Bone 44 (2009) 145–152

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High resolution computed tomography of the vertebrae yields accurate informationon trabecular distances if processed by 3D fuzzy segmentation approaches

Andreas Krebs a,⁎, Christian Graeff a, Isolde Frieling c, Bodo Kurz d, Wolfram Timm b,Klaus Engelke b, Claus-C. Glüer a

a Medizinische Physik, Klinik für Diagnostische Radiologie, Universitätsklinikum Schleswig-Holstein, Germanyb Synarc Inc, Hamburg, Germanyc Osteoporosezentrum Hamburg - Neuer Wall, Hamburg, Germanyd Anatomisches Institut, Universität Kiel, Germany

⁎ Corresponding author. Fax: +49 431 597 3127.E-mail address: andreas.krebs@rad.uni-kiel.de (A. Kr

8756-3282/$ – see front matter © 2008 Elsevier Inc. Aldoi:10.1016/j.bone.2008.08.131

a b s t r a c t

a r t i c l e i n f o

Article history:

Introduction: The structure Received 20 March 2008Revised 20 August 2008Accepted 27 August 2008Available online 23 September 2008

Edited by: H. Genant

Keywords:OsteoporosisTrabecular boneHigh resolution computed tomography3D architectureFuzzy distance transformation

of trabecular bone represents an aspect of bone properties that affects vertebralbone strength independently of bone mineral density [M. Kleerekoper, A. Villanueva, J. Stanciu, D. Rao, and A.Parfitt. The role of three-dimensional trabecular microstructure in the pathogenesis of vertebral compressionfractures. Calcif. Tissue Int., 37:594–597, Dec 1985; E. Seeman and P. Delmas. Bone quality—the material andstructural basis of bone strength and fragility. N. Engl. J. Med., 354:2250–2261, May 2006.]. Using themathematical concept of fuzzy distance transformation (FDT), we evaluated the accuracy of measurements oftrabecular distance (Tb.Dif) which can be determined for vertebrae in vivo using high resolution computedtomography (HRCT).Methods: In a first step extrema voxels with a very high likelihood of representing bone or marrow areidentified. A probability level of being a bone voxel is assigned to all other voxel. This probability is based onthe FDT of the voxel's gray-level, preprint submitted to Elsevier June 10, 2008; revised July 15, 2008 i.e. theshortest gray-value weighted distance to the marrow background. Next, the resulting bone structure isskeletonized. The space between the ridges of the skeleton is filled with the largest possible spheres. Theaverage over the radii of the spheres defines Tb.Dif, a measure of trabecular distance. 14 whole vertebraeembedded in polymethyl methylacrylate were scanned by HRCT (voxel size 156×156×400 μm3) inside ananthropomorphic abdomen phantom. Scans obtained on Scanco Xtreme CT (XCT, voxel size 823 μm3) withoutthe phantom were used as reference.Results: Tb.Dif calculated on XCT data were almost identical to trabecular distance values (1/Tb.N⁎)determined with the manufacturer's standard software (r2=0.98). Tb.Dif values obtained with HRCTcorrelated strongly with Tb.Dif values obtained by XCT (r2=0.89). Over the range from 400 to 1400 μmtrabecular distance could be estimated with a residual error of 78 μm.Conclusions: The FDT based variable Tb.Dif provides 3D estimates of trabecular distances with residual errorsof less than 100 μm using a HRCT protocol which also can be employed in vivo for assessing vertebralmicroarchitecture.

© 2008 Elsevier Inc. All rights reserved.

Introduction

Monitoring of osteoporosis therapy based solely on bone densito-metry is insufficient to assess anti-fracture efficacy. The structure oftrabecular bone represents an additional aspect of bone propertiesthat affects bone strength independently of bone mineral density(BMD) [12,29]. Bone biopsies, high resolution magnetic resonanceimaging (MRI), or dedicated peripheral quantitative computedtomography (pQCT) imaging systems for measurements in peripheralregions of the skeleton such as the forearm or the tibia provide

ebs).

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insights into the trabecular structure. As can be expected because ofthe different loading conditions, structural measures from biopsies orperipheral sites show limited correlations with the clinically impor-tant fracture sites of the proximal femur and the vertebrae.

Recent advances in computed tomography allow high resolutionimaging (HRCT) at central fracture sites such as the spine, withimproved spatial resolution. Pilot studies have shown promisingperformance in discrimination of subjects with and without recentvertebral fractures [10] and excellent responsiveness to bone anabolictreatment [5]. In vivo assessment of trabecular bone structure islimited by image noise and radiation exposure and it is unclear towhat extent the resulting images reflect the true trabecular bonestructure.

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The high level of noise and the limited spatial resolution requirespecific software hat avoids artificial thresholds used for segmentationof bone versus bone marrow and which is less sensitive to noise andresolution limits. Using the mathematical concept fuzzy distancetransformation (FDT), we propose to estimate trabecular ridge distancebased on the structural variable trabecular distance Tb.Dif. The aim ofthis work is to quantify the residual error of this method in a settingthat resembles the in vivo situation very closely.

Materials and methods

HRCT scan

14 vertebral bodies obtained from the Anatomical Institute of ouruniversity were embedded in polymethyl methylacrylate (PMMA).The embedded vertebral bodies were shaped in such a way that theycould be inserted without air gaps into an anthropomorphic CIRSabdomen phantom with tissue equivalent organ structure. Anadditional attenuator ring could be fit around the phantom to emulatein vivo conditions of an obese patient (see Fig. 1 (left)). The embeddedvertebral bodies were measured by HRCT (Siemens SomatomSensation 16,120 kV, 360mAs, pixel size 156×156 μm2, slice thickness400 μm). HRCT datawere calibrated tomineral scale [mg K2HPO4/cm3]using Mindways' calibration phantom (Mindways Software, Austin,TX, USA) depicted in the Fig. 1.

Reference measurements for the trabecular structure wereobtained on a Scanco Xtreme CT (XCT, ScancoMedical AG, Bassersdorf,Switzerland) with the voxel size 823 μm3 and adjusted tomineral scale[mg calcium hydroxiapatite (CaHA)/cm3] by the Xtreme CT calibrationprocedure. Note: Unless otherwise stated in this publication [mg/cm3]units of BMD are always specified on a CaHA equivalent scale.

Image preprocessing

All image preprocessing was performed using the softwareStructuralInsight V1.48 developed in-house. The StructuralInsightRegistration Add-on used the registration algorithm provided by theInsight Segmentation and Registration Toolkit (ITK) [9, Chapter 8].

Using the XCT images of the vertebrae, the complete trabecularbone volume was masked excluding hyper-dense degenerativecalcifications and the cortical rim of the vertebral body. This maskingwas based on polygons manually defined by the user on a limitednumber of nonadjacent slices (typically 4–8). These polygons were

Fig. 1. Left: PMMA embedded vertebra in CIRS model 235 abdominal phantom (gray) with thethe CT calibration phantom (white) permitted the conversion of the image's gray-valuesdetermined based on manually defined polygons (black) excluding cortical rim. The black spvertebrae during the PMMA embedding. The air gap between the abdominal phantom and

subsequently interpolated linearly to cover all reconstructed slices(typically 170–220 per vertebral body).

For assessment of local subvolumes we subdivided every maskedXCT image into pairwise disjoint adjacent axially oriented cuboids ofdimensions 12.3 mm×12.3 mm×height of vertebra, such that theunion of the cuboids was centered in the image. Since the 14 XCT scanswere of different voxel dimensions, the number of cuboids obtainedfrom an XCT scan varied from four to nine. 66 of the 86 cuboids (four tonine per vertebra) remained after the exclusion of regions in whichthe volume of interest (VOI) determined by polygonal masking wastoo small to provide robust statistics (less than 65% of the volume ofone cuboid).

A second set of smaller cuboidswith dimensions 6.2×6.2×5.95mm3

was obtained in a similar fashion. 608 of the 970 cuboids remained afterthe exclusion of regions in which the VOI determined by polygonalmasking was too small to provide robust statistics (less than 85% of thevolume of one cuboid).

Using ITK registration routines a 3D translation and a 3D rotationwere computed for every HRCT image such that its cortical rimmatched its counterpart in the XCT image down-sampled to the voxelsize of the HRCT. Since the cortical rim represented an object with athickness of more than 5 voxel in HRCT image, it could clearly beidentified on both XCT and HRCT. Visual inspection of 3D compositeimages [9, Chapter 8, ITK checkerboard] of the registered XCT andHRCT images showed an almost perfect matching of the cortical rimfor the 14 vertebrae of the dataset.

Every mask defining the trabecular bone volume in an XCT imagewas transferred to the corresponding HRCT image based on thetranslation and rotation parameters determined by the registrationprocedure. Analogously, the cuboid regions were transferred to thecorresponding HRCT image.

Fuzzy distance based trabecular distance

The top and middle plots of Fig. 2 show what happens to ahistogram of a vertebra image when moving from μCT to XCT or HRCTmeasurements: Due to partial volume effects and noise the bone peakmelts into the marrow peak and the bone/marrow binarizationbecomes ambiguous.

Fuzzy segmentation approaches may overcome these limitations. Asigmoidal membership function maps the voxel's gray-value onto the[0; 1] interval (cf. bottom plot of Fig. 2). The assigned value representsthe probability of the voxel to be bone. The fuzzy distance concept

attenuator ring to simulate obese patients. Five rods of reference material embedded into BMD in [mg K2HPO4/cm3]. Right: HRCT reconstruction. The trabecular bone wasots inside of the displayed polygon were induced by air bubbles which remained in thethe PMMA embedding yielded the black circle.

Fig. 3. Virtual rod-plate phantom depicted with a voxel size of 20 μm. The top left plotshows an unrotated rod-plate phantom masked by sphere with 4 mm diameter withrod diameter dR=100 μm, rod spacing sR=700 μm, plate thickness dP=100 μm, and platespacing sP=900 μm. The top right plot shows the same phantom rotated 50°counterclockwise around the axis given by the vector (0.35; 0.2; 1.). Voxels with a z-coordinate N0.6 were not rendered for better illustration. The following six 3D plotsvisualize the effect of an increasing voxel size on the rotated phantom.

Fig. 2. Histograms of bone mineral density values for μCT (top) and HRCT (middle)images. Min., max., and medial densities were arbitrarily chosen to document a typicalrange of values of 94 mg/cm3, 162 mg/cm3, and 125 mg/cm3, respectively. Instead ofbinary decisions a membership function (bottom) can be defined to assign aprobability value from [0, 1] of belonging to the bone phase to each voxel accordingto its HRCT gray-value.

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allows the probability weighted measurement of distances: A 2 mmlong line of voxels with amembership value 1 leads to a fuzzy distanceof 2 mm. If the same line consists of voxels with a membership value0.3, this yields a fuzzy distance of 0.3 · 2 mm=0.6 mm. The FDTassignsto every potential bone voxel (membership valueN0) the minimalfuzzy length over all curves connecting the bone voxel to the marrowbackground (membership value=0) [cf. 23]. Appropriate choice of theshape of the sigmoidal curve (example at bottom of Fig. 2) ensuresthat the FDT of the line is optimally calibrated.

To determine the ridges of the trabeculae, we adapted a methoddeveloped by Hildebrandt and Rüegsegger [8]. They employed anordinary distance transform of an object in a binary image to identifyridges of the object. In their approach, each voxel was assigned agray-value corresponding to the shortest distance to bone marrow.This gray-value can also be interpreted as the radius of a spherewhich is centered at the voxel and completely contained in the bonephase. In this concept, ridge points have a larger distance to marrowcompared to adjacent bone voxel, i.e. are associated with a largerradius. Ridges then can be defined as the set of center points ofall non-redundant spheres filling the object, i.e., a ridge point wasdefined as a center point of a sphere which was not completelycontained in any other sphere. In our adapted approach, insteadof the ordinary distance transform on binary images, we used theFDT on gray-scale images to calculate spheres: Bf (c, r) :={x∈R3 |distFuzzy(c, x) ≤ r} instead of B(c, r):={x ∈R3 | distEuclidean(c, x) ≤ r}.This provides the basis to define FDT weighted ridges analogously toridges based on ordinary distance transforms. As a result we obtaineda binary image where only the ridges of the trabeculae are set to 1and all other voxels to 0.

To determine the spacing of these ridges, we computed the largestsphere for each non-ridge voxel which contained the non-ridge voxel(not necessarily as the sphere's center) and which did not contain anyridge voxel. The diameter of this sphere was taken as the local fuzzydistance based trabecular distance (local Tb.Dif) for this non-ridge voxel.Taking the mean value of Tb.Dif over all non-ridge voxels of the VOIyields the mean fuzzy distance based trabecular distance (mean Tb.Dif).

The calculation of Tb.Dif was implemented as the FDT Add-on toStructuralInsight V1.48. Tb.Dif values were determined for the VOIdetermined by the image preprocessing for the XCT images and theircorresponding HRCT images, either on entire vertebral bodies or onthe larger or smaller cuboids.

Virtual phantom

To verify that our algorithm determines the structural parameterTb.Dif accurately, we implemented a virtual phantom which allows togenerate artificial structures of known spacing and topology mimick-ing the structure of cancellous bone. The phantom enables us to

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generate 3D images of rods with diameter dR arranged perpendicularto the xy-plane and uniformly spaced in a square or triangular gridwith a spacing sR, sRNdR.

Using the fuzzy method described above, this phantom shouldyield a trabecular distance Tb:Dif =

ffiffiffiffiffiffiffiffiffi

2dsRp

in case of a uniform squaregrid, Tb:Dif = 2

3

ffiffiffiffiffiffiffiffiffi

3dsRp

in case of a uniform triangular grid.Furthermore, the phantom makes it possible to generate 3D

images of parallel plates of thickness tP and uniform spacing sPbetween the center of neighboring plates. The combination of the rodand the plate images allows for the simulation of mixed rod-platemodels, providing the flexibility to generate structural patternssimilar to those observed in cancellous bone (Fig. 3).

The phantom was directly constructed as a 3D gray-value imagewith 20 μm voxel side length. Initially, the rods were oriented parallelto the z-axis, the plates perpendicular to the z-axis. To determinewhether the accuracy of Tb.Difmeasurements depends on orientation,this high resolution image was rotated around an arbitrary axis by anarbitrary angle and sampled to the target voxel size of the phantom. Toavoid the influence of the six cutting planes of the image border atdifferent angles of rotation, the phantom was masked by a sphere.

The successive rotation around an axis allows us to simulatetrabecular rods which are not aligned cranio-caudal. Here, it is worthto note that it is sufficient to explore rotations around one axis. Due tothe laws of linear algebra successive rotations around different axescan always be reduced to one translation given by a vector or to onerotation defined by an axis and an angle.

Reference measurements

The Rüegsegger group has established model-independent vari-ables for characterizing trabecular bone structure for their micro-CTwork [7,13,14]. Scanco devices, including the Xtreme CT scanner, areusing these variables. Since they have the largest base of publishedpapers, we chose to use Scanco algorithms as a reference againstwhich we wanted to compare our algorithms.

Fig. 4. Sagittal cuts through two vertebrae each represented by a quadruple set of images. Thclose to dataset's mean BMD, andwith somewhat more different Tb.Dif (top vertebra 1023 μmby XCT (first and third row) and by HRCT (second and fourth row). The right column depict

Differing from our fuzzy method, Hildebrand et al. determinedthe ridges of the bone phase after a bone/marrow binarization [7].Using these ridges local ridge distances and the binary basedtrabecular distance Tb.Did can be computed analogously to theprocess mentioned above. Hildebrand et al. defined the structuralvariable Tb.N⁎=1/Tb.Did [mm−1] “as the inverse of the meandistance between the mid-axes of the observed structure” [7](average of the local ridge distances) over the VOI. The ScancoXtreme CT software calculates Tb.N⁎. We used its inverse Tb.Did

[μm] as the XCT reference for the entire vertebrae. For the Tb.Did

values the masking of the trabecular region of interest wasperformed by the Scanco Xtreme CT evaluation Software.

The accuracy error of an HRCT-based Tb.Dif measurement wasdetermined in the following steps. The correctness of the algorithmwas first tested by comparing the measurement results of Tb.Dif withthe known nominal values of the virtual phantom and second bycomparison with results of the Scanco Tb.Did algorithm (both Tb.Dif

and Tb.Did applied to an XCT dataset of the 14 vertebral bodies).Subsequently we then correlated the HRCT results processed with theTb.Dif algorithm with the XCT results processed with the Tb.Did

algorithm. The residual error of this regression analysis provided anestimate of the accuracy error of the HRCT approach (including bothalgorithm and image technique related errors).While Tb.Did datawereonly available for masks including entire vertebrae, Tb.Did data forsubregions could be derived from Tb.Dif data using the tight relation-ship of Tb.Did and Tb.Dif results. The statistical analyses were carriedout using MATLAB 7.3.0.298 (R2006b) (The MathWorks, Inc., Natick,MA, USA) and JMP 7.0 (SAS Institute, Cary, NC, USA).

Results

Image quality

In single slices obtained from a HRCT scan trabecular elementswere hard to distinguish from noise (cf. Fig. 1 (right)). Without further

e vertebrae had similar BMD (top vertebra 125 mg/cm3, bottom vertebra 134 mg/cm3),, bottomvertebra 932 μm). The left column displays the BMD calibrated images scanneds the fuzzy distance transformations of their respective left neighbors.

Fig. 5. BMD calibrated in units of [mg calcium hydroxiapatite/cm3] from Xtreme CTversus BMD in units of [mg K2HPO4/cm3] from HRCT.

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image processing only larger trabeculae, particularly those orientedperpendicular to the slices, were visible in coronal and sagittal cutsthrough a vertebra.

The two image quadruples of Fig. 4 show sagittal cuts of twovertebrae scanned by XCT (pixel size 82×82 μm2) and by HRCT(pixel size 156×400 μm2). The registration was performed in threedimensions and checked by visual inspection of the cortical rimusing a composite image from the HRCT and the XCT reference. Thesagittal cuts of the XCT images were taken after registration.

Fig. 6. Accuracy errors of Tb.Dif as a function of rotation simulated by the virtual phantom. Rescenarios ranged around 0 μm for two cases and around 100 and 200 μm for the other two

The right column of Fig. 4 depicts the FDT of their leftneighbors. The FDT of the XCT scan was calculated before theregistration process to avoid a loss of image information due to theimplicit low pass filtering of the registration sampling. The sagittalcuts of XCT's FDT (right column, first and third row) were obtainedby moving the FDT image according to the registration parametersto the HRCT FDT image and cutting exactly at the HRCT sagittal cutpositions after the move.

The FDT maintained the coarser trabecular structure. Noise wasreduced since small clusters of foreground voxels got small FDT values.As can be seen noise structures outside the vertebral bodies werequite effectively reduced, both for XCT and HRCT. The bottom rightimages of the quadruples of Fig. 4 clarify that this effect worked alsowhen applying the FDT to a HRCT scan.

BMD

The XCT BMD values of the 14 entire vertebrae spanned a rangefrom 96 to 163 mg/cm3. To extend the range we also included theBMD values of the 12.3 mm×12.3 mm×height of vertebra cuboids.This way we obtained a sample of 80 data points which XCT valuesranged from 74 to 191 mg/cm3 with mean±standard deviation (SD)of 128±26 mg/cm3 (±20% of the reference mean). These BMD valuescorrespond to a T-score varying from −3.0 to 0.9 with mean±SD of−1.2±1.0 T-scores (using the reference data of [11] to calculate T-scores). These T-score ranges are only meant as rough estimates todocument that the vertebrae span a reasonable BMD range. The trueT-score would be expected to differ somewhat due to the differencesin image resolution, region of interest, and the calibration; more-over, air bubbles which remained in the vertebrae during the PMMAembedding may also have affected BMD results.

The regression line of calibrated XCT values versus Mindways-calibrated HRCT data is shown in Fig. 5: BMDXCT=0.94 ·BMDHRCT

sults are obtained for isotropic voxels of 160 μm side length. Accuracy errors for the fourcases, i.e. around 10–20% of the nominal spacing values listed in the figures.

Fig. 8. Tb.Did versus Tb.Dif regression for the complete trabecular volume, regions of size12.3 mm×12.3 mm×height of vertebra, and regions of size 6.2×6.2×5.95 mm3. Tb.Did ofcuboids were calculated from the relationship of Tb.Did versus Tb.Dif obtained on XCTscans of entire vertebrae. HRCT voxel size was 156 μm×156 μm in-plane and 400 μmslice thickness.

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−12 mg/cm3 with a RMSE=11 mg/cm3 (9%), and r2=0.88 (pb10−16).The regression line reflects all plotted points. As the smaller cuboidsare contained in the region of interest of the entire vertebrae, theredundant measurements may have led to a bias of the regressionanalysis. However, the regression solely using the points from thecomplete vertebrae and the regression solely using the points fromthe cuboids yielded very comparable results.

Trabecular distance

Test of algorithm using virtual phantomThe accuracy of the fuzzy distance based assessment of Tb.Dif

was evaluated by simulation using the virtual phantom setting of6 mm mask diameter, rod diameter dR=100 μm, plate thicknesstP=100 μm, rod or plate spacing between 900 and 1400 μm,isotropic voxels with 160 μm side length. This phantom was rotatedcounterclockwise in increments of 15° around the axis given by thevector (0.35; 0.2; 1.) (Fig. 3). As can be seen, the rotation and theresampling of the voxels led to partial volume effects. These effectsincrease with increasing voxel sizes. Please note that all quantitativecalculations were performed on gray-scale image data while in Fig. 3bone was delineated by a lower threshold (gray-scale value of 26) forvisualization purposes only. The top left diagram of Fig. 6 shows thatTb.Dif was underestimated by 105 μm on average for a phantommade up solely of rods, i.e. that the measurement error was smallerthan one voxel side length. This procedure was repeated for aphantom consisting only of plates (see top right diagram of Fig. 6)and here almost no systematic bias in the accuracy error wasobserved. The lower diagrams of Fig. 6 show the influence of rotationfor mixed rod-plate phantoms. Here, the accuracy error rangedbetween 0 and 200 μm.

Test of algorithm by comparison with Tb.Did

We evaluated the correspondence of the Tb.Did values computedby Scanco Xtreme CT's software with its FDT based analogon Tb.Dif

calculatedwith our in-house implemented algorithm. Both algorithmswere run on the XCT scans with 82 μm isotropic voxel side lengthacquired for the 14 vertebrae.

The results are plotted in Fig. 7. The Scanco Tb.Did values rangedfrom 813 to 1471 μm with mean±SD of 1091±204 μm (±19%).Using linear regression, the reference values Tb.Did could bepredicted by Tb.Dif using the equation Tb.Did=0.998 ·Tb.Dif−1 μmwith a RMSE of 32 μm corresponding to 3% of the Tb.Did

Fig. 7. Tb.Did (based on Scanco algorithm) versus Tb.Dif (based on FDT algorithm)correlation for 14 PMMA embedded vertebrae imaged with the Scanco Xtreme CT.

distribution mean, and r2=0.98 (p≤10−10). Forcing the interceptthrough zero resulted in a slope of 0.998 and a RMSE of 32 μm (3%of the mean).

Regression of XCT versus HRCTFig. 8 depicts the relationship of Tb.Did of XCTdata (cubic voxelswith

82 μm side length) versus Tb.Dif of HRCT data (156×156×400 μm3) forthree types of regions: entire vertebrae and larger and smaller cuboids.The reason for adding cuboids is apparent from the figure: data of entirevertebrae did not extend below a spacing of about 750 μm. Whereassubregions happened to fall in areas of higher and lower density andspanned awider range, in our case down to about 400 μm. On the otherhand, small volumes may contain very few trabeculae if located inregions of low density. In such cases dominance of edge effectsmay leadto biased results. To ensure that enough individual trabeculae remainedin the smaller cuboids to provide statistically robust and unbiasedresults for average spacing, we excluded most of the smaller cuboidsleaving only those that were located in the densest regions of thevertebrae.

We accepted only small cuboids with Tb.Didb750 μm and withb1136 μm (1136 μm corresponded to the 750 μm ordinateaccording to the regression for the complete vertebrae). A spacingof less than 750 μm resulted in more than 8 intersections along acuboid of 6 mm side length, a reasonable level to calculatestatistics. 36 of the 970 small subvolumes fulfilled this criterion. Wemerged the results for the three types of regions by a jointregression for all data points. The target variable Tb.Did rangedfrom 399 to 1410 μm with a mean±SD of 841±231 μm (±27.5%).The linear regression was given by Tb.Did=1.29·Tb.DifHRCT−725 μmand approximated the data with a RMSE of 78 μm (9.3%), r2=0.89(pb10−16).

In this analysis, the regression line reflects all measurement pointsplotted in Fig. 8. As the smaller cuboids are contained in the biggercuboids and all cuboids are contained in the region of interest of theentire vertebrae, the redundant measurements may have led to bias inthe regression analyses. Nevertheless, the regression solelyover the Tb.DifHRCT values from the entire vertebrae, solely over the Tb.DifHRCTvalues from the 12.3 mm×12.3 mm×height of vertebra cuboids, andsolely over the Tb.DifHRCT values from the 6.2 mm×6.2 mm×5.9 mmcuboids yielded comparable results for the residual errors, with RMSEsof 31 μm, 90 μm, and 84 μm, respectively.

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Discussion and conclusions

Trabecular structure is a determinant of bone strength indepen-dent of BMD [4,16,18,29,31] although the evidence of themagnitude ofthe contribution needs further evaluation. Therefore, it is likely thatmeasures of trabecular structure improve the prediction of fracturerisk in vivo beyond BMD results as measured by DXA or QCT [12,15,22].

The assessment of the structure of cancellous bone in humans ispresently limited to biopsies of the iliac crest or the use of highresolutionMRI or pQCTapproaches for themeasurement in peripheralregions of the skeleton such as calcaneus, tibia, radius, or ulna. Bonebiopsies can be analyzed at very high resolution but are invasive,cannot be repeated at the same location which is necessary to showtreatment effects in longitudinal studies, suffer from a limited andpoorly localizable sampling volume, and represent a site notsusceptible to fracture risk.

pQCT or MRI measurements have limited value for the assessmentof bone strength or structure at the main fracture sites of the spine orthe femur, since bone structure is adapted to local loading patternswhich differ substantially between the long bones of the peripheryand the central skeleton. Consequently the topology of the cancellousnetwork differs considerably [30] and it is not surprising that mixedresults have been reported regarding the added value of peripheralstructural measure in improving fracture discrimination [2,17].

pQCTandMRI allowedmeasurementswith voxel sizes of around 80–130 μm, respectively. This allowed depiction of trabeculae spacing withhigh accuracy. However, even for best image quality with 145 μmisotropic spatial resolution of the Xtreme CT (Scanco Medical AG,personal communication about technical specifications) other cancel-lous microarchitectural measures such as trabecular bone volumefractionBV/TVor trabecular thickness Tb.Thwere notmeasured directly,but were derived from BMD and trabecular number, i.e., they did notprovide independent information.Corticalmeasures, specificallycorticalthickness, could provide valuable information, at least for local strength.

HRCT allowed direct measurements at one of the main fracturesites, the vertebrae, but the assessments had some limitations. Thesampling theorem limits resolution of adjacent individual trabeculaeto a spacing of twice the voxel size. According to the manufacturerinformation the spatial resolution as characterized by the modula-tion transfer function (MTF) at 10% contrast is about500×500×650 μm3 for the kernel employed in our study [21]. Forcomparison, the corresponding MTF of the Xtreme CT is specified as100 μm [28]. Thus, for HRCT the spatial resolution was larger thanthe typical diameter of individual trabecular but lower thantrabecular separation. In addition, one should consider that it wasnot our aim to measure the spacing of individual trabeculae. Rather,we wanted to examine the limits for characterizing the average oflocal trabecular distances over a VOI that contains tens if nothundreds or thousands of structures. Here, we expected and indeedshowed that using a scan protocol with in-plane voxel side length of160 μm and a slice thickness of 400 μm the average trabeculardistance over the VOI could be assessed with a residual error ofabout 80 μm, less than the voxel size. This result still was limited bythe level of noise present.

To the best of our knowledge, our earlier study [5] was the firstpublication showing the feasibility of HRCT-based structural analysisof the trabecular bone in vivo as a tool for monitoring osteoporosistreatment. There, a 3D adaption of the parallel plate model [19,20] andthe mean intercepts length methods were used to calculate standardstructural variables including bone volume fraction (app. BV/TV),trabecular number (app. Tb.N), and trabecular separation (app. Tb.Sp).Here, the prefix “app.” for “apparent” was added to standardnomenclature [cf. 20] to indicate the influence of limited resolutionand low signal-to-noise ratio. In this contribution we used a similarHRCT scan protocol and analyzed a measure of trabecular spacingusing a direct 3D and model-independent method, the FDT approach.

In an earlier work based on directly measured distances in 3Dspace, Hildebrand et al. [7] had introduced the comparable measuresTb.N⁎ defined by Tb.N⁎=1/Tb.Did and Tb.Sp⁎. Here, the “⁎” labels thedifference to the corresponding structural variable stemming from the3D adaption of the stereological methods. A comparison presented in[13] between μCT data with 28 μm isotropic voxel size and scaled μCTdata with 165 μm isotropic voxel size indicated that the model-independent directly measured indices (e.g. Tb.N⁎ and Tb.Sp⁎) wereinfluenced very little by the coarser voxels (r2 between 0.93 and 0.95).The directly measured indices proved to work better than theiranalogues Tb.N and Tb.Sp based on the plate model assumption ifimaged at lower resolutions [13, Table 3]. A numerical experimentwhich is not presented in this publication, with the XCT images down-sampled to 165×165×300 μm3 and correlated with the originalisotropic 80 μm voxel size confirmed the good performance of thedirectly measured Tb.Dif under HRCT-like voxel sizes, if noise waslimited (RMSE=26 μm, r2=0.97). A further advantage of the directlyderived indices was that they did not rely on an assumed model typeandwere therefore not biased by eventual changes from a plate-like toa more rod-like structure.

The difficulty of assessing trabecular structure on CT images iswell established [6]. A part of the problem is the binarization stepemployed by most structural algorithms including the oneintroduced by Laib and Rüegsegger. Here fuzzy classificationmethods have proved useful [3,26,27] as an alternative approachmaintaining the gray-level information as long as possible. Sahaand Wehrli [23] used the FDT to assess trabecular bone thickness invivo from μ-MR images of human distal radii acquired at137×137×350 μm3 voxel size. They employed a skeletonizationapproach [24] that differed from our ridge identification approachwhich was more similar to the one introduced by Hildebrandt andRüegsegger [8]. Also their definition of trabecular bone thicknesswas based directly on the FDT whereas we followed an adaptationof the maximum sphere method by Laib and Rüegsegger. Unlikethese authors we applied the maximal sphere method to themarrow instead of the bone phase, since our spatial resolution wasmuch poorer. We applied the FDT to obviate information loss dueto an early bone/marrow binarization, used it to compute ridges,and combined it with the Tb.Dif calculation which required ridgesof the bone phase. Utilizing our FDT approach to 14 wholevertebrae scanned under ex-vivo conditions in a Scanco XtremeCT with 82 μm isotropic voxel side length, we got almost identicalresults as the Scanco Software (see Fig. 7) and our method could beused at much lower levels of spatial resolution.

Simulating in vivo conditions of an obese patient by a CIRSabdominal phantom with an attenuator ring obtained with a typicalHRCTscanner used in clinical practice, the numerical regression (Fig. 8)demonstrates that Tb.Did down to 400 μm could be predicted highlysignificantly (p≤10−16) with a RMSE of 78 μm and r2=0.89. Thedeviation of the regression line of XCT versus HRCT in Fig. 8 is in partcaused by image noise. The relative RMSE accounted for 9% of thereference's mean. As the standard deviation of reference datasetaccounted for 28% of reference's mean, this means that the RMSE wassubstantially smaller than the sample standard deviation. The samplewith an approximate T-score range from about −3 to +1 was quitesimilar in variability in BMD as the typical populations examined inosteoporosis studies.

Our results also demonstrate that HRCT permits the assessment ofsome aspects of structural inhomogeneity. Trabecular distanceassessed in cuboids of dimensions of 12 mm×12 mm×height ofvertebra spanned a wide range of values and thus reflects inhomo-geneity in the axial plane. The results obtained on smaller cuboidssuggest that it may be possible to study even smaller volumesprovided that the trabecular network is sufficiently dense for ouralgorithm to provide robust and unbiased results. Performance ofinhomogeneity measures should be evaluated in future studies to

152 A. Krebs et al. / Bone 44 (2009) 145–152

determine whether they represent biomechanically relevant mea-sures, potentially revealing weak subregions of a vertebra.

Our study has limitations. Most importantly we validated theapproach using ex-vivo data. Although the noise level of the in vivomeasurement of an obese patient was already simulated by the CIRSabdominal phantomwith an attenuator ring, unpredictable motion ofthe patient during the assessment will likely reduce image qualitymaking the quantification of trabecular spacing even more challen-ging. Unfortunately, there is no gold standard available that could beemployed in vivo. Moreover radiation exposure consideration limitsour ability to test performance measure like precision errors onpatients by taking repeated measurements. However, in our patientstudy [5] we calculated long-term precision bias based on repeatedmeasurements over 2 years and fitting of the treatment inducedchanges. The residual errors around those fit curves represent a worstcase estimate of technique related precision errors because they alsoinclude a component of true biological deviation from the fittingcurve. In that study the estimated long-term precision for Tb.Spranged around 360 μm or 12%, a level that is commensurate with thetechnique related errors of 80 μm or 9% of our technologically moresophisticated FDT method. Further improvements of the conceptcombining fuzzy concepts like the iterative fuzzy relative connected-ness [3], topological concepts [24,25], and Bayesian approaches ofsubvoxel tissue classification [1,32] could offer perspectives for evenbetter performance.

In summary, our study documents the feasibility to calculate Tb.Dif

as a measure of trabecular spacing using an HRCT protocol that can beimplemented and used in vivo on state of the art CT scanners. We havevalidated this method as a tool that permits assessment of trabeculararchitecture at one of the main osteoporotic fracture sites, thevertebrae. Our method can be used to study the effect of treatmenton bone structure. Further studies are warranted to evaluate whetherTb.Dif is a valuable independent predictor of fracture risk.

Acknowledgments

We would like to express our sincere thanks to the X-raytechnicians of the Klinik für Diagnostische Radiologie, Universitätsk-linikum Schleswig-Holstein, Campus Kiel, Christiane Henge, FrankRachau, and Gérard Morvan who have provided immense help withthe image acquisition. This work benefited from the use of the InsightSegmentation and Registration Toolkit (ITK), an open source softwaredeveloped as an initiative of the U.S. National Library of Medicine andavailable at www.itk.org [9]. Synarc Inc, Hamburg, Germany, theEuropean Regional Development Fund (ERDF), and the Innovationsstif-tung Schleswig-Holstein (ISH) supported us by Grant 2005-41T (e-region Schleswig-Holstein plus).

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