Introduction

Carotid atherosclerosis can cause hemodynamic impairment in intracranial circulation as well as artery-to-artery embolisms [1]. Currently, the severity and degree of luminal stenosis are the main factors influencing therapeutic decision making in patients with atherosclerosis [2–4]. However, recent studies have revealed that plaque morphology and tissue components are important additional factors in risk assessment [5, 6]. In fact, plaques causing only minimal stenosis may still present a significant risk for distal ischemic events [7]. Evidence is building supporting the concept of the vulnerable associated with high-risk plaque in the carotid circulation, similar to coronary artery disease [8]. Therefore, noninvasive characterization of plaque composition, such as the amount of calcification, the lipid content, the presence of necrosis or haemorrhage, neovascularization, inflammation, and thickness of the fibrous cap, can better determine the risk of stroke [9–12].

Table 1 The number and characteristics of the calcified plaques detected via pathology that were missed by CT are reported by X-ray energy for mono-energetic-synthesized images and for standard poly-energetic CT images.
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Magnetic resonance imaging (MRI), positron emission tomography (PET), and ultrasound have been used to evaluate the soft tissue component of plaque with good results; however, these techniques have significant limitations in evaluating and even visualizing the calcified portion of plaque [13–22]. Computed tomography (CT) is able to image calcifications, and it may have a specific role in evaluating this portion of the plaque [23–30].

In CT imaging, objects are examined with a polychromatic x-ray beam represented by the highest (peak) energy in the beam, e.g., 120 kVp [31]. Objects preferentially absorb x-rays with lower energy, resulting in a change in the x-ray energy spectrum [32]. The higher energy portion of the x-ray beam is what is ultimately detected [33]. Current CT systems correct this phenomenon, called beam-hardening effective energy shift, by using calibration data measured in specific phantoms and calculated with those specific functions during the image reconstruction process [34]. Polychromaticity of the x-rays causes loss of information because of energy averaging [35–37]. In dual energy CT, objects are examined with two polychromatic x-ray beams of different kVp peak energy, resulting in measurements of the linear attenuation coefficients at two different average energies. The energy dependence of x-ray absorption properties of various materials allows these two images to be used as a basis for calculating synthesized images that represent specific energy-dependent properties of the object such as different materials or different x-ray interactions (photoelectric effect vs. Compton scattering). They can also be used to synthesize images at specific energies, yielding virtual monochromatic spectral (VMS) images [38–43]. While beam-hardening still affects data acquisition of dual-energy CT, the images can yield additional information potentially useful for better tissue and morphology characterization.

Since calcium attenuation is dependent on energy level, different x-ray spectra will have different absorption by calcified plaques, potentially resulting in additional information for tissue and morphology characterization [33]. While this additional information may be derived from conventional CT that uses different polychromatic spectra (PS-CT), this is impractical because multiple scans would be required. We hypothesize that a single scan using dual-energy CT can be used to create VMS images of carotid plaque calcifications that match histology better than PS-CT techniques.

This study focuses on the evaluation of the calcific portion of atherosclerotic plaque. Thus, the objectives of this ex vivo study were the following:

  1. (1)

    to use human endarterectomy specimens of carotid atherosclerotic plaques to determine if changes occur in the perceived size of carotid plaque calcifications on dual-energy VMS CT images reconstructed at different energy levels (keV) and different polychromatic CT images (kVp);

  2. (2)

    to compare the size and number of carotid plaque calcifications measured via CT to histology; and [3] to quantify the change in perceived calcification size with CT beam energy (VMS and PS).

In this paper the unit ‘keV’ is used to describe the virtual monochromatic-energy of the VMS-CT images. The term ‘kVp’ is used to describe the maximum energy of a polychromatic spectrum. Thus, ‘keV’ and ‘kVp’ are associated with VMS-CT and PS-CT, respectively.

Method and materials

Specimens

After approval from the institutional review board, five ex vivo carotid endarterectomy (CEA) specimens were obtained from five patients with advanced atherosclerosis (Fig. 1). Samples were fixed in 10 % neutral buffered formalin. After CT imaging, the endarterectomy specimens were specially processed to preserve the plaque calcifications. This calcium-preserving processing required that the specimens first be embedded in plastic. Then, 8-μm cross-sections were ground at 1-mm intervals and stained with Toluidine Blue/Basic Fuchsin to demonstrate plaque calcifications (Fig. 1). The sections were photographed and regions of calcifications were manually traced on digitized images of the sections by an experienced histopathologist blinded to the CT results [23, 44, 45]. All calcified areas on each histology slide were summed to obtain the calcification area for that slice.

Fig. 1
figure 1

Toluidine Blue/Basic Fuchsin stained section and polychromatic (140, 120, 100, 80 kVp) and reconstructed CT VMS images (40, 60, 80, 100, 120, and 100 keV) of the same location as matched by the human observer. The magnification factors are different for CT and histology

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CT

Each specimen was placed in formalin within a separate sample compartment and imaged with the long axis of the carotid plaques aligned with the longitudinal (z) axis. The five endarterectomy specimens were simultaneously imaged using single-source rapid tube switching dual-energy 64-channel CT (Discovery CT750 HD; GE Healthcare, Waukesha, Wisconsin, USA). Data sets were acquired with the following parameters: gantry rotation 0.6 s; detector collimation 0.625 × 64 mm; helical pitch 0.984; field of view (FOV) 12.6 × 12.6 cm; 640 mA; and tube voltage switching between 80 and 140 kVp with the tube voltage switched every 0.5 millisecond. The acquired dual-energy data were used to reconstruct seven VMS image sets at different energy levels (40, 60, 77, 80, 100, 120, and 140 keV). Images were reconstructed as contiguous 1-mm thick axial images with a standard kernel. The same specimens were also imaged with a conventional polychromatic source at different tube potentials (80, 100, 120, and 140 kVp) with the same acquisition parameters as the dual energy acquisition. The dual-energy and the conventional image acquisitions were performed with the samples in the same exact position.

Image analysis

The reconstructed VMS CT axial images of the carotid plaques were then analyzed using a custom-designed computer package, CASCADE (Computer-Aided System for Cardiovascular Disease Evaluation), developed to perform quantitative analysis of plaque morphology, composition, and disease burden on cross-sectional images of diseased vessels [14, 22]. With CASCADE, the cross-sectional area of the plaque calcifications within each VMS CT image was semi-automatically measured in square millimetres using a density threshold of 130 Hounsfield units (HU) [46]. All calcified areas on each CT image slice were summed to get the calcification area for that slice.

CT and histology matching

One experienced radiologist with sub-specialty training in cardiovascular imaging matched the VMS CT images to the histology sections on the basis of the shape of the lumen, outer vessel wall, image/slice location relative to the carotid bifurcation, and the size and shape of the calcifications present in the particular image/slice of the plaque [23]. The radiologist had access to all the histological images made by the pathologist (Fig. 1b) and by scrolling through the CT images matched the CT images and histology sections [12]. The histopathologist and the radiologist analyzed the images separately with no interaction between the two. The radiologist was aware of which plaque the histological images were from, but not the level of the histological images within the plaque [23, 33].

Statistical analysis

Calcification detection sensitivity was calculated as the number seen on each CT method divided by the total number seen on the pathology slices. A Pearson correlation coefficient for a linear relationship was calculated between the pathology and CT results, and between different CT techniques. The mean difference (bias) and root-mean-square (RMS) error in CT calcification size was calculated using the calcification sizes measured via histology as the gold standard. The mean percent bias was calculated as 100 %*(ACT – Apath)/(Apath) averaged over the calcifications found by the CT imaging technique of interest, where ACT and Apath were the sizes (areas) of the calcifications measured by CT and pathology, respectively. Note that calcifications not seen on CT images were not used in correlation, bias, or RMSE calculations. Calcifications missing from CT scans were characterized by the detection sensitivity.

We characterized the change in the apparent size of calcifications with CT beam energy. Linear regression (least-squares minimization) was applied to the size-vs-CT beam energy data; the slope of this line indicates how fast the apparent size of the calcifications change with beam energy.

Results

All five CEA specimens studied contained plaque calcifications. Twenty to 35 sections were obtained per specimen. Figure 1 shows an example of changes in the size and appearance of plaque calcifications with different VMS energy levels and different kVp compared to histology. The areas (mm2) of each calcification were measured via histology and on each CT image set (Fig. 1, Table 1).

A total of 146 histology sections were obtained. Nineteen sections were excluded because the carotid wall was partially damaged during plastic processing. Therefore, 127 histology sections were included in the study and matched with the corresponding CT image. Eleven slices did not contain calcifications as determined via pathology. There were a total of 116 slices containing one or more calcifications. The plaque calcium area per image ranged from 0.20 mm2 to 26.4 mm2 with a mean and median of 8.3 mm2 and 6.1 mm2, respectively. Unless otherwise noted, all results are cumulative across all five samples.

Figure 2 is a scatter plot of calcification area measured by histology compared to CT for three CT techniques, as follows: the highest and lowest VMS-CT energies (40 keV and 140 keV), and conventional PS-CT at 120 kVp. While there was a good statistical correlation between the calcium areas measured via histology and all of the CT image sets (Fig. 3), considerable variability is observed. By referencing the line-of-identity in Fig. 2, we see that 40 keV-VMS and 120 kVp-PS images overestimate calcification areas, while 140 keV-VMS images underestimate the calcification area.

Fig. 2
figure 2

Scatter plot of pathology size vs. CT size for mono-energetic CT images at 40 keV and 140 keV, and conventional 120 kVp CT image. The light gray line represents an ideal correlation between CT and pathology

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Fig. 3
figure 3

Correlation coefficient (ρ light gray) between calcification sizes found by pathology and CT imaging using different CT techniques. The error bars represent the 95 % CI on ρ. CT detection rate of calcifications (dark gray bars) is the fraction of calcifications seen on pathology that were also identified on CT images. Using 140 keV VMS, only 35 % of the slices containing calcifications at pathology were detected (see also table I)

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The PS-CT image detection rate was essentially the same at 111/116 (95.7 %) for each kVp. The PS-CT images all missed the same five calcifications, with the exception of the lowest PS-CT scan (80 kVp) that missed only four. The VMS-CT image at 40 keV missed only 3 calcifications (97.4 % detection rate); two of these three were in common with calcifications missed on the PS-CT scans. The VMS-CT detection rate decreased steadily with increasing energy. Figure 3 shows the detection rates and correlation coefficients for each CT technique as compared to pathology findings. The error bars represent the 95 % confidence interval on the correlation coefficient.

The RMS error and percent bias are shown in Fig. 4. The VMS-CT with the highest detection rate, 40 keV, also overestimated calcification sizes by ~200 %. On average, the VMS-CT bias decreases steadily with keV until the 100 keV VMS-CT image underestimated calcification size. Figure 4 shows that the lowest RMS error and percent bias occur for VMS-CT images at 80 and 100 keV. All PS-CT images overestimated calcium areas and had higher RMSE and bias than the 80 and 100 keV VMS-CTs.

Fig. 4
figure 4

Root-mean-square error (RMSE) and mean percent (%) error of calcifications sizes measured at CT for the different x-ray energies, with sizes measured on pathology taken as the true size

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The apparent size of calcifications on the VMS-CT images decreased steadily with VMS energy. This can be interpreted as causing the VMS-CT detection rate to decrease with increasing VMS energy. Small calcifications on the low energy VMS-CT images tended to disappear on higher energy images. The mean size of the 27 calcifications that were not detected on the 100 keV VMS-CT was 2.2 mm2 (size on pathology), versus a mean size of 10.2 mm2 (on pathology) for those detected on the 100 keV VMS-CT scan. In theory, the rate at which a calcification changes size with CT energy could be a characteristic measure of the calcification (e.g., related to the linear attenuation coefficient of the constituent material(s)). The maximum rate of change on VMS-CT images was -0.39 mm2/keV. The shrink rate tended to be larger for larger calcifications. The change in calcification size on PS-CT images was very small, with a maximum absolute value in our sample of 0.13 mm2/kVp.

Discussion

In this study we used dual-energy CT imaging to generate VMS CT images of five CEA specimens (Fig. 1), with the goal of estimating the size and number of calcifications and comparing the results to conventional PS CT images and pathological results. For the ex vivo experimental conditions used here, and using histology as the gold standard, we demonstrated the following: [1] The size and number of plaque calcifications measured on VMS-CT images depended on the energy level used for the image reconstruction, whereas on PS-CT images there was very little dependence on x-ray beam peak energy (kVp) (Fig. 3); [2] The calcification detection rate and size estimation was better for VMS-CT than for PS-CT, although detection and size estimation were optimized at a different energy VMS (detection sensitivity was optimized at 40 keV, size estimation was optimized between 80-100 keV) (Figs. 3, 4); and [3] Related to above, the apparent calcification size on VMS-CT images decreased steadily with an increasing keV (Fig. 5), revealing it was smaller calcifications that were not detected on higher keV VMS-CT images where lower detection sensitivity was observed. The missed calcifications were smaller on average, but calcifications as large as 15 mm2 (as measured by pathology) were missed on the 140 keV VMS-CT image.

Fig. 5
figure 5

Calcification sizes vs. CT x-ray beam energy for CEA sample 3. Each line shows the change in apparent calcification size for each image slice of sample 3. Linear regression (least-squares minimization) was applied to non-zero data to measure how fast apparent calcification size changed: across all 5 samples, calcifications shrank at rates between -0.06 and –0.39 mm2/keV on VMS-CT images, whereas the size change was only –0.01 to -0.13 mm2/kVp for PS-CT images

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By interpolating findings between 80 keV VMS-CTs, which overestimate calcification size, and 100 keV VMS-CTs that underestimate size, we believe a zero mean bias could be achieved with a 90 keV VMS-CT; however, the estimate would still carry a RMSE of ~6 mm (Fig. 4). This result applies to the samples scanned alone, and these results would likely change when examining carotid calcifications in vivo.

Calculating how calcifications or other plaque features change apparent size with VMS energy is easily done from multiple VMS-CT images synthesized from a dual-energy CT. This metric is not practical for PS-CT, as it would require multiple scans.

Figure 3 shows the high correlation coefficients between CT and pathology calcification sizes. Figures 2 and 4, however, show that, despite the high correlation coefficient, there is still considerable variability in the relationship between calcification sizes. For example, while the vast majority of calcifications seen on low energy VMS-CT images and on PS-CT images were larger than measured via pathology, a few were also smaller on CT images than as determined by pathology in the same images (Fig. 2, markers below the line of identity). The PS-CT images all overestimate calcification size substantially (percent bias, Fig. 4). This is probably due to inadequate correction of effective energy shift causing the beam-hardening phenomenon in the regions peripheral to calcific atherosclerotic plaques [17, 37, 38]. VMS-CT images at a low keV also suffer from beam-hardening and ‘blooming’ common to PS-CT images, but VMS CT images seem to be able to recover this information [35] at a higher VMS energy. As mentioned above, higher VMS energy examinations have reduced calcification detection sensitivity. However, when using dual-energy CT imaging, VMS-CT at several energies can be reconstructed from a single dual-energy scan; thus, a VMS-CT image that optimizes detection rate, and another that optimizes size estimation can both be generated. An obvious limitation is that the size cannot be estimated for those calcifications that are not detected on the higher energy VMS image. Further analysis of the differences in image characteristics between VMS CT images at different energies could potentially provide additional information on the plaque density and calcium distribution within the calcification. For example, use of low energy levels could increase the imaging sensitivity for small plaque calcifications, while high energy levels could reduce the effects of calcium blooming artefacts, which can obscure the vessel lumen and mask other important plaque components [12].

We used an HU threshold of 130 based on that value being used for coronary artery calcium scoring [45]. Our results did not change for thresholds of 120 HU or 140 HU on two samples where these thresholds were applied. HUs are defined for PS-CT with respect to water and air linear attenuation coefficients for a PS x-ray beam. An examination of the appropriate units for the analysis of VMS-CT images is required. The apparent size of calcifications on VMS-CT images will be thresholddependent with the proper selection of units and range of thresholds. We also used the same convolution filter for all image reconstruction; however, the use of different convolution filters may have an effect on carotid plaque attenuation values [47]. It remains to be determined which convolution filter can optimize carotid plaque size when using VMS images.

This study had several limitations. First, this was an ex vivo study; therefore, further work is needed to establish whether the results apply to in vivo situations. Second, although the number of slices evaluated was high, the total number of carotid samples was small. Third, imperfect matching of plaque slices between pathology and CT images may have led to an increased variance in the results. Lastly, evaluation of the non-calcified portion of the plaques has not been attempted.

There are fundamental challenges in using imaging to measuring quantitative parameters in structures that have dimensions smaller than 2-3 times the intrinsic spatial resolution of the imaging system. In this case, voxel ‘spill-over,’ or voxel partial volume effect, leads to material mixing between adjacent image voxels. The very small calcifications in carotid arteries fall within this limit of smaller than 2-3 times the intrinsic CT spatial resolution. The observed change of calcification size with VMS-CT energy is in part due to inherent and potentially informative properties of the calcification. However, other effects are also at play, including the voxel partial volume effect and, in practice, variability in background conditions (e.g., neck size). These effects could be difficult to calibrate for in in vivo imaging.

In conclusion, there was a high correlation between calcification sizes measured via CT and pathology, but broad variability as measured by the RMSE between the two measurements persisted. VMS-CT images at 80-100 keV had the lowest bias and RMSE for the ex vivo experiments conducted here. The PS-CT images had 95.7 % calcification detection sensitivity, but overestimated calcification size by ~100 %, both nearly independent of peak x-ray beam energy. Results of VMS-CT images were strongly dependent on the (virtual) x-ray energy; the 40 keV VMS-CT had a 97.4 % detection sensitivity but overestimated size by ~200 %, whereas the VMS-CTs with the smallest bias and RMSE, 80 and 100 keV, had only 89.7 % and 76.7 % detection sensitivities, respectively.

We demonstrated that plaque calcifications were missed on higher energy monochromatic images; we speculate that this is likely dependent on two factors, plaque size and total calcium content. The fact that analysis of the plaque size changes using different VMS images could provide additional information on the composition of the calcified portion of the carotid plaque; however, this approach must be validated under in vivo imaging conditions and faces fundamental challenges for the calcifications that are comparable in size to the intrinsic spatial resolution of CT. Dual-energy image data can also be used to generate virtual material composition images (as opposed to virtual monochromatic beam energy images). Evaluation of plaque calcium content using virtual material decomposition is another promising approach [48].