imaging three-dimensional cardiac function - Walter G. O'Dell, PhD

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Annu. Rev. Biomed. Eng. 2000.2:431-456. Downloaded from arjournals.annualreviews.orgby UNIVERSITY OF ROCHESTER LIBRARY on 07/27/09. For personal use only.?IMAGING 3-D CARDIAC FUNCTION 445gradient. This method has the advantage over tagging in that each pixel provides aunique motion measurement, and MR phase-contrast imaging has great potentialfor reconstructing 3-D motion (80). However, current implementation of phasecontrastimaging for 3-D motion measurement is hampered by low SNRs, highsusceptibility to motion artifacts, and, hence, limited accuracy of the reconstructedvelocity profiles.Tissue Doppler Imaging The Doppler shift of the reflected echocardiographicwave also contains velocity information that is analogous to that obtained withMR phase-contrast imaging. Doppler ultrasound provides real-time velocity (81)and velocity gradient (82) information about blood and tissue. The frequency shiftspectrum vs time information, presented as a sonogram, reveals the velocity rangeand distribution. The additional motion information from TDI has been shown toimprove, over transthoracic ECG, detection of anomalous conduction pathwaysin patients with Wolff-Parkinson-White syndrome (83). However, velocity informationis obtained only in the direction parallel to the echo beam and CNR noise(Doppler speckle), and the number of available viewing angles limit the imagequality. Tessler et al (84), using a calibrated 1-D flow phantom, found that theDoppler-measured velocity had a baseline error of 6.8 cm/s (9%–17%) for peakflows that range from 40.5 to 75.3 cm/s. This error was independent of inter- orintraobserver variability or variability that is attributable to different flow probesor the flow phantom. Fleming et al (82) also used a test phantom and showed that3 mm by 3 mm was the smallest region of tissue from which a measurable changein velocity could be detected with Doppler imaging.Velocity vector mapping in two and three dimensions is theoretically possibleby using additional ECG receivers or by electronically separating a linear arrayreceiver into spatially separate subapertures (85, 86). The unidirectional velocitymagnitudes and the angle difference between the subapertures and the source echoare used to derive the direction and true magnitude of the velocity.Accounting for the full 3-D motion of the heart, particularly the motion throughthe fixed short-axis image plane locations, is crucial for 3-D deformation analysis.The approaches mentioned above can accommodate this need by acquiring3-D tagging or velocity data sets. However, alternatives, such as the slice isolationpresented by Rogers et al (41), can also be used. A related technique involvingsubtraction of positive and negative tagged images has been shown byFischer et al (87). In another approach, WeDeen et al (88) implemented a motionlessmovie scheme, in which the same slice was imaged at the same timein the cardiac cycle (to be certain that the same chunk of tissue was always imaged),but the tagging grid (or phase-encoding step) was imparted to the tissueat a sequence of preceding time increments. From this they were able to computethe 2-D Eulerian strain (or strain rate) at that slice location. Hybrid tagging/Slice Motion Correction
446 O’DELL MCCULLOCHAnnu. Rev. Biomed. Eng. 2000.2:431-456. Downloaded from arjournals.annualreviews.orgby UNIVERSITY OF ROCHESTER LIBRARY on 07/27/09. For personal use only.?Model-Based Deformation Analysisvelocity-encoding methods are inherently difficult because the tagged regions oftissue contain no velocity information (are a signal void), and the velocity encodingstep requires a reference and a phase-encoding image; thus it does notoffer an overall time advantage compared with 3-D tagging or 3-D phase-contrastimaging.Reconstruction of the 3-D strain field from discrete samples of displacement requiresan interpolation scheme to describe the motion between samples in space, tocorrect for noise in the sampling, and to compute the local displacement gradientsthat are used for strain calculation (unless explicitly stated, considerations for velocityfield and strain rate reconstruction can be assumed to be analogous to thosedescribed here for displacement field and strain reconstruction). The interpolationmethod usually includes a model of the 3-D displacement field. A priori assumptionsof the displacement field can be used to generate a model that contains theexpected modes of motion, and the displacement or velocity samples can be usedto optimize the magnitude and direction of those modes (55).A more general formulation is to use 3-D basis functions to describe the localmotion within each element of a finite element model of the heart (89), increasingthe number of degrees of freedom in the reconstruction to the number of localbasis functions per element times the number of elements. Taking this globally, amodel containing hundreds of candidate modes can be formulated, and the sampledmotion can be used to solve for the magnitude of those modes over the entireheart. This removes the requirement for a priori assumptions about the modesof motion, useful for reconstructing motions in regions of altered mechanicalstate, such as sites of ischemia. O’Dell et al (53) use a displacement field fittedto a polynomial series in prolate spheroidal coordinates (a 3-D analogy to the2-D surface reconstruction presented earlier) to reconstruct 3-D material pointtrajectories from parallel-tag data sets. As shown in Figure 2 (see color insert), thecontribution of each mode to the overall motion of the heart can be quantified andinterpreted independently by using computer models of the heart (90).Another interesting approach, presented by Denney et al (91), uses samplesof motion along with energy minimization equations that penalize large gradientsin deformation to estimate the motion at each point in a rectangular grid thatencompasses the entire heart. This approach is related to optical-flow techniquesand is a powerful model-free method of computational analysis.Limitations of the ReconstructionsUltimately, the resolution and accuracy of the results from a reconstruction schemeare determined by the deformations of the heart tissue and the density and quality oforiginal motion sampling. First, if the motion is simple, for example, the translationof a solid body, only a few simple parameters and a few samples of motions
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