Effect of Voxel Size on 3D Micro-CT Analysis of Cortical Bone Porosity

David Cooper,1 Andrei Turinsky,2 Christoph Sensen,2 Benedikt Hallgrimsson3

1Department of Orthopaedics, Division of Orthopaedic Engineering Research, University of British Columbia,VGH - Research Pavilion - Room 597, 828 West 10th Avenue, Vancouver, BC, V5Z 1L8, Canada2Department of Biochemistry and Molecular Biology, University of Calgary, 3330 Hospital Drive NW, Calgary, AB, T2N 4N1, Canada3Department of Cell Biology and Anatomy, University of Calgary, 3330 Hospital Drive NW, Calgary, AB, T2N 4N1, Canada

Received: 3 March 2006 / Accepted: 12 May 2006 / Online publication: 5 March 2007

Abstract. This study examines the impact of voxel sizeon 3D micro-CT analysis of human cortical boneporosity. The study is based on computed microto-mography scans of 10 human anterior femoral midshaftspecimens acquired at 5, 10, and 15 lm voxel sizes.Artificial voxel sizes (10, 20, and 40 lm) were generatedfrom the smallest scan voxel size (5 lm) in order tocompare actual scanning with artificial degradation, amethod employed in other similar studies. Canal volumefraction (CaV/TV), canal surface to volume ratio (CaS/CaV), mean canal diameter (CaDm), mean canal sepa-ration (CaSp), canal number (CaN), degree of anisot-ropy (DA), and canal connectivity density (CaConnD)were calculated from matching volumes of interest forall datasets. Qualitatively, the clarity of the actual scandatasets deteriorated rapidly as voxel size increased. Incontrast, within the artificially generated datasets, theclarity of cortical pores was better maintained until thelargest voxel size (40 lm). Mean absolute percent errorvalues, correlation coefficients, and paired t-tests re-vealed a pattern of increasing, and generally significant,differences between the smallest and progressively largervoxel sizes (both scanned and artificial). Relative to theactual scans, however, the artificial datasets were lesssensitive to changing voxel size. These findings indicatedthat subtle changes in voxel size, within the rangeexamined, have a considerable effect on human corticalporosity structural parameters. Additionally, the use ofartificially increased voxel sizes should be viewed withcaution as they may not reflect what can actually beobtained by scanning.

Key words: Micro-CT — Cortical porosity — 3D —Cortical bone — Voxel size — Bone density technology— Bone histology & Histomorphometry — Bonearchitecture/structure

Introduction

Micro-computed tomography (micro-CT) has rapidlybecome a standard technique for the visualization andquantification of the 3D structure of trabecular bone.Scanning systems with voxel sizes at or below 10 mi-crons have now made non-invasive analysis of humancortical bone porosity, on the level of osteonal canals,feasible for the first time [1�7]. Synchrotron radiation-based micro-CT has even facilitated the analysis ofcortical porosity in small animal models such as themouse [8] and rat [9]. 3D analysis of cortical porosityholds great potential for improving our understandingof the role of microstructure in determining materialproperties such as strength [7], as well as providing anovel perspective on the complex spatial nature of theremodeling process [2]. A key advantage offered bymicro-CT is the ability to quantify microstructure in 3D.However, due to the limited number of studies in thisemerging area of inquiry, little is known regarding theeffects of image acquisition parameters on the results ofstructural quantification. For example, scan magnifica-tion and the voxel size at which the image data arereconstructed can have a significant impact on quanti-tative analysis. The impact of such parameters on tra-becular bone analysis has been the focus of research dueto the desire for standardization and inter-study com-parison of micro-CT results [10, 11]. Additionally, thereis interest in establishing the relation between data fromrelatively low resolution clinical imaging technologies(e.g., CT and MRI) and ‘‘true’’ trabecular morphologyas estimated by higher resolution methods [12�17]. Toour knowledge, no study has yet examined the effect ofvoxel size on 3D micro-CT analysis of cortical boneporosity. The purpose of this study was to examine theimpact of varying acquisition voxel size, around themaximum range currently obtainable with commerciallyavailable systems (5�15 lm), on the calculation ofporosity structural parameters in human cortical bone.Trabecular bone resolution dependency studies havefrequently utilized experimental designs where only the

Correspondence to: David Cooper; E-mail: cooperdv@inter-change.ubc.ca

Calcif Tissue Int (2007) 80:211�219

DOI: 10.1007/s00223-005-0274-6

smallest voxel size is actually acquired by directlyscanning the sample, and larger voxel sizes are generatedby subsequent (artificial) image degradation [10�14].For the most realistic comparison, however, it is desir-able to actually acquire scan data at the different mag-nifications and with the different imaging modalitiesbeing compared [14, 17, 18]. Therefore, for the currentstudy, the results obtained by actually scanning at dif-ferent magnifications (yielding 5, 10, and 15 lm voxelsizes) were examined to provide a direct measurement ofwhat can be practically achieved by scanning. Addi-tionally, artificially increased voxel sizes, derived fromthe highest scan magnification (5 lm voxel size), werealso assessed to compare the results from these twoexperimental methods.

Materials and Methods

Cortical bone samples were obtained from the anterior mid-shafts of 10 defleshed adult human femora of unknown ageand sex from the anatomical teaching collection at the Facultyof Medicine, University of Calgary. The samples were 5 mmacross and approximately 8 mm in length (along the long axisof the diaphysis). The samples were scanned with a SkyScan1072 (Aartselaar, Belgium) scanner with an acquisition pro-tocol that consisted of x-ray tube settings of 100 kV and 100lA, exposure time of 5.9 seconds, four-frame averaging,rotation step of 0.45 degrees, and a 1 mm aluminum filter. Theassociated scan times were approximately four hours persample. Following scanning, a 2D reconstruction stage utiliz-ing a cone-beam algorithm [19] was used to produce 1024 serial1024 · 1024 pixel cross-sectional images. This protocol was thesame as that described previously [1] with the exception thateach sample was scanned at varying magnification to generate5, 10, and 15 lm isotropic voxels. With the scanner employed,as magnification was increased, voxel size and the field of view(FOV) decreased. Therefore, in order to ensure that the sam-ples would fit within the FOV for all scan magnifications, theendosteal surfaces were ground away where they exceeded 5mm. This ensured that all samples had standardized 5 · 5 mmcross-sections. After scanning, ImageJ 1.33j [20] was used toapply a 3D median filter (5 · 5 · 5 cubic kernel) to suppressimage noise and preserve detail in three dimensions. Next,matching 2.5 mm · 2.5 mm · 2.5 mm (13.75 mm3) cubicvolumes of interest (VOI) were digitally extracted from themidcortex of each of the scanned datasets. Following this, thehighest magnification VOI (5 lm) from each sample wasartificially degraded using TConv 2.0 (SkyScan, Aartselaar,Belgium) to voxel sizes of 10, 20, and 40 lm using isotropic 3Dunweighted averaging. Due to the isotropic nature of thedataset voxels and the kernel of the averaging algorithm, thisapproach resulted in equal in plane (x,y) and between plane/slice (z) averaging, both in terms of the number of voxels andactual spatial dimensions. The 3D averaging approach waschosen as it most closely simulates the partial volume effectwhich affects actual scans and replicates the approach used insimilar studies of trabecular bone analysis [10, 12, 13]. Alldatasets were segmented with a user-defined global threshold.Due to the consistency of the grayscale values it was possibleto apply a standardized threshold to the 5 lm scan datasetsand all of the derived artificial datasets for each femur. Fluc-tuations in the grayscale distributions between the scan data-sets for each femur necessitated individually determinedthresholds. Finally, 3D surface renders of the scan and artifi-cial datasets was created using Analyze 5.0 (AnalyzeDirect,Lenexa, KS). The 3D parameters developed for the analysis oftrabecular bone [summarized by 21], provided they are model-independent, have proven useful for the analysis of other

structures such as polymer scaffolds [22]. These parameterswere applied to the cortical porosity in the current study usingthe general approach described by Cooper and colleagues [2].For each of the datasets, percent porosity or ‘‘canal volumefraction’’ (CaV/TV), canal surface to volume ratio (CaS/CaV),mean canal diameter (CaDm), mean canal separation (CaSp),canal number (CaN), and degree of anisotropy (DA) werecalculated using CT Analyser 1.3.2.2 (SkyScan, Aartselaar,Belgium). Canal connectivity density (CaConnD), a measureof the number of interconnections or branching points in thecanal network, was measured using custom software [2]. Allparameters were assessed for the entire cubic sample, exceptfor DA, which was measured from the largest spherical volumethat would fit within each cubic sample. Statistical analysis wasperformed using SPSS 12.0 (SPSS Inc., Chicago, IL). Thelarger voxel size datasets (both scan and artificial) were com-pared to the highest magnification scan (5 lm) dataset. Thisvalue was treated as representing the ‘‘truest’’ measure, as itwas assumed that the highest magnification would produce themost realistic result [10, 12, 13, 18]. Therefore, percent errorwas calculated as follows for each of the femora:

Percent Error = ((Scan or Artificial Result � 5lm ScanResult) / 5lm Scan Result) * 100

Kolmogorov-Smirnov tests were employed to determine ifthe distribution of the variables was normal for each dataset.Homogeneity of variance for each of the parameters wasexamined using Levene�s test, both within the methods (scanand artificial degradation) and between them (scan vs. arti-ficial degradation for the 10 lm voxel size). Paired t-testswere used to compare the highest scan magnification (5 lm)against all other datasets (scan and artificial). Due to themultiple tests for each parameter (n = 5), a Bonferroniadjustment [23] was applied, which shifted the alpha valuefrom 0.05 to 0.01. Paired t-tests were also employed toexamine the differences between the two methods for the 10lm voxel size (alpha = 0.05).

Results

Representative 2D cross-sections and 3D reconstruc-tions from the 5, 10, and 15 lm scan and 10, 20, and 40lm artificial voxel sizes are provided in Figures 1 and 2,respectively. Visual comparison of the 2D images qual-itatively demonstrated that the scan magnification had aconsiderable impact. The highest scan magnificationprovided the sharpest detail and, as voxel size increased,the images became progressively distorted (Fig. 1). Incontrast, detail was maintained until the largest (40 lm)voxel size in the artificially degraded images. The 3Drenderings demonstrated the same general pattern, withdecreased detail, loss of 3D continuity in the canals, andthe increasing presence of noise as scan magnificationdecreased. Again, the artificially generated datasets re-sulted in relatively improved 3D renderings comparedwith corresponding actual scan datasets. Overall, theartificially degraded datasets were noticeably better thanthe corresponding scan datasets and the negative effectsof pixelation were not overtly evident until the 40 lmvoxel size. The mean results and standard deviations foreach parameter by voxel size and method are summa-rized in Table 1. Kolmogorov-Smirnov tests revealedthat the results for each dataset did not deviate signifi-cantly from normality (P > 0.05) and thus analysis withparametric statistics was warranted. For the scanned

212 D. Cooper et al.: 3D Micro-CT of Human Cortical Bone Porosity

datasets, variances were not significantly affected byvoxel size, except for CaConnD (P > 0.05). Variancesalso differed significantly (P > 0.05) for CaConnD forthe artificial datasets, as did those for DA. Comparingthe scan and artificial 10 lm results, none of theparameters exhibited significantly different variances.The mean results for each of the parameters obtainedfrom scan and artificial datasets are provided in Fig-ure 3. For all parameters, other than CaV/TV, thegeneral pattern of results was similar for both methods,with the actual scans demonstrating more exaggeratedchanges. For CaV/TV, the scan and artificial resultsshowed opposite patterns, with the artificial resultsdecreasing and the scan results increasing. Pearsoncorrelations between the 5 lm scan results and all othervoxel sizes (scan and artificial) were consistently signif-icant (P < 0.01) for CaV/TV, CaDm, CaSp, and CaN.

For CaS/CaV the artificial datasets were all significantlycorrelated (P < 0.01), while only the 10 lm artificialdataset was significantly correlated for DA. None of thevoxel sizes, scan or artificial, was significantly correlatedwith the 5 lm scan voxel size for CaConnD. Table 2summarizes the differences between the parameters interms of mean percent error from the 5 lm scans. Basedupon this measure, the parameters that were the mostsensitive to change in voxel size were CaConnD, CaDm,while CaSp, and DA were relatively stable. Paired t-testsindicated numerous significant (P < 0.01) differencesfrom the 5 lm results. The exceptions to this were thethe 10 lm artificial datasets for CaV/TV (P = 0.067)and CaSp (P = 0.036), and both scan datasets for DA(P = 0.015) and CaN (P = 0.168). Comparing the twomethods directly, all parameters were significantly(P < 0.05) different for the 10 lm datasets.

Fig. 2. Representative 3D rendering of a1000 lm thick sub-volume (longitudinallyoriented). Scanned datasets along top row: 5(left), 10 (center), and 15 (right) lm voxelsizes. Artificially degraded datasets alongbottom row: 10 (left) 20 (center), and 40(right) lm voxel sizes.

Fig. 1. Representative 2D micro-CT cross-setions at matched magnifications (scaledwithout interpolation). Lower left insertrepresent original image sizes relative to 5 lmscan image. Scanned datasets along top row:5 (left), 10 (center), and 15 (right) lm voxelsizes. Artificially degraded datasets alongbottom row: 10 (left), 20 (center), and 40(right) lm voxel sizes.

D. Cooper et al.: 3D Micro-CT of Human Cortical Bone Porosity 213

Discussion

The primary objective of this study was to explore therelation between scan voxel size and 3D structuralanalysis of the cortical porosity within human boneusing a range of magnifications that are achievable usingcommercial micro-CT scanners. In addition, we com-pared the results from actual scans with artificiallygenerated datasets at varying voxel sizes. All parametersdemonstrated dependency upon voxel size and signifi-cant differences were found between the highest scanmagnification and most others (scan and artificial).However, the scan data were more sensitive to changesin magnification, exhibiting more exaggerated patternsof voxel size dependency. Scan quality is potentiallyimpacted by numerous factors including resolution,magnification, noise, artifacts, and post-acquisitionprocessing (e.g., filtering), all acting synergistically.Notably, scan magnification and resolution are notsynonymous or necessarily linearly related. For exam-ple, the relation between these parameters has beenfound to be non-liner for the SkyScan 1072 scanner,with resolution (measured by 10% Modulation TransferFunction (MTF)) saturating at the level of the x-raysource spot size [24]. It should be noted that the scanneremployed in the current study had a spot size corre-sponding with the smallest voxel size examined (5 lm).The artificial degradation approach bypasses such issuesand the error they introduce. This contributes to theproduction of results that are not necessarily a reflectionof what can be practically achieved by scanning. This isnon-trivial since it has been proposed that such simu-lated results can be used to calibrate inter-study and

even intermodality (e.g. micro-CT to CT) results [10].While meaningful calibration may be possible, particu-larly at high magnifications, this practice should beviewed with caution. For example, extreme changes invoxel sizes, such as those between in vitro micro-CT andin vivo clinical techniques (e.g. MRI and CT), oftenresult in the detection of fundamentally different struc-tures [12]. Additionally, calibrations based upon artifi-cial datasets will be dependent upon the quality of thestarting ‘‘source’’ dataset. Therefore different calibra-tions would likely be produced from images obtainedwith different initial scan conditions. This concern ex-tends to the comparison of actual scan results sincedifferent acquisition protocols can have a considerableimpact on quantitative analysis [25]. Further, Bernhardtand colleagues [26] found considerable differences in theresults obtained from three micro-CT systems (onesynchrotron-based and two microfocus systems), indi-cating that caution should also be exercised whencomparing results from different scanners, even if simi-lar voxel sizes are being compared. As such, studies ofimage parameter dependency, including this one, shouldbe viewed as providing background information to aidin the choice of scan protocols and to draw broadcomparisons in terms of inter-study and inter-modalityresults.

A predictable pattern of dependency can be expectedif a structure is initially imaged at a magnification farhigher than needed to resolve it and then the voxel size isprogressively decreased [10]. At first, partial volume ef-fects would be negligible and measurements would bestable despite increases in voxel size. Then, as voxel sizeis progressively increased, a region of monotonous

Table 1. Mean (Standard Deviation) results for each paramater and voxel size.

Variable CaV/TV Cas/CaV CaDm CaSp

5 lm Scan 4.38 (2.82) 0.0771 (0.0190) 68.0 (30.0) 354.3 (35.8)10 lm Scan 5.44 (3.47) 0.0526 (0.0206) 87.2 (28.2) 381.2 (43.5)15 lm Scan 6.02 (3.82) 0.0360 (0.0218) 111.1 (26.7) 453.7 (57.1)10 lm Artificial 4.21 (2.82) 0.0733 (0.0171) 75.5 (27.0) 368.8 (44.6)20 lm Artificial 3.87 (2.82) 0.0710 (0.0171) 98.0 (27.3) 391.4 (47.0)40 lm Artificial 2.87 (2.77) 0.0678 (0.0172) 110.1 (43.2) 482.3 (60.6)

Units % lm)1 lm lm

Variable CaN DA CaConnD

5 lm Scan 0.64 (0.18) 0.652 (0.071) 30.8 (11.3)10 lm Scan 0.60 (0.16) 0.714 (0.049) 10.5 (2.4)15 lm Scan 0.51 (0.21) 0.655 (0.052) 6.1 (2.4)10 lm Artificial 0.53 (0.18) 0.768 (0.034) 17.7 (4.4)20 lm Artificial 0.37 (0.15) 0.812 (0.024) 8.9 (2.3)40 lm Artificial 0.23 (0.12) 0.795 (0.040) 2.5 (1.4)

Units mm)1 — mm)3

Cav/TV = cortical porosity; CaN = canal number; CaS/CaV = canal surface to volume ratio; DA = degree of anisotropy;CaDm = mean canal diameter; CaConnD = canal connectivity density; CaSp = mean canal separation

214 D. Cooper et al.: 3D Micro-CT of Human Cortical Bone Porosity

change would occur. Finally, as the voxel size ap-proaches and ultimately exceeds the size of the target,measurements would become erratic and eventuallyconverge upon an end point. For trabecular bone andcortical bone porosity, this terminal point represents theresolution at which no trabeculae or cortical canals areresolved, respectively. Different parameters exhibit dif-ferent directions of dependency and also vary in theirsensitivity (rate of change) to shifts in voxel size. For thecurrent study the directions of voxel-dependent changewere found to vary between parameters and, in the caseof CaV/TV, between the scan and artificial datasets. Ingeneral, the patterns of change found in the currentstudy agree well with those from comparable measure-ments of trabecular bone (summarized in Table 3). Acaveat must be added here that, despite the use ofstandardized terminology and symbols, parameters arenot always measured in the same manner. Additionally,

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Fig. 3. Variation in mean results by scannedand artificial voxel sizes. Error bars indicatestandard deviation. (CaV/TV = corticalporosity; CaS/CaV = canal surface tovolume ratio; CaDm = mean canaldiameter; CaSp = mean canal separation;CaN = canal number; DA = degree ofanisotrophy; CaConnD = canalconnectivity density).

Table 2. Absolute mean percent errors (relative to the 5 lmscan) plotted by method and voxel size.

Scan Artificial

10 lm 15 lm 10 lm 20 lm 40 lm

CaV/TV 25.8 38.5 4.0 13.7 41.2CaS/CaV 30.2 54.7 4.8 7.6 12.0CaDm 33.0 73.5 14.6 50.9 64.3CaN 9.6 19.7 17.3 42.5 65.0DA 10.7 14.4 18.8 25.9 23.1CaConnD 63.2 78.9 46.2 68.7 90.8

CaV/TV = cortical porosity; CaN = canal number; CaS/CaV = canal surface to volume ratio; DA = degree ofanisotropy; CaDm = mean canal diameter; CaC-onnD = canal connectivity density; CaSp = mean canalseparation

D. Cooper et al.: 3D Micro-CT of Human Cortical Bone Porosity 215

different studies vary in their usage of the term resolu-tion, with many treating it as synonymous with voxelsize. Therefore, it is important to be aware of the dif-ferent terminologies used when making inter-studycomparisons.

The instability of mean canal diameter (CaDm) canbe attributed to the fact that the diameters of thesmallest canals approached the same size, or were evensmaller (particularly for the 15 lm voxel size), than thescan voxels generated to represent their structure. Assuch, the partial volume effect was likely the primarycause of the dramatic patterns of dependency forCaDm. For the studies listed in Table 3, mean trabec-ular thickness (TbTh) was consistently found to increaseas voxel size increased. This pattern has generally beenattributed to the loss of detection of smaller trabeculaeresulting in elevated mean thickness [12]. However, ageneral thickening of trabeculae has been describedwhen analyzing actual scans [18]. The increase in meanCaDm found in this study for the artificial datasets canbest be attributed to the progressive loss of detection ofsmaller canals, particularly in light of the use of astandardized threshold for each series of datasets. Incontrast, the greater increase in CaDm for the scandatasets can be attributed to a combination of theinability to resolve smaller canals and the thickening ofthe remaining canals. Visual inspection of variousdatasets (Figs. 1 and 2) lend support to this interpreta-tion. The cortical canals appeared larger in the lowermagnification (particularly 15 lm scan) than those in the5 lm scan and artificial voxel sizes.

Merging of trabeculae, due to an increase in theirthickness, can account for the decrease in trabecularnumber (TbN) associated with larger voxel size [18]. Inthe current study, canal number (CaN) decreased withmagnification for both the scan and artificial datasets.While a merging effect can not be ruled out for the

current study, it would likely have a minimal effect onthe measurement of cortical canals which have a morespatially dispersed arrangement than the plates andstruts of trabecular bone. Therefore, the decrease inCaN can be attributed primarily to the loss of detectionof small canals and the resulting increase in the spacebetween those that remained. Similarly, mean trabecularseparation (TbSp) has consistently been found to in-crease as magnification decreases (Table 3). This patternof change is explained by the inability to resolve smallertrabeculae which leads to larger spaces between theremaining struts and plates [11]. With respect to thecurrent study, the apparent loss of small canals waslikely the primary cause of the increase in canal sepa-ration (CaSp).

For trabecular bone, degree of anisotropy (DA) hasbeen found to both increase [12] and decrease [18] withdeclining magnification (based upon recalculated resultsto correspond to DA as measured by CT Analyser). Thediscrepancy between these studies may, in part, be dueto the size and the nature of the voxels (anisotropic vs.isotropic) involved. For the current study, DA measuredfrom the artificial datasets increased non-linearly, rap-idly leveling off as voxel size increased. For the scanseries, DA was elevated at 10 lm and then droppeddown, nearly returning to the starting value by 15 lm.The initial increase was likely due to both the inability todetect some transversely oriented (Volkmann�s) canalsand the thickening of the longitudinally oriented canalsin the 10 lm scan datasets (as discussed above). Thesimilar results for the 5 and 15 lm scan datasets appearsto be due, at least in part, to an increased level of noisein the 15 lm datasets.

Assuming the cross-sectional shape of cortical canalsis circular, canal surface is proportional to the circum-ference and thus increases arithmetically (linearly) ascanal radius increases. However, the cross-sectional area

Table 3. Generalized patterns of resolution/voxel size dependency. Arrows indicate direction of change in parameters as voxel sizeincreases (decrease in resolution).

Trabecular Bone BV/TV BS/BV TbTh TbSp TbN DA

Muller et al. 1996 . - m m . -Kothari et al. 1998 m - m m . ma

Peyrin et al. 1998 . . m m . -Kim et al. 2004 m . m m . .b

Cortical Bone CaV/TV CaS/CaV CaDm CaSp CaN DA

Current Study: Scan m . m m . mCurrent Study: Artificial . . m m . m

a Based upon patterns of change graphically depicted in their Figure 7 (Kotheri et al.,1998)b Recalculated to DA defined in this paper from mean values in their Table 1 (Kim et al., 2004)BV/TV = bone volume fraction; CaV/TV = cortical porosity; BS/BV = bone surface to volume ratio; CaS/CaV = canal sur-face to volume ratio; TbTh = mean trabecular thickness; CaDm = mean canal diameter; TbSp = mean trabecular separation;CaSp = mean canal separation; TbN = trabecular number; CaN = canal number; DA = degree of anisotropy; DA = degreeof anisotropy

216 D. Cooper et al.: 3D Micro-CT of Human Cortical Bone Porosity

of a canal increases geometrically (quadratically). As aconsequence, the ratio of surface area to volume de-creases asymptotically towards 0 as the radius increasestowards infinity. Thus, the decrease in canal surface tovolume ratio (CaS/CaV) as scan magnification droppedwas most likely the result of the increase in mean canaldiameter described above. Trabecular bone studies haveconsistently identified a drop in bone surface to volumeratio (BS/BV) associated with larger voxel size (Ta-ble 3).

The stability of canal volume fraction (CaV/TV) inthe artificial datasets in the current study correspondswell with those of trabecular bone where the parametermost consistently described as the least sensitive tochanging voxel size is bone volume fraction (BV/TV).Indeed, a stable region of dependency has been de-scribed for BV/TV in trabecular bone, when imagedwith voxel sizes below 100 lm [10, 11]. In light of thisstability, it is striking that, in terms of direction, voxel-dependent change in this parameter has been inconsis-tent in past studies (Table 3). Similarly, in the currentstudy, the opposite direction of change in CaV/TV forthe two methods was unexpected. It is intuitively rea-sonable that as magnification decreases there is a thin-ning and loss of trabeculae leading to a decrease in TbNand a simultaneous increase in TbSp. Cumulatively, thisconstellation of changes would result in a decrease inoverall BV/TV. However, as discussed, TbTh can actu-ally increase and thus account for an increase in BV/TVdespite the loss of small trabeculae. The parallel situa-tion was found in the current study for cortical bone.Decreasing magnification resulted in a loss of canals forboth the scan and artificial datasets. For the artificialdatasets, this resulted in a simultaneous drop in CaV/TV. However, the inflated canal diameters in the scandatasets led to an increase in CaV/TV. This represents aclear example of where calibration based upon artifi-cially generated datasets would certainly provide mis-leading results. With respect to the inter-study variationin the direction of change for BV/TV, it is likely thatdifferences in image segmentation were a major factor(see below).

A custom algorithm was employed to directly mea-sure interconnections in the porous canal network andderive the canal connectivity density (CaConnD) [2].Unlike the other parameters measured in this study, thisvalue was a direct count (standardized by volume) ra-ther than a stereological estimate. As such, it is notsurprising that the percent errors associated withchanging voxel size for this parameter were the largestand the correlations between them the lowest. The highvariance for the 5 lm scans reflects the biological vari-ability within the samples. The drop in the mean valuesand standard deviations associated with decreasingmagnification reflected the inability to detect allbranching points, particularly those between smaller

canals. At the lowest magnifications, the largest canalsand branching points were consistently resolved, as re-flected in the lower standard deviation values.

While every effort was made to minimize and controlfor sources of error, there were a number of confound-ing factors that certainly contributed to the differencesbetween the datasets. Due to the fact that the artificialdatasets were derived directly from the 5 lm scandatasets they represented near perfect matches with re-spect to the volume of interest. In contrast, for the dif-ferent scan magnifications the matching volumes ofinterest had to be manually extracted. While the volumematches were generally quite good (see Figs. 1 and 2), adegree of error was unavoidable. Thus, some of thedifference between the scan results can be attributed toimperfect volume of interest matches.

For this study, global thresholding was employed tosegment the grayscale images into binary black andwhite for analysis. It is likely that the differences in thepatterns of resolution/voxel size dependency for tra-becular bone BV/TV summarized in Table 3 can, inpart, be attributed to differences in segmentationmethodology. For example, Peyrin and colleagues [11]used local thresholding, while Kim et al. [18] andKothari et al. [12] used two different adaptive (local)segmentation algorithms. As the aim of this study wasto examine the impact of voxel size, rather than seg-mentation methods, it was deemed best to proceedwith global thresholding which, despite potential lim-itations due to artifacts such as beam hardening, isstraightforward and the most accessible and repro-ducible method available to researchers. For the arti-ficial datasets a standard threshold (determined foreach of the 5 lm scan datasets) was used. For the scandatasets a user defined threshold was determined foreach magnification, which can account for some of theerror between the datasets. However, the homogeneityof variance between the different voxel sizes andmethods for the majority of parameters indicated thatthe user defined global thresholds produced consistentresults.

Micro-CT image data are often plagued with highlevels of noise. A commonly employed method forsuppressing noise is the application of filters (usuallygaussian or median). A filter essentially considers eachpixel with a set number of its adjacent neighbors (de-fined as a kernel) and manipulates its value. In the caseof a median filter, each pixel is replaced with the medianvalue from within its kernel. For isotropic kernels,the size of the neighborhood increases geometrically(squared for 2D and cubed for 3D filters). For example,a 3D 5 kernel involves 125 (5 · 5 · 5) voxels. Filters areeffective at eliminating noise; however, they also have ablurring effect on the image data that increases alongwith kernel size. A 3D 5 kernel median filter was used onall scan datasets in the current study. In calibrated units,

D. Cooper et al.: 3D Micro-CT of Human Cortical Bone Porosity 217

this corresponded to 15625 lm3, 125000 lm3, and421875 lm3 in the 5, 10 and 15 lm datasets, respec-tively. Therefore, while kernel size was standardized interms of voxels, the actual volume increased as magni-fication decreased. This certainly contributed to theprogressively blurred appearance of the lower magnifi-cation scans. Scaling of kernel size may help to improvethe quality of lower magnification scans. However, withthe exception of sub-voxel processing [27], a 3 voxelkernel is the smallest cubic filter possible. Similar studiesof trabecular bone analysis have differed in the use ofpost-degradation filtering [e.g., 10, 12]. For the currentstudy, the 5 lm scan datasets were filtered while theartificial datasets derived from them were not. Thiscertainly contributed to the similarity among the artifi-cial datasets, and the differences between the artificialand scan datasets.

Conclusions

All parameters demonstrated patterns of dependencyupon voxel size, indicating that it is a non-trivial factoraffecting quantitative analysis. While similar findingshave been reported for trabecular bone, analysis of thecortical canal network was generally less stable and moresensitive to subtle changes in voxel size. Further, wefound that the method of simulating lower magnifica-tions through artificial degradation produces results thatare potentially misleading when compared with actualscans. Ultimately, the sensitivity of the structuralparameters to changes in voxel size, suggests that highermagnifications (<5 lm) will be necessary to consistentlyresolve all of the smallest canals within human corticalbone. This should not be viewed as discouraging the useof larger voxel sizes (5�10 lm), only as an indicator thatmeasurements are approximations which are not neces-sarily indicative of ‘‘true’’ values and that standardiza-tion of methods is absolutely critical. Notably, despitethe fact that some trabecular measurements have beenshown to be unstable at 6.65 lm [11], micro-CT analysisutilizing larger voxel sizes (commonly 15�30 lm [21])has contributed a wealth of information to the study oftrabecular architecture. It is hoped that a similar situa-tion will develop with respect to cortical bone, andobtaining a better understanding of current limitations isan important step in this direction.

The dependency of morphological parameters onvoxel size is also affected by the size of the target objects.Thus, as diameters of the cortical canals increase (e.g. asa result of systemic bone loss with advancing age ordisease) lower magnifications may be sufficient to acquirestable results. This phenomenon likely explains the goodcorrelation between cortical bone porosity measured byhistology and micro-CT operating at 30 lm voxel size,demonstrated by Wachter and colleagues [6], on a sam-ple drawn from an elderly and pathological population.

Conversely, small animal models have smaller corticalcanals than humans and require even higher magnifica-tions for consistent visualization [8, 9]. While the highestmagnification possible is desirable, it may come withlimitations including decreased field of view and increasedradiation dose (in the case in vivo imaging). Therefore, theaims of any study should be assessed to determine thenecessary and/or possible image quality, weighing factorssuch as scan time, field of view, and voxel size. In thefuture, we will almost certainly see the development ofhigher resolution scanners capable of increasingly largefields of view. However, provided its limitations areunderstood, micro-CT already offers a powerful new toolfor the 3D visualization and quantification of the canalnetwork within human cortical bone.

Acknowledgements. DMLC would like to thank SSHRC andthe Alberta Provincial CIHR Training Program in Bone andJoint Health for support during the period this study wasconducted. In addition to grant support, BH thanks the Uni-versity of Calgary and the Nat Christie Foundation for sup-port of the 3D Morphometrics Facility. CWS is fundedthrough Genome Canada, Genome Alberta, the WEPA pro-gram, which is a joint project between Western EconomicDiversification and the Alberta Science and ResearchAuthority and the National Science and Engineering ResearchCouncil of Canada. CWS is the iCORE/ Sun Microsystemschair in Applied Bioinformatics.

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