Geometric Calculation of Changes in Cardiac Volumes

The most common volume measurement in the heart is the left ventricular volume because it is the most clinically relevant for evaluating cardiac performance. The method used to make this measurement depends on the type of images that are used. The imaging modality can be a digital contrast angiogram, a radionuclide angiogram, or a set of tomographic images. A geometric calculation of the ventricular volume relies on proper identification of the edges of the ventricular cavities on these images. Several edge detection techniques have been proposed for the automatic or semiautomatic outline of left ventricular borders. For images such as a contrast angiogram where the contrast between the ventricular cavity and the ventricular wall is high, the determination of the ventricular contour is fairly easy. Totally automated methods have been developed and validated. Such methods require a perceivable contrast between the left ventricle and superimposed structures such as ribs, catheter, aorta, and diaphragm in order to define ventricular borders accurately. In addition, inhomogeneous distribution of contrast medium within the left ventricular cavity (especially in diastolic and in mitral regurgitation) also causes significant technical problems for totally automated techniques.

In difficult cases, a good compromise solution is an automated edge detection method, coupled with human interaction to guide the edge detection algorithm and to correct any mistakes made by the computer. The simplest and fastest edge detection technique often used is the "raster" technique [7]. The image is first subdivided into rows where each row is the average of several raster lines. The left ventricular boundary is then extracted for each row by searching for the maximum first derivative of gray level along the row. These investigators have reported that 64% of contrast ventriculograms could be processed totally automatically, and an additional 14% could be analyzed with some human intervention [7]. Raster tracking has a disadvantage that border tracking may fail for portions of the left ventricular boundary that are nearly tangential to the raster lines. Hence, it is essential that the left ventricular image be rotated so that the long axis of the left ventricle is perpendicular to the raster lines. Even at this orientation, the boundary at the left ventricular apex may be discontinued because it is almost parallel to the raster lines. The orientation problem can be avoided if an "omnidirectional tracking" technique is used [8,9].

This omnidirectional edge tracking technique can be relatively computationally intensive and slow, and it may be inaccurate when overlapping structures such as pulmonary vessels or the diaphragm interfere with the proper identification of the ventricular boundaries on projectional images. The desire to compromise between speed and accuracy will determine performance of the chosen technique.

Other contouring techniques rely on more specific geometric assumptions of the shape of the heart. Given the assumption that the heart has an oval convex shape, several specific edge detection techniques were developed based on a "radial" search of ventricular boundaries from a center point in the ventricular cavity. Further refinements of the edge detection technique have been proposed based on the concept of active contours or "snakes," which have the ability to conform to irregular contours in an image [10,11]. This class of algorithms is discussed in Chapter 8 as well as other chapters.

The relatively large size of the left ventricle and the need for global contouring of the ventricular cavity for left ventricular volume and function evaluation facilitates the use of digital image processing techniques that enhance the image quality and lead to improved edge detection accuracy [12]. When using contrast, such as in contrast ventriculograms, the background or overlapping structure can be suppressed by subtracting a mask image from the corresponding ECG-gated, opacified image. Random noise such as quantum noise can also be reduced if images from the same point in several cardiac cycles are averaged [13]. After completion of the edge detection procedure, the left ventricular boundary contours can then be used to generate left ventricular volume and regional wall motion data.

Left Ventricular Volume Measurement

Once edges are located, end-diastolic and end-systolic volumes can be obtained and ejection fraction and stroke volume can be calculated. The most widely used method of measuring left ventricular volume is the area length method introduced by Dodge et al. [14]. This method models the left ventricule as a three-dimensional ellipsoid. The three axes of the ellipsoid are estimated from the antero-posterior (AP) and lateral (LAT) views of biplane left ventricular images. The expression used for the volume calculation is

where Aap and Akt are the projected left ventricular areas in the AP and LAT views, respectively, Lap and Llat are the longest measurable axes in the projected LV, and L is the longer of Lap and Ljat. The errors associated with the volumetric measure ments obtained from these two views are about 8% [15]. This formulation has also been found accurate for oblique RAO/ LAO projections [15-17]. This technique was also applied to other imaging techniques such as gated cine MRI (Fig. 1).

The same technique has been further extended to measurements made from a single projection [18]. In the single plane method, it is assumed that the ellipsoid has rotational or circular symmetry about its long axis. The preceding formula is then reduced to

It was shown that single plane methods can provide the same accuracy as the AP/LAT biplane views if the single plane view is perpendicular to the long axis of the left ventricular. This approximately corresponds to the RAO/30° view. However, in general, single plane studies are inferior to biplane studies. Left ventricular ejection fraction deduced from volumetric measurements obtained from the best views have about a 10% uncertainty.

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