Improving the imaging of calcifications in CT by histogram-based selective deblurring

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1 Improving the imaging of calcifications in CT by histogram-based selective deblurring Empar Rollano-Hijarrubia * a,b a a, Frits van der Meer, Aad van der Lugt, Harrie Weinans c, Henri a,b a,b a,b Vrooman, Albert Vossepoel, Rik Stokking. Departments of a Radiology, b Medical Informatics, and c Orthopaedics. Erasmus MC - University Medical Center Rotterdam, Dr. Molewaterplein 5, 315 GE Rotterdam, The Netherlands. ABSTRACT Imaging of small high-density structures, such as calcifications, with computed tomography (CT) is limited by the spatial resolution of the system. Blur causes small calcifications to be imaged with lower contrast and overestimated volume, thereby hampering the analysis of vessels. The aim of this work is to reduce the blur of calcifications by applying threedimensional (3D) deconvolution. Unfortunately, the high-frequency amplification of the deconvolution produces edgerelated ring artifacts and enhances noise and original artifacts, which degrades the imaging of low-density structures. A method, referred to as Histogram-based Selective Deblurring (HiSD), was implemented to avoid these negative effects. HiSD uses the histogram information to generate a restored image in which the low-intensity voxel information of the image is combined with the high-intensity voxel information of the deconvolved image. To evaluate HiSD we scanned four in-vitro atherosclerotic plaques of carotid arteries with a multislice spiral CT and with a microfocus CT (µct), used as reference. Restored images were generated from the images, and qualitatively and quantitatively compared with their corresponding µct images. Transverse views and maximum-intensity projections of restored images show the decrease of blur of the calcifications in 3D. Measurements of the areas of 27 calcifications and total volumes of calcification of 4 plaques show that the overestimation of calcification was smaller for restored images (mean-error: 9% for area; 92% for volume) than for images (143%; 213%, respectively). The qualitative and quantitative analyses show that the imaging of calcifications in CT can be improved considerably by applying HiSD. Key words: computed tomography, calcification, deconvolution, deblurring, PSF, resolution, µct, quantification. 1. INTRODUCTION Atherosclerosis is the leading cause of death in the Western World. The detection of the disease and the choice of treatment are typically based on imaging of the vessel, followed by visual and quantitative analysis of the vessel and abnormalities such as stenosis and calcifications. For years establishing the degree of stenosis of the artery has been a crucial factor for pre-surgical evaluation, but increasingly coronary artery calcium scoring is being used as an additional important factor. Measuring the amount of calcification may be applied as a risk indicator for the progression, stabilization and/or regression of atherosclerosis; and assessing the morphological characteristics of calcified plaque may help to determine its vulnerability 1-5. For all these reasons, it is now becoming more and more important to develop imaging acquisition and processing techniques to improve the accuracy and reproducibility of the measurements in atherosclerotic arteries. Over the last few years multislice spiral/helical computed tomography (MSCT) has undergone an enormous increase in its use for cardiovascular imaging, and it is rapidly becoming the established technique for minimally invasive imaging of arteries 5,6. The advantages of MSCT in comparison with other tomographic imaging modalities are its higher temporal resolution, thereby minimizing motion artifacts, and its higher density resolution, thereby allowing lower doses of contrast material. Current MSCT allow volumetric images of the human body with high, near isotropic, spatial resolution (about.32 mm in the transverse and longitudinal directions). The spatial and contrast resolution of an MSCT scanner depends on its geometry and on the parameters selected for acquiring the data and reconstructing the image. The choice of these parameters determines the blur, noise and artifacts of the resultant images. This blur can be studied in the three directions of space by measuring the three-dimensional (3D) point-spread function (PSF), which is the volume image of a pointobject given by the system. * m.rollanohijarrubia@erasmusmc.nl; phone

2 The spiral CT imaging process can be mathematically approximated as a convolution of the true object with an isotropic, spatially invariant, 3D separable Gaussian PSF 7-11, plus a superposition of noise and artifacts. When scanning atherosclerotic plaques, the object to be imaged consists of nodules of crystalline calcium, mainly hydroxyapatite, distributed among lipid cores and fibrous tissue 1-4. These nodules ( calcifications ) can resemble any shape: spherical, elliptical, laminar, etc., and their maximum length typically ranges from only a few hundred micrometers to more than half a centimeter. Frequently, several nodules are found very close to each other, forming a cluster of calcifications. Due to the convolution of the calcifications with the PSF (or blur function), the space occupied by the calcification in the image is spread over the true volume 11. This especially affects the imaging of a cluster, where calcifications may be convolved together appearing as one calcification with a volume much larger than the sum of the true volumes. The interrelated consequences of the blur on the imaging of calcifications are 11,12 : i) a decrease of contrast and smoothness of edges of the image leading to a loss of definition of the plaque morphology; ii) an overrepresentation of the size of the calcification, resulting in an underestimation of the lumen area; iii) a strong variation of the quantification of calcification with the selected Hounsfield Units (HU) threshold; iv) a strong dependence of the visualization of the calcifications with the display settings (window level and window width); and v) a loss of small calcifications (especially when they do not extend along the entire slice thickness) that are not dense enough to generate the minimal signal-tonoise ratio (SNR) required for detection. The aim of this work is to evaluate options to improve the visualization and quantification of the calcifications in CT angiography (CTA) by applying digital image deconvolution. This technique performs the inverse imaging process to obtain the best estimate of the true object from its image. The deconvolution amplifies the high-frequency components of the image, thereby improving the imaging of small high-density structures. Unfortunately, it also amplifies noise and artifacts and introduces additional edge-related ring artifacts 13,14, which especially degrade the imaging of low-density structures. To avoid these negative side effects we have developed a method, called Histogram-based Selective Deblurring (HiSD), that generates a new image by combining the low-density voxel information of the image with the high-density voxel information of the deconvolved image In-vitro samples 2. MATERIALS AND METHODS To evaluate the method HiSD, four in-vitro atherosclerotic plaques of carotid were scanned with an MSCT scanner and with a µct scanner. These plaques corresponded to a stenotic site of the artery of four patients who underwent surgery. The in-vitro plaques were categorized according to their total content of calcium: Sample to 3 range from heaviest to least calcified. The samples were fixed using plastic holders so as to avoid movement between scans and allow the correlation between the CT images and the µct images Figure 1. Four atherosclerotic plaques presenting different amounts of calcium were selected and categorized as: Sample heaviest, Sample 1 and 2 moderately calcified and Sample 3 least calcified Multislice Spiral CT system (MSCT) CT images were acquired with an MSCT (Somatom Sensation 16; Siemens Medical Systems). All scans were performed using the same protocol based on the following acquisition and reconstruction parameters: i) for the acquisition of the raw data: voltage of 12 kv and current of 249 mas; beam collimation of 16 slices slice collimation of.75 mm; and table feed of 6.3 mm/sec (with 1 second of rotation time), and ii) for the reconstruction of the images: medium-sharp convolution kernel (B5s); field of view (FOV) of 5. mm; 36 o LI algorithm;.75 mm of effective slice thickness (S eff ) or full width at half maximum (FWHM) of the slice sensitivity profile (SSP); and reconstruction increment (RI) equal to.3 mm. A value of RI=S eff /3 (or 67% of image overlap) is recommended to improve the spatial resolution in the z- direction, however, the increase in resolution with RI<S eff /3 is too small to justify the processing burden 7, Microfocus X-ray Computer Tomography (µct) Images from a desktop µct scanner (SkyScan-1172, were used as reference for the morphology of atherosclerotic plaques instead of conventional histology. Following the same physical principles for image generation

3 that clinical CT scanners do, µct allows nondestructive three-dimensional imaging of small objects (up to 8 cm 3 ) at much higher spatial resolution than current MSCT scanners. Previous research has shown that µct is feasible for analysis of the coronary artery wall, and that it provides quantitative information about plaque morphology equivalent to that provided with histomorphometric analysis 16,17. We concluded that conventional histology would not provide the most optimal reference data for the evaluation of the morphology of calcifications within the soft-plaque due to the following disadvantages: i) histology is a destructive technique; ii) the matching and correlation between histology slides and CT images is more complicated than between CT and µct, since the slide thickness in histology may be very thin (~.5 mm) compared with the sampling interval (~1 mm), and the criterion to characterize different tissues within the plaque using histology is based on a colour code dependent on the staining technique; and iii) the profound effect on the structural integrity of the plaque caused by the histological preparation of the samples, that includes the removal of two significant tissue components; calcium and lipid. The complex layered structure of lipid, hemorrhage and calcium in plaques may cause the loss or fragmentation of the tissue components during histological preparation; and the decalcification of the plaque (necessary to facilitate the cutting of the sections) produces a loss of calcium, which has to be compensated by morphologic and tintorial examinations. Therefore, decalcification could limit the validity of histology to be the gold standard reference for calcification content in atherosclerotic plaques 18. The four plaques were scanned with a µct system that allows a resolution of 8 µm to 2 µm (at 1% of the Modulate Transfer Function, MTF). The data were acquired using 8 kv and 1 µa; a rotation step of o ; and a FOV 18.6 mm (depending on the sample size). The images were reconstructed using a cone-beam volumetric reconstruction (Feldkamp algorithm), and the standard corrections for ring artifacts and beam hardening were applied Histogram-Based Selective Deblurring (HiSD) HiSD generates a restored image through the deconvolution of the CT image, and the subsequent combination of the voxel information of the deconvolved image and the image based on the information of their respective histograms. The method consists of three main parts: 1) Measurement of the 3D PSF; 2) Deconvolution of the image; and 3) Generation of a restored image. 1) Measurement of the 3D PSF of the MSCT: Tungsten beads of.28 mm in diameter (Catphan CTP591 Bead Geometry Module, from The Phantom Laboratory placed approximately in the center of the FOV, were scanned. The intensity profile across the center of the bead was measured along the x-, y- and z-axes. These 3 profiles were fitted with a 1D Gaussian function and corrected by the dimensions of the tungsten beads 19 to obtain the standard deviations: σ x, σ y, and σ z of the PSF. The same operation was performed for 3 additional beads, and the averaged standard deviations were calculated in 3D. From this information a normalized 3D Gaussian PSF was numerically generated, centered within a volume of the same size as the image to be deconvolved,. 2) 3D deconvolution of images: Observed (3D) images were obtained by scanning the four in-vitro calcified plaques of carotid arteries. The ImageJ ( plug-in DeconvolutionJ was subsequently used to deblur the images (see figure 2). DeconvolutionJ effectively implements 3D deconvolution based on a regularized Wiener Filter 13 given by the following equation: r r H ( ν ) G ( ν ) = r (1) 2 H ( ν ) + γ where G (ν r ) is the Fourier transform of the image; H (ν r ) is the complex conjugate of the MTF (obtained from the Fourier transform of the PSF); and γ is a constant that depends on the SNR of the image. This constant γ controls the shape of the Wiener filter and is the user input parameter for DeconvolutionJ. The parameter γ determines the strength of the deconvolution and may be tuned for any desired amount of Wiener type smoothing 13,2. Note that if γ = it reverts to the unconstrained inverse filter. The Wiener filter deconvolution can only be applied in cases involving linear, space-invariant blurring functions and additive, uncorrelated noise. In spiral CT, these conditions are not fully met 19 ; the spatial resolution is not completely isotropic, especially due to rotational acquisition of data 21 and patient movements; and noise and artifacts increase along highly attenuating paths (e.g. along bony structures). However, for a sizable volume ( 1 cm in diameter) located at the center of the CT gantry, it may be assumed that the PSF is approximately isotropic and space-invariant, and noise and artifacts are almost constant 7,1,19. This is the case for our regions of interest (ROI), since the structures to be

4 deconvolved (coronaries, carotids, aorta, etc.) can usually be fitted within a volume 1 cm in diameter, concentric with the CT gantry. Before using the DeconvolutionJ plug-in, we studied how the value of γ affects the restoration of the images. The criterion that was used to select γ was based on the minimization of the FWHM of the calcification peaks, while their intensities were maximized. With this criterion we obtained a γ =.5, which was used to deconvolve the images of the four in-vitro carotid plaques. The effect of the deconvolution is illustrated using the data from the heaviest calcified in-vitro plaque (Sample ). Figure 2 shows the and deconvolved cross-sectional CT images of Sample, and the corresponding reference µct image. Although only 2D cross-sectional images are shown, all the algorithms are applied in 3D. The volumes to be deconvolved were chosen slightly larger than the ROIs (containing the whole plaque), so as to prevent artifacts at borders of the image affecting our structures of interest. Before deconvolution, a constant value of 124 was added to the HU of images to avoid problems with negative intensities during deconvolution microct µct microct Observed Deconvolved dec_g Figure 2. Effect of deconvolution on a cross-sectional image of Sample. Frames on the left: top is the reference µct cross-sectional image (18.6 mm width, 124 pixels); middle is the CT image (affected by blur); bottom is deconvolved image. Frames on the right show the respective intensity profiles along the lines indicated in the left frames. Cross-sectional images show calcifications (high-intensity voxels), soft-plaque (grey values surrounding the calcifications), and the plastic holder (ring enclosing the plaque). The intensity profile representation of the image (middle) shows two calcifications convolved together due to image blurring. After applying deconvolution (Equation 2), these calcifications appear resolved (see intensity profile at the bottom), however amplification of artifacts and noise degrades the imaging of the low-density structures (the contrast of the cross-sectional image at the bottom was increased to show the artifacts: ring artifacts surrounding the plastic holder; ditches around the borders of calcifications; and amplification of noise/artifacts and edges; in the intensity profile at the bottom small peaks due to ring artifacts around highfrequency peaks can be better appreciated.). 3) Generation of restored images: As already mentioned, a strong deconvolution (low values of γ) improves the imaging of high-density small structures, but amplifies noise and artifacts and generates additional edge-related artifacts. Our method HiSD includes an algorithm that selectively deconvolves only high-intensity objects, such as calcifications and bone, while leaving the other structures unmodified. The restored image is subsequently generated from the image (Figure 2a) and the deconvolved image (Figure 2a) following the algorithm here explained. This algorithm selectively combines the low-intensity voxel

5 information of the image and the high-intensity voxel information of the deconvolved image into a restored image. This selective combination of voxel information requires the definition of two intensity values: B and C. These values are used to roughly segment calcifications and bone from other tissues in the and deconvolved images, based on thresholding and 3D region growing. Value C is used to discriminate core parts of calcified structure from other structures, image noise and artifacts (if a volume structure has a maximum intensity, I max > C, it is classified as true calcified structure). Value B indicates the intensity of the voxels at the borders of the volume of the calcified structure (i.e. intensity at the transition between the calcified structure and its surrounding tissue). Therefore, with these definitions of B and C, a 3D region growing of image cores with I>C until reaching value B theoretically determine the volume of the calcified structure. The algorithm itself consists of 3 main steps: i) Determination of the values B and C to roughly indicate the volumes of the calcified structures in the image thereby preserving the low-intensities; ii) Determination of values B and C to roughly indicate and preserve the volumes of the calcified structures of the deconvolved image; iii) Integration of the voxel information preserved in the and deconvolved images into the restored image. i) The current implementation of HiSD does not require an accurate determination of B and C. This means that B and C can be measured from the last peak of the histogram, which corresponds to the tissue with the highest density surrounding the calcifications. This surrounding tissue consists of soft-tissue: blood, fibrous tissue, etc., with intensities, I ~ 3-5 HU, and/or contrast material (~3 HU) used to enhance the vessel. (Note: in our images I=HU+124). A fast and more accurate way to determine the values of B and C almost automatically is using the histogram information of the maximum intensity projection (MIP) of the image for an arbitrary angle. Essentially, only the right side of the peaks of the original histogram are displayed in the MIP histogram. This means that the contribution to the last peak of the MIP histogram is almost exclusively due to the noise and artifacts above the mean intensity value of the highest density material surrounding the calcifications, and to the voxels belonging to the borders of the calcifications. This allows us to determine B and C from, respectively, the mean intensity and from the highest intensity of the last peak of the MIP image histogram. Figure 3 shows the MIP image of Sample and its corresponding MIP histogram with the thresholds B and C indicated B C Figure 3. From left to right: MIP of image of Sample and its histogram with the thresholds B and C. Once thresholds B and C are measured, the calcifications of the image are subsequently segmented using thresholding and 3D region growing. Thus, all voxels with I B within the volume of a calcification (I max >C) are set to I=B. Figure 4 shows a cross-sectional view of the thresholded image. Figure 4. Observed image after thresholding with B. Figure 5. Mask generated from thresholded volume of image. Figure 6. Multiplication of the mask with the deconvolved image.

6 ii) Following the same procedure, the thresholds corresponding to B and C (now referred to as B and C ) are estimated for the deconvolved image from its MIP histogram (see Figure 7). Deconvolution changes the histogram due to the amplification of noise and artifacts, resulting in a slightly higher value for B and a substantially higher value for C, compared with their respective values B and C in the image B C Figure 7. From left to right: MIP of masked deconvolved image of Sample and its histogram. The last peak of the histogram contains the contribution of the highest intensities of noise and artifacts surrounding the calcifications, and the contribution of the borders of the calcifications. B is taken at the mean of the peak, and C over the highest-intensity artifacts. iii) Low intensities of the image and the high intensities of the deconvolved image are integrated in the restored image. To achieve this, several steps are followed: First, a 3D mask is generated from the thresholded volumes of the image (see Figure 5). The multiplication of this mask with the deconvolved image performs as a filter, which only preserves in the image those voxels belonging to the volumes of calcifications and their immediate surrounding tissues (see Figure 6). Second, to avoid residual artifacts, region growing of image cores with I >C until reaching B is done, roughly indicating true deconvolved calcifications. Finally, the value of B is subtracted, and the result is added to the thresholded image (see Figure 8). Note: To smooth the transition between the voxels thresholded with B and their adjacent voxels with original values, a Gaussian filter of 1 pixel width was applied restored Figure 8. Left: 2D CT restored image. Right: Intensity profiles of the and restored images along the line indicated in the left image. The images show that the blur of the calcifications is reduced in the restored image and that closed calcifications are better resolved Evaluation of the image quality In order to evaluate HiSD, qualitative and quantitative analyses were performed on the, restored and µct images of four in-vitro calcified plaques. For the qualitative evaluation we visually compared the restored images with the and µct images. We examined several effects: artifacts introduced by HiSD; blur reduction in the xy-plane and z-direction; missed true calcifications; and introduced false calcifications. For the quantitative analysis we measured the area of 27 calcifications using a threshold equal to 276 HU. This threshold was chosen to be above the HU level of noise and artifacts superimposed on the soft-tissue plaque (that has the same mean intensity in the and restored images), thereby preventing any effect of these factors on the area measurements. The 27 calcifications were classified into four different groups according to their maximum area in the µct cross-sectional images: i) small calcifications (<1mm 2 ); ii) medium calcifications (1-2mm 2 ); iii) big calcifications (>2mm 2 ); and iv) clusters of calcifications (defined as a group of 2 or more calcifications so close to each other that their contributions appear

7 convolved in the image). In addition, the total volume of calcification was measured for each of the four invitro samples using the threshold of 276 HU. 3.1 Input parameters. 3. RESULTS In this section we provide the input parameters for HiSD, i.e.: i) parameters for the Wiener filter (PSF and γ); and ii) thesholds B, C, B and C. i) Parameters for the Wiener filter: First, the standard deviations of the PSF along the x-, y- and z-axis were measured and the results are given in Table 1. Mean values of the standard deviations are applied to model the 3D Gaussian PSF used in the Wiener filter. Bead σ x (mm) σ y (mm) σ z (mm) 1.363±.1.358±.2.367± ±.2.365±.4.367± ±.1.362±.1.367±.2 σ.364±.1.362±.2.367±.2 Table 1. Values of the standard deviation of the PSF in 3D. These values are the outcome of the 1D Gaussian fit (R 2 =.999) of the image intensity profiles of three different tungsten beads, and the correction of the resultant mean standard deviation for the non null standard deviation of the beads. Subsequently, the γ input parameter for the Wiener Filter was determined. The optimum value of γ was empirically determined 14,2 so as to maximize the SNR and minimize the FWHM of the calcifications in the deconvolved images. The SNR was found to vary little with large (one order of magnitude) variations of γ. For our images, the best results were achieved with γ [.5,.1]. The effect of γ on the deconvolution of calcifications is shown for several values of γ in Figure 9. Intensity g=.4 g=.5 g=.5 g=.5 invers filter (g=) pixel (.1 mm) Figure 9. Intensity profiles of two nearby calcifications is shown. These intensity profiles were obtained from the deconvolution of an image (continuous dark line) using different values for the γ parameter. With γ.4 the image was smoothed, resulting in larger blur. As the value of γ was reduced, the intensity of the peaks increased and the blur decreased. The optimal representation of the calcifications was found for γ [.5,.1]. For values of γ<.1, the signal began to decrease at the expense of amplifying noise and artifacts. Finally, with γ= (for which the Wiener filter becomes the inverse filter) the noise completely overwhelmed the signal. ii) Thresholds used in HiSD to generate the restored images. The values for the thresholds B, C, B and C measured in the histograms of the MIP and deconvolved images are given for the four in-vitro carotid plaques (Sample -3) in Table 2. Observed image Deconvolved image Threshold B C B C Sample Sample Sample Sample Table 2. Thresholds used to restore the images of the four invitro plaques. The thresholds measured on the images were more similar than the thresholds measured on the deconvolved images. B and C were noticeably larger for Sample. The reason may be that Sample contains more calcifications than the other samples, leading to the generation of more ring artifacts during deconvolution.

8 3.2. Qualitative evaluation The visual comparison of the and restored images with their corresponding reference µct images showed: i) the blur of calcifications was reduced in 3D; ii) in all cases the high-density structures classified as true calcifications in the image corresponded to calcifications in the µct images; iii) no false calcifications were introduced in the restored images; iv) No true calcifications were missed in the restored images. The only exceptions being two small calcifications (see discussion bellow). Next, results are illustrated with cross-sectional and MIP images. Cross-sectional views of a slice of Sample are given in Figure 1. Two different display settings show that the contrast of the calcifications is increased and the blur is reduced in the restored images. It can also be that artifacts and noise amplification due to the deconvolution process does not affect the imaging of low densities. Figure 1. From left to right: µct cross-sectional image; corresponding CT image; and corresponding restored image. The two last images display the same and restored slices with a higher contrast for the low densities. Intensity profiles along the and restored images show (see Figure 11) that the representation of the calcifications becomes sharper in the restored images and that adjacent calcifications are better resolved (see graphic on the left). Intensity along line 2 (right frame) shows that artifacts due to thresholding do not exceed the intensity of edgerelated artifacts originally present in the image (see the intensity background of third peak). intensity Near calcifications restored 1 2 intensity restored Thresholding artifact Edge artifact pixel pixel Figure 11. Intensity profiles of and restored images along line 1 (left frame), and line 2 (right frame). Intensity profiles along the lines 1 and 2 (middle frame) are represented: from top to bottom of line 1; and from left to right of line2. Two small calcifications detected in the and µct images were missed in the restored images. The first small calcification (area=.23 mm 2 and length=.81 mm along the z-axis in the µct image) could be detected in the and µct images of Sample 1 (see arrows in Figures 12a and 12b). This calcification was still shown in the deconvolved image (12c), but it was finally lost in the restored image (12d) because its I max =1424 was lower than C =145, and consequently it was considered to be an artifact. The same happened with the second small calcification, and the reason why other small calcifications were not missed in the restored images is that these were longer in the z-direction. a b c d Figure 12. (From left to right) cross-sections of µct,, deconvolved and restored images of Sample 1.

9 MIP images of the µct,, and restored volumes of Samples and 2 are shown in Figures 13 and 14, respectively. These MIP images are taken along the z-axis and allow us to show the effect of HiSD on the imaging of calcifications that appear in different longitudinal planes. It can be seen that: i) the blur of calcifications along the z-axis was reduced; ii) the contrast of the calcifications was increased, leading to a better visualization of small calcifications; iii) clusters of calcifications were better resolved; iv) no small true calcifications were missed; and v) No false calcifications were introduced. Figure 13. (Left to right) MIP images of µct,, and restored volumes of Sample Quantitative evaluation Figure 14. (Left to right) MIP images of µct,, and restored volumes of Sample 2. Area of calcifications: The areas of 27 calcifications were measured from several cross-sections of the and restored images, and compared with the corresponding areas measured in the µct images. The mean areas of the calcifications were calculated for each of the four groups: small (<1mm 2 ); medium (1-2mm 2 ); big (>2mm 2 ); and clusters of calcifications. The results are given in Table 3. area (mm 2 ) restored area (mm 2 ) reference (µct) (mm 2 ) relative error relative error (%) () (%) (restored) I max (obs.) I max (rest.) Small calc Medium calc Big calc Clusters Table 3. Mean value of the area calculated for the four groups of calcifications. The results are given for the and restored images and for the reference µct images. The mean relative errors of the areas (obtained from the relative errors of the areas of each group) have been calculated for the and restored areas with respect to the µct areas. These results show that the areas measured on the restored images are overestimated (mean error of 9%) with respect to the areas measured on the µct images. However, this overestimation is considerably smaller when compared with the results of the areas measured on the images (mean relative error of 143%). The maximum intensities of the calcifications were considerably higher in the restored images than in the images (~1 HU on average). Figure 15 shows the areas of the 27 calcifications, measured in the, restored CT and µct images. We found that the areas measured on the restored images were smaller and closer to the µct values than the areas measured on the images. Only the areas of two small calcifications were found to be slightly larger for the restored image than for the image. However, when we repeated the measurements using the thresholds corresponding to half of the

10 maximum intensity of each calcification, the areas of the restored calcifications were smaller than the areas of the calcifications restored microct big (>2 mm 2 ) clusters 7. Area (mm 2 ) medium (1-2 mm 2 ) small (<1 mm 2 ) Area reference µct (mm 2 ) Figure 15. Area of 27 calcifications measured in the images (dark), restored images (grey), and µct images (light). Total volume of calcifications per sample: Table 4 presents the total volume of calcifications for the four in-vitro carotid samples measured using the threshold of 276 HU. The results show that the total volume of calcifications is overestimated in both and restored images. However, the measured volumes in the restored images (mean error of 92%) were more accurate than the measured volumes in the images (mean relative error of 213%). volume (mm 3 ) restored volume (mm 3 ) reference volume (µct) relative error (%) (observ.) relative error (%) (rest.) Sample Sample Sample Sample Table 4. Quantification of the total volume of calcium for each of the four in-vitro carotid plaques. Volumes are measured on the, restored, and µct images. Results show that the volumes measured in restored images are smaller and closer to the µct volumes than the volumes measured in the images. 4. DISCUSSION Digital image deconvolution is a technique frequently used in many disciplines, such as microscopy and astronomy, to increase the image spatial resolution in those applications that exceed the imaging capabilities of current systems. Several authors 1,14,22,23 have applied deconvolution to improve the clinical analyses of MSCT images, most notably of small bony structures of human anatomy, and they already suggested its further application to improve the visualization of vessels in CTA images. However, the specific application of deconvolution to improve the visualization and quantification of calcifications in atherosclerotic plaques has not been evaluated until the present study. This work for the first time raises the potential of 3D deconvolution to improve the visualization and analysis of vessels and the quantification of the calcified plaques. Many deconvolution algorithms aimed to reduce the blur while increasing the SNR have recently been developed. Most of them are based on the iterative minimization of the difference between the image and the imaged estimated object obtained in each iteration. These methods are powerful in improving the SNR, but unfortunately at the expense of very long computational processing times 1,14. Iterative deconvolution techniques require many iterations to effectively improve the resolution of the image, and this fact limits their application on large image volumes. Opposed to

11 this, direct deconvolution using the regularized Wiener filter requires relatively short processing times, which makes its application especially interesting when the deconvolution has to be done in 3D. The disadvantage of non-iterative deconvolution techniques (like the Wiener filter) is that the improvement in spatial resolution of the image is done at the expense of amplifying both noise and ring artifacts. Furthermore, to implement the Wiener filter the PSF of the system and the parameter γ (related to the SNR of the image) have to be calculated. These two parameters can be assumed approximately constant for a relatively large volume of interest, and can be standardized for each imaging protocol of a given CT system. We found that small values of γ reduced the blur of the calcifications more effectively, but noise and ring artifacts surrounding high-contrasted structures became more dominant. To avoid these negative effects, we developed the HiSD method and evaluated it on the images of four in-vitro carotid plaques. The method includes an algorithm that combines the low-density structures of the image with the high-density structures of the deconvolved image using thresholds B and C, and B and C, determined from the histograms of the and deconvolved images. We found that the thresholds B and C had similar values for the four samples, which suggests that their values may be standardized under similar levels of image noise and artifacts. This condition is fulfilled when a given CT acquisition and reconstruction parameters are selected, a given contrast material administration protocol (in enhanced scans) is applied, and similar attenuating objects are scanned (this means that regions of the body like thorax and neck would require different settings of the thresholds). On the other hand, B and C were in general different for the four samples depending on their structural characteristics: the more calcifications and discontinuities the sample had, the more ring artifacts were generated thereby increasing the values of B and C. Theoretically, if the tissue surrounding the calcifications is larger than the system PSF, its mean intensity would remain approximately constant after deconvolution, and consequently B and B would be approximately equal. This assumption was satisfied by the least calcified plaque (Sample 3), but the differences between B and B seemed to increase with the percentage of calcification in the plaque. It was more noticeable for the heaviest plaque (Sample ), where the artifacts introduced by the deconvolution resulted in a shift of the threshold B of 169 HU. These results indicate that the standardization of the values B and C may be somewhat more complicated and further research in this direction must be done by means of simulations and phantom experiments. Nevertheless, it must be pointed out that small variations of the values B and C hardly affect the quality of the restored image. This is due to the fact that: i) the volumes of the deconvolved calcifications do not depend strongly on the threshold B because their edges have been sharpened by the deconvolution; and ii) The use of C is not relevant for the restoration of the image, since almost all edge-related artifacts of the deconvolved image are previously eliminated by the masking process, thereby avoiding their introduction as false calcifications. Therefore, B and B are the approximated mean intensity values at the borders of the calcifications in the and deconvolved images, respectively. The image quality and reliability of the restored image depend on the accuracy with which the limits between the calcifications and their surrounding tissues are calculated in both images: i) the more accurate the value of B, the less evident the thresholding artifacts in the restored image; and ii) the more accurate the value of B, the more accurate the measurement of the calcification volume. Since the mean intensity of the denser tissue surrounding the calcifications may change along the volume image (soft-plaque may contain thrombus, and contrast material may not be completely homogenous), an improvement of HiSD would involve the determination of the local values of B and B for each calcification of the image, while C and C would still be determined from the histograms of the MIP images of the whole and deconvolved volumes, respectively. Further work aims to standardize and automate setting the thresholds. The area measurement of 27 calcifications showed that HiSD reduced the overestimation of the calcification sizes in the xy-plane, which lead to better accuracy in vessel lumen assessment. The problem with these measurements is that in some cases the partial volume in the z-direction may contribute, together with the xy-blur, to the overestimation of the areas of the calcifications. However, the contribution of the partial volume in the z-direction would affect the areas of the and deconvolved images in the same way. The quantification of the volume of the calcification is more rigorous and representative, since volume measurements counteract the decrease of blur both in the xy-plane and in the longitudinal direction. Quantification of the total volume of calcification for the four samples showed that the overestimation of the values with respect to the reference µct was lower for the restored images (mean 192%) than for the images (mean 313%). Additional measurements of the volume of calcification are needed for a rigorous evaluation of HiSD. Although current quantification methods use standard thresholds for area/volume measurements, more accurate results would probably be obtained by setting the threshold for each imaged object to half of its maximum intensity 24,25. The application of this new definition of the threshold for the quantification of calcifications will be considered in future works.

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