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Automatic 3D tracking of cardiac material markers using slice-following and harmonic-phase MRI
Automatic 3D tracking of cardiac material markers using slice-following
and harmonic-phase MRI
B
Smita Sampath4, Jerry L. Prince
Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Received 7 June 2006; accepted 15 September 2006
Abstract
A method to track a grid of cardiac material points in three dimensions using slice-following (SF) tagged magnetic resonance imaging
(MRI) and harmonic-phase MRI is presented. A three-dimensional grid of material points on the lines of intersections of short-axis (SA) and
long-axis (LA) planes is automatically tracked by combining two-dimensional pathlines that are computed on both SA and LA image planes.
This process yields the true three-dimensional motion of points originating on the image plane intersections. Experimental data from normal
volunteers, each obtained in four short breath-holds using the SF harmonic phase MRI pulse sequence, is presented. A validation of two-
dimensional in-plane tracks using this pulse sequence on a moving phantom is also presented.
D 2007 Elsevier Inc. All rights reserved.
Keywords: Magnetic resonance tagging; HARP; Slice-following; Cardiac motion; Cardiac strain
1. Introduction
Visualizing and quantifying cardiac motion are important
steps in the diagnosis and management of heart disease.
Current practice is largely limited to two-dimensional
analyses (2-D), despite the availability of relatively straight-
forward protocols for three-dimensional (3-D) imaging. In
magnetic resonance imaging (MRI), for example, tagging
[1,2]
, phase contrast
[3 5]
and stimulated echo
[6,7]
methods are capable of detailed 2-D imaging and analysis.
Three-dimensional visualization and quantification, howev-
er, is not readily available, largely because of a lack of fast,
automatic image acquisition and processing approaches.
This deficiency is addressed in this article.
Routine, 3-D visualization and quantification of cardiac
motion should be clinically useful. For example, it has been
shown that in hypertrophic cardiomyopathy, torsion in the
left ventricle (LV) is reduced, with significantly less rotation
in the posterior region of the equatorial and apical planes
[8]
. Ischemia and infarction are known to affect the motion
of the endocardial wall
[9]
, to correlate well with wall
thickening
[10]
, and to reduce regional rotational and
translational motion
[11,12]
. Patterns of normal basal and
apical rotations a bwringingQ action of the LV have
been studied
[13]
, and alterations in these rotational patterns
in hypertrophic cardiomyopathy
[14,15]
after myocardial
infarction
[11]
have been reported. Mechanical activation of
the paced heart has been imaged and analyzed to reveal
significant asynchrony and heterogeneous contraction,
depending on the location of the pacemaker lead
[16]
.
Magnetic resonance imaging has been at the core of the
most sophisticated and detailed analyses of 3-D myocardial
motion. Data derived from magnetic resonance (MR)
tagging, phase-contrast velocity images and stimulated echo
images have all been used to infer global 3-D motion
properties of the heart, including strain and strain rates,
displacement, velocity, streamlines and pathlines
[17]
. But
there are still significant challenges. For example, tracking
of dense 3-D displacement inevitably requires long imaging
times
[3,7,18,19]
, manually intensive postprocessing
[18,20,21]
and/or interpolation techniques
[22 24]
.
0730-725X/$ see front matter
D 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.mri.2006.09.033
Jerry L. Prince is a founder of and owns stock in Diagnosoft, a company
which seeks to license the HARP technology. The terms of this arrangement
are being managed by the Johns Hopkins University in accordance with its
conflict of interest policies.
B
This work was supported by a National Heart, Lung, and Blood
Institute grant (R01HL47405; PI Jerry Prince).
4 Corresponding author. Laboratory of Cardiac Energetics, National
Institutes of Health, National Heart, Lung, And Blood Institute, Bethesda,
MD 20892-1061, USA. Tel.: +1 301 496 1159.
E-mail address: sampaths@mail.nih.gov (S. Sampath).
Magnetic Resonance Imaging 25 (2007) 197 208 In this article, we back off from the goal of dense
tracking and propose a new method for automatic tracking
of a sparse collection of myocardial points. The method,
which we call slice-following harmonic phase (SF-HARP)
imaging, applies 2-D harmonic phase (HARP) analysis
methods
[25,26]
to complementary spatial modulation of
magnetization (CSPAMM)-tagged MR images that have
been acquired using the slice-following (SF) technique
[27,28]
. Acquiring multiple (orthogonal) images permits the
3-D tracking of points at the intersections of these image
planes. We use this approach as the basis for computing
global quantities such as myocardial rotation and twist, but
it could also be used for computing regional strain by
acquiring multiple image planes in a small region.
In the following, we briefly describe both SF with
CSPAMM (SF-CSPAMM) and HARP (which are estab-
lished techniques), and then describe SF-HARP. The
performance of SF-HARP is then demonstrated by present-
ing results on both normal volunteers and a moving phantom.
2. Theory
2.1. Slice-following and 2-D HARP
The SF-CSPAMM technique
[28,29]
was introduced to
take through-plane motion into consideration while imaging
spatial modulation of magnetization (SPAMM)-tagged
slices
[2]
. In SF-CSPAMM, a thin slice is tagged at the
initial time frame while imaging a large slab that always
encompasses the moving tagged slice even at later time
frames [see
Fig. 1
(A)]. Two image sequences with
complementarily signed (1-1 SPAMM) tagging modulations
are acquired at each slice location: the A sequence uses a
[+908, +908] tagging pulse, and the B sequence uses a
[+908,
908] tagging pulse.
Consider two SF-CSPAMM image sequences, one
acquired in the short-axis (SA) plane and the other in the
long-axis (LA) plane within the heart. It is useful to define an
anatomic coordinate system for these two orthogonal planes.
Let (e
1
, e
2
, e
3
) be a 3-D orthonormal frame, and let (e
1
, e
2
) be
coordinate directions in the SA plane and (e
2
, e
3
) be
coordinate directions in the LA plane. Suppose x = (x
1
, x
2
)
is a 2-D vector representing a position within a given image
plane. In the SA plane, x
1
gives the position in the e
1
direction
and x
2
gives the position in the e
2
direction. On the other
hand, in the LA plane, the first and second elements of
x correspond to the e
2
and e
3
directions, respectively. All
positions are measured relative to an origin, which is taken to
be somewhere on the intersection of the two planes. It is
observed that the coordinate direction e
2
is common to the
two coordinate systems, and because of our choice of origin,
e
2
defines the direction of the line created by the intersection
of the two image planes.
The spatial distribution of the longitudinal magnetization
at any time t for the images A and B (in either image plane)
is given by
A x; t
ð
Þ ¼ ÂM
0
x
ð Þcos u x; t
ð
Þ
½
e
t=T 1
þ M
0
x
ð ÞÀ1
e
t=T 1
ÁÃf cos aðÞ;tÃ
Â
ð1Þ
and
B x; t
ð
Þ ¼ ÂM
0
x
ð Þcos u x; t
ð
Þ
p
½
e
t=T 1
þ M
0
x
ð Þð1
e
t=T 1
ÞÃf cos a
ð Þ; tÃ
Â
ð2Þ
where M
0
(x) is the initial longitudinal magnetization,
f [cos(a); t] is a function of the imaging flip angles a and
cos[/(x, t)] and cos[/(x, t) p] are the modulated
motion-related tagging functions. The complex subtraction
A B prescribed by CSPAMM
[27]
yields a series of SF-
CSPAMM images given by
I
SF CSPAMM
x; t
ð
Þ
¼ 2M
0
x
ð Þe
t=T 1
cos u x; t
ð
Þ
½
f cos a
ð Þ; t
½
:
ð3Þ
Slice-following guarantees that this signal arises from the
tagged slice itself rather than from tissues that might have
entered the image slab as the result of through-plane motion.
The Fourier transform of each image in Eq. (3) has two
harmonic peaks. Although cardiac motion causes local shifts
in the frequency and/or broadening of these harmonic peaks
during the cardiac cycle, the motion information is largely
contained within small regions in k-space surrounding these
harmonic peaks. HARP techniques
[25]
typically use a
band-pass filter to isolate regions of interest around one of
Fig. 1. Tagged slices are encompassed by the imaged slices in SF with
CSPAMM. (A) Single imaged slice at time frames t
0
and t
n
. (B) Two
orthogonal imaged slices at the two time frames.
S. Sampath, J.L. Prince / Magnetic Resonance Imaging 25 (2007) 197208
198 these peaks (see
Fig. 2
) to compute a sequence of (complex-
valued) harmonic images given by
I x; t
ð
Þ ¼ 2M
0
x
ð Þe
t=T 1
e
ju x;t
ð
Þ
f cos a
ð Þ; t
½
:
ð4Þ
The phase /(x, t) of these images the so-called harmonic
phase images are directly related to the motion of the
tagged slice in the direction perpendicular to the tag lines.
Two-dimensional pathlines of any point in the image plane
can be comput