Patent Publication Number: US-8970578-B2

Title: System and method for lesion-specific coronary artery calcium quantification

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. provisional Application Ser. No. 61/139,165, entitled, “System and Method for Lesion-Specific Coronary Artery Calcium Quantification”, filed on Dec. 19, 2008. 
    
    
     TECHNICAL FIELD 
     The present system and method is a lesion-specific quantification tool for coronary artery calcium scans that can enhance or supplant other predictive indicators. 
     BACKGROUND OF THE INVENTION 
     Atherosclerosis is the leading cause of morbidity and mortality worldwide. It is a complex disease initiated and propagated by lipoprotein deposition and inflammation. Later stages of atherosclerosis are characterized by progressive deposition of calcium in the coronary arterial vessel-wall. Histopathology, computed tomography and intravascular ultrasound studies have confirmed that the extent of coronary calcification is closely correlated to the atherosclerosis plaque burden. 
     A cardiac tomography (CT) based coronary artery calcium (CAC) scan is a non-contrast-enhanced, three dimensional imaging technique that has been introduced as a non-invasive, low-radiation method for the assessment of the overall coronary arterial atherosclerotic burden, by quantifying calcium in the coronary vasculature. CAC has been validated to be independent of, and additive to, the Framingham Risk Score (FRS) in predicting major cardiovascular events. CAC is also considered safer and more appropriate for the primary prevention setting than invasive modalities, such as intravascular ultrasound (IVUS), and non-invasive and high-radiation modalities, such as CT angiography. 
     A three dimensional CAC image volume contains a large amount of clinically relevant information, such as the geometric and morphologic characteristics of each calcific lesion, which can be of high diagnostic and therapeutic value. However, current measurements of CAC, such as the Agatston score and the volume score, only quantify the whole-heart calcium burden. 
     SUMMARY OF THE INVENTION 
     Embodiments of the system and method described herein utilize the significantly greater data provided by a non-contrast-enhanced CAC scan; data that is left unused by the “whole-heart” Agatston or volume scores. While the Agatston score and volume score summarize overall coronary calcium burden, they are blind to the number of vessels involved, to the geographic distribution of the lesions, to the size and shape of the individual lesions and to the distance of the lesions from the coronary ostium. However, such information is inherently present in these clinically acquired scans. Embodiments of the systems and methods described herein extract and use the enhanced information provided by 3-D CAC scan data to improve prediction and assessment of cardiac risk. 
     Systems and methods described herein demonstrate that utilizing lesion-specific CAC (LS-CAC) and distance-weighted lesion-specific CAC (DWLS-CAC) improves prediction and assessment of obstructive coronary artery disease and prediction of cardiovascular events. Accordingly, these systems and methods significantly increase the clinical predictive value of traditional coronary artery calcium scanning. 
     An advantage of the systems and methods described herein is the ability to use standard imaging protocol. Embodiments of the lesion-specific calcium scoring systems and methods work on datasets acquired with typical clinical imaging protocols on conventional CT scanners. There is no need to modify the CT hardware or update the imaging protocol. Accordingly, there is no increased radiation exposure for the patients. 
     The described systems and methods also achieve fast semi-automatic calcific lesion-labeling and fully automated geometric and morphologic lesion measurements. Embodiments use a graphical user interface with automatic 3D propagation algorithm, to enable users to analyze a CAC volume rapidly (e.g., within 5 minutes), which is similar to, or even faster than using conventional CAC software while providing enhanced diagnostic capability. 
     In one embodiment, the system and method presents traditional measures such as total Agatston and volume scores as well as enhanced information comprising: statistics specific to each individual, such as each lesion&#39;s individual Agatston score, volume score, length, width, average and maximum attenuation values in Hounsfield unit (HU), as well as the distance of each lesion from corresponding vessel&#39;s ostium. These lesion-specific measurements highly correlate with the instances of coronary artery stenosis, and plaque volumes and compositions. Using a Naïve Bayesian approach, a distance-weighted measurement of the lesion-specific CAC was developed. This lesion specific CAC is more predictive of cardiovascular events compared to the overall CAC scores. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The claimed subject matter is described with reference to the accompanying drawings. A brief description of each figure is provided below. Elements with the same reference number in each figure indicated identical or functionally similar elements. Additionally, the left-most digit(s) of a reference number indicate the drawing in which the reference number first appears. 
         FIG. 1  is a block diagram of an embodiment of the system for lesion-specific CAC quantification. 
         FIG. 2  is a flowchart of an embodiment of a method for lesion-specific CAC quantification. 
         FIG. 3  is a flowchart of another embodiment of a method for lesion-specific CAC quantification. 
         FIG. 4   a  depicts a model illustrating 6-connectiveness in a 3D volume. 
         FIG. 4   b  depicts a model illustrating artifact mapping in a 3D volume utilizing 6-connectiveness. 
         FIG. 5  is an example of segmented 3D calcific lesion, and the measurement of the lesion&#39;s length and width. 
         FIG. 6  illustrates an exemplary cross-section of an artery with lesions of varying geometries. 
         FIG. 7  is an example of a graphical user interface allowing a physician to interact with the systems and methods described herein. 
         FIG. 8  is an exemplary report highlighting details quantified by the systems and methods described herein. 
         FIG. 9  illustrates ROC curves of whole-heart, vessel- and lesion-specific CAC scores. 
         FIG. 10  depicts a ROC curve analysis associated with the ROC curve depicted in  FIG. 9 . 
         FIG. 11  depicts an exemplary graph of marginal event probability based upon distance of a calcific lesion from the ostium of an artery. 
         FIG. 12  depicts an exemplary graph of marginal event probability based upon calcium score of a calcific lesion. 
     
    
    
     DETAILED DESCRIPTION 
     Conventional CAC image volume analysis reduces the three-dimensional (3D) volume, to a stack of two-dimensional (2D) slices that form the 3D volume to facilitate processing. The stack 2D slices of 3D data are evaluated and used to identify and quantify the presence of artery calcium, indicative of atherosclerosis. Typically, the presence of calcium within the CAC image volume is evaluated as a whole to determine the calcium burden on the heart depicted in the CAC image volume. These conventional techniques ignore the position of the calcium lesions as well as the geometry and size of individual calcium lesions. To minimize processing, risks of atherosclerosis are evaluated based upon these 2D images and averaged data. 
     In contrast, systems and methods described herein use the 3D volume of image data without reducing it to 2D data, avoiding potential errors introduced by representation of 3D data using sets of 2D images. For example, when 3D data is treated as a stack of 2D images, artifacts, such as lesions of calcium, whose major axis are aligned with the axis of the stack of 2D images may appear as a relatively small artifact in each 2D image, but may extend through a significant number of images. For a lengthy, but narrow lesion aligned with the axis of the stack of 2D images, only a small cross-section of the lesion would appear in each 2D image. A lesion may be overlooked or identified as relatively minor, even though it has significant length, due to the orientation of the artifact and the stack of 2D images. If the cross-section is sufficiently narrow, the appearance of the lesion in each 2D image could be filtered as noise within the data, resulting in the elimination of a significant lesion from the data and a significant, false reduction in the calculated risk. Maintaining the 3D nature of the image volume eliminates this potential source of error in image analysis. 
     In further embodiments, the systems and methods described herein analyze CAC image volumes on a lesion specific basis, evaluating individual lesions present within the CAC volume, rather than analyzing the presence of calcium within the CAC volume representing the heart as a whole. In conventional methodologies, lesions appearing throughout the heart are evaluated and averaged to determine the calcification of the volume and risk to the heart. While averaging may generally provide reasonable predictions of the effects of the lesions, in situations where the lesions vary significantly, averaging may not accurately reflect the risks to the heart. For example, if the set of lesions includes a single large lesion and one or more smaller lesions, the average of the set will appear the same as a set of mid-sized lesions; however, the risk of that large lesion negatively impacting the heart is significantly greater. In contrast, in embodiments of the lesion-specific CAC quantification systems and methods, lesions are evaluated individually, such that the risk posed by the large lesion is recognized and reflected in the resulting analysis and risk profile. As used herein, the term risk profile means data indicative of the risk of a negative result, e.g. a coronary event or other negative impact of the presence of a lesion. 
     In other embodiments, the size, geometry and position of individual lesions is analyzed to provide a more accurate risk profile associated with the lesions. For example, lesions located proximate to an artery origin are more likely to adverse effects than those which are located distal from the artery origin. In addition, those lesions that protrude further into the ostium of an artery, causing a greater obstruction of the ostium, are more likely to result in adverse effects on the imaged individual than lesions that protrude only minimally into the ostium itself. By analyzing not just statistics describing the average presence of calcium in the CAC volume, but rather lesion specific information describing geometry, size and/or location of each individual lesion, the systems and methods described herein increase accuracy of predictions of risk to the individual imaged by the CAC volume. 
       FIG. 1  is a block diagram of an embodiment of a system  100  for lesion-specific CAC quantification, also referred to here in as LS-CAC quantification. In an exemplary embodiment, the system  100  includes a CT scanner system  102 . As used herein, the term “exemplary” indicates a sample or example. It is not indicative of preference over other aspects or embodiments. The CT scanner is used in a conventional manner to scan or image a portion of the human body, in particular the coronary system, resulting in CAC image data. In an embodiment, the CAC image data is maintained in a first storage device  104  associated with the CT scanner system  102 . The CAC image data can be maintained for later processing and analysis. As used herein the term storage device includes any suitable form of memory, including but not limited to static memory such as erasable programmable read only memory (EPROM), electronically erasable programmable read only memory (EEPROM), flash or bubble memory, hard disk drive, CD-ROM, a USB drive, tape drive or any combination of static memory and dynamic memory. 
     In another embodiment, the CAC image data is transmitted from the first storage device  104  to a processor  106  that performs lesion specific analysis of the CAC image data. In an alternate embodiment, the image data is provided directly from the CT scanner system  102  to the processor  106 . Although system  100  is depicted as including a CT scanner system  102  in connection with the processor  106  that performs lesion-specific CAC quantification, the CT scanner system  102  may be completely independent, such that CAC image data is provided for processing, but no direct connection occurs between the CT scanner system  102  and the processor  106 . The processor  106  can be implemented using a microprocessor, microcontroller, or central processor unit (CPU) chip and printed circuit board (PCB). Alternatively, the processor  106  can include an application specific integrated circuit (ASIC), programmable logic controller (PLC), programmable logic device (PLD), digital signal processor (DSP), or the like 
     In an embodiment, the processor  106  is encoded with a method for lesion-specific analysis of the CAC image data as a 3D volume. As discussed above, such image data is typically analyzed as 2D slices of the 3D volume represented by the image data. Conventional systems analyze CT image data as a stack of 2D images to facilitate processing. In contrast, embodiments of the system  100  for lesion-specific CAC quantification, analyze the image data as a 3D volume of data. This 3D analysis avoids the inaccuracies introduced in analysis due to the limitations of 2D analysis. 
     In embodiment, the system  100  includes a user interface  108 . In an embodiment, the user interface  108  includes a monitor, LED screen, touch screen or other display mechanism that displays 3D CAC image data. The user interface  108  can also include input devices such as a keyboard, mouse, trackball, pointer or any other input device. The user interface  108  allows users (e.g., physicians or technicians) to view the 3D CAC image data. As described in further detail below, through the user interface  108  users can move through the 3D CAC image data, and identify lesions. In a further embodiment, users utilize a cursor to identify a lesion by selecting point on the displayed image. Based upon the value of the selected point, the processor  106  processes the 3D CAC image data to determine the boundaries of the identified lesion. In an alternative embodiment, the processor  106  is able to identify lesions within the 3D CAC image data without requiring selection of initial points by users. 
     In a further embodiment, the user interface  108  depicts the selected lesion boundaries, such that the user can view the lesion geometry. In other embodiments, the user interface  108  provides users with the ability to adjust or confirm the presented boundaries of the lesion. In still other embodiments, the user interface  108  provides users with the opportunity to identify the relative location of the identified lesion. For example, the user can indicate that the lesion corresponds to the left main ostium using the user interface  108 . 
     In other embodiments, the identification of lesions and associated information regarding the lesion location is stored along with the 3D CAC image data in a second storage device  110 . Although the system  100  is depicted with two separate storage devices,  104 ,  110 , a number of storage devices can be utilized with the system  100 . The resulting information regarding location and geometry of lesions within the 3D CAC image can be further evaluated by the processor  106  to determine a risk profile for the individual and heart scanned to produce the 3D CAC image data. The resulting risk profile can be maintained in the storage device  110  and/or displayed to a user via the user interface  108 . 
     Referring now to  FIG. 2 , an exemplary methodology for lesion-specific CAC quantification is illustrated. At step  202 , CAC image data is obtained, either from a CT scanner system  102  or storage device  104 . For example, a user can utilize the user interface  108  to select a particular CAC image data set from a storage device  104  for analysis and processing. At step  204 , the processor  106  generates a model for display from the CAC image data. In particular, the CAC image date is transformed, such that the calcium levels are illustrated in the model. 
     In an embodiment, a user identifies a lesion within the displayed model via the user interface at step  206 . For example, the user can select a point, or pixel, on the display, clicking or otherwise selecting the point to indicate the presence of a lesion at that point. The selected pixel corresponds to a voxel within the 3D CAC image data, where a voxel is a three-dimensional pixel. A voxel represents a quantity of 3D data just as a pixel represents a point or cluster of points in 2D data. In another embodiment, the processor  106  identifies likely lesions based upon the 3D CAC image data. In a further embodiment, a user confirms or rejects processor  106  identified lesions. 
     At step  208 , the processor  106  maps the boundaries of the identified lesion within the displayed model. In an embodiment, the boundaries are determined through the use of a flood-fill operation. For example, each voxel adjacent to the user-selected voxel is evaluated. If the value of the adjacent voxel is determined to be within a predetermined range, the voxel is identified as part of the lesion identified by the user-selected voxel. This adjacent voxel is marked as a lesion, and voxels adjacent to this newly identified lesion voxel or analyzed to determine whether they too are a part of the lesion. If the adjacent voxel is not part of the lesion, the processor  106  continues to evaluate the remaining voxels adjacent to the earlier identified lesion voxel, until all of the edges of the lesion have been identified. 
     At this point, a 3D map or model of the user identified lesion volume has been created. At step  210 , the geometric characteristics of the identified lesion are measured. For example, the processor  106  can calculate the width, length, height and location of the lesion with respect to one or more arteries. At step  212 , a determination is made as to whether there are addition lesions to process. In an embodiment, the user indicates via the user interface  108  that identification of lesions is complete or continues to select additional points identifying lesions. If further lesions are to be identified, the process returns to step  206 ; if all the lesions are selected or identified, the process continues to step  214 . 
     In an embodiment, at step  214 , the processor  216  determines a risk profile associated with the identified and mapped lesions. In a further embodiment, in addition to the analysis of the lesions as a whole, the processor  106  evaluates the individual lesions, including lesion geometry and location to generate a risk profile and analysis of the CAC volume. 
       FIG. 3  illustrates another embodiment of a methodology  300  for lesion-specific CAC quantification. At step  302 , the CAC volume from image files in (Digital Imaging and Communications in Medicine (DICOM) format are parsed and loaded. In an alternative embodiment of the methodology, there is an option to load in image data and LS-CAC quantification results from previously saved studies. For example, LS-CAC results can be maintained in the storage device for further analysis. 
     At step  304 , the CAC image is converted to a binary calcium volume based on HU thresholding. This conversion is based upon selection of an intensity threshold of the calcific lesions. In an embodiment, a conventional threshold equaling 130 HU is defined as the default value. In other embodiments the default intensity threshold is selectable by the user via the user interface  108 . In one embodiment, at step  306 , a determination is made as to whether an adjustment to the intensity threshold is necessary to allow for identification of lesions within the calcium volume. If yes, the intensity threshold is adjusted and the process returns to step  304  where the calcific volume derived again. Once an appropriate intensity threshold is selected, the calcific volume is displayed at step  308 . 
     In an embodiment, in the converted volume, calcific lesions are displayed by overlaying the color-encoded binary calcium volume onto the gray-scale CAC volume. In this example, the CAC volume is depicted in gray-scale, where the intensity of a particular pixel indicates the density of calcium for the voxel within the CAC volume. Accordingly, areas of greater calcium density, such as lesions will appear as higher intensity areas in the display of the user interface  108 . In an embodiment, the intensity threshold selected above is a value such that calcium densities that are too low to be part of a lesion are not shown on the display. By selecting the proper threshold, the boundaries of lesions are easier more noticeable on the display and easier to detect. Once a lesion is positively identified it may be encoded in color to further hi-light the lesion. 
     In an embodiment, a graphical user interface  108  (GUI) allows users to easily browse through the entire 3D CAC volume at step  310 . By interactively clicking on the GUI&#39;s three orthogonal cross-section views, described in detail below, users are able to localize and annotate the four major coronary arteries&#39; ostia, i.e., left main (LM) ostium, left anterior descending (LAD) and left circumflex (LCx) ostium, and right coronary artery (RCA) ostium. At step  312 , a determination is made whether the user identified and annotated an ostium, or lesion. If the user identified and annotated an ostium, the position of the ostium is recorded with respect to the CAC volume at step  314 . 
     At step  316 , a determination is made as to whether all of the ostium and lesions have been identified and annotated. If not, the process returns to step  310 , where users can continue to identify ostium or can interactively localize calcific lesions and annotate their corresponding arteries, i.e., LM, LAD, LCx, and RCA by clicking and specifying a seed point within each coronary calcific lesion via the user interface  108 . For lesions that cover two or more arteries, the corresponding artery is defined as the artery that is more proximal to the lesion. For example, if a lesion locates at the ostium of LAD and LCx, and covers all three LM, LAD and LCx arteries, this lesion is labeled as LM. 
     If the user selects another point, identified as a lesion at step  312 , then after selection of a user-specified seed point as a lesion, a 3D 6-connected flood-fill operation is applied to segment the 3D calcific lesion at step  318 . This 3D flood-fill operation automatically propagates through slices in 3D using a 6-connectiveness criterion, which will be explained in detail below. As a result of this flood-fill, users are not required to label the lesion slice by slice, as required in conventional 2D analysis of CAC volume. In this manner, the described methodology  300  can vastly expedite the image analysis process. 
     Another advantage of the described 3D approach is that the de-noising method using volume-size-thresholding in 3D is more accurate than in 2D. In conventional 2D approaches, for de-noising purposes, lesions in a single 2D slice with volume size smaller than 1 mm 2  are treated as noise and discarded. However, this is may be inaccurate, since these small-sized 2D lesions could be parts of larger 3D lesions. As discussed above, a long but narrow lesion might appear as less than 1 mm 2  in multiple slices. The lesion would be classified as noise within the individual 2D slices and discarded, reducing the accuracy of the resulting risk profile. 
     In an embodiment, at step  320 , for each segmented 3D lesion, a set of statistics are calculated, such as 2D and 3D Agatston scores, volume, length, width, average HU value, maximum HU value, and the Euclidian distance to its corresponding arterial ostium. Compared to the conventional 2D Agatston score, which takes the maximum HU value in each 2D slice, the 3D Agatston score takes the maximum HU value in the whole 3D lesion or plaque volume. Therefore, theoretically, 3D Agatston score is more robust and reliable than 2D, because the 2D approach could be affected by changes in the orientation of the imaging plane/patient in highly inhomogeneous lesions. 
     After the statistics for the identified lesion are calculated, the process continues to step  316  to determine whether all ostia and lesions have been identified. If no, the process returns to step  310 . If yes, then at step  322 , the results of such calculations are saved to a storage device  110  and/or output as a report to the user. In an embodiment, the output is displayed on the user interface  108  or stored in the storage device  110 . 
     Based on the lesion-specific quantification methodology  300  described herein, a prototype system and method was developed that has been successfully tested on CAC scans from two clinical CT scanners (Siemens Somatom 64-MSCT and Toshiba Aquilion ONE 320-MSCT). The methodology  300  can be adapted for use with a variety of models of CT scanners. 
     To facilitate use with multiple manufacturers&#39; scanners, in an embodiment, the system  100  is adapted to parse and load in DICOM images with both DICOMDIR and XML structures. Alternative CAC volume image formats are adaptable to the LS-CAC systems and methods by one of ordinary skill in the art. Once the CAC volume is loaded, calcific regions are extracted using a HU threshold of 130. In an embodiment, this predefined threshold is user adjustable. For example, if the CAC volume is V, and x, y, and z are integral indexes in the X, Y and Z coordinates of the 3D volume, the binary calcific volume C can be derived by: 
     
       
         
           
             
               
                 
                   
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     In an embodiment, the calcific volume is encoded with a color (e.g., red) and is overlaid on the gray-scale CAC images. 
     Referring now to  FIG. 4   a , a model illustrating 6-connectiveness in 3D volumes is depicted. A central voxel  402  is surrounded by adjacent voxels  404 , with an adjacent voxel  404  on each of its six sides. In an embodiment, during the flood-fill process, if the central voxel  402  is selected as a lesion point, each of these adjacent voxels  404  will be evaluated to determine whether they are part of the lesion as well. 
       FIG. 4   b  illustrates a path  406  connecting individual voxels, shown as a first voxel  408  and a second voxel  410 , identified as part of a lesion. For two calcific voxels, such as the first voxel  408  and second voxel  410 , voxels are 6-connected if they are 6-connected by a path  406  of calcific voxels. Accordingly, if the voxels along the path  406  are calcific voxels, the first voxel  408  is 6-connected with the second voxel  410 . 
     In an embodiment, a 3D 6-connected flood-fill algorithm is adapted to segment the calcific lesion. There are many different implementations of the flood-fill operation known to those of ordinary skill in the art. One embodiment of a flood-fill method suitable for use with embodiments of the present system and method is detailed in Table 1. 
                     TABLE 1               An exemplary 3D flood-fill algorithm.                                    1. Initialize an empty queue L to store the group of calcific voxels       in the lesion of interest. Initialize an empty queue T.       2. If the seed point in the calcium volume C(x s , y s , z s ) = 0, return;       Otherwise, add voxel v s  = (x s , y s , z s ) to L and T.       3. While T is not empty, repeat the following steps:                         For each element v = (x, y, z) of T, observe its 6 neighbors:                         If C(x − 1, y, z) = 1, and v′ = (x − 1, y, z) ∉ L: add v′ to L and T.           If C(x + 1, y, z) = 1, and v′ = (x + 1, y, z) ∉ L: add v′ to L and T.           If C(x, y − 1, z) = 1, and v′ = (x, y − 1, z) ∉ L: add v′ to L and T.           If C(x, y + 1, z) = 1, and v′ = (x, y + 1, z) ∉ L: add v′ to L and T.           If C(x, y, z − 1) = 1, and v′ = (x, y, z − 1) ∉ L: add v′ to L and T.           If C(x, y, z + 1) = 1, and v′ = (x, y, z + 1) ∉ L: add v′ to L and T.                         Delete v from T.                 4. Output L as the resulting calcific lesion.                    
Geometric and Morphologic Measurements
 
     In embodiments, the length, width, volume, 2D/3D Agatston score, and the distance to its corresponding artery ostium of each segmented calcific lesion is measured after identification and mapping. Suppose lesion L contains N voxels: v i =(x i , y i , z i )εL, i=1, 2, . . . N, where x i , y i , z i  are the integral indexes in the 3D volume. Suppose the voxel&#39;s resolution is r=(r x , r y , r z ), which is specified in the DICOM image files. An individual voxel v i &#39;s physical coordinates can be obtained by: p i =(r x ·x i , r y ·y i , r z ·z i ), i=1, 2, . . . N. Suppose lesion L&#39;s corresponding artery ostium O=(x o , y o , z o ). The physical coordinates of the ostium O can be derived as based upon the physical coordinates or position within the 3D volume and the resolution of individual voxels r=(r x , r y , r z ) such that physical coordinates are derived as: p o =(r x ·x o , r y ·y o , r z ·z o ). 
     The lesion&#39;s length and width is defined by calculating the lesion&#39;s thickness in the orthogonal directions along the lesion mass&#39;s first and third Eigen Vectors, described in further detail with respect to  FIG. 5  below. Suppose 
               p   _     =         ∑       i   =   1     ,   2   ,           ⁢     …   ⁢           ⁢   N         ⁢     p   i       N           
is the center of mass of the lesion. We define the covariance matrix B as:
 
 B=[p   1   −  p ,p   2   −  p ,p   N   −  p ]·[p   1   −  p ,p   2   −  p ,p   N   −  p ]   T   (2)
 
Note that the dimension of B is 3×3. We apply principal component analysis on B and get the Eigen vectors v 1 , v 2 , v 3 , and Eigen values, λ 1 , λ 2 , λ 3 , respectively, and λ 1 ≧λ 2 ≧λ 3 .
 
       FIG. 5  is an example of a segmented 3D calcific lesion  500 . Eigen vectors, v 1 , v 2  and v 3 ,  502 - 506 , associated with the lesion  500  are depicted. In an embodiment, the processor  106  calculates a set of statistics relevant to the risk profile of the lesion, based upon the geometry and location of the lesion  500 . In an embodiment, the length, width, volume, 2D and 3D Agatston score, as well as the distance to its corresponding artery ostium (not shown) of each segmented calcific lesion  500  are computed. 
     In an embodiment, an ellipsoid shape is assumed or used as an initial model of a lesion to determine Eigen vector  502 ,  504  and  506  axes. The longest axis can be assumed to be oriented parallel with the artery, due to the nature of lesion growth patterns. In an embodiment, the assumption of ellipsoid shape is utilized to determine the orientation of the Eigen vectors  502 ,  504 , and  506 . In another embodiment, length of the lesion is determined based upon the first Eigen vector  502 . In a further embodiment, width is determined based upon the extent of the lesion along the direction of the axis of the third Eigen vector  506 , but because lesions are often irregularly shaped, the width is not assumed to be greatest on the Eigen vector  506  itself. In this embodiment, the maximal width in the direction of the third Eigen vector  506  along the length of the first Eigen vector  502  is considered the width of the lesion, and indicates the protrusion of the lesion into the ostium of the artery, as described further with respect to  FIG. 6 . 
     As discussed above, each representation of a lesion  500  contains N voxels, or a certain quantity of 3D data, v i =(x i , y i , z i )εL, i=1, 2, . . . N, where x i , y i , z i  are the integral indexes in the 3D volume of N. Accordingly, the position of a given lesion voxel, i, within the matrix defined by the 3D volume is defined by the coordinates x i , y i , z i , also referred to herein as the position coordinates. The voxel&#39;s resolution, or relationship of the voxel to real world distance measurements can be represented as r=(r x , r y , r z ). The voxel&#39;s physical coordinates within the physical world can then be obtained by the dot product of the voxel position coordinates and the resolution of the voxel: p i =(r x ·x i , r y ·y i , r z ·z i )=1, 2, . . . N. The lesion&#39;s corresponding artery ostium, O=(x o , y o , z o ), can then be located by deriving: p o =(r x ·x o , r y ·y o , r z ·z o ), where x o , y o , z o  are the position coordinates of the artery ostium voxel and the voxel&#39;s resolution is represented as r=(r x , r y , r z ). 
     In an embodiment, the lesion&#39;s length and width is defined by calculating the lesion&#39;s thickness in the orthogonal directions along the lesion mass&#39;s first  502  and third  506  Eigen vectors. Lesion&#39;s length, as determined along the first Eigen vector  502 , is defined as the maximum distance between any two lesion voxels along the direction of the first Eigen vector  502  v 1 : 
                   L   =       max       i   =   1     ,   2   ,           ⁢     …   ⁢           ⁢   N     ,     j   =   1     ,   2   ,           ⁢     …   ⁢           ⁢   N     ,     i   ≠   j         ⁢              (       p   i     -     p   j       )     T     ·     v   1                      (   3   )               
The width  506  of the lesion is defined as the maximum distance between any two lesion voxels along the direction of the third Eigen vector  506  v 3 :
 
                   W   =       max       i   =   1     ,   2   ,           ⁢     …   ⁢           ⁢   N     ,     j   =   1     ,   2   ,           ⁢     …   ⁢           ⁢   N     ,     i   ≠   j         ⁢              (       p   i     -     p   j       )     T     ·     v   3                      (   4   )               
The lesion&#39;s volume is defined as the number of voxels within the lesion N, multiplied by the resolution of the voxel:
 
 Vol=N·r   x   ·r   y   ·r   z   (5)
 
     To remove noise in conventional Agatston scores, 2D calcific lesions in a single 2D slice, where lesions with an area size smaller than 1 mm 2  are treated as noise, and can be discarded. As discussed above, where a lesion is narrow but long, if the axis of the lesion is oriented in the same direction as the stack of 2D slices, a lesion may appear to be less than 1 mm 2  in each individual slice. Accordingly, a lesion of significant size overall may be eliminated as noise from the set of 2D slices since it fails to appear as larger the noise threshold in the individual 2D slices. 
     In embodiments of the LS-CAC systems and methods, this de-noising strategy of conventional 2D systems is adapted for 3D processing. In an embodiment, calcific lesions are evaluated as volumes, such that if the 3D volume of a lesion is smaller than a defined noise threshold, e.g., 1 mm 3 , the lesion is treated as noise, and be discarded. Because the volume of the lesion is evaluated, this particular embodiment would retain the data regarding the long, narrow lesion that would have been discarded in the 2D conventional system. In another embodiment, according to the imaging quality, users can also actively adjust the noise threshold. In a further embodiment, the LS-CAC system  100  can utilize conventional 2D Agatston scores, as well as 3D Agatston scores. 
     In an embodiment, the 3D Agatston scoring method is similar to the conventional 2D method for Agatston scoring, except that the whole 3D volume and the highest HU value in the whole 3D lesion are used as opposed to calculating 2D Agatston scores for each individual 2D slice of the 3D volume and then summing the 2D Agatston scores for each slice. 
     The distance to the ostium is defined as:
 
 D=|p   o   −  p |   2   (6)
 
where p o  is the position of the ostium within the 3D volume and p is the position of the lesion within the 3D volume.
 
     The lesion&#39;s maximum HU value is defined as: 
     
       
         
           
             
               
                 
                   
                     HU 
                     max 
                   
                   = 
                   
                     
                       max 
                       
                         
                           i 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                             
                         
                         ⁢ 
                         … 
                         ⁢ 
                         
                             
                         
                         , 
                         N 
                       
                     
                     ⁢ 
                     
                       C 
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             i 
                           
                           , 
                           
                             y 
                             i 
                           
                           , 
                           
                             z 
                             i 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The lesion&#39;s average HU value is defined as: 
     
       
         
           
             
               
                 
                   
                     HU 
                     mean 
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           i 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                             
                         
                         ⁢ 
                         … 
                         ⁢ 
                         
                             
                         
                         , 
                         N 
                       
                     
                     ⁢ 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           
                             
                               x 
                               i 
                             
                             , 
                             
                               y 
                               i 
                             
                             , 
                             
                               z 
                               i 
                             
                           
                           ) 
                         
                       
                       / 
                       N 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In an embodiment, the LS-CAC system  100  computes a detailed set of statistics or measurements regarding each lesion within the CAC volume. For example, the system  100  computes lesion level measurements including, but not limited to, Lesion Volume, Lesion Agatston Score, Lesion 3D Agatston Score, Lesion Length, Lesion Width, Distance to corresponding vessel&#39;s ostium, Maximum HU and Mean HU. In addition, the system  100  can compute statistics and measurements associated with each of the four major arteries. These vessel level measurements include, but are not limited to, Lesion Number, Total Volume, Total Agatston Score, Total 3D Agatston Score, Maximum Lesion Volume, Maximum Lesion Agatston Score, Maximum Lesion 3D Agatston Score, Maximum Lesion Length, Maximum Lesion Width, Mean Lesion Volume, Mean Lesion Agatston Score, Mean Lesion 3D Agatston Score, Mean Lesion Length, Mean Lesion Width, Shortest Distance to corresponding vessel&#39;s ostium, and Largest lesion&#39;s (with maximum Agatston Score) distance to corresponding vessel&#39;s ostium. In a further embodiment, the system  100  computes whole heart level measurements including, but not limited to, Total Lesion Number, Whole Heart Volume Score, Whole Heart Agatston Score, and whole Heart 3D Agatston Score. 
       FIG. 6  illustrates a cross section of an artery  600 , including the artery walls  602  and ostium  604 . The illustrated artery  600  has a first lesion  606  and a second lesion  608  of varying geometries. As shown, second lesion  608  is slightly larger than the first lesion  606  and protrudes further into the ostium  604  of artery  600 . The first Eigen vector  502  of each of the first lesion  606  and second lesion  608  is generally oriented substantially parallel with the artery wall  602 . This is typical lesion geometry. 
     In an embodiment of the LS-CAC system  100 , conventional statistics such as total 2D Agatston and over-all CAC volume scores are computed for the CAC volume. In addition, lesion-specific statistics or measurements, including lesion geometry data, are computed. For example, the LS-CAC system  100  computes a 2D and 3D Agatston score, volume score, length, width, average maximum attenuation values in Hounsfield (HU), and the distance from corresponding artery ostium  604  for each of the first lesion  606  and second lesion  608 . These statistics can be maintained in the storage device  110 . These lesion specific measurements highly correlate with the instances of coronary artery stenois, and plaque volumes and compositions. 
     In an embodiment, a lesion-specific volume, 2D and 3D Agatston score for each lesion is measured along with its distance from the corresponding coronary ostia  604 . A first distance  610  is indicative of the distance that the first lesion  610  extends into the ostium  604  and the portion of the ostium  604  that remains unobstructed by the first lesion  606 . A second distance  612  is indicative of the distance that the second lesion  612  extends into the ostium  604  of the artery  600 , and the portion of the ostium  604  that remains unobstructed by the second lesion  608 . This measure of obstruction by lesions is highly indicative of the risk posed by individual lesions. This information can serve as a model to evaluate the overall event risk by combining the risks from all the lesions using a Naïve Bayesian technique, which assumes that the event risk caused by each lesion is independent to each other. 
     Referring now to  FIG. 7 , an embodiment of a graphical user interface  700  for a system  100  that performs lesion-specific CAC quantification is illustrated. The depicted graphical user interface  700  is one possible embodiment of the user interface  108  of the LS-CAC system  100 . In an embodiment, the user interface  700  includes an editable field  701  (A) of the HU threshold of calcific regions. In a further embodiment, the graphical user interface  700  includes a view or window  702  (C) that displays the binary calcium volume. In an alternate embodiment, the binary calcium volume is displayed in gray-scale, where intensity of the pixels indicates the density of calcium at a particular location. Areas identified as lesions can be indicated using color to allow users to easily recognize lesions. For example, an annotated calcific lesion  706  appears as a shaded region to indicate a lesion in the LAD artery. In a further embodiment, the user interface  108  includes a mouse, trackball or other control device that allows the user to scroll through the binary calcium volume and select one or more points. 
     In other embodiments, the graphical user interface  700  includes a status panel  704  (B) that allows users to label three arterial ostia. Users can select individual points within the binary calcium volume utilizing the window  702  and a control device, such as a mouse to select a point. In a further embodiment, upon selection of a point, the user can right-click with a mouse, or otherwise use a control device to initiate a popup menu  708  (D), which allows for the classification of specific regions of the calcific volume  702 . 
     In an embodiment, the graphical user interface  700  allows users to easily browse through the entire 3D CAC volume. By interactively clicking on the GUI&#39;s three orthogonal cross-section views, users are able to localize and annotate the four major coronary arteries&#39; ostia, i.e., left main (LM) ostium, left anterior descending (LAD) and left circumflex (LCx) ostium, and right coronary artery (RCA) ostium. 
     By clicking and specifying a seed point within each coronary calcific lesion, users can interactively localize calcific lesions and annotate their corresponding arteries, i.e., LM, LAD, LCx, and RCA. For lesions that cover two or more arteries, their corresponding artery is defined as the artery that is more proximal. For example, if a lesion locates at the ostium of LAD and LCx, and covers all three LM, LAD and LCx arteries, the lesion is labeled as LM. 
     In an embodiment, from the user-specified seed point, a 3D 6-connected flood-fill operation is applied to segment the 3D calcific lesion. This 3D flood-fill operation automatically propagates through the 3D CAC volume using a 6-connectiveness criterion. Accordingly, users are not required to label the lesion slice by slice, as in required in the conventional 2D methodology, in which the CAC volume is represented as a stack of 2D slices. In this manner, the described method can vastly expedite the image analysis process. Another advantage of the described 3D approach is that the de-noising method using volume-size-thresholding in 3D is more accurate than in 2D. In conventional 2D approaches, for de-noising purposes, lesions in a single 2D slice with volume size smaller than 1 mm 3  are treated as noise and discarded. However, this is may be inaccurate, since these small-sized 2D lesions could be parts of larger 3D lesions, as discussed in detail above. 
     In an embodiment, for each segmented 3D lesion identified by the user, 2D and 3D Agatston scores, volume, length, width, average HU value, maximum HU value, and the Euclidian distance are calculated to its corresponding arterial ostium. Compared to the conventional 2D Agatston score, which takes the maximum HU value in each 2D slice, 3D Agatston score takes the maximum HU value in the whole 3D plaque volume. Therefore, theoretically, 3D Agatston score is more robust and reliable than 2D, because the 2D approach could be affected by changes in the orientation of the imaging plane/patient in highly inhomogeneous plaques. 
     In the embodiment illustrated in  FIG. 2 , the graphical user interface  700  allows the user to freely browse through the 3D volume by interactively clicking on the three orthogonal cross-section views, including the window  702  and additional displays of 3D image data  710 . In an embodiment, users can save the resulting data, describing the location and geometry of one or more lesions, to a storage device  110 . 
       FIG. 8  depicts an exemplary lesion specific CAC quantification report  800 , which presents traditional measures such as total Agatston and volume scores as well as enhanced information, such as each lesion&#39;s 3D Agatston score, volume score, length, width, average and maximum attenuation values in Hounsfield unit (HU), and the distance of each lesion from corresponding vessel&#39;s ostium. In an embodiment, each segmented 3D lesion, 2D/3D Agatston score, volume, length, width, average HU value, maximum HU value, and the Euclidian distance are calculated to its corresponding arterial ostium. The 3D Agatston score takes the maximum HU value in the whole 3D plaque volume. These lesion-specific measurements highly correlate with the instances of coronary artery stenois, and plaque volumes and compositions. The results provide a comprehensive report that describes risk profile rather than basic output from existing 2D systems. Using a Naïve Bayesian approach, a distance-weighted measurement of the lesion-specific CAC was developed, which is more predictive of cardiovascular events compared to the overall CAC scores. 
     Clinical Applications and Results 
     Laboratory testing data was used to demonstrate that vessel-specific and lesion-specific coronary artery calcium scores generated by the method/process described above and implemented using the described systems and methods, but not total Agatston or volume scores, are accurate in predicting obstructive coronary artery stenosis. In this study, 100 patients with CAC and invasive angiography (XRA) data were investigated. Vessel-specific CAC was determined for each major artery, i.e., the left main, the left anterior descending, and the right coronary artery. Average lesion-specific score was calculated by dividing the vessel-specific score by the number of lesions within the corresponding vessel. Coronary artery stenosis greater than 50% on XRA was used as the criterion to label the corresponding vessel with obstructive CAD. It was noted that the Agatston and volume scores were similar in patients with/without obstructive CAD (335.8±74.1, vs. 652.4±186.5; p=0.13 and 299.5±61.4 vs. 539.9±147.9; p=0.14). In contrast, vessel-specific score, vessel-specific volume, average lesion-specific score and average lesion-specific volume were significantly different between patients with/without obstructive CAD (77.8±12.1 vs. 309.5±65.2, p=0.001; 69.3±10.1 vs. 252.9±50.9, p=0.001; 22.5±3.1 vs. 69.8±15.0, p=0.004 and 20.3±2.6 vs. 57.6±11.6, p=0.003). As shown in Table 2, ROC analysis also showed superiority of vessel- and lesion-specific scores over the total Agatston and volume score. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 ROC analysis of the vessel-specific/lesion-specific CAC scores and total scores 
               
               
                 with respect to vessel stenosis. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Optimal 
                   
                 Standard 
                 95% confidence 
                 p- 
                   
                   
               
               
                   
                 Cupoint 
                 AUC 
                 deviation 
                 interval 
                 value 
                 Sensitivity 
                 Specificity 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Vessel-specific 
                 28.9 
                 0.789 
                 0.0479 
                 0.724-0.844 
                 0.0001 
                 88.6 
                 59.9 
               
               
                 score 
               
               
                 Vessel-specific 
                 24.2 
                 0.786 
                 0.0481 
                 0.721-0.842 
                 0.0001 
                 91.4 
                 58.0 
               
               
                 volume 
               
               
                 Average lesion- 
                 12.5 
                 0.761 
                 0.0498 
                 0.694-0.820 
                 0.0001 
                 82.9 
                 59.9 
               
               
                 specific score 
               
               
                 Average lesion- 
                 11.8 
                 0.762 
                 0.0497 
                 0.696-0.821 
                 0.0001 
                 85.7 
                 58.6 
               
               
                 specific volume 
               
               
                 Total Agatston 
                 594.5 
                 0.584 
                 0.0834 
                 0.433-0.724 
                 0.3145 
                 36.4 
                 84.6 
               
               
                 score 
               
               
                 Total volume 
                 580.6 
                 0.582 
                 0.0835 
                 0.431-0.723 
                 0.3250 
                 36.4 
                 88.5 
               
               
                   
               
            
           
         
       
     
     In another study, the total CAC scores with lesion-specific calcium quantification were compared by validating against intravascular ultrasound (IVUS) virtual histology (VH) with radiofrequency analysis. It was demonstrated that lesion-specific measures correlate with values of lumen stenosis and plaque composition by virtual histology (VH), while total CAC scores only correlate with the overall plaque burden on IVUS. In this study, 24 patients with CAC, IVUS/VH and Framingham Risk Score (FRS) were investigated. On CAC scans, the total Agatston and volume scores (AS, VS) were determined. Each lesion was scored individually and determined lesion-specific AS, lesion-specific VS, width and length. Minimal lumen diameter (MLD) and area (MLA), percent atheroma volume (PAV) and percent area stenosis (% AS) were measured on IVUS. Fibrous (FI), fibrofatty (FF), necrotic core (NC) and dense calcium (DC) volume and percent were measured on VH. The correlation coefficients r and p value were calculated. A value of p&lt;0.05 was considered significant. It was found that the Framingham Risk Score (FRS) was not predictive of IVUS/VH parameters. As shown in Table 3, it was found that the whole-heart 2D and 3D Agatston and volume score significantly correlated with the overall percent atheroma volume on IVUS, but not with measures of lumen stenosis. However, lesion-specific measures correlated with minimal lumen diameter and percent area stenosis; such measures also correlated with percent atheroma volume. Furthermore, whole-heart measures did not correlate with VH parameters, except volume score vs. fibrofatty percentage. However, several lesion-specific values correlated with necrotic core and dense calcium volume. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Comparison of whole-heart and lesion-specific calcium quantifications by 
               
               
                 validating against IVUS/VH parameters. 
               
               
                 Whole-Heart and Lesion-Specific CAC vs IVUS/VH Parameters 
               
            
           
           
               
               
               
               
               
            
               
                   
                 CAC 
                 IVUS/VH 
                 r-value 
                 p-value 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Whole-Heart Score 
                 Agatston 
                 PAV 
                 0.6059 
                 0.0046 
               
               
                   
                 Volume Score 
                 PAV 
                 0.5869 
                 0.0065 
               
               
                 Lesion-Specific Score 
                 Lesion Width 
                 MLD 
                 −0.5490 
                 0.0122 
               
               
                   
                 Lesion Length 
                 PAV 
                 0.4376 
                 0.0325 
               
               
                   
                 Agatston 
                 % AS 
                 −0.4780 
                 0.0330 
               
               
                   
                 Lesion Width 
                 % AS 
                 −0.4641 
                 0.0393 
               
               
                   
                 Volume 
                 % AS 
                 −0.5041 
                 0.0234 
               
               
                   
                 Volume 
                 DC Volume 
                 0.5463 
                 0.0057 
               
               
                   
                 Volume 
                 NC Volume 
                 0.4071 
                 0.0483 
               
               
                   
               
               
                 Only significant correlations are listed. 
               
            
           
         
       
     
     Another study tested the hypothesis that DWLS-CAC is more predictive of cardiovascular events than the whole-heart Agatston score. This study demonstrated that distance-weighted lesion-specific evaluation of CAC is more predictive of cardiovascular events compared to the total Agatston and volume scores. In this study, 30 patients (10 with events and 20 without events) were investigated. Their total AS and VS. Lesion-specific were measured. VS and AS were also measured for each lesion and its distance from the corresponding coronary ostia. A model was developed to predict risk of each lesion based on its lesion-specific AS/VS and its distance from the ostium, assuming a sigmoid-shaped increasing relationship between risk and lesion-specific AS/VS and a sigmoid-shaped decreasing relationship between risk and distance, where the sigmoid shapes were modeled by single-sided Gaussian curves. 
     Suppose the event probability caused by a lesion i is p i . which is a function of its lesion-specific AS/VS s i  and its distance to the ostium d 
                     p   i     =     {               a   i     ·     exp   (       -     d   1   2         2   ⁢     σ   d   2         )       ,             if   ⁢           ⁢     s   i       &gt;     3   ⁢     σ   s                       a   i     ·     exp   (       -     d   1   2         2   ⁢     σ   d   2         )     ·     exp   (       -       (       s   i     -     3   ⁢     σ   s         )     2         2   ⁢     σ   s   2         )       ,             if   ⁢           ⁢     s   i       ≤     3   ⁢     σ   s                         (   9   )               
where a is a coefficient, σ d  and σ s  are the Gaussian standard deviations of the AS/VS and distance sigmoid-shaped models. A model was developed to evaluate the overall event risk by combining the risks from all the lesions using a Naïve Bayesian technique, which assumes that the event risk caused by each lesion is independent to each other. Therefore, the overall event probability P can be derived by:
 
                   P   =     1   -       ∏       i   =   1     ,   2   ,           ⁢   …   ⁢           ,   N       ⁢     (     1   -     p   i       )                 (   10   )               
P where p i  is the event risk (probability) caused by lesion i and N is the total number of calcific lesions presented in the heart. P should be optimized by tuning parameters a, σ d  and σ s  to achieve the smallest p-value between patients with/without events using an unpaired t-test.
 
     For the 30 CAC positive scans, we calculated their overall event risk Pk; (k=1; 2 . . . 30) using Equations 9 and 10. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     t 
                     = 
                     
                       
                         
                           
                             P 
                             _ 
                           
                           event 
                         
                         - 
                         
                           
                             P 
                             _ 
                           
                           no_event 
                         
                       
                       
                         
                           
                             
                               s 
                               event 
                               2 
                             
                             10 
                           
                           + 
                           
                             
                               s 
                               no_event 
                               2 
                             
                             20 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     v 
                     = 
                     
                       
                         
                           ( 
                           
                             
                               
                                 s 
                                 event 
                                 2 
                               
                               / 
                               10 
                             
                             + 
                             
                               
                                 s 
                                 no_event 
                                 2 
                               
                               / 
                               20 
                             
                           
                           ) 
                         
                         2 
                       
                       
                         
                           
                             
                               ( 
                               
                                 
                                   s 
                                   event 
                                   2 
                                 
                                 / 
                                 10 
                               
                               ) 
                             
                             2 
                           
                           / 
                           9 
                         
                         + 
                         
                           
                             
                               ( 
                               
                                 
                                   s 
                                   no_event 
                                   2 
                                 
                                 / 
                                 20 
                               
                               ) 
                             
                             2 
                           
                           / 
                           19 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     { 
                     
                       
                         a 
                         i 
                       
                       , 
                       
                         σ 
                         s 
                       
                       , 
                       
                         σ 
                         d 
                         LAD 
                       
                       , 
                       
                         σ 
                         d 
                         LCx 
                       
                       , 
                       
                         σ 
                         d 
                         RCA 
                       
                     
                     } 
                   
                   = 
                   
                     
                       argmin 
                       
                         
                           α 
                           i 
                         
                         , 
                         
                           σ 
                           s 
                         
                         , 
                         
                           σ 
                           d 
                           LAD 
                         
                         , 
                         
                           σ 
                           d 
                           LCz 
                         
                         , 
                         
                           σ 
                           d 
                           RCA 
                         
                       
                     
                     ⁢ 
                     
                       B 
                       ⁡ 
                       
                         ( 
                         
                           
                             v 
                             
                               v 
                               + 
                               
                                 t 
                                 2 
                               
                             
                           
                           , 
                           
                             v 
                             2 
                           
                           , 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where  P   event  and  P   no     —     event  are the means of the P k s of the 10 patients with cardiac events and the 20 patients without event, respectively, and similarly, s 2   event  and s 2   no     —     event  are P k s&#39; standard deviations. B is the incomplete beta function. The optimization is implemented through a brutal force approach with multiple resolutions and a local gradient-descent refinement step, which make the convergence faster. 
     Utilizing a lesion-specific CAC quantification system and the event risk model, the optimized overall distance-weighted lesion-specific Agatston score and volume score (DWLS-AS/DWLS-VS) was derived from the 30 CAC scans. The Framingham Risk Score (FRS), AS, VS, maximum lesion AS/VS were compared in each vessel and distance weighted lesion-specific AS/VS between patients with/without events using unpaired t-test and ROC analysis. As shown in Table 4, FRS, total AS/VS, and maximum lesion AS/VS were similar in patients with and without events. However, distance weighted lesion-specific AS/VS Ps were significantly different (0.1078±0.055 vs. 0.0607±0.043; p=0.03 and 0.1085±0.055 vs. 0.0611±0.044; p=0.03). 
     Distance from ostium was more important in LCx and RCA compared to LAD (3σ d : 33 mm, 30 mm, &gt;100 mm, respectively). The conclusion was drawn that more proximal calcified lesions have higher risk of cardiac events; therefore, distance-weighted lesion-specific evaluation of standard CAC scans significantly improves predictive value. Such evaluation can be easily implemented in clinical practice by using the lesion-specific calcium quantification framework described herein. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Statistics of different calcium quantification 
               
               
                 measures in patients with/without event. 
               
            
           
           
               
               
               
               
            
               
                   
                 Mean ± SD (Event vs. No Event) 
                 p-Value 
                 AUC 
               
               
                   
               
               
                 Total Volume Score 
                 683.8 ± 642.3 vs. 480.0 ± 628.0 
                 0.4201 
                 0.66 
               
               
                 Total Agatston Score 
                 826.5 ± 819.2 vs. 539.8 ± 687.1 
                 0.3553 
                 0.64 
               
               
                 Framinghan Risk Score 
                 6.44 ± 4.61 vs. 6.30 ± 4.89 
                 0.9399 
                 0.50 
               
               
                 Maximum Volume Score 
                 333.1 ± 354.8 vs. 226.5 ± 316.8 
                 0.4335 
                 0.64 
               
               
                 Maximum Agatston Score 
                 433.3 ± 471.9 vs. 301.8 ± 415.9 
                 0.4687 
                 0.64 
               
               
                   Distance weighted Lesion - Specific   
                 
                   0.1085 ± 0.055 vs. 0.0611 ± 0.044 
                 
                 
                   0.0315 
                 
                 
                   0.75 
                 
               
               
                 
                   Volume Score 
                 
                   
                   
                   
               
               
                   Distance weighted Lesion - Specific   
                 
                   0.1078 ± 0.055 vs. 0.0607 ± 0.043 
                 
                 
                   0.0317 
                 
                 
                   0.75 
                 
               
               
                 
                   Agatston Score 
                 
               
               
                   
               
               
                 Distance weighted lesion-specific scores (highlighted) are significantly different (p = 0.03) in patients with/without event, which could be of event-predictive value. 
               
            
           
         
       
     
     As shown in  FIG. 9 , the areas under the ROC curve (AUC) of DWLS and AS/VS were both 75%, which are significantly larger than the AUC of total-AS/VS, which were 64% and 66%. At the specificity point of 80%, which is commonly used as the clinical cutpoint for choosing interventional treatment, the sensitivity of the DWLS-AS/VS measurements are 20%±30% higher than the whole-heart scores. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 The σ d  and σ s  values of DWLS-AS/VS. 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 σ s   
                 σ d   LAD   
                 σ d   LCx   
                 σ d   RCA   
                 a i   
               
               
                   
               
               
                 DWLS-AS 
                 3030 
                 &gt;100 cm 
                 12.6 mm 
                 10.1 mm 
                 1 
               
               
                 DWLS-VS 
                 2301 
                 &gt;100 cm 
                 12.1 mm 
                 10.0 mm 
                 1 
               
               
                   
               
            
           
         
       
     
     In Table 5, the parameters derived from the optimization process of the DWLS-AS/VS models are listed. The more proximal calcified lesions have higher marginal risks of cardiac events in LCx and RCA, where σ d   LCx =12.6 mm in DWLS-AS, σ d   LCx =12.1 mm in DWLS-VS, σ d   RCA =10.1 mm in DWLS-AS and σ d   RCA =10.0 mm in DWLS-VS. Suppose that 36 is the cutoff point of the Gaussian model, then most of the culprit lesions locate within the proximal 3 to 4 cm segments of the LCx and RCA, which is in good accord with clinical observations. For LAD, we observe that σ d   LAD  s of DWLS-AS/VS are both &gt;100 cm, which shows that lesions in LAD have the same high marginal event probability as in LM, in regard of their geometric locations. This is in accord with clinical observations as well: LAD is a more important major coronary artery that supplies the largest cardiac territory; physicians tend to choose revascularization treatment, which is one instantiation of MACE, for LAD atherosclerosis, even if the plaque location is relatively dismal. σ s  is the standard deviation of the AS/VS scores. 
     As shown in  FIGS. 11 and 12 , σ s-As  is larger than σ s-As , since AS is usually larger than VS.  FIGS. 11 and 12  illustrate marginal probabilities versus σ d , for  FIG. 11 , and σ s , for  FIG. 12 , curve of DWLS-AS/VS. It is also interesting to observe that in the single-lesion AS/VS ranges of 0˜1000, which are most common in clinical CAC scans, the marginal risk probability and the AS/VS score have an approximate linear relationship, which agrees with the findings in whole-heart CAC AS/VS studies. 
     In a retrospective, single-center, observational study; 91 consecutive patients referred to the Piedmont Heart Institute between January 2005 and June 2006 for both coronary artery calcium scoring and invasive X-ray coronary angiography within 12 months were included. This study was designed to investigate the diagnostic accuracy of different CAC measurements for obstructive CAD in patients with positive CAC; those with negative calcium scores were excluded (7 patients). Enrollment criteria were met by 84 patients. Demographic and clinical information was collected from medical records. 
     CAC examinations were performed on a 32×2 multi-detector (MDCT) system (Siemens Somatom 64; Erlangen, Germany). Non-contrast CAC scans were performed during end-respiratory breath hold with retrospective electrocardiographic (ECG)-gating. CAC images were acquired using 3 mm collimation with a 2 mm inter-slice gap. Other acquisition parameters included a gantry rotation of 375 ms, pitch 0.24, tube voltage 120 kV and tube current of 250 mAs. 
     Invasive X-ray coronary angiography was performed by using the Judkins technique based on institutional protocols, acquiring a minimum of five views of the left coronary system and two views of the right coronary system. The absence or presence of discrete coronary artery stenoses was examined in two orthogonal views and obstructive disease was confirmed by visual assessment. Two criteria for obstructive CAD, ≧50% diameter stenosis and ≧70% diameter stenosis, were used. The coronary vasculature was divided into 4 territories, i.e., left main coronary artery (LMCA), left anterior descending artery (LAD), left circumflex artery (LCx), and right coronary artery (RCA). Presence of obstructive CAD was recorded for each corresponding vessel. 
     Total Agatston score was calculated by standard methods. The area of calcification was multiplied by an arbitrary weighted density score based on the maximum Hounsfield unit (HU) value in the identified 2D calcified lesion, as follows: 1=130-199 HU; 2=200-299 HU; 3=300-399 HU; 4=400 HU and above. Calcium scores in all 2D calcified lesions along the major epicardial arteries were summed to derive the whole-heart Agatston score. Volume score was calculated as the total volume of the calcification in the major epicardial arteries, where calcification was identified as voxels with attenuation values equal to or greater than 130 HU. Lesion-specific Agatston and volume scores were measured in each single calcified lesion. A single calcified lesion was defined as a complete group of connected calcified voxels based on the 6-connectedness criterion in 3D. A software system has been developed to allow users to manually annotate calcified lesions followed by automated lesion segmentation. Vessel-specific CAC was determined as the sum of the lesion-specific CAC scores in the corresponding vessel. Lesions that covered two or more vessels were divided according to their locations. The maximum lesion-specific CAC was specifically recorded and the mean lesion-specific CAC in each vessel was calculated (vessel-specific score divided by the number of individual lesions). 
     Since patients with negative CAC scores were excluded in the study cohort, in order to achieve comparable sample distribution, only vessels with positive CAC scores were investigated in the vessel/lesion-specific CAC study. Normal vs. non-normal distribution was assessed by the Kolmogorov-Smirnov test. Normally distributed continuous variables were compared by unpaired two-tailed t-test. Non-normally distributed values were compared by independent Mann-Whitney test. Receiver operating characteristics (ROC) curves and the area under the curve (AUC) were used to evaluate and compare the diagnostic performance of different CAC parameters in diagnosing obstructive CAD. ROC cut-points were also selected to achieve 80% specificity or sensitivity, and the corresponding positive predictive value (PPV), negative predictive value (NPV), and sensitivity/specificity were compared between the whole-heart and vessel/lesion-specific approaches. Statistical significance was determined by a p-value &lt;0.05. 
     Results 
     Overall Patient Characteristics 
     Of the 91 patients screened, 84 met enrollment criteria with positive CAC results. Mean age was 66.1±8.5; 52 (61.2%) of patients were male. Clinical factors were not different between patients with and without obstructive CAD by either definition (≧50% or ≧70% diameter stenosis) (Table 6). 
                     TABLE 6                  Demographic data.                                     No. of   No. of &lt;50%   No. of ≧50%   No. of ≧70%           Patients   Stenosis   Stenosis   Stenosis               All   84   27 (32%)   57 (68%)   33 (39%)       Male   52 (62%)   14 (27%)   38 (73%)   22 (42%)       Female   32 (38%)   13 (41%)   19 (59%)   11 (34%)       Mean age ± SD(yrs)   66.1 ± 8.5   65.3 ± 10.0   66.6 ± 7.8   65.8 ± 8.2               SD: standard deviation; No: number. Age distribution was similar in patients with and without obstructive CAD by X-ray angiography using unpaired Welch-tests, with p = 0.55 (based on ≧50% diameter stenosis) and 0.74 (based on ≧70% diameter stenosis). Gender distribution was similar in patients with and without obstructive CAD by X-ray angiography based on frequency table analysis and χ 2  tests, with p = 0.29 (based on ≧50% diameter stenosis) and 0.62 (based on ≧70% diameter stenosis).            
Coronary Artery Disease by Invasive Coronary Angiography
 
     242 calcium positive coronary vessels were evaluated, including 38 LMCA, 79 LAD, 68 LCx, and 57 RCA, in 84 patients. Based on a criterion of ≧50% stenosis, 57 out of 84 patients (67.9%) and 83 out of 242 vessels (34.3%) had obstructive CAD (1 LMCA, 47 LAD, 17 LCx, and 18 RCA); based on a criterion of ≧70% stenosis, 33 out of 84 patients (39.3%) and 36 out of 242 vessels (14.9%) had obstructive CAD (15 LAD, 11 LCx, and 10 RCA). 
     Whole-Heart CAC Scores, Vessel-Specific and Lesion-Specific CAC Scores 
     CAC scores were non-normally distributed in the overall study population (Kolmogorov-Smirnov test for normal distribution: p=0.001); mean(±SD) whole heart Agatston score was 641(±709), median was 400. Mean(±SD) whole-heart volume score was 536(±570); median was 338. Using a criterion of ≧50% stenosis for obstructive CAD by XRA, whole-heart Agatston score and volume score were not significantly different between patients with and without obstructive CAD (median [interquartile range]: 436 [95,1177] vs 309 [84,574], p=0.23; and 374 [108,988] vs 265 [76,480], p=0.18, respectively). However, vessel-specific and lesion-specific values were significantly higher in patients with obstructive CAD (maximum lesion specific Agatston score: 165 [53,294] vs 47 [15,110]; p&lt;0.0001). 
     Diagnostic Characteristics of Whole-Heart, Vessel- and Lesion-Specific CAC Scores by ROC Analysis 
     ROC curves of whole-heart, vessel- and lesion-specific CAC scores in predicting ≧50% and ≧70% obstructive CAD are shown in  FIG. 9 ; corresponding optimal cut-points with corresponding sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) are shown in  FIG. 10 . For the prediction of 50% stenosis by XRA, all vessel- and lesion-specific scores had higher AUC&#39;s as compared to whole-heart values (whole-heart AgSc AUC: 0.58; maximum lesion-specific volume score AUC: 0.72). Statistically defined, optimal cut-point for whole-heart AgSc was 986; corresponding sensitivity and specificity were 32% and 93%. Optimal cut-point for maximum lesion-specific VolSc was 132 with 51% sensitivity and 88% specificity. A similar pattern was also seen for the prediction of ≧70% stenosis by XRA, although the performance of whole-heart AgSc improved (AUC 0.66) as compared to ≧50% stenosis. 
       FIG. 10  depicts the ROC curve analysis associated with the ROC curve of  FIG. 9 , where WH is whole-heart; VS is volume-specific; Max LS is maximum lesion-specific; Mean LS is mean of lesion-specific; AUC is area under ROC curve; Sens is sensitivity; Spec is specificity; PPV is the positive predictive value; and NPV is negative predictive value. Cut-points were selected to achieve maximum summation of sensitivity and specificity. Conventional cut-points of 100 and 400 of WH-AgSc were also tested. 
     Since the “optimal cut-point” of 986 for whole-heart AgSc is not very clinically meaningful, the diagnostic performance of each of the parameters with either sensitivity or specificity fixed at 80% was examined (see Tables 7 and 8). This analysis showed that when sensitivity was fixed at 80%, specificity increased from 22.2% (whole-heart AgSc) to 42.1% (maximum lesion-specific VolSc) for the detection of ≧50% stenosis; for the detection of ≧70% stenosis, specificity increased from 43.1% (whole-heart AgSc) to 62.1% (maximum lesion-specific VolSc). When specificity was fixed at 80%, sensitivity increased from 35.1% (whole-heart AgSc) to 61.4% (vessel-specific VolSc) for the detection of 50% stenosis; for the detection of ≧70% stenosis, sensitivity increased from 48.5% (whole-heart AgSc) to 61.1% (maximum lesion-specific AgSc). 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Comparison of CAC predictive values while specificities are fixed at 80%. 
               
            
           
           
               
               
               
            
               
                   
                 50% stenosis 
                 70% stenosis 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Cut- 
                   
                   
                   
                   
                 Cut- 
                   
                   
                   
                   
               
               
                   
                 point 
                 Sens 
                 Spec 
                 PPV 
                 NPV 
                 point 
                 Sens 
                 Spec 
                 PPV 
                 NPV 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 WH-AgSc 
                 790 
                 35.1% 
                 80% 
                   80% 
                 37.3% 
                 770 
                 48.5% 
                 80% 
                 61.5% 
                 70.7% 
               
               
                 WH-VolSc 
                 661 
                 36.8% 
                 80% 
                 80.8% 
                 37.9% 
                 661 
                 48.5% 
                 80% 
                 61.5% 
                 70.7% 
               
               
                 VS-AgSc 
                 194 
                 60.2% 
                 80% 
                   61% 
                 79.9% 
                 264 
                 61.1% 
                 80% 
                 34.9% 
                 92.2% 
               
               
                 VS-VolSc 
                 158 
                 61.4% 
                 80% 
                 61.4% 
                 79.4% 
                 238 
                 58.3% 
                 80% 
                 33.9% 
                 91.7% 
               
               
                 Max LS-AgSc 
                 119 
                 56.6% 
                 80% 
                 59.5% 
                 77.9% 
                 155 
                 61.1% 
                 80% 
                 34.9% 
                 92.2% 
               
               
                 Max LS-VolSc 
                 97 
                 55.4% 
                 80% 
                   59% 
                 77.4% 
                 127 
                 61.1% 
                 80% 
                 34.9% 
                 92.2% 
               
               
                 Mean LS-AgSc 
                 63 
                 48.2% 
                 80% 
                 55.6% 
                 74.7% 
                 76 
                 55.6% 
                 80% 
                 32.8% 
                 91.2% 
               
               
                 Mean LS-VolSc 
                 53 
                 48.2% 
                 80% 
                 55.6% 
                 74.7% 
                 67 
                 52.8% 
                 80% 
                 31.7% 
                 90.7% 
               
               
                   
               
               
                 WH: whole-heart; 
               
               
                 VS: volume-specific; 
               
               
                 Max LS: maximum lesion-specific; 
               
               
                 Mean LS: mean of lesion-specific; 
               
               
                 AUC: area under ROC curve; 
               
               
                 Sens: sensitivity; 
               
               
                 Spec: specificity; 
               
               
                 PPV: positive predictive value; 
               
               
                 NPV: negative predictive value. 
               
            
           
         
       
     
                     TABLE 8                  Comparison of CAC predictive values while sensitivities are fixed at 80%.                             50% stenosis   70% stenosis                                                             Cut-                   Cut-                           point   Sens   Spec   PPV   NPV   point   Sens   Spec   PPV   NPV                                                                 WH-AgSc   71   80%   22.2%   68.7%   35.3%   232   80%   43.1%   48.2%   78.6%       WH-VolSc   63   80%   22.2%   68.7%   35.3%   127   80%   41.2%   47.4%   77.8%       VS-AgSc   34   80%   35.8%   39.6%   78.1%   114   80%   63.1%   27.6%   94.9%       VS-VolSc   47   80%   42.1%   42.1%   80.7%   110   80%   60.7%   26.4%   94.7%       Max LS-AgSc   34   80%   40.3%   41.4%   80.0%   78   80%   59.7%   25.9%   94.6%       Max LS-VolSc   31   80%   42.1%   42.1%   80.7%   71   80%   62.1%   27.1%   94.8%       Mean LS-AgSc   20   80%     44%   42.9%   81.4%   24   80%   45.1%   20.4%   93.0%       Mean LS-VolSc   18   80%   42.1%   42.1%   80.7%   23   80%   46.6%   20.9%   93.2%               WH: whole-heart;       VS: volume-specific;       Max LS: maximum lesion-specific;       Mean LS: mean of lesion-specific;       AUC: area under ROC curve;       Sens: sensitivity;       Spec: specificity;       PPV: positive predictive value;       NPV: negative predictive value.            
Classification of Patients
 
     Another measure of improved diagnostic accuracy is the overall correct classification of patients. Assuming that the 80% sensitivity and specificity cut-points are clinically meaningful and patients above and below the respective cut-points are considered positive or negative and those who fall between those values are indeterminate, the proportion of indeterminate patients significantly decreased with the lesion-specific approach from 50% to only 17.9%, compared to the whole-heart AgSc. 
     This study tested the hypothesis that a more detailed analysis of CAC datasets based on vessel- and lesion-specific measurements has superior diagnostic accuracy for the prediction of obstructive CAD, using invasive coronary angiography as reference standard. Indeed, the main finding of this study was that maximum lesion-specific AgSc resulted in a significantly increased diagnostic accuracy compared to the whole-heart Agatston score, as evidenced by a higher AUC on ROC analysis (0.72 vs 0.58). Therefore, when specificity was fixed at 80%, as often necessary in clinical practice, sensitivity of vessel- and lesion-specific values increased by about 20%, which is a clinically significant improvement. 
     The whole-heart Agatston and volume scores are a simple summation of all calcified lesions in the three major epicardial arteries and are therefore inherently limited in the geographic localization of specific stenoses. Accordingly, in this study, whole-heart AgSc and VolSc were not different in patients with and without obstructive CAD, when CAD was defined based on 50% stenosis. Furthermore, the diagnostic accuracy of whole-heart AgSc and VolSc based on ROC analysis was poor for the prediction of obstructive CAD, either using 50% or 70% to define obstructive CAD ( FIG. 10 ). 
     However, the 3-dimensional CAC dataset contains significantly more information beyond the whole-heart Agatston and volume scores and therefore has the potential to improve diagnostic accuracy. Indeed, both for the detection of 50% and 70% stenoses, the AUC for vessel- and lesion-specific values were greater than 0.70, compared to the AUC of 0.58 for whole-heart AgSc. 
     The diagnostic performance of both vessel-specific and lesion-specific parameters were evaluated. Based on AUC calculations alone, vessel-specific parameters were slightly better than lesion-specific values both for the prediction of 50% and 70% stenosis ( FIG. 10 ). For lesion-specific parameters, maximum values were better than means ( FIG. 10 ). Comparing the sensitivities of each parameter when specificity was fixed at 80%, vessel-specific AgSc, maximum lesion-specific AgSc and maximum vessel-specific VolSc had the highest sensitivity for the prediction of 70% stenosis by XRA. Since vessel-specific measurements are more readily available on current, clinical, commercial workstations, such measurements may be more practical in clinical practice today. The prediction of obstructive CAD with vessel- and lesion-specific parameters was improved compared to the whole-heart approach, whether 50% of 70% was used for the definition of obstructive CAD, although the degree of improvement was larger for the detection of 50% stenosis. 
     From a clinical perspective, an AUC of 0.70 or greater—which was seen with all vessel- and lesion-specific parameter—is comparable to other clinically useful diagnostic tests, such as radionuclide myocardial perfusion imaging (87% sensitivity and 73% specificity) or stress echocardiography (70% sensitivity and 89% specificity). Therefore, it is proposed that a vessel- and lesion-specific approach is more acceptable for clinical decision-making as compared to traditional whole-heart AgSc, given the finding of a 61% sensitivity with an 80% specificity. 
     It is interesting to speculate how vessel- and lesion-specific scores may be incorporated in clinical practice. CAC imaging is currently recommended for asymptomatic subjects without known—but with intermediate likelihood of—CAD for the purposes of refined risk stratification. The apparent paradox is, however, that revascularization is typically reserved for patients with symptoms due to myocardial ischemia and therefore, it has been a clinical challenge to recommend further diagnostic testing on the basis of CAC scanning in asymptomatic subjects. It has been suggested that since many patients may be asymptomatic due to physical inactivity, provocative testing may be performed to uncover potential ischemia in patients with elevated CAC scores (ie. Agatston score 400 or greater). However, as we pointed out earlier, the specificity and positive predictive value of the whole-heart AgSc, whether using a cut-point of 400 or even 1000, are quite low. Therefore, it is proposed that the improved diagnostic accuracy of vessel- and lesion-specific scores may be helpful in refining clinical decision making. As shown, using cut-points for 80% sensitivity (to rule out obstructive CAD) and for 80% specificity (to rule in obstructive CAD), a vessel- and lesion-specific approach significantly reduces the number of patients with an “indeterminate” CAC for the prediction of ≧50% obstructive CAD ( FIG. 5 ). As a potential clinical approach, patients below the cut-point corresponding to 80% sensitivity (eg. vessel-specific VolSc&lt;47) clearly do not need further workup for ischemia or obstructive CAD, while those above the cut-point corresponding to 80% specificity (e.g. vessel-specific VolSc&gt;158) could be referred for myocardial perfusion imaging or for coronary angiography. Those in the intermediate zone could be referred for myocardial perfusion imaging. In this regard, it is important to point out that significantly less patients fall into the intermediate zone using the vessel- and lesion-specific approach, compared to the whole-heart Agatston score. 
     Although to our knowledge, no previous investigation has evaluated the diagnostic accuracy of a vessel- and lesion-specific approach, the Calcium Coverage Score (CCS) has been previously introduced to improve the predictive value of CAD events beyond the whole-heart Agatston score. In a study, Brown et al. showed that the percentage of coronary arteries affected by calcific plaque was significantly associated with coronary heart disease events. However, there was no difference in the prediction of hard cardiac events (myocardial infarction or death) when CCS was compared to the whole-heart Agatston and mass scores. 
     The study showed that a lesion-specific CAC approach was superior to the whole-heart AgSc in the prediction of obstructive CAD, using invasive coronary angiography as a reference standard. Such an approach may also be superior for the detection of obstructive CAD using intravascular ultrasound as reference standard, and even for the prediction of a hemodynamically significant stenosis, as measured by fractional flow reserve (FFR). 
     While various embodiments of the present system and method have been described above, it should be understood that the embodiments have been presented by the way of example only, and not limitation. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined. Thus, the breadth and scope of the present invention should not be limited by any of the above described exemplary embodiments.