Improving the imaging of calcifications in CT by histogram-based selective deblurring *
Empar Rollano-Hijarrubia a,b, Frits van der Meera, Aad van der Lugta, Harrie Weinansc, Henri Vroomana,b, Albert Vossepoela,b, Rik Stokkinga,b. a Departments of Radiology, bMedical Informatics, and cOrthopaedics. Erasmus MC - University Medical Center Rotterdam, Dr. Molewaterplein 50, 3015 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 observed 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 observed 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: 90% for area; 92% for volume) than for observed 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 vulnerability1-5. 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 arteries5,6. 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 0.32 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. *
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The spiral CT imaging process can be mathematically approximated as a convolution of the true object with an isotropic, spatially invariant, 3D separable Gaussian PSF7-11, 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 tissue1-4. 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 volume11. 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 are11,12: 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 artifacts13,14, 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 observed image with the high-density voxel information of the deconvolved image.
2. MATERIALS AND METHODS 2.1. In-vitro samples 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 0 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.
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Figure 1. Four atherosclerotic plaques presenting different amounts of calcium were selected and categorized as: Sample 0 heaviest, Sample 1 and 2 moderately calcified and Sample 3 least calcified.
2.2. 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 120 kV and current of 249 mAs; beam collimation of 16 slices × slice collimation of 0.75 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 (B50s); field of view (FOV) of 50.0 mm; 360oLI algorithm; 0.75 mm of effective slice thickness (Seff) or full width at half maximum (FWHM) of the slice sensitivity profile (SSP); and reconstruction increment (RI) equal to 0.3 mm. A value of RI=Seff /3 (or 67% of image overlap) is recommended to improve the spatial resolution in the zdirection, however, the increase in resolution with RI 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 observed 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 observed 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 ~ 30-50 HU, and/or contrast material (~300 HU) used to enhance the vessel. (Note: in our images I=HU+1024). 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 0 and its corresponding MIP histogram with the thresholds B and C indicated. 3500
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Figure 3. From left to right: MIP of observed image of Sample 0 and its histogram with the thresholds B and C.
Once thresholds B and C are measured, the calcifications of the observed image are subsequently segmented using thresholding and 3D region growing. Thus, all voxels with I≥B within the volume of a calcification (Imax >C) are set to I=B. Figure 4 shows a cross-sectional view of the observed thresholded image.
Figure 4. Observed image after thresholding with B.
Figure 5. Mask generated from thresholded volume of observed image.
Figure 6. Multiplication of the mask with the deconvolved image.
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 observed 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 observed image. B’ C’ 800 700 600 500 400 300 200 100 0 0
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Figure 7. From left to right: MIP of masked deconvolved image of Sample 0 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 observed 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 observed image (see Figure 5). The multiplication of this mask with the deconvolved image performs as a filter, which only preserves in the observed 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 observed 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. 0
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Figure 8. Left: 2D CT restored image. Right: Intensity profiles of the observed 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.
2.5. Evaluation of the image quality In order to evaluate HiSD, qualitative and quantitative analyses were performed on the observed, restored and µCT images of four in-vitro calcified plaques. For the qualitative evaluation we visually compared the restored images with the observed 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 observed 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 (2mm2); and iv) clusters of calcifications (defined as a group of 2 or more calcifications so close to each other that their contributions appear
convolved in the observed image). In addition, the total volume of calcification was measured for each of the four invitro samples using the threshold of 276 HU.
3. RESULTS 3.1 Input parameters. 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 1 2 3
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0.363±0.001
0.358±0.002
0.367±0.002
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Table 1. Values of the standard deviation of the PSF in 3D. These values are the outcome of the 1D Gaussian fit (R2=0.999) 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 determined14,20 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 observed images, the best results were achieved with γ∈[0.005, 0.001]. The effect of γ on the deconvolution of calcifications is shown for several values of γ in Figure 9. 6000
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Figure 9. Intensity profiles of two nearby calcifications is shown. These intensity profiles were obtained from the deconvolution of an observed image (continuous dark line) using different values for the γ parameter. With γ≥0.4 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∈[0.005, 0.001]. For values of γ2 mm )
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