A Comparative Study of Trabecular Bone Micro-Structural Measurements using Different CT Modalities

Abstract

Purpose:

Osteoporosis, characterized by reduced bone mineral density (BMD) and micro-architectural degeneration, significantly enhances fracture-risk. There are several viable methods for trabecular bone micro-imaging, which widely vary in terms of technology, reconstruction principle, spatial and temporal resolutions. Also, there are different methods for computing representative bone micro-structural features. We have performed a post-mortem study to evaluate different methods of CT-based trabecular bone micro-structural measurements.

Method:

Cadaveric bone specimens from the distal radius were scanned using micro-CT and four in vivo CT imaging modalities: HR-pQCT, dental CBCT, whole body MDCT, and extremity CBCT. Trabecular bone micro-structural measures were computed from CT scans using in vivo modalities, and their agreement with corresponding reference measures from micro-CT imaging was examined. A new algorithm was developed to optimize soft thresholding parameters for individual CT modalities for computing bone volume fraction images.

Results:

Observed values of most trabecular measures, including trabecular bone volume, network area, transverse and plate-rod micro-structure, thickness, and spacing, for in vivo CT modalities were higher than their reference values derived from micro-CT imaging. In general, the values of trabecular bone measures derived from HR-pQCT imaging were closer to their reference values as compared to other in vivo CT modalities. Despite large differences in observed values of measures among modalities, high linear correlation (r ∈ [0.94 0.99]) was found among micro-CT and in vivo CT-derived measures of trabecular bone volume, transverse and plate micro-structural volume, and network area. All HR-pQCT-derived trabecular measures, except erosion index, showed high correlation (r ∈ [0.91 0.99]). Erosion index using in vivo modalities showed weaker correlation (r ∈ [0.65 0.81]) as compared to the plate-width measure (r ∈ [0.72 0.91]).

Conclusion:

The strong correlations found, demonstrate the potential of in vivo CT modalities for trabecular bone micro-structural imaging. However, large shifts in observed values of trabecular bone measures for in vivo imaging modalities suggest that proper scanner calibration is necessary before using in multisite and longitudinal studies. The wide range of performance of different measures with different imaging modalities suggests the need for a judicious choice of measures depending on the imaging modality used.

1. INTRODUCTION

Osteoporosis is a bone disease characterized by reduced bone mineral density (BMD), degenerated bone micro-structure, and enhanced fracture-risk.^1-3 Although osteoporosis is a disease across all ages and both genders, its prevalence grows with aging, especially, among Caucasians and women after menopause.⁴ Nearly 40 percent of women and 13 percent of men suffer one or more fragility fractures in their lifetime. The continued increase in life-expectancy has tilted human age distribution toward older ages, increasing the prevalence of age-related conditions, e.g., osteoporosis, and the annual incidence of hip fractures is expected to rise to 6.3 million by 2050.⁵ Commonly, osteoporotic fractures occur in the hip, spine, wrist, and upper arm. Osteoporotic hip fractures are especially devastating, reducing life expectancy by 15-20 percent and adding an annual healthcare cost of nearly 19 billion dollars in the United States alone.⁶ Osteoporosis mostly remains non-symptomatic until a fracture occurs, often due to already advanced disease stage with porous and weaker bone. Early and accurate diagnosis of osteoporosis and assessment of fracture-risk is fundamental to handle the disease, and bone imaging plays an important role to accomplish this goal.⁷

Dual-energy X-ray absorptiometry (DXA) computed BMD is clinically used to characterize osteoporosis. It has been shown that BMD explains 60-70% of the variability in bone strength and fracture-risk, and the remaining variability comes from the collective effect of other factors such as cortical and trabecular bone distribution, and their micro-structural basis.^8,9 Roles of trabecular bone micro-structure in determining bone strength and fracture-risk have been convincingly established in histologic studies. ^10-15

In a histologic study among osteoporotic men, Legrand et al.¹⁰ observed significant differences in trabecular bone micro-structural measures between fracture and non-fracture groups, while the differences in age and body mass index (BMI) between the groups were non-significant; differences in BMD between the groups were non-significant by study design. In another study involving men with low BMD (T-score < −2.5) and different risk factors including age, BMI, alcohol intake, corticosteroid therapy, hypogonadism, and chronic diseases, Legrand et al.¹¹ observed that men with three or more risk factors had low trabecular bone volume, cortical bone thickness, and a marked disorganization of the trabecular network. Based on a post-menopausal study, Moore et al.¹² characterized women with vertebral fractures by loss of individual trabecular elements and increased trabecular spacing leading to significant decrease in trabecular bone volume.

Trabecular bone is composed of structures called “rods” and “plates”. Also, trabecular bone mostly consists of “longitudinal” and “transverse” structures. Longitudinal trabeculae run parallel to the long axis of the radius, and transverse structures are perpendicular to the axis. Most trabecular plates are longitudinal, and transverse trabeculae are mostly rods.¹⁶ There is histological evidence confirming relationships between gradual conversion of trabecular plates to rods and increased fracture risk.^13-15 In a study among post-menopausal women, Kleerekoper et al.¹³ observed that women with vertebral fractures have significantly lower trabecular plate density than BMD-matched controls without fracture. Parfitt et al.¹⁴ observed that age-related loss in trabecular bone volume is mainly due to reduction in plate density, and further reduction in plate density was observed in patients with osteoporotic vertebral fracture. Chappard et al.¹⁵ observed trabecular plate thinning and perforation in patients with corticosteroid-induced osteoporosis. Silva et al.¹⁷ observed that loss of transverse trabeculae is associated with a marked reduction in bone strength leading to failure due to buckling of longitudinal trabeculae.

In the last two decades, there has been remarkable progress in high-resolution imaging and analytic technologies enabling in vivo assessment of trabecular bone micro-structure.¹⁸ State-of-the-art imaging modalities for trabecular bone micro-structural assessment include magnetic resonance imaging (MRI),^8,19,20 high-resolution peripheral quantitative computed tomography (HR-pQCT),^21,22 flat-panel cone beam CT (CBCT),²³ and whole-body multi-row detector CT (MDCT).²⁴ A major advantage of CT-based methods is that they provide quantitative BMD assessment. Also, these methods are relatively easy to apply and calibrate for data uniformity in multi-site studies. However, major challenges with CT-based methods for trabecular bone micro-structural analysis emerge from wide differences in image noise and spatial resolution characteristics among the HR-pQCT, CBCT, and MDCT modalities, and even among different CBCT scanners. Therefore, there is a need to evaluate the performance of different CT-based methods for trabecular bone micro-structural analysis and understand the relationship of different trabecular bone measures with image noise and spatial resolution of different CT modalities.

In this paper, we examine the performance of HR-pQCT, CBCT, and MDCT imaging modalities in computing trabecular bone micro-structural measures, especially those related to trabecular plate/rod and longitudinal/transverse distribution, as compared to reference trabecular bone measures derived from micro-CT imaging at 8.61 μm isotropic voxel size. Also, we present a generalized approach to derive optimum segmentation parameters, for individual CT modalities generating non-binary bone volume fraction (bvf) image from a CT scan, that maximizes the agreement with the corresponding registered micro-CT data.

2. METHODOLOGY

To evaluate the performance of different in vivo CT-based modalities for quantitative trabecular bone micro-structural analysis, we compared the performance of four in vivo CT imaging modalities: HR-pQCT, dental CBCT, whole body MDCT, and extremity CBCT. Cadaveric bone specimens from distal radius were used for the experiments, and trabecular bone measures derived using micro-CT imaging were considered as reference. These cadaveric specimens have been previously used in several studies.^25-32 In this study, we focus on the performance of different trabecular bone micro-structural measures, especially those related to trabecular plate/rod and longitudinal/transverse distribution. Roles of trabecular plate/rod and longitudinal/transverse micro-structural measures have been convincingly demonstrated in histological studies.^10-15,11 Also, in this paper, we present a new generalized method for computing soft thresholding parameters for any given CT modality that maximizes agreement of segmented bvf maps with trabecular bone micro-networks captured in reference micro-CT imaging. The experimental design adopted in this paper did not involve a large homogeneous tissue region. Therefore, contrast-to-noise ratio (CNR) was determined as the ratio of the difference in mean bone and background skeleton voxel intensity, and the standard deviation of the background skeleton voxels. Both image voxel size and true resolution determined at 10% modulation transfer function (MTF) are reported for different imaging modalities. It may be clarified that resolution (lp/mm) at 10% MTF is an intrinsic feature of the technology implemented in an imaging modality defining its detectability of structural resolution. On the other hand, voxel size is defined during image reconstruction, which is often varied to control image noise and matrix size; however, reducing voxel size beyond true resolution may not further enhance the resolution of structure detectability. Also, CT dose index (CTDI) is provided as the measure of radiation dose output for each scanner except micro-CT.

2.A. Cadaveric Specimens

We used 14 cadaveric human radii bone specimens, donated to medical research at the University of California, San Francisco in accordance with the ethical guidelines regulating such donations. The specimens were defatted and preserved in plain water at normal room temperature. Each specimen is approximately cubic with at least one side containing some cortical bone. The side lengths are 12-15 mm. They were stored individually in marked test-tubes containing water. See Figure 1 for an example.

Figure 1.

An example of cadaveric bone specimen and acquired CT scans. (a) A photographic representation of a distal radius bone specimen. (b) A 3D volume rendition of micro-CT scan of the same specimen. (c-g) Volume renditions of matching VOIs from registered images acquired using different scanners: (c) micro-CT, (d) HR-pQCT, (e) dental CBCT, (f) whole body MDCT, and (g) extremity CBCT.

2.B. Micro-CT Imaging

Each specimen was scanned in a SkyScan1176 micro-CT (SkyScan, Kontich, Belgium) scanner. The following micro-CT scan parameters were used – tube voltage 65 kV, tube current 385 μA, 1 mm Al filter for beam hardening, 30×23 mm² field of view, 0.3° rotation step, 1100 ms per rotation, total scan time per specimen 2 hours. This scanner had a true resolution (10% MTF) of 100 lp/mm = 5 μm; all scans were reconstructed at 8.67 μm isotropic voxel size using filtered back-projection; and the observed CNR was 24.12 ± 3.68 (mean ± std.). Intensity values were acquired as an uncalibrated linear attenuation coefficient over the range of [0 65535].

2.C. HR-pQCT Imaging

HR-pQCT images were acquired in an XtremeCT (Scanco Medical AG, Brüttisellen, Switzerland) scanner. The following scan parameters were used: tube voltage 60 kVp, tube current 0.9 mA, field of view 126x126 mm², imaging time 336 s. Acquired images were associated with the following properties — voxel size: 82 μm isotropic, true resolution: 5 lp/mm = 100 μm, CNR: 4.07 ± 0.53, and CTDI: 5.5 mGy. Intensity values were acquired in mg HA¹ unit after rescaling with slope: 0.197 and intercept: −393.5.

2.D. CBCT Imaging

3D Accuitomo 80 (J. Morita MFG., Kyoto, Japan):

A dental CBCT device. The following CBCT parameters were used for all scans on this device: tube voltage 85 kV, tube current 5 mA, field of view 40x40 mm², exposure time 17 s. Images were associated with the following properties — voxel size: of 80 μm isotropic, true resolution: 2 lp/mm = 250 μm, CNR: 7.37 ± 1.26, CTDI: 4.9 mGy.

Verity (Planmed, Helsinki, Finland):

An extremity CBCT device. For all scans on this device, the following parameters were used: tube voltage 90 kVp, tube current 12 mA, Sharp Light filter, field of view 160x160 mm², exposure time 6 s. Images were initially reconstructed at 250 μm isotropic voxel size. The reconstructed images were later resampled at 125 μm isotropic voxel size using a cubic B-spline filter implemented in the MatLab software; other image properties were as follows — true resolution: 1.25 lp/mm = 400 μm, CNR: 4.53 ± 0.59, CTDI: 5.4 mGy.

For both CBCT scanners, image intensity values were acquired in gray values similar to the Hounsfield unit (HU).

2.E. MDCT Imaging

A Siemens SOMATOM Force (Siemens AG, Erlangen, Germany) scanner was used, with the following parameters: tube voltage 120 kVp, tube current 62 mA, filter type WEDGE_2, field of view 500x500 mm², slice thickness 400 μm, spacing between slices 200 μm, rotation time: 1 s, pitch 0.8. Axial MDCT images were reconstructed using an ultra-sharp kernel UR69u and advanced modeled iterative reconstruction (Admire) setting 3. The reconstructed field of view was 50x50 mm² with a 98x98 μm² in-plane pixel size and a slice thickness of 400 μm. Images were resampled at 98 μm isotropic voxel size using a cubic B-spline filter within the MatLab software; other image properties were as follows — true resolution: 2.48 lp/mm = 202 μm (in-plane) and 2.1 lp/mm = 238 μm (z-direction),² CNR: 4.91 ± 0.82, CTDI: 8.5 mGy. Intensity values were acquired in HU.

2.F. Image Processing and Trabecular Bone Micro-Structural Measures

Three major image processing steps were performed in our experiments—(1) registration of HR-pQCT, CBCT, and MDCT images to corresponding micro-CT data, (2) optimization of soft threshold parameters (i.e., upper and lower thresholds) for individual modalities to convert raw scan data into bvf images, and (3) computation of different trabecular bone micro-structural measures. These steps are briefly described in the following.

Image Registration:

The images from different in vivo CT scanners, i.e., an HR-pQCT, two CBCT, and an MDCT scanner, were manually registered to matching micro-CT images in a two-step process implemented in MeVisLab (MeVis Medical Solutions AG, Bremen, Germany) using the Registration Manual module. ³³ In the first step, three dimensional (3D) rigid transformation was used for rough registration of the whole specimen including cortical bone. The registration transformation matrix was applied on the physical image space, which accounted for voxel size difference in different modalities. During the second step, registration results were fine-tuned by manually matching trabecular micro-structures through the MeVisLab toolkit. The resulting volumes can be seen in Figure 1 and matching slices in Figure 2.

Figure 2.

Trabecular bone micro-structure on matching slices from post-registered images using different CT scans of a cadaveric distal radius specimen. (a,b) Raw and bvf image slice pairs from micro-CT imaging. (c-j) Same as (a,b) but using other CT modalities: (c,d) HR-pQCT, (e,f) dental CBCT, (g,h) whole body MDCT, and (i,j) extremity CBCT.

Computation of bvf:

A “bvf map” is a truncated function that maps CT number to bone volume fraction (bvf); the function is characterized by a lower and upper threshold values; bvf is 0 below the lower threshold, 1 above the upper threshold, and is a linear function in between. In this paper a new bvf computation algorithm is presented that optimizes the lower and upper threshold parameters t_l and t_h for soft thresholding for a given in vivo CT modality, while maximizing overlaps of both bone and non-bone micro-structures in reference micro-CT scans and the matching scans using the target CT modality. See the APPENDIX for detail description on formulation of an accuracy function in terms of the parameters t_l and t_h. Figure 3 illustrates the optimum parameter selection method and the surface plot of the accuracy function at different soft thresholding parameters.

Figure 3.

Optimization of soft thresholding parameters for bvf computation. (a,b) Down-sampled micro-CT image (a) and its bvf map (b) computed using manually selected-threshold parameters. (c,d) Matching image slice from the HR-pQCT scan (c) of the same specimen and corresponding bvf map (d) using the optimum threshold parameters. (e,f) Computed bvf maps using two non-optimum threshold parameters. (g) Computed accuracy surface plot at different combinations of soft thresholding parameters 〈t_l, t_h〉. Note that the accuracy value is non-existent for parameters t_l ≥ t_h, which creates a sharp fall of the accuracy surface along the diagonal line t_l = t_h.

2.G. Computation of Bone Micro-Structural Measures

Trabecular bone measures examined in this paper are listed in Table 1. Each CT image was processed through the following image-processing steps to compute different trabecular bone measures—(1) conversion of CT numbers into bvf values using the optimum threshold parameters derived from the new threshold optimization algorithm and computation of overall bvf (Tb.BVF) measure; (2) fuzzy skeletonization³⁹ and computation of trabecular network area density (Tb.NA) measure; (4) volumetric topological analysis (VTA)³⁶ and computation of mean plate-width (Tb.PW) and plate bvf (Tb.pBVF) measures; (5) tensor scale analysis³⁵ and computation of transverse bvf (Tb.tBVF) measure, (6) digital topological analysis (DTA) ^38,40,41 of fuzzy skeleton and computation of erosion index (Tb.EI) measure; (7) star-line analysis for computation of trabecular thickness (Tb.Th) and trabecular spacing (Tb.Sp) measures.³⁷ To avoid edge artifacts, image VOIs were padded with full-bone planes before applying fuzzy skeletonization, VTA, tensor scale, DTA, and star-line analysis. Finally, the padded VOIs were eroded by 5 voxels before computing different summary measures. A global value of each measure was derived from the VOI volume of each specimen.

Table 1.

List of CT-derived trabecular bone measures examined in this paper. The nomenclature of trabecular bone measures used by Bouxsein et al.³⁴ and Chen et al.²⁴ is followed here, wherever possible.

Parameter (unit)	Description
Tb.BVF (%)	Trabecular bone volume fraction
Tb.tBVF (%)	Trabecular bone volume fraction contributed by transverse trabeculae characterized using tensor scale analysis35
Tb.pBVF (%)	Trabecular bone volume fraction contributed by trabecular plates computed using VTA36
Tb.NA (mm2/mm3)	Trabecular bone network area density, i.e., the average area of the medial surface of segmented bone per unit VOI
Tb.PW (μm)	Mean trabecular plate-width computed using VTA36,37
Tb.Th (μm)	Mean trabecular thickness computed by star-line analysis37
Tb.Sp (μm)	Mean trabecular spacing, i.e., the space between trabecular micro-structures computed by star-line analysis37
Tb.EI (no unit)	Erosion index—a summary measure of DTA of trabecular bone aimed to represent the extent of bone erosion38

VOI: volume of interest, VTA: volumetric topological analysis, DTA: digital topological analysis

2.H. Data Analysis

For each imaging modality, different trabecular bone micro-structural measures were calculated for each specimen, and the population used for these measures was the set of specimens. Summary statistics of individual trabecular bone measures for every CT modality, including the reference micro-CT imaging, were computed in terms of the mean and standard deviation of different measures. For each trabecular bone measure, the linear correlation of its measured values from a given in vivo CT modality with its reference values derived from micro-CT imaging was examined. Note that erosion index measure was computed from binary segmentation of the trabecular bone; but for all other trabecular bone measures, fuzzy segmentation of the trabecular bone was used.

3. RESULTS AND DISCUSSION

Photographic display and volume renditions of matching VOIs from different CT scans of a cadaveric distal radius bone specimen are presented in Figure 1. These VOIs were used for computing different trabecular bone measures for our analysis. Matching trabecular bone micro-structures are visible in volume renditions from different modalities. However, loss of thinner trabeculae is noted at relatively lower resolution imaging, especially, in volume renditions derived from whole body MDCT and extremity CBCT scans. Also, the presence of high noise in HR-pQCT scans are visible in (d), which is more apparent in the slice-display of Figure 2(c).

Results of our optimum bvf computation method are illustrated in Figure 2, Figure 3, and Table 2. Table 2 shows the computed thresholds for different imaging modalities in both intensity units as well as in the unit of mineral density (mg/cm³); the optimum intensity threshold values were searched at an interval of ten. For HR-pQCT, intensity values were converted to mg HA using the slope and intercept parameters, which was then converted to mg/cm³ by adding 1000. MDCT image intensity values were converted to the mg/cm³ unit using the calibration curve derived from MDCT scans of a Gammex RMI 467 Tissue Characterization Phantom (Gammex RMI, Middleton, WI, USA).²⁴ The same calibration curve was applied for dental and extremity CBCT modalities for approximate conversion of their intensity values into mineral density unit. The threshold values on third column of the table in the unit of mineral density are significantly different for different in vivo CT modalities. This observation suggests that modality-specific choice of optimum threshold values is important for in vivo CT-based quantitative micro-structural analysis. Due to the availability of a limited number of bone specimens, the same specimens, which were used for the threshold optimization process, were also used for our main experiments. It should be clarified that the thresholds selected through the optimization process may not be appropriate for other bone samples or in vivo bone imaging modalities. A comprehensive validation of generalizability of the threshold optimization process is beyond the scope of the current paper. However, a repeat experiment was performed to examine the dependence of computed threshold values on the set of specimens used for optimization. Specifically, for each given imaging modality, ten specimens were randomly selected and used for threshold optimization, and this process was repeated ten times. Mean and standard deviation of computed optimum threshold values obtained in this repeat experiment are shown in Table 3. It may be noted that mean values of lower and upper thresholds for different modalities are close to the optimum threshold values obtained using the complete set of specimens. Moreover, for all imaging modalities, the values of standard deviation of computed optimum threshold intensities for different sets of specimens are small.

Table 2.

Results of optimum threshold computation for different imaging modalities in both image intensity and mineral density units (mg/cm³).

Modalities	Threshold values in intensity [tl th]	Threshold values in mg/cm3 [tl th]
HR-pQCT	[2,980 3,970]	[1,194 1,389]*
MDCT	[100 390]	[1,217 1,768]*
Dental CBCT	[200 420]	[1,407 1,825]*
Extremity CBCT	[−40 150]	[951 1,312]*

^*Approximate values

Table 3.

Mean and standard deviation of computed optimum threshold intensity values in a repeat experiment using ten random specimens.

Modalities	Lower Threshold value in intensity (mean ± std.)	Upper Threshold value in intensity(mean ± std.)
HR-pQCT	2995 ± 26.0	3972 ± 12.0
MDCT	82 ± 14.3	384 ± 6.3
Dental CBCT	200 ± 0.0	407 ± 18.3
Extremity CBCT	−38 ± 9.6	160 ± 8.4

Figure 3 illustrates the results of the optimization process for HR-pQCT imaging. The accuracy surface, used for soft thresholding parameter optimization, is shown in (g). As noted in (g), the accuracy function generates a smooth surface. Computed bvf map using the optimum parameters obtained from the global maxima of the accuracy curve is shown in (d), while the same at two non-optimal parameters are presented in (e) and (f). Matching trabecular bone micro-structures between the optimum bvf map in (d) and the reference bvf map in (b) are noticeable. Results of bvf computation for different modalities studied in this paper are presented in Figure 2. Image intensity units for original images were different for different imaging modalities. Therefore, different display windows were adopted for different images to generate visually similar brightness and contrast of trabecular bone micro-structures. For all bvf images, the same display window was applied.

Results of trabecular plate-rod classification at individual trabeculae, as derived from different CT scans of a bone specimen, are illustrated in Figure 4. As visually noted in the figure, fully computerized classification of individual trabecular plates and rods from target CT images are satisfactory. It is difficult to visually establish the correspondence of micro-structures at the level of individual trabeculae among the plate-rod classification renditions from different modalities. However, the correspondence of regions with higher rod (or, plate) densities is noticeable among the renditions from different modalities. Results of longitudinal-transverse orientation classification of individual trabeculae from different CT scans of a bone specimen are illustrated in Figure 5. As noted from the renditions using different CT modalities, the results of fully automated characterization of longitudinal (green) and transverse (red) trabeculae are visually satisfactory. Like Figure 4, regional agreement of longitudinal and transverse trabecular classification from different CT modalities is visible.

Figure 4.

Illustration of trabecular plate-rod classification using different CT imaging modalities: micro-CT (a); HR-pQCT (b); dental CBCT (c); whole body MDCT (d); and extremity CBCT (e).

Figure 5.

Illustration of trabecular bone orientation characterization using different CT imaging modalities: micro-CT (a); HR-pQCT (b); dental CBCT (c); whole body MDCT (d); and extremity CBCT (e).

Summary statistics of different trabecular bone measures from different CT modalities in terms of their mean and standard error are illustrated in Figure 6. The observed mean of Tb.BVF, Tb.tBVF, as well as Tb.pBVF demonstrates that all in vivo CT modalities overestimate the three bvf measures compared to their reference values derived from micro-CT scans. The increase in measured mean bvf values may be explained by structure blurring at lower image resolution causing structure thickening. More importantly, the increase in the three bvf measures is non-monotonic with the resolution-change in different CT modalities, and their highest values occur for dental CBCT imaging with intermediate image resolution. This observation suggests that, beyond the resolution regime of dental CBCT, some of the thinner trabecular micro-structures are lost, and its negative contribution to the value of mean bvf supersedes the effects of blurring. This argument is further supported by the following observation. Generally, transverse trabeculae are rod-like structures and thinner as compared to trabecular plates mostly occurring as longitudinal structures.^42,43

Figure 6.

Mean and standard error plots for different trabecular bone measures derived from micro-CT and four in vivo CT modalities.

For micro-CT, HR-pQCT, as well as dental CBCT, observed mean Tb.tBVF is approximately 30% of respective mean Tb.BVF values, while mean Tb.tBVF fall to 24% and 19% of Tb.BVF for MDCT and extremity CBCT, respectively. Tb.pBVF was computed to be approximately two-third of Tb.BVF for micro-CT and HR-pQCT but much higher for other CT modalities. These observations indicate that at low resolution loss of transverse trabeculae is much higher than the loss of plate-like structures. In case of Tb.NA, no significant relationship between mean network area and image resolution was observed. The value of mean Tb.NA measure from HR-pQCT scans is significantly higher than its values derived from other modalities, which is primarily contributed by noise artifactually increasing trabecular network area after skeletonization. In general, observed mean Tb.PW and Tb.Th using an in vivo imaging modality are higher than their values obtained using micro-CT imaging. Compared to other in vivo modalities, the observed mean values of Tb.PW using HR-pQCT is closer to the micro-CT-based value. Mean Tb.PW measures using dental CBCT, MDCT, and extremity CBCT imaging are more than double of its micro-CT-based value. The observed differences in the mean values of Tb.Th measure using in vivo modalities are even greater. A probable reason behind this is the composite effect of two factors—increased blurring as well as loss of thinner trabeculae at lower resolution—both increasing the mean Tb.Th values. The mean of the trabecular spacing measure Tb.Sp derived using the HR-pQCT imaging is smaller compared to its reference value using micro-CT, which may be an attribution of noise. The observed mean values of the erosion index measure Tb.EI using in vivo imaging modalities show a similar trend as the trabecular network area measure Tb.NA.

We compared our observed values for Tb.BVF, Tb.Th, and Tb.Sp measures with their values available in the literature for micro-CT and HR-pQCT modalities (Table 4); for other measurements, we could not find data in literature. It is worthy to mention that, although the observed differences in trabecular bone micro-structural measures are primarily explained using differences in spatial resolution of different imaging modalities, effects of noise and unmatched radiation exposure on these measures, partially contributing to the observed differences, may not be overruled.

Table 4.

Comparison of our observed values for different trabecular bone measures with the literature.

	Micro-CT		HR-pQCT
Measures	Observed mean ± std.	Mean values in literature [min max]25,44,45*	Observed mean ± std.	Mean values in literatur [min max]44-46*
Tb.BVF (%)	10.8 ± 3.3	[10 14]	18.5 ± 6.6	[20.2 27]
Tb.Th (μm)	172 ± 34	[130 173]	233 ± 49	[173 250]
Tb.Sp (μm)	727 ± 174	[650 942]	656 ± 221	[730 942]

^*Reported values at tibia and radius are used

Results of linear correlation (r) analysis of different trabecular bone measures using different in vivo modalities relative to the reference micro-CT scans are illustrated in Figure 7. As shown in the figure, the three bvf measures Tb.BVF, Tb.tBVF, and Tb.pBVF, as well as the trabecular network area measure Tb.NA, using all four in vivo modalities are highly correlated (r ∈ [0.94 0.99]). The plate-width measure Tb.PW using HR-pQCT scanner show high correlation (r = 0.91) with its micro-CT-based values, while the correlation for the measure using other in vivo modalities are acceptable (r ∈ [0.72 0.85]). Similar results of correlation analysis are observed for the thickness measure Tb.Th except for extremity CBCT imaging, where the correlation is relatively weak (r = 0.60). For all imaging modalities, the observed linear correlation (r ∈ [0.66 0.93]) for the spacing measure Tb.Sp is higher than their respective r-values for Tb.Th. This suggests that the Tb.Sp measure is relatively more reliable than the thickness measure at lower resolution, which seems plausible because trabecular spacing is larger than thickness; see the observed mean values in Figure 6 for micro-CT imaging. In general, the erosion index measure Tb.EI resulted in lower linear correlation (r ∈ [0.65 0.81]) for all in vivo modalities as compared to the plate-rod measures Tb.pBVF and Tb.PW. The algorithms for computing Tb.pBVF and Tb.PW account for partial voxel voluming and characterization of plates and rods on the continuum, which improves its performance at a lower resolution as compared to the algorithm for computing erosion index which needs binarization, and hard classification of plates and rods. All trabecular bone measures using HR-pQCT, except Tb.EI, show high correlation (r ∈ [0.91 0.99]). Also, it is notable that, although most of the trabecular bone measures show large shift in their mean values at in vivo resolution, several trabecular bone measures, namely Tb.BVF, Tb.tBVF, Tb.pBVF, and Tb.PW, are strongly to moderately correlated (r ∈ [0.72 0.99]) with the reference micro-CT values. It is worthy to mention that the ranges of x- and y-axes in the plots of Figure 7 are different. Thus, slopes of different trend lines in these plots may not indicate the relationships of measured values using micro-CT and corresponding in vivo modalities; see Figure 6 for relationships among values measured using different modalities. Finally, it may be clarified that micro-CT, HR-pQCT, and dental CBCT images were processed at their original voxel size generated at image reconstruction. On the other hand, extremity CBCT and MDCT images were interpolated to generate an isotropic voxel size smaller than human trabecular thickness, which is around 150 μm.⁴⁷ It is worth mentioning that observed differences in various trabecular bone micro-structural measures are due to differences in various aspects of different imaging modalities including spatial resolution, radiation dose, noise as well as principle and algorithms of image reconstruction. Dispersing all these effects is a challenging task. However, to examine the effects of spatial resolution on trabecular bone micro-structural measures, we conducted an experiment where images at different voxel size were generated from micro-CT images using interpolation, and effects on different trabecular measures were examined in terms of linear correlation. Specifically, we applied interpolation on original micro-CT images to generate test images at 75, 100, 125, 150, 175, 200, 225, 250 μm, and results of linear correlation analysis (r-values) for different measures with corresponding values obtained from original micro-CT images are presented in Figure 8. Beside the Tb.BVF measure, Tb.tBVF, Tb.pBVF, Tb.NA, and Tb.Sp show high linear correlation (r > 0.9) for all resolution. On the other hand, the measure Tb.EI show relatively low correlation with the original micro-CT values beyond 100 μm voxel size. At a voxel size of 200 μm or larger, r-values for both Tb.PW and Tb Th measures fall rapidly. These observations are mostly in agreement with the results presented in Figure 7 except for Tb.Sp. In the actual in vivo imaging experiment, Tb.Sp showed relatively low linear correlation at MDCT and extremity CBCT imaging resolution with micro-CT derived values. This difference in observations may be explained as follows. For simulated degeneration of voxel size by image interpolation, no noise was added, and therefore, likelihood of loss of individual trabeculae at lower resolution was low. However, for in vivo imaging at lower resolution using MDCT or extremity CBCT modalities, noise and radiation exposures were different lifting the likelihood of loss of individual trabeculae.

Figure 7.

Correlation among the values of different trabecular bone measures derived from target CT modalities and the corresponding reference values from micro-CT scans. Pearson correlation coefficient (r) values are reported. It may be noted that the ranges of x- and y-axes in these plots are not matched.

Figure 8.

Effects of voxel size on different trabecular micro-structural measures. Images at different voxel sizes were generated by interpolating original micro-CT images. Linear correlation of various measures at different voxel sizes with their original micro-CT derived values are shown.

4. CONCLUSION

Using different in vivo CT modalities for quantitative trabecular bone micro-structural imaging and trabecular bone measures, this study has focused on unique measures related to trabecular plate/rod and longitudinal/transverse distribution. Although the measured values of trabecular features at in vivo resolution differ greatly from their reference values from micro-CT imaging, there is, in general, strong to moderate correlation between the measurements from in vivo CT and micro-CT imaging. The performance of different in vivo modalities, in terms of linear correlation of derived trabecular bone measures with reference measurements, is dependent on their resolution. HR-pQCT imaging has the highest true spatial resolution, and all trabecular bone measures, except Tb.EI, derived using this modality show high correlation (r ∈ [0.91 0.99]) with micro-CT based reference values. Strong to moderate correlation of measures derived from in vivo CT methods suggest the great promise of in vivo CT imaging for quantitative trabecular bone micro-structural analysis. On the other hand, large shifts in observed values of trabecular bone micro-structural measures using different in vivo modalities suggest that data from different scanners may introduce modality-specific data-shift which must be carefully considered during experimental and data analysis planning. For a study with limited statistical power, it is recommendable to use a single imaging modality throughout the study to avoid modality-specific variability. For large multi-site and longitudinal studies involving different imaging modalities due to option limitations, it is recommendable to use different modalities only with proper linear calibration. Further, the wide range of performance of individual measures at different imaging modalities suggests the need for judicious selection of target trabecular bone measures depending upon imaging modalities available to individual studies. The experimental design adopted in this study shows modality-specific influence factors including spatial resolution, noise and radiation exposure on different trabecular bone micro-structural measures. It will be worthy to investigate the effects of different imaging factors and artifacts separately on micro-structural measures; however, such experiments are outside the scope of the current study.

APPENDIX

Accuracy Function for Soft Thresholding of CT Images

An accuracy function for a given CT modality at specific values of lower and upper thresholds are defined as follows. Let Z³ denote the image space and τ_ref(s, p) ∣ p ∈ Z³ denote the reference voxel-wise bvf map for a given specimen s derived from its micro-CT scan; the bvf map was computed from micro-CT scans using manually selected soft-threshold parameters and connectivity analysis to eliminate isolated noisy components. Let τ_t(s, p, t_l, t_h) ∣ p ∈ Z³ denote the voxel-wise bvf map for the same specimen s derived from its scan using the target CT modality and soft threshold parameters t_l < t_h. Voxel-wise agreement and disagreement functions A and D, respectively, are defined as follows:

$$A(p,t_{\mathrm{l}},t_{\mathrm{h}})=\left({\tau }_{\text{ref}}(s,p){\tau }_{\mathrm{t}}(s,p,t_{\mathrm{l}},t_{\mathrm{h}})+\left(1-{\tau }_{\text{ref}}(s,p)\right)(1-{\tau }_{\mathrm{t}}(s,p,t_{\mathrm{l}},t_{\mathrm{h}}))\right)\alpha (t_{\mathrm{l}},t_{\mathrm{h}}),$$ (1)

$$D(p,t_{\mathrm{l}},t_{\mathrm{h}})=\left(\left(1-{\tau }_{\text{ref}}(s,p)\right){\tau }_{\mathrm{t}}(s,p,t_{\mathrm{l}},t_{\mathrm{h}})+{\tau }_{\text{ref}}(s,p)(1-{\tau }_{\mathrm{t}}(s,p,t_{\mathrm{l}},t_{\mathrm{h}}))\right)\left(1-\alpha (t_{\mathrm{l}},t_{\mathrm{h}})\right),$$ (2)

where α(t_l, t_h) represents the global agreement in the volume of core bone micro-structure derived from micro-CT scans of all specimens and that derived from all specimen scans using the target modality and the soft threshold parameters t_l < t_h. Specifically, α(t_l, t_h) is computed as follows:

$$\alpha (t_{\mathrm{l}},t_{\mathrm{h}})=f_1\left(\frac{{\sum }_{s\in S}\mid \{p\mid p\in Z^3\wedge {\tau }_{\text{ref}}(s,p)=1\}\mid }{{\sum }_{s\in S}\mid \{p\mid p\in Z^3\wedge {\tau }_{\mathrm{t}}(s,p,t_{\mathrm{l}},t_{\mathrm{h}})=1\}\mid }\right),\text{where}{f}_1(a)=\text{min}\left(a,\frac{1}{a}\right),$$ (3)

where the symbols ‘∈’ and ‘∧’ represent ‘belongs to’ and ‘and’; S is the set of all specimens. In the above equation, the argument of the function f₁(·) calculates the ratio of the total volume of core bone (summed over all specimens) in the reference data to the total volume of core bone in the target data (summed over all specimens). Further, it may be noted that, in Eqs. (1) & (2), A(·) captures both voxel-wise true positive, i.e., the term τ_ref(·) τ_t(·), and true negative or the term (1 – τ_ref(·))(1 – τ_t(·)). In other words, A(·) represents a weighted measure of voxel-wise accuracy of soft thresholding, where τ_ref(·) and τ_t(·) represent the true and computed bvf values, respectively. Similarly, D(·) is formulated to capture the voxel-wise weighted disagreement of τ_t(·) with τ_ref(·). An accuracy function of soft threshold parameters 〈t_l, t_h〉 is defined as follows:

$$accuracy(t_{\mathrm{l}},t_{\mathrm{h}})=\frac{{\sum }_{s\in S}{\sum }_{p\in Z^3}A(p,t_{\mathrm{l}},t_{\mathrm{h}})}{{\sum }_{s\in S}{\sum }_{p\in Z^3}A(p,t_{\mathrm{l}},t_{\mathrm{h}})+{\sum }_{s\in S}{\sum }_{p\in Z^3}D(p,t_{\mathrm{l}},t_{\mathrm{h}})}.$$ (4)

Finally, the soft threshold parameters 〈t_l, t_h〉 are determined at the global maximum of the accuracy map.