Temporal Evaluation of Ventricular Wall Motion

The clinical usefulness of global evaluation of ventricular function through the measurement of ventricular volume and ejection fraction is well demonstrated and widely accepted. However, from a clinical point of view, a better evaluation of the ventricular function should allow the detection and the measurement of regional dysfunctions in ventricular wall motion [35]. A wide number of wall motion and regional ventricular function evaluation methods have been reported. Regional ejection fraction [36] and segmental shortening measurements using radial [8] or centerline [37] methods have been applied and showed that regional assessment of ventricular performance yield greater accuracy in the evaluation of cardiac diseases.

However, in order to discriminate between alterations in systolic and diastolic behavior, a quantitative analysis of regional ventricular wall motion should include a temporal analysis of the complete heart cycle. The three conventional parametric images described in the previous section have proven quite useful and have been utilized in several centers for several years. However, none of these images give information about synchrony of contraction. Of course, some indirect information exists in the sense that areas of abnormal wall motion have implicitly abnormal synchrony. Nevertheless, these images detect abnormal wall motion based on abnormal amplitude of contraction and not because of asynchrony. As a consequence, if the contraction amplitude is normal in a certain area, an existing asynchrony will be missed, which occurs in most cases of electrophysiologic or ischemic disturbances. The two specific aspects mentioned earlier have been among the principal reasons for the success of the next category of images [38].

Phase Analysis of Ventricular Wall Motion

A technique based on pixel-by-pixel Fourier-phase analysis of radionuclide angiograms [39] was found to be very useful for the detection of regional asynchrony in wall motion. Phase and amplitude are obtained by what is commonly referred to as phase analysis; a more appropriate term could be "first harmonic analysis," while an inappropriate yet often-used term is "Fourier analysis". The latter term implies that multiple harmonics are used, which is not the case. The results of this analysis technique are displayed in color-coded parametric images representing two-dimensional maps of the sequence of contraction in the different regions of the heart.

The amplitude image reflects the extent of contraction on a pixel-by-pixel basis. The phase image is nothing more than a topographical representation of relative values of timing of count rate changes. This in turn means that on a phase image, only the information pertaining to synchrony-asynchrony of motion is displayed. Being thus free of the amplitude characteristics, the phase image is in general no longer dependent on anatomy. Since 1979, phase imaging has been investigated for detection of ventricular wall motion abnormalities, evaluation of the cardiac electric activation sequence, and for many other applications [40-42].

Commonly, the phase analysis technique is applied to gated blood pool images obtained in the LAO projections (Fig. 3). Some investigators however, have applied phase analysis in as many as three cinegraphic image projections [40]. The value of the pixel within a blood pool image represents the sum of the radioactivity along a line perpendicular to the camera through the patient's chest. If a pixel value is plotted against time (frame number), the resulting plot is a time activity curve for this pixel. To derive phase and amplitude images, each time-activity curve is approximated by a single cosine function.

The amplitude and phase of the first Fourier harmonic, used

FIGURE 3 Schematic illustration of the generation of the phase and amplitude images from a set of radionuclide angiogram images. The time-activity curve of each pixel is approximated by a single cosine function using discrete Fourier transforms. The phase shift and amplitude of this cosine function are then used to generate color-coded parametric maps. See also Plate 50.

in constructing the cosine approximation, are derived by subjecting the time-activity curve f(n) to discrete Fourier transform analysis:

Fm N- f( ^ (2Kkn\ -V1 f2Ukn F(k) = 2^f(n) cos - ] (n) sin n=0 V N / n=0 V N

F(k) is the kth harmonic of the time-activity curve and in general is a complex number, and N is the number of frames in the study. The amplitude (A) and phase (0) of the kth harmonic are defined by

arctan b(k)

The amplitude of the first harmonic contains information about the regional stroke volume (changes in counts form end-diastole to end-systole), while the phase contains information about the sequence of contraction. The amplitude and phases derived from first harmonic analysis of time-activity curves are used to form amplitude and phase images. Since pixels outside the heart tend to have small amplitudes and random phases, they are deleted by thresholding the amplitude images and using the threshold amplitude image to mask the phase image. Thresholds from 6 to 15% of the maximum amplitude have been found suitable [4,31]. Several methods have been used to represent graphically the results of phase analysis. Color-coded phase images are often displayed to facilitate visual discrimination of subject changes. Dynamic displays or "activation movies'' are very helpful in assessing the patterns of phase changes over the ventricles [31,43]. Activation movies can be constructed in two ways. In one method, the displayed phase image itself is static, but the color scale used to display the image is rotated. This technique is based on the argument that since phase is a periodic parameter, phase images should be displayed using a cyclic color scale.

A second method, described by Verba et al. [44], displays an end-diastolic image of the heart and superimposes upon it black dots which are turned on and off in a temporal sequence determined from the phase of each pixel. An activation movie constructed in this fashion gives one the impression of a wave of contraction spreading over the heart (Fig. 4).

A useful adjunct to these images is the phase distribution histogram. The shape and color of its components help both qualitative and quantitative evaluation of the phase image [4]. The phase histogram has two peaks, one corresponding to pixels in the ventricles and the other to pixels in the atria. Clearly, phase analysis distinguishes between the onset of ventricular and atrial contraction. Of more interest is the extent to which it distinguishes the onset of contraction within the ventricles (Fig. 5).

Medical Imaging Processing

Time I Aclivliy Curte

Radionuclide angiogram

Pa ram elfte linages

Radionuclide Angiography Heart
FIGURE 4 Two different representations of the phase image. In diagonal a sequence of maps where the phase progression is indicated as a "wave" of a different color. On the lower left, a composite color-coded phase image of the same sequence. See also Plate 51.

The main purposes for which this parametric imaging technique has been employed are the evaluation of global and left ventricular function and the assessment of the cardiac electric activation sequence. Both amplitude and phase images appear to be useful for the assessment of ventricular function. The rationale for using the amplitude image is clear; this image is simply a picture of the pixel-by-pixel stroke volume. The rationale for using the phase images rests on the observation that ischemia reduces the velocity of myocardial contraction, and thus, local abnormalities of wall motion are frequently associated with changes in the time of wall movement [4]. Phase analysis has also been employed in a wide variety of settings in which the electric activation sequence is altered. Several studies have investigated phase imaging for non-invasively identifying the location of pacemakers [45-47] or for evaluating the effect of different pacing techniques [48]. These studies have shown a gross correspondence between the side of stimulation by a ventricular pacemaker and the first motion of the ventricular wall as identified by the phase images. Some studies have shown that the activation sequence determined by phase imaging correlated well with the actual electric activation sequence measured by epicardial mapping [45]. Conduction abnormalities have also been extensively studied using phase analysis. Although phase analysis measures mechanical motion and not electrical activation, it does appear useful for inferring electrical events.

Phase analysis has been applied to a variety of different imaging modalities and also to organs other than the heart. It has been used, for example, to study renal perfusion from

Radionuclide Ventriculography Heart

FIGURE 5 Example of phase analysis applied to a radionuclide ventriculogram at rest (A,B) and during exercise (C,D); in a patient with coronary artery disease. Images A and C show the phase map of the whole cardiac silhouette, and images B and D show the phase map of the isolated left ventricular region. The phase images clearly show the areas with perturbed ventricular wall motion as bright sections (arrows). The histogram of phase distribution also shows a wider ventricular peak during exercise. See also Plate 52.

FIGURE 5 Example of phase analysis applied to a radionuclide ventriculogram at rest (A,B) and during exercise (C,D); in a patient with coronary artery disease. Images A and C show the phase map of the whole cardiac silhouette, and images B and D show the phase map of the isolated left ventricular region. The phase images clearly show the areas with perturbed ventricular wall motion as bright sections (arrows). The histogram of phase distribution also shows a wider ventricular peak during exercise. See also Plate 52.

radionuclide images [3]; it was also used to study lung perfusion patterns [49]. Some investigators have also reported the applicability of this technique to dynamic CT and MRI images of the heart [50].

Fourier Analysis of Contrast Ventriculograms

The usefulness of the temporal phase analysis of radionuclide angiograms has been well demonstrated [4,51,52] for the detection of regional alterations in wall motion in coronary artery disease (CAD). A similar pixel-by-pixel analysis of digitized cineangiogram images was also attempted, but was found to be valid only if one assumes that changes in density of each picture element are proportional to changes in blood volumes in the ventricular cavity. This is true only if the contrast medium is homogeneously mixed with the blood in all the images selected for the analysis. With careful selection of studies with homogeneous opacification of LV by intravenous injection, a pixel-by-pixel phase analysis was, however, reported to be useful for the detection and quantification of regional asynchrony [53]. A similar technique developed for the assessment of the synchronicity of regional wall motion based on a multiharmonic Fourier analysis of the ventricular edge displacement was also proposed [54]. This alternative technique is based on the measurement of the radial motion of the ventricular endocardial edge (see Fig. 6) and can therefore be applied to images obtained either after intravenous or after conventional intraventricular injection, regardless of the homogeneity of the dilution of the contrast material [55].

Temporal analysis of ventricular wall motion from contrast angiograms was studied in patients with coronary artery disease [56]. The display of Fourier parametric images allows the visualization of the spatial distribution of this temporal behavior and the detection and localization of segmental abnormalities of wall motion by depicting abnormal synchro-nicity of contraction and relaxation, even in the absence of significant reduction in the amplitude of contraction.

The temporal analysis of myocardial wall motion can also be applied to tomographic images such as two-dimensional echocardiogram or MRI images, provided that adequate delineation of myocardial contours is obtained from the images. Some difficulties and limitations of automated analysis of ultrasound images must, however, be considered. The mechanism underlying image degradation must be clearly understood before algorithms can be developed to account for them. Gray-scale manipulation, smoothing, and integration of information from several heartbeats are methods that have been borrowed from other imaging systems and applied to echocardiographic images. The two major problems are the location of a pictorial boundary on the image, and the determination of the relation of this pictorial boundary to an anatomic one. MRI images provide a better delineation of the

FIGURE 6 Phase analysis of dynamic X-ray contrast ventriculogram. Parietal wall motion is analyzed in a radial way from the center of the ventricle. See also Plate 53.

different anatomical structures and are more suitable for automatic analysis of myocardial wall motion (Fig. 7).

Assuming that an adequate edge detection algorithm is implemented, additional analysis of ventricular wall motion can be applied to the detected ventricular contours. We have demonstrated that motion analysis techniques similar to the one developed for contrast angiograms can be applied to cardiac MRI images. The inward-outward motion of the ventricular wall is analyzed along a user-selectable number of radii (usually between 60 and 120 sectors) drawn automatically from the geometric center of the ventricular cavity. The motion curve along each radius is analyzed and the corresponding Fourier coefficients are calculated. The phase of the first harmonic is calculated and used to generate a parametric image representing the extent of wall motion of each segment that is color-coded according to the phase. The color assigned to each sector corresponds to the delay in time of the calculated phase for that particular sector (see Fig. 7). The full color scale corresponds to the RR interval of the study. The analysis program also plots a histogram of the number of sectors with a given phase value. This histogram represents the homogeneity and synchrony of wall motion, where a narrow peak reflects a very synchronous motion of all ventricular segments while a wider peak will indicate the presence of asynchronous or delayed segments. A standard deviation of the main peak (SDp) on the phase histogram is used as an index of homogeneity of phase distribution.

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