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[Brain Mapping] [Cardiac Motion Estimation][Image Processing and Analysis]
Harmonic Phase Magnetic Resonance Imaging
Nael F. Osman and Jerry L. Prince
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Overview
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Tagged cardiac magnetic resonance
imaging (MRI) produces images of the heart which can be analyzed to yield
detailed maps of motion and mechanical strain, describing regional
function of the heart. Harmonic phase (HARP) analysis is a fast and
minimally-interactive method for processing tagged MR images to yield
a rich collection of functional measures including pathlines, circumferential
and radial strains, velocity maps, high-density "synthetic"
tags, and principle strains. These measures are useful for visualization
and quantifying the heart's performance and are being evaluated for clinical
applications in diagnosing and monitoring heart disease. Also, the principles
behind HARP have laid the foundation for a variety of new, emerging MR
imaging techniques.
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Introduction
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resonance imaging can be used to create temporary features, called
tags, within the body's tissues. These features are not harmful because
they are created using the same principles by which images are created
in MRI. Several different tag styles are shown in Figure 1. The tags,
while visible over their (approximately) one second lifetime, move
with the motion of the heart. The pattern of tags can in turn be analyzed
to understand the motion of the heart during its contraction and dilation.
Usually tags are created at the beginning of a heart beat and data
to create images are acquired during systole and part of diastole.
Typically, several heart beats are required, over a brief breath-hold,
to gather enough data to form a high-resolution MR image sequence
of the tag motion. Heart motion is highly repeatable, which makes
this method of data acquisition possible.
There have been many
methods proposed to analyze the motion of tags within these image
sequences. To this date, all methods rely on the localization of
"tag lines" and subsequent inferences about what takes
place between the tag lines. Because of pixel size, tag size, noise,
and tag fading, the research community has had limited success in
producing robust, fast, and highly accurate and repeatable algorithms.
Important research has been conducted over the last decade or so,
typically using painstaking manually-assisted analysis of tagged
MR images, pointing to the very high potential for MR tagging to
be used clinically for the quantification of regional function and
diagnosis and monitoring of heart disease. Unfortunately, slow image
acquisition times and slow and tedious processing methods, have
prevented migration of this useful research tool into a practical
clinical protocol.
Harmonic phase magnetic
resonance imaging (HARP-MRI) is a promising new method that overcomes
the drawbacks of the other existing methods and makes it possible
to use MR tagging possible in clinical applications. HARP-MRI is
based on a different perception and understanding of the tagging
process. Moreover, HARP-MRI is not limited to an image processing
tool, but it paves the way to new imaging techniques based on its
principles.
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The Harmonic Image
Consider the tagged
cardiac images shown in Figure 2, showing the same slice at the
reference time and later near the end of systole. These images have
two-dimensional Fourier transforms that have collections of spectral
peaks, as shown in Figure 3 (truncated in the vertical direction).
Assuming that the spectral peaks are well separated, it is possible
to isolate a single peak in each image and take the inverse Fourier
transform of just the spectral contents within this single peak,
yielding a harmonic image. The circles shown in Figure 3
represent the pass regions of a bandpass filter used to isolate
spectral peaks for HARP analysis. A harmonic image is a complex
image, which therefore has real and imaginary images or, equivalently,
magnitude and phase images. In HARP analysis, it is necessary to
consider both the magnitude and phase of harmonic images.
The Harmonic Magnitude Image
The magnitude of a harmonic
image is called a harmonic magnitude image, to distinguish
it from the usual magnitude MR image. Figure 4 shows the magnitude
images of the harmonic images corresponding to the filtered peaks
in Figure 3. These harmonic magnitude images look similar to the
tagged images in Figure 2 except that the tag lines are absent,
and the images are blurry. The blurriness is due to the filtering
process, which reduces the resolution of the harmonic magnitude
image. Despite this loss of resolution, harmonic magnitude images
can be used for segmentation by thresholding. The segmentation masks
shown in Figure 5 roughly separate tissue from non-tissue.
The Harmonic Phase Image
The other component
of a harmonic image is called the harmonic phase image, or
simply the HARP image. The HARP images corresponding to the
harmonic images from Figure 2 are shown in Figure 6. The phase is
depicted only on the masks shown in Figure 5 for visualiation purposes.
The phase can only be computed between the -180 to 180 degrees,
which means that the measured phase is a "wrapped" version
of the true harmonic phase. This accounts for the "sawtooth"
appearance of the images in Figure 6. In particular, the "crisp"
lines that are apparent in these images are due to the changing
phase value from 180 to -180 degrees caused by wrapping. Careful
observation of these HARP images shows bending of the phase wrapping
artifact in the later HARP image. These resemble the tag lines in
the original image in Figure 2. It can be shown that the harmonic
phase actually depends on the underlying motion as well as the tagging
parameters. In fact, the underlying motion is not only represented
at the points of phase wrapping, but all other points as well. Mathematically,
it can be shown that the phase of the harmonic images is linearly
related to the tissue motion in a direction orthogonal to the tag
lines.
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time
= 0
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time
= 320 ms
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Figure 2. Vertical
tags at two times.
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Figure 3. Central
slab of the Fourier transform magnitudes.
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Figure 4. Harmonic
magnitude images.
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Figure 5. Mask
derived from the harmonic magnitude images.
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Figure 6. Harmonic
phase images (masked).
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Producing Harmonic Images
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The spectrum of a harmonic
image is spread over all spatial frequencies; but most of the spectral
energy is concentrated around the spectral peaks (Figure 3). The HARP
bandpass filter should be properly positioned in order to capture a certain
fraction of the spectral energy (for example, 90%). The size and position
of this bandpass region will be affected by the underlying motion of the
heart as well. For example, a contraction of the heart causes an increase
in spectral spreading, a tissue stretching orthogonal to the tag lines
will cause a decrease in the magnitude of the central frequency of a spectral
peak, and a tissue contraction will cause an increase in the central frequency.
In the heart, the mechanical
strain is bound by the local contractility of the myocardial fibers. Thus,
the expected size and position of a harmonic peak is limited. After conducting
an extensive set of simulations, we found that it is nearly optimal to
position the bandpass filter at the spatial tagging frequency itself,
and the radius of the bandpass filter should be about X % of the spatial
tagging frequency, where X % is the magnitude of the maximum expected
strain (typically around 30%).
Other factors affect the computation
of harmonic images. For example, the intensity of harmonic images fades
in accordance with the tag fading, which reduces the SNR of the harmonic
image. Also, interference from other harmonic peaks also produces artifacts.
Fortunately, imaging parameters can be found that effectively balance
these effects, yielding images that are capable of producing very accurate,
reasonably high-resolution regional cardiac function measurements.
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| Principle
of HARP Analysis |
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Harmonic images are very
similar to tagged images, except that they appear to have tags that are
sinusoidal patterns, and there are two of them – a cosine pattern
and a sine pattern, corresponding to the real and imaginary parts of the
harmonic image. When the heart moves, the underlying pattern of each harmonic
image changes. For example, compression of the heart muscle causes the
crests of the sinusoidal pattern to move closer together while stretching
or elongation causes the crests to move farther apart. This means that
there is a relationship between the frequency of a harmonic image and
the compression and elongation – in other words, the strain –
of the heart muscle.
Consider the tag patterns
shown in the top row of Figure 7. The initial sinusoidal pattern changes
under both fading and deformation so that it has both a lower amplitude
and different frequencies. If one looks at the phase of this sinusoid,
as shown in the bottom row of Figure 7, it is clear that the phase of
the pattern changes as well, but in a more limited way. In fact, the phase
of a given point does not change due to motion — the phase is a material
property. The slope of the phase change, however, in direct correspondence
to the change in frequency of the sinusoid, which in turn reflects the
underlying strain.
HARP analysis methods exploit
the following two properties: 1) for a given point, harmonic phase is
constant with time and 2) the slope of the harmonic phase is linearly
related to the underlying mechanical strain.
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Figure 7. Principle of HARP.
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Motion
Tracking Using HARP
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Once imposed by the tagging
process, the harmonic phase of a point in the tissue is constant throughout
a motion or deformation. Motion tracking using HARP exploits this fact
by using a phase-based optical flow formulation, which we refer to as
CINE-HARP. We use a pair of tagged image sequences, usually with vertical
and horizontal tags. These tag orientations provide sufficient information
to track points in the plane. Out-of-plane motion is not tracked ordinarily,
and therefore the tracking result must be interpreted as an apparent
two-dimensional motion. This is consistent with the tag motion that
we actually see in two-dimensional images, so HARP tracking can be used
to track tag lines, or anatomical features that we see in the images.
Motion tracking uses an iterative
algorithm that searches for the point in a second image that has the same
two phase values as the point of interest in the first image. This process
is repeated throughout the entire tag image sequence, yielding a pathline
for the selected point. Points can be tracked both forward and backward
in time as well. Figure 8 shows a collection of tracked points overlayed
on the product of vertical and horizontal tagged images at end-diastole.
The points have been manually selected to correspond to tag intersections,
but they could be placed anywhere. Notice that points in the right ventricular
myocardium can also be tracked.
Figures 9 and 10 show images
of horizontal and vertical tagged images to show like a grid. A collection
of points lying on two tag lines have been selected in the first time
frame. The points were tracked through an image sequence to the last time
frame at endsystole. We observe that, except for the point on the top,
the points tracked successfully to lie on the same tag lines. The top
point strayed from tagging due to the out-of-plane motion causing some
tag lines, respectively the corresponding phase values, to disappear.
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Figure 8
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Figure 9
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Figure 10
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Measuring Lagrangian Strain
The tracking method
can be used to measure Lagrangian strain by observing the change
in distance between a pair of tracked points. Because of the special
geometry of the heart and its function, it is common to measure
the strain in the radial and circumferential directions. For this,
we place a collection of points on a circular grid that fits the
LV wall. The grid, shown in Figure 11, is three concentric circles
representing the endocardium, midwall, and epicardium, Each circle
has 16 points uniformly distributed on the circumference. All the
points are tracked through the cardiac cycle and by measuring the
change in distance between neighboring point on a circle provides
a measure of circumferential strain. The distance between points
neighboring on the radial direction produce the radial strain.
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Figure 11
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Figure 12 shows the
computed circumferential strain for the different octants of the circles
and for each circle. This special experiment represents a mechanically
activated canine dog with a pacing lead sewed at location 5 in Figure
11 close to the base. The pacing lead causes early contraction at
location 5 accompanied with stretching on the other side (location
1). Soon, the whole LV starts contracting, with less shortening in
the early contraction octant 5.
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Figure 12.
Lagrangian strain in different octants.
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Measuring Eulerian Strain
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Now we focus on the second
principle of HARP: that the slope of the harmonic phase is related to
strain. We refer to the measurement of strain made using this technique
as Single-shot HARP because it does not require an image sequence.
Instead, only one pair of harmonic phase images (vertical and horizontal)
are required, both corresponding to a single time in a cardiac cycle.
After calculating the slopes of these harmonic phase images at a given
point, we can compute a two-dimensional strain tensor at that point. This
is repeated over all points (pixels) in an image so that a strain tensor
map is produced. Several measurements can be produced from these strain
tensors: circumferential strain, radial strain, maximum and minimum strains,
and the contraction angle. The contraction angle is the anglebetween the
maximum contraction direction and the circumferential direction.
Figure 13 shows the circumferential
strain map for a 20 time frames of a mechanically activated canine heart
(described above). The darker regions indicates circumferential shortening,
while the yellowish color indicates stretching. Starting from the second
time frame we can observe a darker spots at the 5 o'clock, the position
of the pacing lead. On the other hand, we can observe stretching at the
10 o'clock region.
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Figure 13. A sequence
of Eulerian strain maps.
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In order to quantify the Eulerian
strain maps, we used the grid defined in Figure 11, tracked the grid using
the previous method, and averaged the Eulerian strain by octant. The resultant
plots, shown in Figure 14, are similar to those computed using the Lagrangian
tracking method (Figure 12). A minor difference is that at the first time
frame in Figure 14 strain can be detected that is not apparent in the
first time frame of Figure 12. This is because the Lagrangian frame-of-reference
is the first time frame while the Eulerian frame-of-reference is the time
in which the tags were place.
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Figure 14. Time evolution
of Eulerian Strain by Octant.
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HARP Analysis Program
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a program using MATLAB that uses HARP ideas to measure myocardial function.
The computations are fast and the program requires minimal human intervention.
We computed the motion of the mechanically activated using a Pentium II
PC 366MHz. Filtering 40 images to produce the harmonic magnitude and HARP
images takes 15 seconds. Computing the Eulerian strains takes 3 seconds.
Tracking a point takes a fraction of a second, and to compute the Lagrangian
strain it takes 10 seconds. The tracking grid requires user intervention
to place the circles inside the wall muscle. The total analysis for an image
slice can be finished in less than 10 minutes. With MR imaging settings
tuned for HARP, the measurements would be available in less than 10 minutes.
Development of real-time HARP software written in C/C++ is underway. |
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Conclusion
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that allows the assessment of cardiac regional function using tagged MRI
for clinical applications. So far, HARP has been successful in analyzing
motion from conventional tagged MR images. HARP can also be used in conjuntion
with special acquisitions for real-time acquisition and processing of myocardial
function. |
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Acknowledgments
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We are grateful to Dr. Elliot
R. McVeigh and Tony Z. Faranesh for making these tagged images available
for us. This research was supported by the National Institute of Health,
National Heart, Lung, and Blood Institute.
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| Publications |
- 1. N. F. Osman and J. L. Prince, "Direct calculation of 2D components
of myocardial strain using sinusiodal MR tagging", Proc. SPIE Vol. 3337,
Medical Imaging 1998: Physiology and Function from Multidimensional
Images, pp. 142-152, San Diego, February 21-27, 1998.
- N. F. Osman and J. L. Prince, "Angle Images for Measuring Heart Motion
from Tagged MRI", Proceedings of IEEE Int. Conf. Image Proc., vol. 1,
pp. 704-708, Chicago, October 1998.
- N. F. Osman, A. Z. Faranesh, E. R. McVeigh, and J. L. Prince, "Tracking
cardiac motion using cine harmonic phase (HARP) MRI", Proc. Intl. Soc.
Mag. Reson. Med. 7 (ISMRM), pg. 24, Phiadelphia, PA, May 1999.
- N. F. Osman, W. S. Kerwin, E. R. McVeigh, and J. L. Prince, "Cardiac
Motion Tracking Using CINE Harmonic Phase (HARP) Magnetic Resonance
Imaging", Mag. Res. Med., vol. 42, pp. 1048-1060, 1999.
- J. L. Prince, S. N. Gupta, and N. F. Osman, "Bandpass Optical Flow
for Tagged MRI", Medical Physics, vol. 27, issue. 1, pp. 108-118, January
2000.
- N. F. Osman, J. Garot, and J. L. Prince, "Assessment of Regional Cardiac
Function From Tagged MRI Using Harmonic Phase (HARP) Software" Supplement
to Journal of the American College of Cardiology February 2000, Vol.
35, Issue 2, Suppl. A, page 540, 2000.
- J. Garot, D. A. Bluemke, N. F. Osman, C. E. Rochitte, E. R. McVeigh,
E. A. Zerhouni, J. L. Prince, J. A. Lima, "Fast determination of regional
myocardial strain fields from tagged cardiac images using harmonic phase
MRI ," Circulation, 101(9):981-988, Mar 7 2000.
- N. F. Osman and J. L. Prince, "An Integrated System for Measuring
Regional Cardiac Function Using Harmonic Phase MRI," Proc. Int'l Soc.
Magn. Reson. Med. 8 (ISMRM), Denver, April 2000.
- J. Garot, D. A. Bluemke, N. F. Osman, C. E. Rochitte, E. R. McVeigh,
E. A. Zerhouni, J. L. Prince, J. A. C. Lima, "Fast automated assessment
of regional left ventricular function from tagged cardiac images by
Harmonic Phase magnetic resonance imaging," Supplement to Journal of
the American College of Cardiology February 2000, Vol. 35, Issue 2,
Suppl. A, page 464, 2000.
- N. F. Osman, E. R. McVeigh, and J. L. Prince, "Imaging Heart Motion
Using Harmonic Phase MRI", IEEE Trans. on Medical Imaging, vol. 19,
No. 3, pp. 186-202, March 2000.
- N. F. Osman and J. L. Prince, "Visualizing Myocardial Function Using
HARP MRI", Physics in Medicine and Biology, vol 45, issue 6, pp. 1665-1682,
June 2000.
- W. S. Kerwin, N. F. Osman, and J. L. Prince "Image Processing and
Analysis in Tagged Cardiac MRI", in Handbook of Medical Image Processing
and Analysis, ed. Isaac N. Bankman, Academic Press, pp.375-392, 2000.
- N. F. Osman and J. L. Prince, "On the Design of the Bandpass Filters
in Harmonic Phase MRI," Proc. IEEE Int'l Conf. Image Proc., Vancouver,
Sept 10-20, 2000.
- J. Garot, D. A. Bluemke, N.F. Osman, C. E. Rochitte, B. L. Gerber,
J. L. Prince, J.A.C. Lima. "Dobutamine stress HARP MRI differentiates
myocardial stunning from necrosis after reperfused acute MI." AHA Annual
Meeting, November, Circulation, 2000.
- J. Garot, D. A. Bluemke, N.F. Osman, C. E. Rochitte, B. L. Gerber,
J. L. Prince, J.A.C. Lima. "Detailed analysis of transmural LV function
and recruitable myocardial deformation in subendocardial vs transmural
infarcts using tagged-MRI." AHA Annual Meeting, November, Circulation,
2000.
- N. F. Osman, J. L. Prince, E. A. Zerhouni, J. Garot, J. A. Lima, D.
A. Bluemke, "Cardiac MR: New Methods and Applications for Quantitative
Analysis", RSNA 2000: 86th Scientific Assembly and Annual Meeting, Educational
Exhibit, November 26 - December 1, 2000.
- N. F. Osman and J. L. Prince, "Analyzing Tagged MR Images of the Heart
Using HARP Software Package," RSNA 2000: 86th Scientific Assembly and
Annual Meeting, InfoRad Exhibit, November 26 - December 1, 2000.
- J. Garot, D. A. Bluemke, N. F. Osman, C. E. Rochitte, E. A. Zerhouni,
J. L. Prince, J. A. C. Lima, "Transmural Contractile Reserve After Reperfused
Myocardial Infarction in Dogs," Journal of the American College of Cardiology,
vol.36, no.7, pp. 2339-2346, 2001.
- N. F. Osman and J. L. Prince, "Improving HARP to Produce Smooth Strain
Maps of the Heart", Joint Annual Meeting ISMRM-ESMRMB, April 21-27,
2001.
- N. F. Osman, J. L. Prince, E. A. Zerhouni, J. Garot, J. A. Lima, D.
A. Bluemke, "Cardiac MR: Methods and Applications for Quantitative Analysis
Using Harmonic Phase Imaging," Annual Meeting of the American Roentgen
Ray Society (ARRS), Abstract 173, Seattle, April 29 - May 4, 2001. This
abstract won a Certificate of Merit.
- S. Sampath, J. A. Derbyshire, N. F. Osman, E. Atalar, and J. L. Prince,
"Real-Time Imaging of Cardiac Strain using Ultra-Fast HARP Sequence,"
Joint Annual Meeting ISMRM-ESMRMB, April 21-27, 2001.
- D. Kraitchman, S. Sampath, J. A. Derbyshire, A. W. Helman, E. A. Zerhouni,
D. A. Bluemke, J. L. Prince, and N. F. Osman, "Detecting the Onset of
Ischemia Using Real-time HARP," Joint Annual Meeting ISMRM-ESMRMB, April
21-27, 2001.
- N. F. Osman, S. Sampath, J. A. Derbyshire, E. Atalar, and J. L. Prince,
"Synthetic Tagged MR Images For Real-time HARP Imaging," Joint Annual
Meeting ISMRM-ESMRMB, April 21-27, 2001.
- N. F. Osman, S. Sampath, E. Atalar, and J. L. Prince, "Imaging Longitudinal
Cardiac Strain on Short-Axis Images using 3D-HARP," Joint Annual Meeting
ISMRM-ESMRMB, April 21-27, 2001.
- J Garot, D. A. Bluemke, N. F. Osman, C. E. Rochitte, E. A. Zerhouni,
J. L. Prince, and JAC Lima, "Transmural segmental contractility and
inotropic reserve in subendocardial and transmural experimental infarcts
using Harmonic Phase MRI", EUROPEAN SOCIETY OF CARDIOLOGY - XXIII Annual
Congress, Stockholm, September 1-5, 2001.
- D. L. Kraitchman, S. Sampath, J.A. Derbyshire, D.A. Bluemke, B.L.
Gerber, J. L. Prince, and Nael F. Osman, "Quantitative Ischemia Detection
During Cardiac MR Stress Testing," American Heart Association Annual
Meeting, Anaheim, CA, November 11-14, 2001.
- N. F. Osman and J. L. Prince, "Harmonic Phase MRI," in Measurement
of Cardiac Deformations from MRI: Physical and Mathematical Models,
A. A. Amini and J.L. Prince (editors), Dordrecht: Kluwer Academic Publishers,
2001.
- N.F. Osman, J.Garot, S. Sampath, B. Gerber, K. Wu, E. Atalar, J. Lima,
and J. L. Prince, "Direct Imaging of Left Ventricular Regional Dysfunction
Using SENC MRI," SCMR 2002 meeting.
- N.F. Osman, S. Sampath, A. Derbyshire, E. Castillo, D. Bluemke, E.
Zerhouni, J. L. Prince, and D. Kraitchman, "Real-time SENC for the Detection
of Regional Dysfunction during Dobutamine Stress Test," SCMR 2002 meeting.
- K. Abd-Elmonieum, S. Sampath, N. Osman, and J. L. Prince, "Tool for
automatic real-time regional cardiac function analysis using HARP,"
in Proc. SPIE's Medical Imaging, San Diego, CA, Feb. 15-20, 2003.
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