## Quantitative Analysis

OF FUNCTION, PERFUSION, AND VIABILITY

Postprocessing of cardiac MRI studies represents the stage at which the full potential of the cardiac MRI examination may be best realized. Postprocessing is composed of two major steps: image postprocessing and data postprocessing. The first step largely involves segmentation algorithms to delineate and extract features and structures of interest from the collected images. The second step consists mainly of applying mathematical and statistical methods to aid in a given diagnosis. We focus here on the analysis of MR cine and perfusion studies.

For many cardiac protocols, the myocardium is the area of interest for analysis, so the myocardium must be segmented

Fig. 20. Example of myocardial segmentation for two images corresponding to the end-diastolic (left) and end-systolic (right) phases in a patient with poor cardiac function. The red contours are drawn around the blood pool demarking the endocardium. The green contour is drawn around the epicardium. The yellow contour delineates the right ventricular blood pool. For this particular patient, the cross-section of ventricular cavity with the short-axis view changed significantly less than in a healthy normal. Also shown are chords connecting the endocardial and epicardial borders. The chords are orthogonal to a centerline between the two contours. The chords measure the true thickness of the myocardium as opposed to radial chords, which emanate from the center of the left ventricle.

Fig. 20. Example of myocardial segmentation for two images corresponding to the end-diastolic (left) and end-systolic (right) phases in a patient with poor cardiac function. The red contours are drawn around the blood pool demarking the endocardium. The green contour is drawn around the epicardium. The yellow contour delineates the right ventricular blood pool. For this particular patient, the cross-section of ventricular cavity with the short-axis view changed significantly less than in a healthy normal. Also shown are chords connecting the endocardial and epicardial borders. The chords are orthogonal to a centerline between the two contours. The chords measure the true thickness of the myocardium as opposed to radial chords, which emanate from the center of the left ventricle.

from the rest of the image to extract further information, such as to utilize contrast enhancement in a perfusion study or monitor systolic thickening of the wall for a MR cine study.

### 6.1. Analysis of Ventricular Function by MRI

The quantitative analysis of ventricular function is based on the segmentation of the myocardium. In general, this is achieved by drawing contours on the endocardial and epicardial borders of the myocardium (Fig. 20).

The ventricular volumes of interest are the end-diastolic and end-systolic volumes, as well as derived parameters such as the stroke volume and ejection fraction. Although ventricular volumes have been computed from differently oriented views of the heart, analysis of the short-axis views is most widely used in cardiac MRI because of its proven accuracy (43-46). In the simplest case, myocardial segmentation is performed only for the images corresponding to the end-diastolic and end-systolic phases. The end-diastolic phase is defined as the phase containing the largest blood pool area in the left ventricle. The end-systolic phase is identified as the image containing the smallest blood pool area (Fig. 21).

Once the end-diastolic and end-systolic phases are fixed, the contours are drawn in the images for the end-diastolic and end-systolic phases for all slices containing the left ventricle. In images for a basal slice of the left ventricle, part of the aorta and aortic valve may be visible. It should be noted that inclusion of contours above the mitral valve plane will significantly overestimate the values for myocardial mass and ventricular volume. Thus, the careful inclusion or exclusion of slices near the base of the heart for determination of the volumes at end-diastole and end-systole is of considerable importance for an accurate deter mination of the ventricular volumes. Once all contours are drawn and verified, the ventricular volume can be computed by simple slice summation using Simpson's rule with the slice thickness as an increment.

Young et al. (46) proposed a method of speeding up the process of contour drawing by placing guide points on the endocardial and epicardial borders instead of drawing continuous contours for both borders. The algorithm then automatically detects the myocardial borders by interpolation between the guide points. This user-friendly method reduces the burden of generating contours compared to the conventional tracing of the contours. Swingen et al. (47) modified the guide point technique by including feedback from continuously updated 3D models of the heart to evaluate both the placement of guide points and the accuracy of the computed volumes. They showed that the combined use of short- and long-axis views results in more accurate estimates of the ventricular volumes and the myocardial mass compared to exclusive reliance on short-axis views.

Parameters of interest for volumetric analyses are as follows:

• Left ventricular mass: the myocardial mass is obtained by multiplying the myocardial volume by the myocardial specific gravity (1.05). Myocardial volume is calculated as the difference between the epicardial and endocardial volumes. The normal mean for left ventricular mass is 92 ± 16 g/m2 of body surface area.

• Stroke volume: the stroke volume is calculated as the difference between end-diastolic and end-systolic blood or chamber volumes, and it represents the volume of blood ejected by a ventricle per heartbeat (in the absence of aortic regurgitation).

Unless shunts and valvular regurgitation are present, the calculated stroke volumes of the two ventricles should be nearly equal. This is a rule of thumb for verification of the volume computation.

• Ejection fraction: this is the ratio of the ventricular stroke volume to the end-diastolic volume. The normal range is between 55 and 65%. An ejection fraction of less than 40% is considered to indicate impaired ventricular function.

• Cardiac output: this is the product of stroke volume and heart rate. It is a measure of the volume of blood ejected by the heart per beat. For an average adult, it is 4-8 L/min. Cardiac output is often corrected by normalization with respect to the body surface area.

### 6.2. Analysis of Wall Motion

Wall motion analysis is performed to measure the changes in thickness of the left ventricular wall from diastole to systole (9,48-52). Wall motion abnormalities are commonly associated with many cardiac diseases, including dilated cardiomy-opathy, end-stage valvular disease, and ischemic heart disease.

The assessment of myocardial wall thickness, thickening, and wall motion abnormalities proceeds from the segmentation along the endocardial and epicardial borders. A centerline is drawn between the myocardial contours (53). Approximately 100 chords are then drawn orthogonal to the centerline at equal intervals to intersect the two myocardial contours (Fig. 5). With the centerline technique, the chords are optimally placed to measure the exact thickness of the transmural myocardium (53).

Parameters of interest for wall motion analyses include the following:

• Myocardial thickness: the lengths of the orthogonal chords, from the endocardial to the epicardial borders, measure myo-cardial thicknesses.

• Myocardial thickening: differences in end-diastolic and end-systolic thicknesses, as a percentage of end-diastolic thickness, are a measure of thickening.

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