boe ad trabecular boe separated. I the femoral head ad eck regios, most of the boudaries were distiguishable o the cross sectio. I the femoral codyle, clear boudaries were ot always available ad therefore we oly reded the tical thickess at poits where a clear boudary was visible. The distace was the coverted to tical boe thickess i referece to the agle ruler. The tical boe thickess values at the respodig poits were also calculated usig a customised MATLAB code based o the CT images. I this study, 44 poits were selected i the photos ad CT images. The tex coefficiet K was determied through optimisatio to miimise the mea squared errors betwee the calculated thickess values ad measured oes. Additioally, 19 more measurig poits were selected to cross validate the coefficiet K. Fig. 5a. Cuttig plaes i the experimet. Fig. 5b. Cortical boe thickess measuremet. For a give poit P m, the local threshold respodig to its HU profile was determied by Equatio (3). Assume K K , where was a iteger ad 0,1000. Let T ad exp, m, T represet cal, m, thickess measured at the poit P m i the experimet ad from the CT sca, respectively. The calculatio error at poit P m with K could be deoted as, E m, Tcal, m, Texp, m, (4) For all possible tex coefficiets K, the mea squared errors betwee the measured ad calculated

6 thickess values were computed by Equatio (5), SS 1 M M m1 E 1 M 2 2 m, ( Tcal, m, Texp, m, ) M m1 (5) where SS is the mea squared error ad M 44, represetig the total umber of measured poits i this study. The K that miimised SS would be the tical coefficiet K. Parametric Femur ad Tibia Thickess Models Pricipal Compoet Aalysis was performed to fid out fewer, but sufficiet variables called pricipal compoets (PCs) that best explaied the variace i the origial thickess data set usig a built i MATLAB fuctio. All the pricipal compoets were orthogoal to each other ad formed a ew basis to describe the origial data i reduced dimesios. A regressio aalysis was the performed o the PCs with respect to age, BMI ad stature ad thus parametric femur ad tibia thickess models could be developed. III. RESULTS Cortical Boe Thickess Measuremet Fig. 6 shows that the respodig cuttig cross sectios i the experimet ad the CT image matched well. For each cross sectio, a poit was marked ad measured o the most aterior, posterior, medial ad lateral edge. Twelve more poits ad 19 additioal validatio poits were put where ecessary ad easily distiguishable. All measurig poits ad validatio poits were carefully checked to make sure that they were at the same locatio i the photos as i the CT slices. Three repeated measuremets were performed at each measurig poit usig a caliper. Table I lists some of the thickess results i differet femur regios. The percetage errors are show i the paretheses. Fig. 6. Femur cuttig cross sectio i the experimet ad the CT image. Left: cross sectio C; Right: cross sectio D. Blue dots: from the experimet; Red dots: from the CT image. Cortical Boe Thickess Calculatio For the global thresholdig method, the HU threshold was set from 300 to 1,000 with a iterval of 100. The mea squared errors betwee the calculated thickess values ad measured oes were also calculated for each HU threshold value. For the local thresholdig method, the tex coefficiet K was if all 44 measurig poits were icluded ad the miimised mea squared error was mm 2. The average estimated thickess based o CT

7 was 4.26 mm, while the average measured thickess was mm. The average thickess error was mm (0.685%) ad the mea squared error i the validatio was mm 2. However, the calculatio results showed a uderestimatio i the femur diaphysis where tex was thick ad a overestimatio i the femur epiphysis where tex was thi. It could also be derived from Equatio (3) that a larger K would lead to a larger HU threshold, which could cotribute to the uderestimatio of thickess i the femur diaphysis. We the proposed to specify two tex coefficiets, ad 0.522, for thi tex ad thick tex areas, respectively. These tex coefficiets were optimised separately. At this time, the mea squared error reduced to mm 2. The average thickess was mm from calculatio agaist mm from experimet. The average thickess error dropped to mm (0.4%) ad the mea squared error i the validatio was reduced to mm 2. These results suggested that K for femur ad tibia shafts was ad for femur ad tibia eds. Partial results of both calculatio methods are listed i Table I. Femur Regio epiphysis (head) epiphysis (eck) diaphysis (shaft) epiphysis (codyle) TABLE I CORTICAL BONE THICKNESS (IN MILLIMETERS) Local Thresholdig Method, Global Thresholdig Method K Measured Value ± (115.2%) 0.8( 18.0%) ± (25.0%) 0.9( 6.25%) ± (78.1%) 1.1( 27.4%) ± (238.7%) 1.6(50.5%) ± (4.7%) 2.7(22.9%) ± (54.2%) 1.4(2.8%) ± (60.6%) 1.1( 1.9%) ± ( 2.7%) 3.1(7.8%) ± ( 2.1%) 3.9(6.0%) ± ( 6.7%) 6.5( 3.7%) ± ( 3.4%) 9.2(5.7%) ± ( 14.4%) 6.4( 3.8%) ± ( 14.7%) 3.9( 4.9%) ± ( 6.9%) 7.8( 1.8%) ± (69.8%) 1.0( 15.1%) ± (5.8%) 0.7( 47.1%) ± (48.7%) 1.3( 7.9%) Parametric Femur ad Tibia Thickess Models I this study, parametric thickess models were established for femur ad tibia, respectively. Fifty six PCs were selected for the male femur model ad 34 for the female model. The selected PCs were able to accout for 99% of all the variace i each model. The coefficiet of determiatio R squared values were computed for each parametric model usig Equatio (6), 2 RSS R 1 (6) TSS where RSS is the sum of squared errors betwee the observed ad predicted thickess values, ad TSS is the sum of squared differeces betwee the average ad observed thickess values. The R squared values were ad for the male ad female femur thickess models, respectively. The R squared values were

8 0.186 ad for the male ad female tibia thickess models, respectively. The p values of the predictors o the first five PCs for each regressio model were summarised i Table II. The regressio results showed that age ad BMI were sigificat predictors for the femur thickess models while age was the oly sigificat characteristic for the tibia thickess models. Stature was excluded i the predictors because it did ot show sigificat effect o tical boe thickess distributio. TABLE II P VALUES OF PREDICTORS IN THE THICKNESS MODELS (* P<0.05) Model Predictor p value 1st PC 2d PC 3rd PC 4th PC 5th PC Male femur Age 0.048* 0.000* BMI 0.009* Female femur Age * 0.006* BMI * Male tibia Age 0.035* * 0.003* BMI Female tibia Age 0.001* * BMI IV. DISCUSSION BMD is the determiig factor that distiguishes tical boe ad trabecular boe, ad the HU value i CT scas is positively related to BMD. Sice boes are ot made of homogeeous materials, tical boes i differet body areas may sustai differet BMDs ad thus HUs. Studies [13,14,16] idicate that HU (maximum A value of the HU profile) may drop cosiderably i thi tex areas because of the resolutio limits ad blurrig effect. Therefore, thresholds that separate tical ad trabecular boe are supposed to vary with local BMDs/HUs i differet areas. Covetioal global thresholdig method fails to cosider such local effects. The 50% relative threshold method is robust ad effective whe tex is thick eough. However, if the tex is thi, a fixed ratio of 0.5 may overestimate the tical thickess. The ewly proposed local thresholdig method determies the thresholds based o the local backgroud ad maximum HUs, i which case the desity variaces are cosidered. The ratio is derived based o a PMHS experimet idepedet of model assumptio. I this study, two differet ratios were determied for thi ad thick tex regios, respectively. which ca overcome the limitatios of the 50% relative threshold method. Sice the profile of HU values distributio is obtaied i this method idepedet of pixel sizes, a tex thickess value ca be estimated eve if it is thier tha or close to the size of oe pixel as show i Fig. 7. Figure. 7 The local thresholdig method i thi tex area (femoral eck, pixel size = mm). I [18], accuracy levels of the 50% relative threshold method, the model fittig decovolutio method [16 17] ad the model based profile aalysis method [18 19] were reported ad compared usig the stadard Europea Forearm Phatoms. Whe the true thickess was 1 mm, the smallest percetage error usig these three methods was 152.2%, 19.3% ad 22.8%, respectively. The error decreased to 18.9%, 0.3% ad 0.3%,

9 respectively whe the true thickess became 2 mm. It should be oted that these error levels were from the best estimatios uder specific scaig coditios which usually could ot be met i the cliical CT scaig process. Geerally speakig, the local thresholdig method proposed i this study is more accurate tha the global thresholdig method ad the 50% relative threshold method i the literature. It may ot be as accurate as the model based methods i [16 19], but is still at a acceptable level. However, the accuracy of methods i refereces [16 19] was quite sesitive to the assumed tex BMD. A 20% icrease of the assumed tex BMD could lead to a icrease of estimatio error from +4.3% to 13.1% uder the same coditio [18]. I cotrast, the local thresholdig method was more robust as o assumed tex BMD was eeded. The complex model based methods maily focus o the measuremet of boe material desity or disease diagosis, such as osteoporosis. The regios of iterest are small local areas where fractures are proe to happe. I this study, we focused more o the FE modelig to provide better computatioal huma body models, thus the etire boe is of great cocer. Due to radiatio dose restrictio, resolutio of cliical CTs of the etire boe is iferior. Compared the image pixel sizes i this study (0.623 to mm) to that metioed i [16] (0.589 mm), the model based techiques may ot be robust i low resolutio cliical CTs. Time efficiecy is also importat whe it comes to modelig. It took a desktop PC aroud 5 mi to process thickess values for 17,000 locatios o the femoral eck aloe i [16] but less tha 1 mi to process 9,140 locatios o the etire femur i this study. Therefore, eve if some complex model based methods ca estimate tex thickess i sub millimetre level if coditio permits, the local thresholdig method proposed i this study that ca efficietly estimate thickess results at a acceptable accuracy level still has great potetials i the field. I this study, two differet tical coefficiets were recommeded for thi tex ad thick tex areas. I thi tex areas, the gap betwee HU ad A HU was smaller tha that i thick tex areas, but C HU was C similar i all areas. This preseted a dilemma, i which a lower K was expected for HU profiles i thick tex areas but this might overestimate the thickess i thi tex areas ad vice versa. I order to resolve this issue, thi tex ad thick tex areas were studied separately. Referece [22] used the similar local thresholdig method to quatify the tical boe thickess for huma ribs. The average measuremet thickess value from the PMHS was mm idicatig tex i huma ribs was very thi. The tex coefficiet was i their study which is close to the value of i this study. I thick tex areas, a recommeded threshold to accurately segmet the boe geometry was 49% of the differece of the desity betwee the adjacet tissues [13]. This percetage could be treated as the tex coefficiet K, which was agai close to the value of i this study. Eve though i the thi tex areas, the global thresholdig method was ot reliable, it could still provide acceptable results i the boe shaft areas with a properly selected threshold value. Followig the optimisatio procedure i this paper, the threshold value ca be set to 770. The mea squared error is mm 2 compared to mm 2 usig the local thresholdig method i the femur shaft area (cross sectios B to F). Oe of the major deficiecies of the global thresholdig method is that it caot guaratee o zero thickess values at all odes/poits i the model. If this happes, a arbitrary value is usually specified which ca itroduce obvious errors. The femur ad tibia thickess models did ot have high R squared values. It idicated that the variaces i femur ad tibia tical thickess are ot well accouted by the curret predictors. Therefore, more subject characteristics should be icluded as predictors i the regressio model to icrease the relatio. Boe related diseases, such as osteoporosis ad eatig habits, may have sigificat effects o tical boe thickess distributio. This study idicated that BMI played a sigificat role i the femur tical thickess distributio which agreed with the coclusio i [8]. Age was also foud to be a sigificat factor i this study which is ot surprisig. I [23], it was cocluded that the tical thickess reduced as age advaced for wome while tical thickess was similar at all ages for me. Cortex geerally becomes thier as healthy adults age due to the expasio of marrow area [24]. No results of tibia regressio models were give i [8], but this study idicated that BMI was ot a sigificat predictor i tibia tical thickess. Several limitatios existed i this study. First, oly oe PMHS was used to calibrate ad validate the tex coefficiet. More PMHS will be eeded to calibrate the tex coefficiet ad validate the proposed method o a larger scale. The sample size of female subjects was small, ad o female subjects aged from 30 to 40 were icluded i this study. Future work will iclude addig more female cliical CTs to the data set. However, the curret sample is at the same level as the previous study (62 male subjects ad 36 female subjects i [8]). I the

10 future, the established parametric exteral geometry models ad thickess models ca be itegrated as part of the parametric whole body huma body model. Future work may also iclude extedig the proposed method to other body regios. V. CONCLUSIONS This study proposed a ew local thresholdig method to accurately ad efficietly estimate tical boe thickess usig cliical CT scas ad a method to validate the thickess calculatio agaist experimetal results. This study also developed a parametric tical thickess model accoutig for sex, age, stature ad BMI effects for huma femur ad tibia. The models developed i this study ca serve as a statistical basis for buildig parametric FE huma models represetig a diverse populatio. VI. ACKNOWLEDGEMENT The authors would like to thak Ae Boifas ad Nichole Orto at the Uiversity of Michiga Trasportatio Research Istitute i the US for their great help ad support i the experimet of femur tical boe thickess measuremet. The authors would also like to thak Chia Scholarship Cousel for their fiacial support for this study. VII. REFERENCES [1] Mora S G, McGwi G Jr, Metzger J S, Aloso J E, Rue L W 3rd. Relatioship betwee age ad lower extremity fractures i frotal motor vehicle collisios. The Joural of Trauma, 2003, 54(2): [2] Kuppa, S, Fessahaie, O. A overview of kee thigh hip ijuries i frotal crashes i the Uited States. Proceedigs of the 18 th Iteratioal Techical Coferece o the Ehaced Safety of Vehicles, 2003, Nagoya, Japa. [3] Zimmerma, E A, Busse, B, Gludovatz, B, Ritchie, R O. O the stregth ad toughess of huma tical boe. 14 th Iteratioal Coferece o Fracture, 2017, Rhodes, Greece. [4] Zioupos P, Currey J D. Chages i the stiffess, stregth, ad toughess of huma tical boe with age. Boe, 1998, 22(1): [5] Shi X, Cao L, Reed M P, Rupp J D, Hu J. Effects of obesity o occupat resposes i frotal crashes: a simulatio aalysis usig huma body models. Computer Methods i Biomechaics ad Biomedical Egieerig, 2015, 18(12): [6] Wag Y, Cao L, Bai Z, Reed M P, Rupp J D, Hoff C N, Hu J. A parametric ribcage geometry model accoutig for variatios amog the adult populatio. Joural of Biomechaics, 2016, 49(13): [7] Shi X, Cao L, Reed M P, Rupp J D, Hoff C N, Hu J. A statistical huma rib cage geometry model accoutig for variatios by age, sex, stature ad body mass idex. Joural of Biomechaics, 2014, 47(10): [8] Klei K F, Hu J, Reed M P, Hoff C N, Rupp J D. Developmet ad validatio of statistical models of femur geometry for use with parametric fiite elemet models. Aals of Biomedical Egieerig, 2015, 43(10): [9] Hu, J, Fata, A, Neal, M O, Reed, M P, Wag, J. Vehicle crash simulatios with morphed GHBMC huma models of differet stature, BMI, ad age. Proceedigs of 4 th Iteratioal Digital Huma Modelig Coferece, 2016, Motreal, Caada. [10] Utaroiu C D, Yue N, Shi J. A fiite elemet model of the lower limb for simulatig automotive impacts. Aals of Biomedical Egieerig, 2013, 41(3): [11] Takahashi, Y, Kikuchi, Y, Mori, F, Koosu, A. Advaced FE lower limb model for pedestrias. Proceedigs of the 18t h Iteratioal Techical Coferece o the Ehaced Safety of Vehicles, 2003, Nagoya, Japa. [12] Iwammoto, M, Tamura, A, et al. Developmet of a fiite elemet model of the huma lower extremity for aalyses of automotive crash ijuries. SAE Techical Paper, 2000, Detroit, Michiga, USA. [13] Hagarter T N. Thresholdig techique for accurate aalysis of desity ad geometry i QCT, pqct ad uct images. Joural of Musculoskelet Neuroal Iteract, 2007, 7(1):9 16. [14] Prevrhal S, Egelke K, Kaleder W A. Accuracy limits for the determiatio of tical width ad desity: the ifluece of object size ad CT imagig parameters. Physics i Medicie & Biology, 1999, 44(3): [15] Prevrhal S, Fox J C, Shepherd J A, Geat H K. Accuracy of CT based thickess measuremet of thi structures: Modelig of limited spatial resolutio i all three dimesios. Medical Physics, 2003, 30(1):

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