An integral method for the analysis of wall motion in gated myocardial SPECT

studies

Michael L. Goris, Robert L Van Uitert Jr.

Division of Nuclear MedicineStanford University School of Medicine

Stanford California

Ventricular wall motion is generally defined as the displacement of the intersection of a wall edge and an axis of the cardiac coordinate system. The result is that motion is detected only in-plane and only in a preferred direction. Complex motion, defined as off-plane and in multiple directions, cannot be detected by those classical approaches. What we present here is an alternative, based on the fact that during the cardiac cycle there is conservation of densities and of volumes. The method detects complex motion and the detection is independent of the heart’s orientation in the image.

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Our aim was to investigate and develop a system of analysis of complex left ventricular wall kinetics. The proposed method is specifically adapted to gated myocardial perfusion SPECT data. The unique properties of gated SPECT data in this respect are the lack of fiduciary points, the relatively low spatial resolution and the conservation of total counts during the cardiac cycle.

The method will be illustrated first on two synthetic cases. The first is characterized by symmetrical motion towards a single intra-ventricular center point.On the left the central orthogonal slices (horizontal long axis, transverse and vertical long axis) for 8 time bins.

The three dimensional image for each time bin t is collapsed into the x-axis, so that the counts in the image are represented by a one-dimensional vector A(x,t). The integrated A(x,t) becomes the function P(x,t)

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The total image activity is constant for all values of t (and all projection directions).The integral function P(x,0) defines the percentile activity at x in time-bin 0. The location in x of the percentile P at t >0 is found by linear interpolation. The displacement vector D(x,t) is the function showing the difference in location of a given percentile P between image 0 and image “t”. The values of D(x,t) are periodic over “t” for all values of x.

The black curve is the cumulative density function at t=0 P(x,0) The location of the same percentiles in P(x,t) is indicated by the green dots. The displacement D(x,t) is indicated by the green horizontal lines.

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The function P(x,t) is redefined after rotation of the image volume in space (in this case 12 rotations).For each of the passes the function D(x,t) is decomposed into its x, y, and z components, and those components are re-expanded into the volume.

The first pass (Red on Right) has only an X component. Since the collapse was in x, all pixels with a common x position have the same value. The second pass (Red, middle) is at 45 degrees and has an x and y component (Green). The y component is projected in the y volume (Right), the x component is added to the x volume (Left). The values are not constant for pixels with a common x coordinate.

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X-motion Y-motion

Z-motion First harmonic analysis of the motion in the x , y, and z directions separately.Since the motion is centripetal in this case, the phases (lower row) are opposite on either side of the midline

Figure 5 c

For each pixel we have a motion vector for each time bin and for x and y (and z) motion. The model predicts that by combining the vectors (x, y and z in 3D), the path of the activity in that pixel can be followed through complex motion

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Anterior Vertical long axis Inferior Septal Horizontal Long Axis Lateral

Septal Short Axis Lateral In this synthetic case, motion is entirely centripetal, and reflected in the tracing of the motion for all pixels in three orthogonal central planes (except at the outer edge where discretization of the digital image comes into play).

And the radial phases for centripetal motion are homogeneous

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In the second synthetic model motion is asymmetrical, mimicking inferolateral hypokinesis. The result is in fact that all x and y motion are in the same direction during systole

Surface Rendering of Diastole and Systole

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The phases for x and y motion are homogeneous. For the motion in z there are two phases, with the apex in opposite phase to the body of the myocardium.

When all motion is reduced to the centripetal motion component, the infero-lateral hypokinesis is easily identified.

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The three middle orthogonal planes are shown here with the tracings of the total motion within the plane for all the voxels. In this tracing end-systole is in red.

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An actual case where the traditional analysis shows some apical hypokinesis

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The model easily accommodates the right

ventricle. The analysis of the centripetal component

of the motion identifies apical dyskinesia

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In this case the in-plane motion is displayed for 1 voxel in 16 and on an enlarged scale. The color coding of time is green to blue to red to white. Motion is clearly not wholly centripetal, but more towards the apex, and there is in fact no single convergence point. If the center of the ventricle is taken as the reference point for motion, there is apical dyskinesis.

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If the image of the heart is reoriented differently in the image volume, the centripetal motion remains the same, and also the complex motion.

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Clinical Case

Page 15: In the central short axis slice, all the volume elements tend to move towards the right ventricle. The larger X-motion component is in the lateral wall, and the phases are uniform. Most of the motion in the y-direction comes from the inferior wall, but the y component is in different direction in the anterior and inferior wall. There are opposite phases in the y-motion. The centripetal motion has homogeneous phases, except in the septum, where the motion is away from the center.

Page 16: In the central horizontal long axis slice, most motion is again towards the right ventricle. The x-motion phases are homogeneous. Also, in the z-motion, most motion is towards the apex, which makes the phases of the z-motion homogeneous. The largest motion is at the base. But apical motion toward the apex, and septal motion towards the right ventricle, are seen as opposite phases in the centripetal motion analysis.

Page 17: In the central vertical long axis slice, the opposite phases between anterior and inferior wall (for Y) are seen, as well as the larger motion amplitudes inferiorly at the base. Z-motion phases are again homogeneous. The antero-apical motion away from the center is easily detected.

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Clinical Case: Central short axis slice

Temporal encoding is green to blue to red to whiteX-motion Y-motion Z-motion Centripetal

Amplitude Amplitude Amplitude Amplitude

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Phase Phase Phase Phase

Temporal encoding is green to blue to red to whiteClinical Case: Central Horizontal Long Axis slice

X-motion Y-motion Z-motion CentripetalAmplitude Amplitude Amplitude Amplitude

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Phase Phase Phase Phase

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Temporal encoding is green to blue to red to whiteClinical Case: Central Vertical Long Axis slice

X-motion Y-motion Z-motion CentripetalAmplitude

Phase

Amplitude

Phase

Amplitude

Phase

Amplitude

Phase

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Conclusions (tentative)1. The method works in so far as recovering

spatial resolution from motion measurements that are global.

2. The motion defined in image coordinates is indeed independent of the orientation of the ventricle relative to the image coordinates.

3. The results illustrate that the motion of individual elements cannot be totally described within any plane.

4. The collective of elements cannot said to move to and from a single point in space.

Hence there has to be some loss of information when ventricular kinetics are measured only in-plane, and with a single collective convergence focus. The method here is proposed as an alternative.

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