Bone 54 (2013) 133–140

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Bone

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Original Full Length Article

Computational identification and quantification of trabecularmicroarchitecture classes by 3-D texture analysis-based clustering☆

Alexander Valentinitsch a,c,⁎, JaninaM. Patsch a,c, Andrew J. Burghardt c, ThomasM. Link c, SharmilaMajumdar c,Lukas Fischer a, Claudia Schueller-Weidekamm b, Heinrich Resch d, Franz Kainberger a,b, Georg Langs a

a Computational Image Analysis and Radiology Lab, Department of Radiology, Medical University of Vienna, Vienna, Austriab Division of Musculoskeletal Radiology and Neuroradiology, Department of Radiology, Medical University of Vienna, Vienna, Austriac Musculoskeletal Quantitative Imaging Research Group, Department of Radiology & Biomedical Imaging, University of California San Francisco, San Francisco, CA, USAd Medical Department II, St. Vincent Hospital Vienna, Vienna, Austria

Abbreviations: HR-pQCT,High-resolution peripheral qphy; MUW, Medical University of Vienna; UCSF, UniversTb.ROI, Trabecular region of interest; TMAC, Trabecular mcoefficient; GLCM, Gray level co-occurrence matrix; PMGMM, Gaussian mixture model; PE, Precision error; ICC, In☆ Funding: NIH RC1 AR058405; NIH R01AR060700; NIHFund (FWF) Erwin-Schrödinger Grant J-3079; Philips Clinic⁎ Corresponding author at: Computational ImageAnalysi

of Radiology, Medical University of Vienna, Währinger GürtFax: +43 1 40 400 4898.

E-mail addresses: alexander.valentinitsch@meduniwjanina.patsch@ucsf.edu (J.M. Patsch), andrew.burghardtthomas.link@ucsf.edu (T.M. Link), sharmila.majumdar@lukas.a.fischer@meduniwien.ac.at (L. Fischer),claudia.schueller-weidekamm@meduniwien.ac.at (C. Scheinrich.resch@bhs.at (H. Resch), franz.kainberger@medgeorg.langs@meduniwien.ac.at (G. Langs).

8756-3282/$ – see front matter © 2013 Elsevier Inc. Allhttp://dx.doi.org/10.1016/j.bone.2012.12.047

a b s t r a c t

a r t i c l e i n f o

Article history:Received 13 June 2012Revised 20 December 2012Accepted 22 December 2012Available online 10 January 2013

Edited by: Harry Genant

Keywords:HR-pQCT3D-Texture analysisUnsupervised clusteringTrabecular microarchitecture classes

High resolution peripheral quantitative computed tomography (HR-pQCT) permits the non-invasive assess-ment of cortical and trabecular bone density, geometry, and microarchitecture. Although researchers havedeveloped various post-processing algorithms to quantify HR-pQCT image properties, few of these techniquescapture image features beyond global structure-based metrics. While 3D-texture analysis is a key approachin computer vision, it has been utilized only infrequently in HR-pQCT research. Motivated by high isotropicspatial resolution and the information density provided by HR-pQCT scans, we have developed and evaluateda post-processing algorithm that quantifies microarchitecture characteristics via texture features in HR-pQCTscans. During a training phase in which clustering was applied to texture features extracted from each voxel oftrabecular bone, three distinct clusters, or trabecular microarchitecture classes (TMACs) were identified. TheseTMACs represent trabecular bone regions with common texture characteristics. The TMACs were then used toautomatically segment the voxels of new data into three regions corresponding to the trained cluster features.Regional trabecular bone texture was described by the histogram of relative trabecular bone volume coveredby each cluster. We evaluated the intra-scanner and inter-scanner reproducibility by assessing the precisionerrors (PE), intra class correlation coefficients (ICC) and Dice coefficients (DC) of the method on 14 ultradistalradius samples scanned on two HR-pQCT systems. DC showed good reproducibility in intra-scanner set-upwith a mean of 0.870±0.027 (no unit). Even in the inter-scanner set-up the ICC showed high reproducibility,ranging from 0.814 to 0.964. In a preliminary clinical test application, the TMAC histograms appear to be agood indicator, when differentiating between postmenopausal women with (n=18) and without (n=18)prevalent fragility fractures. In conclusion, we could demonstrate that 3D-texture analysis and feature cluster-ing seems to be a promising new HR-pQCT post-processing tool with good reproducibility, even between twodifferent scanners.

© 2013 Elsevier Inc. All rights reserved.

uantitative computed tomogra-ity of California, San Francisco;icroarchitecture class; DC, DiceMA, Polymethylmethacrylate;traclass correlation coefficient.RO1AG17762; Austrian Scienceal Research; EU FP7 KHRESMOI.s andRadiology Lab, Departmentel 18–20, A-1090Wien, Austria.

ien.ac.at (A. Valentinitsch),@ucsf.edu (A.J. Burghardt),ucsf.edu (S. Majumdar),

hueller-Weidekamm),uniwien.ac.at (F. Kainberger),

rights reserved.

Introduction

Osteoporosis is a metabolic bone disease characterized by boneloss resulting in high fracture susceptibility due to reduced bonemass, bone density, and bone quality. Bone quality refers to surrogateparameters such as bone microarchitecture, turnover, damage accu-mulation, and mineralization, that contribute to bone strength andfracture risk independently of bone mass [1]. In the last two decades,high-resolution magnetic resonance imaging (HR-MRI) and high-resolution peripheral quantitative computed tomography (HR-pQCT)have emerged as non-invasive research techniques that allow thequantification of bone microarchitecture without bone biopsy [2].The non-invasive investigation of bone microarchitecture has providedsubstantial insights to gender-, age- [3–5] and compartment-specificbone morphology, in health, various forms of osteoporosis [6–8], and

134 A. Valentinitsch et al. / Bone 54 (2013) 133–140

othermetabolic bone diseases [9]. In particular, HR-pQCT has been usedto identify novel discriminative characteristics between patients withprevalent osteoporotic fractures and non-fracture controls that exhibitalmost similar areal bone mineral density (aBMD) by dual-energyX-ray-absorptiometry (DXA) [6,10].

Along with the increasing use of HR-pQCT in clinical research,novel image processing techniques have been developed [4,11–14].Fixed quadrant models have been used to identify regional variationsin bonemicroarchitecture [14] and to capture subtle treatment effectsthat remained undetected by global standard evaluations [15]. In con-trast to this method, which subdivides scan regions into quadrants,three-dimensional (3D) texture analysis of HR-pQCT data is able torecognize morphological pattern groups without the definition ofpreset geometric regions of interest. 3D texture analysis thereforehas the potential to contribute unique quantitative information onthe spatial distribution of bone mass that is not captured by assess-ment of bone density or structure metrics. Two-dimensional (2D)texture analysis has been previously applied to conventional radio-graphs and CT scans and has been able to distinguish patients withprevalent osteoporotic fractures from non-fracture controls [16,17].In bone research, fractal analysis has been the most widely usedtexture-analysis technique [18,19] and has shown a strong relationshipwith histomorphometry and measures of bone strength [20,21]. Inradiographs of the spine, the proximal femur and the calcaneus, fractalanalysis yielded good discrimination between patients with and with-out prevalent fragility fractures [22,23]. Another texture-based quanti-fication method is the trabecular bone score (TBS) which is applied toDXA-derived projection images of the spine and relates to some extentto μCT-based microstructure measures [24–26]. Recently, Bachettaet al. [27] applied 2D texture analysis to radial and tibial radiographsand found significant associations with trabecular microarchitectureassessed byHR-pQCT. Fouque-Aubert et al. [28] used a similar approachto correlate 2D texture of hand radiographs with local 3D bone micro-structure in patients with rheumatoid arthritis. To our knowledge, 3Dtexture analysis, which can deliver more spatial image informationthan 2D techniques, has not been applied to HR-pQCT scans. Therefore,contributions of our study include 1) the introduction of a novel post-processing technique of HR-pQCT data based on 3D-texture-analysisand clustering, 2) the validation of our technique by assessment ofsingle-site, short-term, and cross-site reproducibility in cadaveric spec-imens, and 3) a preliminary application of the technique to a small set ofHR-pQCT scans of postmenopausal women with and without fragilityfractures.

Materials and methods

Samples, HR-pQCT acquisition and standard evaluation

Fourteen human distal radius sections were acquired from anon-profit, NIH-funded American tissue bank (NDRI, Philadelphia,Pennsylvania) and embedded into polymethylmethacrylate (PMMA)to construct structure realistic phantoms at theDepartment of Radiologyof the University of California, San Francisco (UCSF) [29]. The bonespecimens were approximately 1-cm thick and were obtained fromthe anatomical site consistentwith the standard in vivo HR-pQCT acqui-sition protocol (i.e. 9.5 mm proximal to the distal radius endplate).Using XtremeCT (Scanco Medical AG, Brüttisellen, Switzerland), eachsection was scanned with a nominal isotropic voxel size of 82 μm. TheX-ray source potential was 60 kVp with a current of 900 μA. A two-dimensional detector containing 3072×256 CCD elements was usedto acquire 750 projections at a 200 ms integration time per projection.To evaluate short-term reproducibility, all specimens were scannedthree times, with repositioning performed before each acquisition.For cross-site reproducibility experiments, an additional scan wasacquired, after which the embedded samples were shipped to theMedical University of Vienna and scanned using the same imaging

protocol. Densitometric and morphometric standard evaluationswere performed according to Laib et al. [11]. We calculated trabecu-lar bone volume fraction (BV/TV) from the volumetric BMD of thetrabecular compartment (Tb.BMD) using the assumption that com-pact bone has a matrix mineral density of 1200 mg HA/cm3. Addi-tionally, trabecular BMD was calculated for a peripheral regionadjacent to the cortex (pTb.BMD) and central trabecular region(mTb.BMD) [30]. From the binary image, trabecular number (Tb.N)was measured using the direct 3D distance transform (DT) approach[31,32]. Based on the densitometric BV/TV and direct Tb.N, trabecu-lar thickness (Tb.Th) and trabecular separation (Tb.Sp) were derivedusing traditional plate model assumptions. Cortical thickness (Ct.Th)was defined as the mean cortical volume divided by outer bordersurface.

Cortex segmentation and definition of the trabecular region of interest

Cortical and trabecular bone compartments were segmented byan in-house threshold-independent segmentation tool (TIST) [33].In order to avoid inclusion of the subcortical compartment in ourcalculations we peeled 8 voxels from the extracted trabecular mask.We refer to the mask volume after peeling (i.e. our defined trabecularregion of interest — Tb.ROI) as the total volume (TV). In this manu-script we report microarchitectural properties of the Tb.ROI basedon texture analysis.

Image registration and normalization

In order to assess short-term (i.e. intra-scanner) and cross-site(i.e. inter-scanner) reproducibility, all scan data (USCF and MUW)for each sample were co-registered. We used a standard monomodalintensity-based medical image registration algorithm that minimizesthe sum of squared intensity differences (SSD) between the registeredvolume images [34]. The transformation applied to register was rigiddue to our rigid object (i.e. bone). The software was implemented inMATLAB (Mathworks, Natick, MA). To eliminate scanner site detectordifferences, all imageswere converted from their original grayscale at-tenuation values to equivalent hydroxyapatite densities (mgHA/ccm)using a linear relationship derived from a calibration phantom. Thecalibration phantom contained five different cylinders with varyingconcentrations of HA-resin (0, 100, 200, 400, 800 mgHA/ccm). Thedynamic range of the imageswas−500 mgHA/ccm to 1500 mgHA/ccm.

Feature extraction of trabecular bone

The three-dimensional gray scale image properties of HR-pQCTvolumes were evaluated in order to quantify microarchitecturalcharacteristics in the defined trabecular region of interest (Tb.ROI)(i.e. the peeled trabecular mask). We refer to these characteristicsas texture patterns. For each volume unit (voxel) a local texture de-scriptor was calculated based on the surrounding 15×15×15 voxels.Voxels outside the Tb.ROI were not included in any neighborhoodcalculations. We used two methods for feature calculation: 1. Three-dimensional gray level co-occurrence matrix (3D GLCM) [35–37],2. partial derivatives [38].

A GLCM extracts statistical image information regarding the distri-bution of the differences in intensity values between voxels separatedby a certain distance and/or direction. For the 3D GLCM 13 differentpossible directions were extracted at three different scales definedby the radius of the neighboring voxels (radius: 1, 2, 4 voxels). Linearbinning was applied in order to map 12-bit gray-level intensities to8 gray levels. The calculation resulted in rotation invariant featuresby averaging over all directions: energy, entropy, correlation, con-trast, variance, sum average, inertia, cluster shade, cluster promi-nence, homogeneity, maximal probability and inverse variance [39].

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The partial derivatives of an image volume in structure tensor(first order derivatives) and Hessian matrix form (second order deriva-tives) capture local structural image properties, such as structureness,tubularity, orflatness. Features extracted from the partial derivatives in-cluded the mean and standard deviation of two geometric ratios of thederived eigenvalues (i.e. tubularity and flatness) aswell as the Euclidiannorm of the eigenvalues as structureness [40].

Computational identification of trabecular bone classes

Feature extraction resulted in a 102-dimensional feature vectorthat described the local texture pattern for each voxel. Unsupervisedclustering [41] was performed in this feature space, to identify trabec-ular bone characteristics that recur within a majority of the study data(i.e. phantom or subject cohort). Clusters were based on a Gaussianmixture model (GMM) [42]. The GMM considers each cluster as amultivariate Gaussian distribution in the feature space. Clusters corre-spond to sets of voxels that exhibit similar texture patterns. In thisman-uscript, we refer to such clusters as Trabecular microarchitecture Classes(TMACs). The stability index of the clustering [43] was used to choosethe optimal number of TMAC in the data set. This index is based on aninformation theoretic approach (mutual information) and assesses thevariation of the clustering result due to the different clustering parti-tions obtained from different data sub-samples. In the validation exper-iment we refer to the computational identification of TMAC as training.Training resulted in an unsupervised partitioning of the feature spaceinto three different texture clusters, whichwas the optimal number de-termined by the stability index algorithm [43]. The number of clusters(k) was determined by using 10 repetitions of two-fold cross validationto find the minimum standard deviation of the mutual information fordifferent numbers of clusters (i.e. k=2–7). Each repetition was usedon a different set of 4000 voxels randomly chosen from all availabledata (i.e. specimens). Because each cluster reflects unique patterns ofmicroarchitecture and texture, we decided to use the term trabecularmicroarchitecture classes (TMACs) to refer to the individual clusters(Fig. 1).

Fig. 1. Representatives of the cluster centroids: The centroids for each texture classof the learned GMM are represented as the three dimensional texture patches witha cubic neighborhood of 15×15×15 voxels. Each voxel in a cubic neighborhood isassigned to one of the three classes/clusters, which has the highest probability accordingto the GMM. Each centroid represents a different 3D microarchitectural texture pattern(i.e. trabecular microarchitecture class — TMAC).

Calculating the TMAC distribution in new cases

We assumed that the TMACs represented the variability of trabec-ular bone patterns present in the study training population, and couldbe further generalized to new cases. For analysis of new cases, theclustering algorithm was applied as follows: Each voxel in theTb.ROI was scored with regard to its a posteriori probability definedwith the Gaussian mixture distribution of belonging to either of thethree classes, and class assignment was defined by the highest prob-ability score. A histogram of class membership frequencies served as aglobal descriptor of the Tb.ROI. From the histogram of class member-ship frequencies we derived the cluster volume (CL.V) and the clustervolume fraction (CL.V/TV) per TMAC. In the experimental validationwe refer to this step as testing. Note that in each run of these cross-validation experiments (see Evaluation of single-site, short-term,and cross-site reproducibility section) the training data set used forTMAC clustering and the test data used for mapping TMACs in anew case are disjoint.

Evaluation of single-site, short-term, and cross-site reproducibility

Validation of the class reproducibility was performed using threeseparate experiments. For each experiment the Dice coefficient (DC),precision error (PE), and intraclass correlation coefficient (ICC) werecalculated in order to quantify the spatial overlap (i.e. agreement) ofTMACs calculated for repeated scans. A Dice coefficient value of zeroindicates no spatial overlap of the trabecular classes in the Tb.ROI,whereas a value of 1 indicates complete overlap.

Single-site reproducibilityTo validate the TMAC single-site reproducibility and generaliza-

tion across subjects, two leave-one-out cross-validation experimentsfor all 14 samples on two different scanners (Medical University ofVienna [MUW]; University of California, San Francisco [UCSF]) wereperformed. For each scanner, unsupervised training was performedon 13 samples, and the Tb.ROI of the remaining sample was classifiedaccording to the trained TMAC (testing). For each of the three TMACswe report overlap (DC) of the cluster region when the sample was inthe test set (i.e., when training was performed without the sample),and the 13 occasions when it was part of the training set.

Short-term reproducibilityEach specimen was scanned three times (i.e. intra-scanner set-up),

with the first scan from each series of three used as a reference scan(RS) for training the TMAC. The remaining 2 scans from each serieswere then classified according to the TMAC obtained from the trainingstep. We report the mean overlap (DC) of the trabecular classes be-tween the RS and the two repeated scans. PE and ICC of all three scansare also assessed.

Cross-site reproducibilityTo validate the cross-site (i.e. inter scanner) reproducibility

we evaluated, co-registered images obtained at both sites (MedicalUniversity of Vienna; University of California, San Francisco) wereevaluated. In a leave-one-out cross validation we performed trainingon images from one site (e.g. samples 2–14 from MUW), but theimage used for testing came from the other site (e.g., sample 1 fromUCSF), and vice versa (e.g. samples 2–14 from UCSF for training andsample 1 fromMUW for testing). To compare the cross-site reproduc-ibility, for each sample we calculated DC, PE and ICC of the TMAC cal-culated during testing at the two different sites.

Patients

In the second part of the evaluation we applied the proposed clus-tering technique on a small clinical data set. The data included HR-

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pQCT scans and clinical data of postmenopausal women with andwithout fragility fractures fromanongoingNIH-funded studyperformedat theUniversity of California San Francisco (NIHRC1AR058405; Clinicaltrials identifier NCT00703417). Inclusion criteria were defined as post-menopausal status, age between 50 and 75 years, body mass index(BMI) 18–37 kg/m2, and the ability to walk without assistance. Fragilityfractures were defined as fractures having occurred after a low-impacttrauma (e.g. a fall from standing height). Fractures were required tobe postmenopausal and documented by previous radiographs. In addi-tion, vertebral fractures were classified according to using a semi-quantitative technique described by Genant et al. [44]. Exclusion criteriafor both groupswere juvenile or premenopausal idiopathic osteoporosis,a history of severe neuropathic disease, recent history of immobilization(>3 months), hyperparathyroidism, hyperthyroidism, immobilization,alcoholism, chronic drug use, chronic gastrointestinal disease, significantchronic renal or hepatic impairment, unstable cardiovascular disease,uncontrolled hypertension, chronic treatment with antacids, estrogen,rosiglitazone, pioglitazone, adrenal or anabolic steroids, anticonvulsants,anticoagulants, pharmacological doses of vitamin A supplements,fluorides, bisphosphonates, calcitonin, and/or tamoxifen. In addition tobasic patient demographics, bonemineral density (BMD)measurementsby Dual-Enerergy X-ray Absorptiometry (DXA; hip, spine, and radius;Prodigy, GE/Lunar, Milwaukee, WI, USA), were collected as a part ofeach subject's exam. The study was approved by the Committee ofHuman Research of the University of California, San Francisco. Allpatients gave written informed consent before participation.

HR-pQCT acquisition (in vivo) and standard image analysis

HR-pQCT scans (XtremeCT, Scanco Medical AG, Brüttisellen,Switzerland) of the ultradistal radius were used. All scans were ac-quired according to the standard in vivo protocol [3,6]. Unless thesubject reported a local fracture history, the non-dominant radiuswas imaged. Acquisition settings were 60 kVp, 900 μA, and 100 msintegration time. The 126 mm field of view (FOV) was reconstructedacross a 1536×1536 matrix, giving an isotropic nominal resolutionof 82 μm voxels. All scans were visually graded with regard to mo-tion artifacts. Grade five scans were excluded from subsequentimage analysis [45]. The same standard densitometric and micro-structural indices were automatically calculated as described forbone specimen in the previous section (see Samples, HR-pQCT acqui-sition and standard evaluation section) [11].

Table 1Summary of standard protocol microstructural measurements of HR-pQCT imagesbetween of the different scanner sites (UCSF, MUW) of the sample data.

Parameters Units Mean SD

Age [years] 76.4 8.6BMD [mg HA/ccm] 332.0 74.3Tb.BMD [mg HA/ccm] 215.7 55.2pTb.BMD [mg HA/ccm] 259.1 52.5mTb.BMD [mg HA/ccm] 185.7 59.5Ct.BMD [mg HA/ccm] 788.2 133.3Ct.Th [mm] 0.656 0.302Ct.Ar [mm2] 48.9 22.6Tb.Ar [mm2] 266.6 108.0BV/TV [1] 0.180 0.046Tb.N [1/mm] 1.704 0.416Tb.Th [mm] 0.106 0.012Tb.Sp [mm] 0.533 0.233Tb.Sp.SD [mm] 0.271 0.177

In vivo clustering of trabecular bone microarchitecture

This experiment was designed to assess whether the TMAC his-togram is informative with regard to fracture vs. non-fracture. We in-cluded the entire patient data set (n=36; Fx: n=18, Non-Fx: n=18)for training a general GMM (i.e. computational identification ofTMACs in our in-vivo cohort). Clustering was performed to identifythree TMAC (i.e. class memberships) in the in-vivo data (consistentwith previous experiments described in Feature extraction of trabecularbone to Evaluation of single-site, short-term, and cross-site reproducibil-ity sections). Per patient, absolute and relative TMAC volumes (CL.V;CL.V/TV) were quantified.

To describe cluster-specific bone microarchitecture within thethree texture-clusters, we imported the binary cluster masks to theVMS workstation and assessed cluster-specific morphometry by IPL.The same analytical step was performed for the entire Tb.ROI. Giventheir broad use in HR-pQCT image analysis, trabecular bone volumefraction (BV/TV), trabecular number (Tb.N), trabecular thickness(Tb.Th), trabecular separation (Tb.Sp), and the standard deviation ofthe trabecular separation (Tb.Sp.SD) were used to describe cluster-specific morphometry [11,46].

Statistics

General reproducibilitywas tested by leave-one-out cross-validation.In each iteration of the cross-validation, one sample was excluded fromthe training set, and was used as a testing sample. Overlap of cluster re-gions identified when a sample was part of the training set (i.e. includedin training), and when the same sample was part of the testing set(i.e. not included in the training) were quantified with dice coeffi-cients (DC) between each respective TMAC volume.

In addition, we reported precision errors (PE), which are morecommon to describe intra- and inter-scanner reproducibility. Forcluster volume fractions precision errors (PE) were expressed inabsolute values (PESD) and as root mean square coefficient of varia-tion (PE%SD) [47]. Moreover, we calculated the intra-class correlationcoefficient (ICC) with a two-way mixed model [48]. For the statisticalcomparison of class-specificmorphometric properties, we used one-wayANOVAmodelswith subsequent Bonferroni correction. A Student's t-testwas used to compare CL.V/TV per TMAC between fracture and non-fracture patients. In addition, we applied two different multivariatediscrimination methods to the clinical data set: On one hand, linear dis-criminant analysis (LDA) [49] was performed using combined pairs ofCL.V/TV features. On the other hand, naive Bayes classification with sin-gle Gaussians and diagonal covariance matrix [50] was performed usingall three CL.V/TV features.

Results

Sample characteristics

The reproducibility experiment included 14 samples with an agerange from 60 to 88 years and an average of 76.4 years (male:72.9 years, female: 80.0 years). The male to female ratio was 1:1.The mean values of the standard bone morphometry parametersderived from HR-pQCT imaging of the different scanner sites arepresented in Table 1.

Evaluation of reproducibility

Table 2 shows the performance evaluation of the trabecular boneclasses for both scanners separately (single-site: MUW; UCSF). TheDice coefficient (DC) between corresponding trabecular classes iden-tified in repeated measurements after unsupervised learning rangedfrom 0.922±0.017 to 0.977±0.007 (no unit). The mean overlap ofthe short-term reproducibility experiment was 0.870±0.027 (DC,no unit). For the cross-site experiment we reported an overlap of0.812±0.042 (DC, no unit). Mean short-term and cross-site results(i.e. intra- and inter-scanner reproducibility) are presented in Fig. 2.

Table 2Single-site reproducibility. The unsupervised learning is evaluated with a leave-one-out cross-validation for both sites (MUW, UCSF) by Dice coefficients for each trabecularmicroarchitecture class (TMAC) based on phantom scans.

MUW UCSF

Parameters Units mean SD mean SD

Overall [1] 0.974 0.007 0.972 0.007TMAC 1 (red) [1] 0.977 0.007 0.975 0.007TMAC 2 (green) [1] 0.946 0.020 0.922 0.017TMAC 3 (blue) [1] 0.973 0.012 0.971 0.011

Table 3Precision errors, expressed as absolute values (PESD), root mean square coefficient ofvariation (PW%CV), and interclass correlation coefficient (ICC) per cluster. Individualoverlap is expressed as dice coefficient (DC). Note that the two studies represent slightlydifferent sections of the bone, and thus the TMAC distribution is only consistent withineach study.

Cluster volume faction (CL.V/TV)

Parameters TMAC 1 (red) TMAC 2 (green) TMAC 3 (blue)

Intra-scannerMean 0.285 0.379 0.336PESD 0.024 0.026 0.013PE%CV 5.76 12.19 6.24ICC 0.881 0.969 0.995DC 0.870 0.775 0.861

Inter-scannerMean 0.390 0.270 0.339PESD 0.047 0.036 0.026PE%CV 11.68 11.69 12.84ICC 0.849 0.814 0.964

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Cluster-specific mean values, PESD, PE%CV, ICC, and DC are given inTable 3. ICC showed high reproducibility of both (e.g. intra- and interscanner) measurements, ranging from 0.881 to 0.995. PE%CV washigher in the intra scanner reproducibility measurements, except inTMAC 2 (PE%CV: 12.19%).

DC 0.800 0.754 0.796

Table 4Clinical patient characteristic with areal BMD measurements and T-scores, and HR-pQCTstandard parameters. Data are expressedwithmean and standard deviation (SD) patientswith fractures (Fx) and controls (Non-Fx).

Non-Fx Fx

Parameters Units mean SD mean SD

Age [years] 58.9 4.7 64.9b 5.9BMI [kg/m2] 26.2 4.8 25.3 3.5

Subject characteristics

Patient characteristics and DXA results are given in Table 4. Onaverage, fracture cases were significantly older than controls (p=0.002). Body mass index (BMI) was similar between the two groups.In the control group there were thirteen Caucasians (72%), fourAsians (22%), one African-American woman (6%). 89% of controlswere Non-Hispanic (n=16), and 11% were Hispanic (n=2). Thefracture group was composed of 16 Caucasians (89%) and 2 Asians(11%), with one patient being Hispanic (6%) and 17 (94%) Non-Hispanic. In 18 fracture patients there were 20 prevalent low impactfractures involving the spine (n=4), ankle (n=8), foot (n=3),elbow (n=1), finger (n=1), hip (n=1), humerus (n=1), and pelvis(n=1). Two patients had more than one postmenopausal fracture.62% of fracture cases reported a positive family history of osteo-porosis, 11% of fracture patients had parents with a history of a hipfracture. In the control group, one subject had a history of a postmen-opausal ankle fracture following moderate impact trauma. 28% ofcontrols reported a positive family history of osteoporosis, 17% ofcontrols stated that either of their parents had sustained a hip frac-ture. At the lumbar spine, fracture patients had osteopenic and signif-icantly lower areal bone mineral density (aBMD; −14.6%; p=0.002)than healthy controls that exhibited normal mean T-scores at thisscan site. At the ultradistal radius and 1/3 radius, the mean T-scoreswere osteopenic in fractures and controls and did not show signifi-cant group differences.

Fig. 2. Visualization of short-term and cross-site reproducibility of relative class/clustervolumes after unsupervised learning.

HR-pQCT standard evaluations

Visual inspection of image quality was performed in all patientsand yielded the following motion grades: Grade 1: 11%, Grade 2:61%, Grade 3: 17%, Grade 4: 11%. HR-pQCT standard evaluations indi-cated significantly lower cortical BMD (Ct.BMD; −5.8%, p=0.044)and lower Tb.Th (Tb.Th; −10.1%; p=0.035) in fracture cases. Theremaining geometric, densitometric, and morphometric indices weresimilar between the two groups (Table 4).

Trabecular bone clustering in postmenopausal women with and withoutprevalent fragility fractures

All patients exhibited each of the three trabecular bone classes.TMAC-specific morphometry is reported in Fig. 3. In line with visual

DXAaBMD [g/cm2] 1.149 0.195 0.981b 0.156(spine L1–L4) [T-score] −0.3 1.6 −1.5a 1.3aBMD [g/cm2] 0.640 0.083 0.606 0.095(radius 1/3) [T-score] −1.1 1.1 −1.5 1.3aBMD [g/cm2] 0.335 0.066 0.322 0.084(ultradistal) [T-score] −1.2 1.8 −1.5 2.3

HR-pQCTBMD [mg HA/ccm] 282.7 64.9 255.1 52.9Tb.BMD [mg HA/ccm] 146.2 43.0 133.4 29.3pTb.BMD [mg HA/ccm] 201.5 40.0 191.1 32.8mTb.BMD [mg HA/ccm] 107.9 46.1 93.5 29.1Ct.BMD [mg HA/ccm] 826.5 64.0 778.2a 73.9Ct.Th [mm] 0.644 0.178 0.559 0.182Ct.Ar [mm2] 44.5 11.5 39.2 12.4Tb.Ar [mm2] 215.8 51.3 217.8 39.3BV/TV [1] 0.122 0.035 0.112 0.025Tb.N [1/mm] 1.761 0.402 1.771 0.244Tb.Th [mm] 0.069 0.012 0.062a 0.007Tb.Sp [mm] 0.536 0.183 0.515 0.095Tb.Sp.SD [mm] 0.284 0.281 0.242 0.078

Significant difference in mean values with a pb0.05: b pb0.01 using a Student's t-Test.

Fig. 3. Class/cluster specific morphometry. Data are expressed as mean and SD. Letters denote significance of multi comparisons between trabecular microarchitecture classes(a TMAC 1 vs. TMAC 2; b TMAC 1 vs. TMAC 3; c TMAC 2 vs. TMAC 3 with pb0.05).

138 A. Valentinitsch et al. / Bone 54 (2013) 133–140

inspection, trabecular bone class 1 (TMAC 1 — red) could be seento represent a region of dense, thick, and homogenous trabeculae(Fig. 3). On the other hand, TMAC 3 (blue) represented the otherend of the morphometric spectrum and displayed the highest trabec-ular heterogeneity and the lowest trabecular density, number, andthickness (BV/TV: −67.3%; Tb.N: −26.9%; Tb.Th: −58.4% versusTMAC 1). Although only indirectly indicated by low regional bonevolume, TMAC 3 (blue) corresponded to skeletal regions that ex-hibited a local shift from bone towards bone marrow. TMAC 2(green) represented regions of intermediate trabecular density andthickness but relatively high number and homogeneity of trabeculae.There was a significant difference in mean cluster volume fraction(CL.V/TV) of TMAC 1 (red) between postmenopausal women withand without prevalent fractures (0.272±0.015 versus 0.235±0.015;p=0.046) (Fig. 4). Fracture patients displayed a numerical but insignif-icant trend towards larger cluster volume fractions for TMAC 3. ForTMAC 2, there were no significant differences between the two meancluster volume fractions (p=0.560) (Fig. 3). Multivariate linear dis-criminant analysis with pairs of TMAC, achieved correct clinical groupassignment in 63.9%. A naive Bayesian classification based on the fullTMAC histograms yielded correct classification of 67% of patients withregard to fracture/non-fracture status in the leave-one-out cross valida-tion. Using only DXA, correct discrimination ranged from 44.5% to61.1%, depending on the measurement region (ultradistal (UD) radius:44.5%; radius 1/3 region: 52.8%; lumbar spine 1–4 (L1–L4): 61.1%).

Fig. 4. Cluster volume fractions (CL.V/TV) in woman with and without prevalent fragilityfractures. Error bars showstandarderror inmeasurements. The star (*) indicates statisticalsignificance between the two groups (Non-Fx versus Fx).

Discussion

In this study we have demonstrated that clustering of trabecularbone by 3D-texture analysis is a feasible and reproducible post-processing option for HR-pQCT data. Applying the technique toultradistal radius scans of postmenopausal women with and withoutprevalent fragility fractures we found that fracture patients displayeda significantly smaller “high quality” cluster volume (TMAC 1) thannon-fracture controls. Vice versa, fracture cases had a larger low qual-ity cluster volume (TMAC 3), although the differences did not reachstatistical significance.

In our approach, the identification of microarchitectural patternswas data-driven. Avoiding the need for a priori pattern definitionand segmentation, we automatically obtained microstructural 3Dpatterns from the isotropic HR-pQCT scans. The optimal number ofclusters was determined based on the computational stability indexintroduced by Pascual [43] and resulted in three clusters (TMACs).The appropriate and automatic choice of the number of clusterswith regard to the study population is a crucial step in the develop-ment of clustering algorithms, as it determines variability, and repro-ducibility. However, in clustering it is possible that with largerpopulations more clusters (e.g., sub-classes), for which stable differ-entiation is possible, will emerge. In general, data driven approachesto texture pattern identification have several advantages over a prioripattern definitions including optimal yield in information extractionas well as high class stability in repeated runs (Fig. 2).

The single-site reproducibility experiment demonstrated thatthe TMACs remained stable if the training set of specimens was per-muted. This suggests that the cluster estimates obtained from thespecimens (i.e. the training set) appear to reflect the textural key fea-tures and some of the variability found in elderly humans (Table 1).The single-site reproducibility results also indicate that a clustermodel (i.e. Gaussian mixture model) that has been learned from anindependent dataset would have similar cluster distributions. Basedon the findings of the validation experiment, we concluded that thethree clusters were stable enough to be applicable to new, unknownHR-pQCT cases that were not included in the training set. The intra-scanner reproducibility tests with sample repositioning had an over-all dice coefficient (DC) slightly below the 0.9 mark and the ICCof TMACs are between 0.881 and 0.995, which represented a goodresults. Reproducibility of the results across two different scannerswas encouraging. Intrinsic scanner characteristics such as detector prop-erties, geometric and density calibrations, and X-ray source differences

Fig. 5. Representatives of differences in the trabecular microarchitecture class (TMAC)distribution between controls (Non-Fx) and fracture patients (Fx).

139A. Valentinitsch et al. / Bone 54 (2013) 133–140

which are important confounders for multi-center studies were indi-rectly reflected in the results, which showed a lower DC, PE and ICC inthe inter-scanner reproducibility experiment than in the intra scannerexperiments (Table 3).

In general, scanner-based artifacts can lower the performance andreproducibility of most post-processing algorithms. Ring artifacts,which are in HR-pQCT imaging caused by minimal misalignment ofadjacent CCD units, are known confounders of 3D-texture analysisbecause they introduce an abrupt gradient in the gray-scale images. Al-though scanner-based artifacts are frequent in computed-tomography(CT) [51] and have also been described for micro computed-tomography (μCT) [52,53], they have never been specifically addressedin HR-pQCT research. Examining our results, we have noticed that thesethin ring artifacts certainly affect texture features; nevertheless, werefrained fromperforming artifact correction in order to avoid unneces-sary datamanipulation. These effects are reflected in the reproducibilityanalysis results of the cluster volume fraction (CL.V/TV) in each TMAC,which have high but consistent PE (e.g. TMAC 2: 12.19%) in comparisonto other reproducibility studies describing morphometric indices[29,54]. In addition, artifacts caused by subjectmotion have a noticeableinfluence on image quality. According to Pialat et al. [45], geometric andmorphometric standard indices of HR-pQCT are strongly affected bymotion. Data on motion-dependence of other post-processing toolshave not been published. Our study was also not designed to assessthe effects of motion on cluster volumes; however, we observed arobust performance of the algorithm across a representative spectrumof images of motion grades accepted for quantitative analysis.

In a preliminary TMAC-application to clinical data, we found thatclustering appeared to reflect fracture status in postmenopausalwomen. Although clinical conclusions about the utility of TMAC forfracture prediction are definitely limited by the small sample size,racial heterogeneity, and older age in fracture than non-fracturepatients, our results can be viewed as initial steps. They illustratethat the TMAC histogram represents characteristics of the cohorts.Larger clinical datasets are needed to gain more insight into the utilityof this measurement. However, it seems promising that TMAC yieldedstatistical differences between trabecular texture in fracture and non-fracture patients while there were no statistical significances fortrabecular BMD. Somewhat different from other postmenopausalfracture cohorts studied by HR-pQCT [6,30,55,56], only trabecularthickness was significantly lower in fracture than non-fracturepatients. From a medical point of view this circumstance might be at-tributable to the relatively young mean age of both fracture patientsand controls. Irrespective of biological explanations, this finding isin line with the clustering results, which primarily indicate a deficitof TMAC 1, the cluster containing the thickest trabeculae.

There were important limitations to our study. From a clinicalperspective, it needs to be stressed that our fracture/non-fracture pa-tients were not age-matched. There was some racial inhomogeneityand the groups were relatively small. Group definition by prevalentfractures remains certainly suboptimal due to self-report of traumaseverity. Taken altogether, our clinical results should be primarilyviewed as first in-vivo data that support the utility of TMAC analysesin HR-pQCT imaging.

From a technical perspective, the TMACs reported in this studyare identified based on the study population. Thus a larger popula-tion might result in more stable sub-categories. In addition, ourcompartment-specific approach included neither cortical bone[12,15] nor the subendocortex [57] and could thus be viewed as bio-logically incomplete. Technically, cortical bone and subendocorticaltrabeculae could be subjected to a similar clustering algorithm.However, we believe that the relatively large sample volume andthe higher local turnover within the trabecular compartment pre-dispose cancellous bone for a targeted application of our technique.The bone sections analyzed in the intra- and inter-scanner experi-ments were different due to re-alignment and subsequent discarding

of regions not covered by all scans, performed in each studyindividually.

Future studies should address the effect of motion artifacts oncluster stability and reproducibility. The combination of HR-pQCTclustering with decomposition techniques (e.g. individual trabecularsegmentation — ITS [58]) might be helpful to improve the structuralcharacterization of the trabecular subvolumes. Besides measuringcluster size, the assessment of the spatial distribution and connectiv-ity of different textural regions and their relation with patient charac-teristics could become investigative steps (Fig. 5). Cluster-specificmicro-finite element analysis [59,60] might help to elucidate the bio-mechanical contribution of different cluster types and their specificrelationship to bone strength. In longitudinal HR-pQCT studies, tra-becular dynamics could also be quantified by measuring changes incluster volume and spatial distribution. Moreover, baseline masksobtained by clustering could be used to study trabecular dynamicswithin predefined subvolumes.

In summary, we have demonstrated the feasibility of 3D-textureanalysis and trabecular bone clustering on HR-pQCT images of theultradistal radius. The method was well reproducible in short-term,single-site, and cross-site validation set-ups. In a preliminary clinicalapplication, clustering increased the yield of HR-pQCTdata andprovideda complementary measure beyond standard evaluations that might aidto differentiate fracture and non-fracture patients by HR-pQCT.

Acknowledgments

The authors thank Thelma Munoz, Melissa Guan, Paran Yap andThomas Baum for their help in recruiting, consenting and scanning.We would also like to thank Dirk Müller (Philips Healthcare) forrelevant input during the development of the method and inspiringdiscussions, and Matthew DiFranco for proofreading. This work waspartially supported by NIH (NIH RC1 AR058405 and NIH R01AR060700), OeNB (13468, BIOBONE), EU (FP7-ICT-2009-5/257528,KHRESMOI), FWF (P 22578-B19, PULMARCH) and Philips Research.JMP was supported by the Austrian Science Fund (FWF; Erwin-Schrödinger Grant J-3079).

References

[1] NIH Consensus Development Panel on Osteoporosis Prevention Diagnosis andTherapy. Osteoporosis prevention, diagnosis, and therapy. JAMA 2001;285:785–95.

[2] Link TM. Osteoporosis imaging: state of the art and advanced imaging. Radiology2012;263:3–17.

140 A. Valentinitsch et al. / Bone 54 (2013) 133–140

[3] Khosla S, Riggs BL, Atkinson EJ, Oberg AL, McDaniel LJ, Holets M, et al. Effects of sexand age on bonemicrostructure at the ultradistal radius: a population-based nonin-vasive in vivo assessment. J Bone Miner Res 2006;21:124–31.

[4] Burghardt AJ, Kazakia GJ, Ramachandran S, Link TM, Majumdar S. Age- andgender-related differences in the geometric properties and biomechanical signif-icance of intracortical porosity in the distal radius and tibia. J Bone Miner Res2010;25:983–93.

[5] Macdonald HM, Nishiyama KK, Kang J, Hanley DA, Boyd SK. Age-related patternsof trabecular and cortical bone loss differ between sexes and skeletal sites: apopulation-based HR-pQCT study. J Bone Miner Res 2011;26:50–62.

[6] Boutroy S, Bouxsein ML, Munoz F, Delmas PD. In vivo assessment of trabecularbone microarchitecture by high-resolution peripheral quantitative computed to-mography. J Clin Endocrinol Metab 2005;90:6508–15.

[7] Vilayphiou N, Boutroy S, Sornay-Rendu E, Van Rietbergen B, Munoz F, Delmas PD,et al. Finite element analysis performed on radius and tibia HR-pQCT images andfragility fractures at all sites in postmenopausal women. Bone 2010;46:1030–7.

[8] Liu XS, Zhang XH, Sekhon KK, Adams MF, McMahon DJ, Bilezikian JP, et al.High-resolution peripheral quantitative computed tomography can assess micro-structural and mechanical properties of human distal tibial bone. J BoneMiner Res2010;25:746–56.

[9] Hansen S, Beck Jensen JE, Rasmussen L, Hauge EM, Brixen K. Effects on bonegeometry, density, and microarchitecture in the distal radius but not the tibia inwomen with primary hyperparathyroidism: a case-control study using HR-pQCT.J Bone Miner Res 2010;25:1941–7.

[10] Liu XS, Stein EM, Zhou B, Zhang CA, Nickolas TL, Cohen A, et al. Individual trabeculasegmentation (ITS)-based morphological analyses and microfinite element analysisof HR-pQCT images discriminate postmenopausal fragility fractures independent ofDXA measurements. J Bone Miner Res 2012;27:263–72.

[11] Laib A, Häuselmann HJ, Rüegsegger P. In vivo high resolution 3D-QCT of thehuman forearm. Technol Health Care 1998;6:329–37.

[12] Burghardt AJ, Buie HR, Laib A, Majumdar S, Boyd SK. Reproducibility of directquantitative measures of cortical bone microarchitecture of the distal radius andtibia by HR-pQCT. Bone 2010;47:519–28.

[13] Liu XS, Cohen A, Shane E, Stein E, Rogers H, Kokolus SL, et al. Individual trabeculaesegmentation (ITS)-based morphological analysis of high-resolution peripheralquantitative computed tomography images detects abnormal trabecular plateand rod microarchitecture in premenopausal women with idiopathic osteoporo-sis. J Bone Miner Res 2010;25:1496–505.

[14] Sode M, Burghardt AJ, Kazakia GJ, Link TM, Majumdar S. Regional variations ofgender-specific and age-related differences in trabecular bone structure of thedistal radius and tibia. Bone 2010;46:1652–60, doi:10.1016/j.bone.2010.02.021.

[15] Burghardt AJ, Kazakia GJ, Sode M, de Papp AE, Link TM, Majumdar S. A longitudi-nal HR-pQCT study of alendronate treatment in postmenopausal women with lowbone density: relations among density, cortical and trabecular microarchitecture,biomechanics, and bone turnover. J Bone Miner Res 2010;25:2558–71.

[16] Vokes TJ, Giger ML, Chinander MR, Karrison TG, Favus MJ, Dixon LB. Radiographictexture analysis of densitometer-generated calcaneus images differentiates post-menopausal women with and without fractures. Osteoporos Int 2006;17:1472–82.

[17] Lespessailles E, Gadois C, Kousignian I, Neveu JP, Fardellone P, Kolta S, et al. Clinicalinterest of bone texture analysis in osteoporosis: a case control multicenter study.Osteoporos Int 2008;19:1019–28.

[18] Peleg S, Naor J, Hartley R, Avnir D. Multiple resolution texture analysis and classi-fication. IEEE Trans Pattern Anal Mach Intell 1984;6:518–23.

[19] Benhamou CL, Lespessailles E, Jacquet G, Harba R, Jennane R, Loussot T, et al. Fractalorganization of trabecular bone images on calcaneus radiographs. J Bone Miner Res1994;9:1909–18.

[20] Lespessailles E, Jullien A, Eynard E, Harba R, Jacquet G, Ildefonse JP, et al. Biome-chanical properties of human os calcanei: relationships with bone density andfractal evaluation of bone microarchitecture. J Biomech 1998;31:817–24.

[21] Chappard D, Guggenbuhl P, Legrand E, Baslé MF, Audran M. Texture analysis ofX-ray radiographs is correlated with bone histomorphometry. J Bone MinerMetab 2005;23:24–9.

[22] Pothuaud L, Lespessailles E, Harba R, Jennane R, Royant V, Eynard E, et al. Fractalanalysis of trabecular bone texture on radiographs: discriminant value in post-menopausal osteoporosis. Osteoporos Int 1998;8:618–25.

[23] Benhamou CL, Poupon S, Lespessailles E, Loiseau S, Jennane R, Siroux V, et al. Fractalanalysis of radiographic trabecular bone texture and bonemineral density: two com-plementary parameters related to osteoporotic fractures. J BoneMiner Res 2001;16:697–704.

[24] Pothuaud L, Carceller P, Hans D. Correlations between grey-level variations in 2Dprojection images (TBS) and 3D microarchitecture: applications in the study ofhuman trabecular bone microarchitecture. Bone 2008;42:775–87.

[25] Hans D, Goertzen AL, Krieg MA, Leslie WD. Bone microarchitecture assessed byTBS predicts osteoporotic fractures independent of bone density: the Manitobastudy. J Bone Miner Res 2011;26:2762–9.

[26] Bousson V, Bergot C, Sutter B, Levitz P, Cortet B. Scientific Committee of the Groupede Recherche et d'Information sur les Ostéoporoses. Trabecular bone score (TBS):available knowledge, clinical relevance, and future prospects. Osteoporos Int2012;23:1489–501.

[27] Bacchetta J, Boutroy S, Vilayphiou N, Fouque-Aubert A, Delmas PD, Lespessailles E,et al. Assessment of bonemicroarchitecture in chronic kidney disease: a comparisonof 2D bone texture analysis and high-resolution peripheral quantitative computedtomography at the radius and tibia. Calcif Tissue Int 2010;87:385–91.

[28] Fouque-Aubert A, Boutroy S, Marotte H, Vilayphiou N, Lespessailles E, Benhamou CL,et al. Assessment of hand trabecular bone texture with high resolution direct digital

radiograph in rheumatoid arthritis: a case control study. Joint Bone Spine2012;79(4):379–83.

[29] Burghardt AJ, Pialat JB, Burrows M, Liu D, Patsch JM, Valentinitsch A, et al.Cross-site reproducibility of cortical and trabecular bone density and micro-architecture measurements by HR-pQCT. Osteoporos Int 2010;21:S45–6.

[30] Vico L, Zouch M, Amirouche A, Frère D, Laroche N, Koller B, et al. High-resolutionpQCT analysis at the distal radius and tibia discriminates patients with recentwrist and femoral neck fractures. J Bone Miner Res 2008;23:1741–50.

[31] Hildebrand T, Ruegsegger P. A new method for the model-independent assess-ment of thickness in three-dimensional images. J Microsc (Oxford) 1997;185:67–75.

[32] Laib A, Hildebrand T, Häuselmann HJ, Rüegsegger P. Ridge number density: a newparameter for in vivo bone structure analysis. Bone 1997;21:541–6.

[33] Valentinitsch A, Patsch JM, Deutschmann J, Schueller-Weidekamm C, Resch H,Kainberger F, et al. Automated threshold-independent cortex segmentation by3D-texture analysis of HR-pQCT scans. Bone 2012;51:480–7.

[34] Hill DL, Batchelor PG, Holden M, Hawkes DJ. Medical image registration. Phys MedBiol 2001;46:R1-45.

[35] Haralick RM, Shanmugam K, Dinstein I. Textural features for image classification.IEEE Trans Syst Man Cybern 1973;3:610–21.

[36] Kovalev VA, Kruggel F, Gertz HJ, Cramon von DY. Three-dimensional texture anal-ysis of MRI brain datasets. IEEE Trans Med Imaging 2001;20:424–33.

[37] Herlidou-Même S, Constans JM, Carsin B, Olivie D, Eliat PA, Nadal-Desbarats L,et al. MRI texture analysis on texture test objects, normal brain and intracranialtumors. Magn Reson Imaging 2003;21:989–93.

[38] Sato Y, Nakajima S, Shiraga N, Atsumi H, Yoshida S, Koller T, et al. Three-dimensionalmulti-scale line filter for segmentation and visualization of curvilinear structures inmedical images. Med Image Anal 1998;2:143–68.

[39] Albregtsen F. Statistical texture measures computed from gray level coocurrencematrices. Image Processing Laboratory; 1995.

[40] Frangi A, NiessenW, Vincken K, ViergeverM.Multiscale vessel enhancementfiltering.Lect Notes Comput Sci 1998:130–7.

[41] PermuterH, Francos J, Jermyn I. A study of Gaussianmixturemodels of color and tex-ture features for image classification and segmentation. Pattern Recognit 2006;39:695–706.

[42] Reynolds D. Gaussian mixture models. Encyclopedia of biometric recognition; 2008.[43] Pascual D, Pla F, Sánchez J. Cluster stability assessment based on theoretic infor-

mation measures. Prog Pattern Recognit Image Anal Appl 2008:219–26.[44] Genant HK, Wu CY, van Kuijk C, Nevitt MC. Vertebral fracture assessment using a

semiquantitative technique. J Bone Miner Res 1993;8:1137–48.[45] Pialat JB, Burghardt AJ, Sode M, Link TM, Majumdar S. Visual grading of motion

induced image degradation in high resolution peripheral computed tomography:impact of image quality on measures of bone density and micro-architecture.Bone 2012;50:111–8.

[46] Laib A, Newitt DC, Lu Y, Majumdar S. New model-independent measures of tra-becular bone structure applied to in vivo high-resolution MR images. OsteoporosInt 2002;13:130–6.

[47] Glüer CC, Blake G, Lu Y, Blunt BA, Jergas M, Genant HK. Accurate assessment ofprecision errors: how to measure the reproducibility of bone densitometry tech-niques. Osteoporos Int 1995;5:262–70.

[48] Vargha P. A critical discussion of intraclass correlation coefficients. Stat Med1997;16:821–3.

[49] Krzanowski W. Principles of multivariate analysis:a User's perspective. New York,USA: Oxford University Press; 1988.

[50] Seber GAF. Multivariate observations. New York: John Wiley & Sons, Inc.; 1984.[51] Barrett JF, Keat N. Artifacts in CT: recognition and avoidance. Radiographics 2004;24:

1679–91.[52] Sijbers J, Postnov A. Reduction of ring artefacts in high resolution micro-CT recon-

structions. Phys Med Biol 2004;49:N247–53.[53] Kyriakou Y, Prell D, Kalender WA. Ring artifact correction for high-resolution

micro CT. Phys Med Biol 2009;54:N385–91.[54] Mueller TL, StauberM, Kohler T, Eckstein F,Müller R, van LentheGH.Non-invasive bone

competence analysis by high-resolution pQCT: an in vitro reproducibility study onstructural and mechanical properties at the human radius. Bone 2009;44:364–71.

[55] Sornay-Rendu E, Boutroy S,Munoz F, Delmas PD. Alterations of cortical and trabecu-lar architecture are associated with fractures in postmenopausal women, partiallyindependent of decreased BMD measured by DXA: the OFELY study. J Bone MinerRes 2007;22:425–33.

[56] Stein EM, Liu XS, Nickolas TL, Cohen A, Thomas V, McMahon DJ, et al. Abnormalmicroarchitecture and reduced stiffness at the radius and tibia in postmenopausalwomen with fractures. J Bone Miner Res 2010;25:2572–81.

[57] Zebaze RMD, Ghasem-Zadeh A, Bohte A, Iuliano-Burns S, Mirams M, Price RI, et al.Intracortical remodelling and porosity in the distal radius and post-mortemfemurs of women: a cross-sectional study. Lancet 2010;375:1729–36.

[58] Liu XS, Sajda P, Saha PK,Wehrli FW, Bevill G, Keaveny TM, et al. Complete volumetricdecomposition of individual trabecular plates and rods and its morphological corre-lations with anisotropic elastic moduli in human trabecular bone. J Bone Miner Res2008;23:223–35.

[59] MacNeil JA, Boyd SK. Bone strength at the distal radius can be estimated from high-resolution peripheral quantitative computed tomography and the finite elementmethod. Bone 2008;42:1203–13.

[60] Mueller TL, Christen D, Sandercott S, Boyd SK, Van Rietbergen B, Eckstein F, et al.Computational finite element bone mechanics accurately predicts mechanicalcompetence in the human radius of an elderly population. Bone 2011;48:1232–8.