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Copyright IMAGING THREE-DIMENSIONAL CARDIAC
FUNCTION
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W. G. O’Dell and A. D. McCulloch
Department of Bioengineering, University of California San Diego, La Jolla, California
92093-0412; e-mail: [email protected]
Key Words review, myocardial strain, myocardial stress, 3D imaging
■ Abstract The three-dimensional (3-D) nature of myocardial deformations
is dependent on ventricular geometry, muscle fiber architecture, wall stresses, and myocardial-material properties. The imaging modalities of X-ray angiography, echocardiography, computed tomography, and magnetic resonance (MR) imaging (MRI) are
described in the context of visualizing and quantifying cardiac mechanical function.
The quantification of ventricular anatomy and cavity volumes is then reviewed, and surface reconstructions in three dimensions are demonstrated. The imaging of myocardial
wall motion is discussed, with an emphasis on current MRI and tissue Doppler imaging
techniques and their potential clinical applications. Calculation of 3-D regional strains
from motion maps is reviewed and illustrated with clinical MRI tagging results. We
conclude by presenting a promising technique to assess myocardial-fiber architecture,
and we outline its potential applications, in conjunction with quantification of anatomy
and regional strains, for the determination of myocardial stress and work distributions.
The quantification of multiple components of 3-D cardiac function has potential for
both fundamental-science and clinical applications.
CONTENTS
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
IMAGING MODALITIES FOR GEOMETRIC MEASUREMENT . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
X-ray Ventriculography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Radionuclide Ventriculography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Echocardiography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Computed Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ANALYSES OF VENTRICULAR SIZE AND GEOMETRY . . . . . . . . . . . . . . . . .
Wall Thickness Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ventricular-Cavity Volume Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surface Modeling with Ellipsoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Volumes from Three-Dimensional Surface Reconstructions . . . . . . . . . . . . . . . . .
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DEFORMATION ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Implanted Markers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Magnetic Resonance Imaging Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Strain Rate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slice Motion Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model-Based Deformation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Limitations of the Reconstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
REGIONAL STRAINS IN DISEASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
MEASUREMENT OF THREE-DIMENSIONAL TISSUE ARCHITECTURE . . . . .
FUTURE DIRECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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INTRODUCTION
The three-dimensional (3-D) nature of heart deformation is well appreciated and
a subject of great interest both to cardiovascular scientists and clinical cardiologists. The application of clinical imaging to cardiac function has traditionally been
limited to global geometric measurements, including left ventricular (LV) wall
mass, ventricular volume, stroke volume, ejection fraction, and wall thickness
(1). These measures of heart function provide invaluable diagnostic information
to the clinician regarding the severity of disease and the long-term prognosis
(2). The ability to measure regional myocardial deformation provides additional
information that is valuable for identifying the location and extent of affected
areas, quantifying the degree of mechanical dysfunction, and differentiating between functionally distinct disease states. Among the investigational tools available, visualization and quantification of regional cardiac mechanical function are
perhaps the most direct and reliable indicators of cardiac health (3). For example, although quantification of coronary artery patency is important in directing
treatment of regional myocardial ischemia, the existence of severe vessel occlusion is not necessarily associated with insufficient mechanical function, owing
to myocardial revascularization and ventricular wall remodeling. The realm of
3-D cardiac mechanical analysis encompasses global and regional myocardial
functions, 3-D fiber tissue architecture, electrical propagation of activation, the
generation of internal wall stresses by the contracting myocytes, and the distribution of those stresses by the surrounding tissue matrix. This article describes and
contrasts the prevailing modalities for monitoring 3-D heart function, describes
the current techniques for manipulating image data to model cardiac anatomy
and deformation, and outlines what lies ahead for the field of functional cardiac
imaging. Length constraints preclude coverage of other areas of cardiac imaging research and applications, such as metabolic imaging [positron emission tomography
(PET) and magnetic resonance spectroscopy (MRS)], electric- and magnetic-field
imaging, electrical propagation and mechanoelectrical feedback, and perfusion
imaging.
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IMAGING MODALITIES FOR GEOMETRIC
MEASUREMENT
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Overview
Various imaging modalities exist to measure heart wall geometry. These can be
compared objectively by the following criteria: signal quality [indicated by the
signal to noise ratio (SNR)], discrimination between myocardial and neighboring
tissue [indicated by the contrast to noise ratio (CNR)], temporal and spatial resolution, susceptibility to image blurring and artifact, acquisition and analysis time,
ease of use, relative cost, and availability. For accurate quantification of heart wall
geometry and ventricular volumes, CNR is often the more informative measure
because it governs the ability to discern tissue boundaries. Spatial resolution is typically given by the pixel dimensions in the two-dimensional (2-D) image (voxel
dimensions for 3-D); however, for some modalities, such as MR imaging (MRI)
and computed tomography (CT), the image slice thickness can be comparatively
large, leading to partial-volume artifacts that diminish the effective in-plane resolution. Temporal resolution relates to both the time interval between successive
images (temporal sampling rate) and the time over which the data for each image
are acquired (acquisition window). In X-ray imaging, motion while the shutter is
open leads to blurring and loss of image quality. In MRI, motion during acquisition
causes a phase dispersion across the image, creating a characteristic artifact.
Generally one needs to acquire data on a time scale that is smaller than the
fastest motions of interest. For a typical heart rate of 1 Hz, the duration of isovolumic relaxation or isovolumic contraction is ∼100 ms; hence a temporal sampling
rate of <50 ms is required to capture these events. In many instances, increasing either spatial or temporal resolution competes with the desire to minimize
acquisition time. Reduction of spurious cardiac motion is critical for all imaging
modalities. Image acquisition during periods of patient breath holding (preferably
at end-expiration) and electro-cardiography gating, either prospective (triggering
the acquisition to occur at a specific point in the cardiac cycle) or retrospective (assigning time stamps to the data after acquisition), can substantially reduce image
blurring and motion artifact. With retrospective gating, image data can be acquired
continuously so that overall imaging time may be reduced, possibly improving patient compliance. However, a longer period of post-processing is then required.
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X-ray Ventriculography
By 1964, X-ray ventriculography with contrast enhancement was considered the
gold standard for ventricular volume and mass measurement (4). In this method,
conventional X-ray images are generated by projecting a wide beam of X-ray
energy onto a film. Radiopaque substances in the tissue absorb and scatter the
incoming energy; hence an X-ray image is an inverse mapping of tissue opacity.
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The theoretical resolution of a film image is dependent on the film grain; however,
the effective resolution depends on the relative opacity of neighboring objects, the
dispersion of the X-ray beam, and the distances of objects from the X-ray tube focal
spot and film. Projection images in orthogonal views depict major heart long- and
short-axis dimensions. X-ray projection imaging with contrast is considered to be
mildly invasive because of both the contrast injection and the ionizing radiation. For
wall geometry measurements, there are the problems of limited CNR at the cavity
boundaries, silhouette hiding of concavities in the ventricular surface, and various
projection and registration artifacts. In biplanar cineradiographic imaging, there
are also technical concerns about temporally and spatially registering the images
from the two cameras. As an example of the potential accuracy of biplanar X-ray
imaging, when implanted bead markers are imaged in canine subjects, singleplane views can distinguish and locate the centers of even partially overlapping
1-mm-diameter beads to an accuracy of 0.2 mm (5). However, a typical bead
registration error between two cameras that are oriented perpendicularly to each
other is 0.1 mm (6, 7). Movie film acquisition rates of 60–90 Hz are common. X-ray
projection systems are relatively inexpensive, easy to use, and widely available,
and they can provide real-time feedback, but the accumulated radiation dose is a
concern for repeated measurements.
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Radionuclide Ventriculography
Blood-pool or equilibrium radionuclide ventriculography is another common
modality for estimating ventricular volumes. Erythrocytes are labeled in vivo with
the radioactive tracer technetium-99m. A large-field gamma camera equipped with
a low-energy collimator records the number of radio-decay counts, which is proportional to the number of erythrocytes and, hence, the blood volume. The resulting
time-activity curves are often filtered in time, normalized by the end-diastolic volume count, and used to compute ejection fraction, peak filling/ejection rates, time
to peak filling/ejection rates, and related indices (8). This technique is easy to use
and measures relative volumes without the need for geometric assumptions, but it
is susceptible to background signal sources, has relatively low spatial resolution,
and is susceptible to variable attenuation during respiration. Long acquisition times
of ∼5 min require a regular cardiac rhythm and/or post-processor elimination of
data from premature beats and temporal and spatial smoothing.
Tomographic radionuclide imaging or gated blood pool single photon emission
CT (SPECT), was first demonstrated in 1980 (9) but so far has had only limited
clinical application. The SPECT acquisition is accomplished within 30 min, with
a rotating gamma camera and 60 projection angles (10). The 3-D images can then
be reconstructed with conventional CT back-projection algorithms.
Echocardiography
Among the current cardiac imaging modalities, echocardiography (ECG) is perhaps the most prevalent because of its cost effectiveness, ease of use, real-time
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IMAGING 3-D CARDIAC FUNCTION
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feedback, portability, and widespread availability. Echocardiographic imaging is
based on the partial reflection of acoustic waves at tissue boundaries and echocardiographic image contrast is governed by the difference in acoustic properties
between adjacent tissues. A pencil-shaped beam (M-mode) is swept though an arc
of ∼80◦ to create a 2-D image at 16–38 frames/s. Transthoracic imaging (in which
the echocardiographic transducer is manually placed on the skin) can be used to
obtain multiple long-axis, short-axis, and oblique-image views, but it is limited to
parasternal and apical windows. Transesophageal imaging (in which an echocardiographic transducer is inserted into the esophagus) overcomes the windowing
constraints and places the transducer in close proximity to the heart.
Many of the limitations of 2-D and M-mode ECG are overcome by 3-D ECG,
including limited viewing angles and imaging obliquely through the LV wall, and
this method is quickly approaching clinical use (11, 12). In 1990, von Ramm &
Smith (13) introduced the first fully 3-D, phased-array cardiac ultrasound imager. Currently, 3-D ECG in patients is generally applied by one of two methods: transthoracic imaging in multiple views with transducer position registration
[with either a mechanical arm or an acoustic spatial-location system (14)]; or
transesophageal imaging with either incremental rotation of the transducer at various long-axis imaging planes or translation of the transducer at various short-axis
imaging planes (11). A typical transthoracic 3-D ECG imaging set, as described by
Gopal et al (14), is composed of 7–10 short-axis images and is acquired in 6–8 min.
Analogous long-axis 3-D image sets acquired from rotated apical views are also
feasible; a method introduced by Ghosh et al (15) in 1982. 3-D ECG can also be
used to assess right ventricular (RV) geometry (16).
ECG image quality is limited by relatively low contrast between myocardial
and adjacent tissues, fading of the endocardial boundaries (typically, ∼25% of
the total boundary in a time-elapsed M-mode recording is indiscernible) (17),
noise, and related artifacts. With a contracting LV phantom, Lange et al (17)
found that the error in volume estimation with multiple parallel ECG slices and
Simpson’s rule was 3% at the larger volume (simulating end-diastole) and 4% at
the smaller volume (end-systole). CNR differences account for a discrepancy of
9% for the end-diastolic volume and 11% for the end-systolic volume between
the ECG-estimated LV volumes and those produced by the more reliable tissue
Doppler imaging (TDI) method for contour detection (17). Without the addition
of contrast agents, ECG CNRs generally tend to be lower than those for MRI and
contrast-enhanced CT.
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Computed Tomography
The conventional CT scanner consists of an array of detectors and a single X-ray
source, which is rotated about the sample. The transmitted fan-shaped X-ray beam
is recorded at several angles, and a 2-D image is reconstructed by using a backprojection algorithm. Radiographic contrast injection and rapid scanning are commonly used to improve image quality. CT with contrast offers very good CNR with
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high spatial resolution (typically 2- × 2- × 5-mm voxel dimensions), high temporal resolution (∼1 s), and the ability to acquire axial images at arbitrary locations
through the chest. CT scanners, however, are more expensive and less available
than ECG imagers. The simultaneous acquisition of multiple 2-D CT images for
3-D–image reconstruction was initially demonstrated in 1980, with the dynamic
spatial reconstructor [DSR (18)]. The DSR uses multiple X-ray sources with coneshaped beams and a hemicylindrical fluorescent screen to acquire volumetric data
with high temporal resolution. Whereas the DSR has remained primarily a research tool, electron-beam CT (EBCT) (19) has become increasingly popular for
clinical use. In EBCT, X-rays are produced by scanning a single-source electron
beam onto a tungsten target that is positioned in a semicircle below the patient
(20). Mechanical motion in the gantry is eliminated (bypassing the typical 1-s
interscan delay), and exposure times of 50–100 ms are possible. In typical multislice mode, four tungsten target rings and two detector rings are used to acquire
up to eight image slices without movement of the patient table, reducing motion artifact. Spiral CT (also known as helical CT) is another emerging technique
for very rapid acquisition of 3-D image data; with higher spatial but lower temporal resolution than EBCT. Spiral CT imaging uses a conventional fan-shaped
beam source, which rotates continuously about the patient, and a fixed array of
receivers. Contiguous 2-D axial images are acquired as the sample moves along
the scanner bore. Multiple receivers are often used to acquire four slices simultaneously. Retrospective gating is commonly used in EBCT and spiral CT to reduce
motion artifact (21). With both multislice EBCT and multislice spiral CT, 3-D
image data sets can be acquired in times on the order of seconds—quickly enough
that susceptibility to remaining motion artifact is significantly reduced. On-line
reconstruction algorithms have been developed to aid in the graphical display of
3-D CT cardiac data sets and in simulating views from obliquely oriented cross
sections (22).
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Magnetic Resonance Imaging
Magnetic resonance (MR) imaging (MRI) both provides high CNRs between soft
tissues and blood without the injection of contrast agents and enables imaging at
arbitrary image angles. MRI scans are relatively expensive and time consuming,
and they require a certain amount of patient cooperation. In-plane spatial resolution
can be high (1 × 1 mm); however, the slice thickness is typically 5–10 mm; thus
the images are highly susceptible to partial-volume artifacts. This is problematic
especially towards the heart apex, where the wall slope is high. The quality and
resolution of MR cardiac images have steadily improved with the inclusion of
breath holding, black-blood saturation (which improves the contrast between the
myocardium and blood in the cavity), rapid imaging techniques (i.e. gradient echo
and echo-planar imaging for quicker acquisition), k-space segmentation (for improved temporal resolution), and dedicated cardiac radiofrequency receiver coils
(for improved SNR) (23). With prospective gating and gradient echo sequences,
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the image data for 10–14 temporal images at a single slice location in the heart
can be acquired within a 16- to 20-s breath hold. Breath holds of this duration are
feasible in cardiac patients, even those with acute myocardial infarction (3). The
acquisition of cine data for 8–10 short-axis slices thus requires ∼10–15 min, allowing for patient recovery after each breath hold. Newer sequences, using SMASH
(simultaneous acquisition of spatial harmonics) for example (24), can cut this time
by a factor of 2 or 3. MRI can also be used to perform retrospective respiratory
gating with navigator echo signals from the diaphragm, although the implementation of this technique is difficult (25). A recent review of MRI applied to cardiac
motion analysis by McVeigh (25) is highly recommended.
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ANALYSES OF VENTRICULAR SIZE AND GEOMETRY
LV volume, ejection fraction, and wall thickness are perhaps the most frequently
used indices of cardiac performance and patient prognosis (26, 27). However, the
pertinent geometric information must first be extracted from the images before 3-D
surface reconstruction. The challenge is to detect, within the image, heart contour
features that are irregular in shape and position, changing with time, and varying in
contrast and whose image intensity gradient profile can change in both magnitude
and sign. Contour segmentation is the most laborious and error-prone part of most
analysis schemes. Real-time clinical application of modern 3-D cardiac mechanics
techniques is going to require faster and better automated segmentation. We refer
the reader to the article in this volume of Annual Review of Biomedical Engineering
that pertains to image segmentation, by Pham et al (27a).
Wall Thickness Measurements
LV wall thickness measurements have been linked to regional ischemia (27) and
lead to estimates of mean wall stress (28) and mean wall stiffness. Wall thickness
measurements were made as early as 1964, by X-ray angiography (4), but more
recently Jakob et al (29) improved the technique by using injected-contrast and
digital-subtraction angiography. In comparison with the more commonly used Mmode ECG, the Jakob method showed good agreement towards end-diastole but
poorer agreement at end-systole.
Although wall thickness changes are often the most apparent geometric indicator of altered mechanical function (30), the relationship between wall thickness and
cardiac health is not as clear. Significant correlations were found by Lawson et al
(31) between thallium uptake and systolic wall thickness in ischemic hearts, but not
with diastolic wall thickness and thallium uptake (31, 32). Similarly, Curiel et al
(33) found that the magnitude of inotropic reserve is not related to diastolic wall
thickness or to basal systolic wall thickening. Heupler et al (34) showed that the
LV end-diastolic cavity diameter, not wall thickness, was associated with thallium
perfusion defects and therefore myocardial ischemia. Dong et al (35) concluded
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that regional and interindividual heterogeneity in wall thickness in diseases such
as hypertrophic cardiomyopathy make meaningful comparisons difficult. Finally,
acute changes in wall thickness do not necessarily indicate chronic dysfunction
because long-term wall remodeling may act to compensate for mild injury by
restoring wall thickness to normal values, as described by Pouleur et al (36) with
LV dilation.
The relationship between wall thickening and fiber shortening is also not clear.
Wall thickening at various wall depths was shown by Hexeberg et al (30) to correlate not with fiber shortening or myocardial perfusion in those layers, but with
thickening of the entire wall and local wall geometry. McCulloch et al (37) supported this conclusion for fiber strains but found that transmural location did have
a significant effect on cross-fiber strains.
The estimate of the contour location in an image is accurate to within 1–2 mm,
typically, with MRI (38). For a 10-mm-thick wall, this error leads to a 10%–20%
uncertainty in the thickness estimation. The apparent wall thickness is increased
in planar images that intersect the heart wall at oblique angles to the local surface
normal, creating a bias in the thickness measurement. Through-plane motion introduces additional error because the same piece of myocardial tissue is not imaged
over time at a fixed cross-sectional location. Both the bias and the through-plane
motion artifact can be corrected with 3-D ventricular surface reconstruction by
using data from orthogonal views (see below).
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Ventricular-Cavity Volume Estimates
Traditionally, the measurement of LV volume by thermodilution techniques (39),
projection ventriculography (40), or radionuclide techniques has been subject to
substantial error, that is, ∼20% (39). Despite many innovations in imaging techniques and computerized analyses, substantial errors of this order remain in clinical
measurements of LV volume. Currently, the task of estimating the volume of the
ventricular cavity often reduces to defining the cavity boundaries and integrating
over the enclosed space. Significant, common sources of error are poorly defined
basal and apical limits of the ventricle, oversimplified geometric models, and uncompensated imaging artifacts.
A common convention is to model the base of the heart as a planar surface
passing through the mitral valve ring. However, the entirety of the valve plane
is not easily imaged with ECG or 2-D CT imaging because the mitral valve is
obliquely oriented in the chest cavity. With MRI, it is possible to orient the imaging
plane to encompass the entire mitral valve ring, but, because the slice thickness
is typically 5–7 mm, there is a ±2.5- to 3.5-mm discrepancy in the plane’s exact
location within the slice. Even if accurately imaged at one time, the mitral valve
ring translates apically ∼10 mm (41) from end-diastole to end-systole; hence
it does not remain within a single, fixed short-axis image volume. For a mitral
valve ring that is 25 mm in diameter (area, 491 mm2), a jump from one slice
location to the next represents an estimated volume change, using Simpson’s rule,
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IMAGING 3-D CARDIAC FUNCTION
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of 2.5–3.4 ml or ∼6.2%–8.5% of the total end-systolic volume (for a representative
end-systolic volume of 40 ml). Similarly, it is difficult to detect the most apical
intracavitary point by using only short-axis images. Both of these sources of error
can be overcome by incorporating planar image data from the orthogonal, long-axis
view.
When referenced to 3-D ECG and equilibrium radionuclide angiography,
limited-plane 2-D ECG methods were no better than subjective visual estimation for determining the LV ejection fraction (14). To compensate for the inherent
limitations, some applications use correction factors that are calibrated to match the
known volume errors as tested on postmortem or experimental heart models (40).
However, these correction factors are computed for a “typical” heart geometry that
may not necessarily be appropriate for abnormal or diseased hearts.
Poor CNRs and partial-volume effects both contribute to errors in the segmentation of heart contour data, which are magnified in the LV volume estimate. For
a sphere of radius 25 mm, a typical LV minor-axis radius dimension, an error of
1 mm (4%) in the estimated radius leads to a volume estimation error of ∼12%.
All imaging modalities suffer misregistration of the heart contour data when the
image data are acquired over many heartbeats or different times, as a result of
beat-to-beat variations in the heart contraction and uncorrected respiration-derived
motions. With projection images, the contrast silhouette obscures most of the indentations in the wall (i.e. at the papillary muscle sites), creating an overestimation
of the true ventricular dimensions. A comparison between cross-sectional ECG and
X-ray ventriculography found that projection imaging leads to an overestimation
in ejection fraction of 22% (42).
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Surface Modeling with Ellipsoids
When only a few ventricular surface measurements are available, it is convenient
to model the LV surface geometry as an ellipsoid. This simplification allows for
rapid calculation of volume but disregards the asymmetry of the actual ventricular
surface, the complexity of the mitral valve plane, and the existence of the papillary
muscles. Elliptical models were initially used with projection ventriculography
(40), but are now also used commonly with 2-D ECG data (43). The volume of an
ellipse is given by:
V =
4
πab2
3
where a is the radius along the major axis and b is the radius of the minor axis.
For single-plane projections, Dodge (40) used the formula
b=
Aproj
πa
where b is the minor
axis dimension and Aproj is the area of the long-axis projection
4A2proj
(making V = 3πa ). An analogous formula exists for biplanar data. Ellipsoidal
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models cannot as readily approximate RV volumes, because their geometry does
not possess such symmetry (44).
The Simpson’s-rule method computes the cavity volume by summing the areas
of 2-D planar slices, scaled by the slice separation. The implied geometric assumption for this method is that the area of the measured cross-section remains constant
over the distance between slices (or at least is representative of the average area),
which becomes increasingly error-prone as the slice separation increases. There
are also the previously mentioned errors associated with the identification of the
mitral-valve plane, through-plane motion, and registration artifacts. A common
modification to the volume equation involves reducing the volume contribution
of the most apical and/or most basal slices by 50%. Many other variations are
commonly used.
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Volumes from Three-Dimensional Surface Reconstructions
Regardless of the modality used to acquire the anatomical data, once these are
attained, 3-D surface reconstructions allow more exact descriptions of the heart geometry than simple elliptical models. Many 3-D surface reconstruction techniques
are also able to incorporate anatomical data from multiple views/projections. Many
recent advances in 3-D surface reconstruction have been driven by computer vision
research (45, 46). Piecewise mathematical constructs have also been proposed, including 3-D splines and finite-element basis functions (47, 48). Deformable sheet
or balloon models (3-D extensions of “snakes”) are able to interact directly with
features of the images to satisfy both the need to match image data and to smooth
out noisy image data. The smoothing is accomplished by incorporating energies associated with stretching and bending into the deformable sheet or balloon (49–51).
Global polynomial representations are also applicable (52, 53). For example, we
have used a surface model expressed as a polynomial series in prolate spheroidal
coordinates. Here the base geometry is an ellipsoid, to which are superposed spatial
modulations as a function of angular position, analogous to spherical harmonics.
Mathematically, the radial coordinate λ is represented as a function of the circumferential and longitudinal angles (θ, φ):
λ=
l
L X
X
a j Plm (cos(θ ))eimφ
(1)
l=0 m=−l
Here Plm are the associated Legendre polynomials. The coefficients ai in the polynomial are fit, in a least-squares sense, simultaneously to contour data points
from multiple views. The goodness/smoothness of the reconstruction can be adjusted to match the expected uncertainty in the contour data, by admitting or
omitting higher-order terms in the series, which is achieved by adjusting the series
limit “L.”
Figure 1A (see color insert) shows the fitted endocardial surfaces for a zerothorder fit, that is, the best-fit prolate spheroid. From left to right in the figure,
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Figure 1 Left ventricular endocardial surface-fitted data sets for canine heart. The light lines are
the raw contour data, and the dark lines are generated from the fitting equation (Equation 1). Top:
Top view; bottom: side view. The order of fitting goes from zero-th to third, sixth, and tenth from
left to right.
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IMAGING 3-D CARDIAC FUNCTION
441
additional polynomial terms are added, giving the model increased spatial modulation (for deformable sheets and balloons, this is analogous to decreasing the
bending energy). The error between the fitted surface and the original contour data
can be computed as a function of the number of fitting parameters. The error will
generally decrease as the number of fitting parameters increases, but there is a
point at which the inclusion of additional high-order terms would fit the noise to
the data rather than to the actual heart geometry. The combination of data from
multiple views and the spatial and temporal smoothing will filter out noise and
misregistration errors, creating a more accurate representation of the 3-D heart
surfaces.
Once the 3-D surface is mathematically reconstructed, the cavity volume and
LV mass can be computed numerically. The time required to compute volume estimates from contour data from multiple views and multiple locations is negligible
compared with the time required for the acquisition and segmentation steps. In
the example shown in Figure 1D (see color insert), the 49 polynomial coefficients
were fit to >1800 contour points in <1 min, using an SGI R5000 Indy workstation.
The 3-D analytical surface representations are also useful for accurate measurement of regional wall thickness, where thickness compared with the true epicardial
surface normal can be quickly and accurately computed.
In review, LV volume and ejection fraction remain two of the most sought-after
clinical indices of cardiac health. However, errors of 20% in LV volume estimation
and ejection fraction are common clinically, although this uncertainty is often overlooked. Modern investigational and computational strategies afford much higher
accuracy with only marginally more effort and time although the necessary imaging
technologies and computation software are not yet widely available.
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DEFORMATION ANALYSIS
Measures of ventricular cavity volume, volume changes over time, and myocardial
mass have traditionally been used to gauge global myocardial mechanical dysfunction and overall patient prognosis. However, the ability to quantify the deformation
of the myocardial tissue locally, for example to describe the amount of shortening
in the direction of the myocardial fibers, is of paramount importance in cardiac
mechanics research and promises to provide clinicians with much more powerful
indices of regional tissue viability.
A material point is a physical piece of myocardial tissue. The description of
the deformation in the neighborhood of a material point begins with the task of
identifying and tracking these points and their neighbors over time and space. The
relative motion of neighboring points away from or toward each other reflects the
amount of stretching or compression of the tissue, and is described by the onedimensional (1-D) displacement gradient, ∇U. If the 1-D displacement (along the
x-axis, for instance) of one material point differs from that of a second, neighboring
point located initially a distance 1x away and the displacement difference is given
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by 1u x , then the displacement gradient is 1u x /1x. The infinitesimal displacement
gradient is δu x /δx. If a second degree of motion is added, along a y-axis, then there
is a potential for stretch or compression along this second axis and for rotation
and/or shearing in the plane of motion. The complete 2-D motion is described by
a nonsymmetric 2-D displacement gradient tensor:


∂u x ∂u x
 ∂x
∂y 

∇U = 
 ∂u y ∂u y 
?
∂x
∂y
At least three points are required to fully describe all of these potential motions in
the neighborhood of a material point. Rigid-body rotations alter the displacement
gradient component values, and therefore a rotation-invariant measure of deformation is generally preferred. One such measure is the Lagrangian strain tensor,
E, computed as
1
[(∇U)T × (∇U) {+} (∇U)T {+} (∇U)]
2
Chen et al (52) and Young & Hunter (48) incorporated both surface geometry
data and coronary tree bifurcation points to model epicardial motion and strains.
McEachen & Duncan (54) used points of curvature extrema similarly. These methods used the tracking of these identifiable surface points along with smoothing
constraints to estimate surface point trajectories. For investigational use, Arts et al
(55) implanted a total of 14 radiopaque surface markers around the heart and computed coefficients in a 14-parameter kinematic model of heart motion. Clinically,
similar studies with transplanted hearts embedded with tantalum helices have been
performed by Moon et al (56) and Hansen et al (57), yielding similar results. The
sparseness of the material markers in these studies severely limited the accuracy
and application of these methods for strain calculation (6), yet they provided novel
shape and shape-change information (50, 58). In canine hearts, Hashima et al (59)
achieved much greater material point density by sewing 25 lead beads into the
LV free wall. The resulting finite element-derived, nonhomogeneous epicardial
strains showed substantial alteration during occlusion of the left anterior descending (LAD) coronary artery, compared with the nonoccluded state. Nevertheless,
the absence of material points within the myocardium limits the conclusions that
can be drawn from such surface analyses.
To compute a local 3-D displacement gradient tensor requires a minimum of
four noncoplanar material points (60). The magnitude and rate of change of these
deformations vary regionally around the heart and throughout the cardiac cycle. To
accurately assess 3-D cardiac function, one must first be able to define and track a
sufficient number of material points with adequate spatial and temporal resolution.
Spatially, a complete description of the local strain requires a sampling interval
that is sufficiently small to recover the smallest fluctuations in the motion field.
Douglas et al (61) estimated, using spherical models and wall motion data from
E=
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IMAGING 3-D CARDIAC FUNCTION
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canine hearts, that a 3-mm sampling interval through the wall is needed to model
transmural wall motion in a healthy subject. Less stringent sampling intervals of
5–6 mm are needed in the circumferential and longitudinal directions. However, in
diseased hearts, in which strong gradients in motion may occur in the border zone
between healthy and ischemic regions, a higher density of points may be needed.
Temporally, some purposes require strain patterns at only a single time point, that
is, from end-diastole to end-systole, to evaluate the strains in the fully contracted
state. However, the evolution of strain may also be critical for clinical diagnosis
(62). Strain evolution may give information on the pattern of contraction and reveal
electrical conduction pathway abnormalities. This requires the acquisition of data
on a time scale that is smaller than the fastest motions of interest. As suggested
earlier, a temporal resolution limit of 50 ms seems reasonable.
?
Implanted Markers
One investigational method that has provided valuable research data is the embedding of arrays of radiopaque markers into the heart wall, which are then imaged by
using biplanar cineradiography. Combining the projection data from two orthogonal views, one is able to reconstruct the 3-D location of each bead in the array at
each time frame (7). The motion of three or more planar beads that are attached
to the surface of the heart give an estimate of the local 2-D surface strain (63, 64).
Additional markers at various depths in the heart wall provide the additional
information necessary for a complete 3-D motion analysis (65–67). Beads are
commonly arranged in stacks of planar triangles, ∼5 mm on a side, with 4 mm of
separation between stacks. Imaging a density of beads becomes difficult, but arrays
with 2- to 3-mm separations have been successfully reconstructed. Implanted arrays of sonomicrometers have been used similarly, although their use is generally
limited to 2-D surface studies. The disadvantage of these approaches is the invasiveness of the procedure, which precludes its routine use on human subjects. The implantation surgery may damage the tissue, the chest wall and pericardium are often
resected, and the mere presence of several 0.5- to 1-mm-diameter beads through a
wall 10–15 mm thick may alter the normal mechanical deformations in the subject.
Magnetic Resonance Imaging Tagging
An MRI tag is a region of the tissue where the net magnetization has been altered
with carefully designed radio frequency pulses (3, 68). Upon imaging, these altered
regions show good signal contrast compared with neighboring untagged regions.
Each tag is created as a 3-D plane that extends through the entire subject, and it
is seen as a tag line when imaged in an orthogonal view. Various tag generation
schemes have been invented for creating numerous tags in a short amount of
time. The more popular tagging schemes include stacks of parallel lines (69, 70),
grids (71), and radial stripes (72). Because the tags result from alterations of the
magnetization of the tissue itself, the motion of the tags matches the motion of the
underlying tissue (73, 74).
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Typically, tags are created at end-diastole when the cavity volumes are largest,
and the image data are acquired at 30- to 50-ms intervals as the heart contracts.
The altered magnetization persists for ∼0.5 s, based on the T1 magnetization
relaxation constant of cardiac tissue. Therefore, 10–12 images can be acquired
during the ejection or filling phase of the cardiac cycle. The segmentation of tags
is far more easily automated than is the segmentation of the heart contours, because
the tags are human-made features of the image, for which the location and image
intensity profile can be well predicted (75). The optimal image intensity profile
and in-plane separation of tag planes can be computed analytically and have been
validated experimentally. For parallel tag data, a tag width of 1–2 pixels with a tag
center-to-center separation of 6 pixels gives an optimal tag centerline detection
accuracy (76), which, for a typical image SNR of 15, is <0.1 pixels (0.1 mm
for a typical clinical cardiac image). The detection of the location of grid tag
intersections is slightly less accurate [∼0.3 mm mean error (77)], owing to the
absence of the tag profiles at the intersections.
Parallel tagging schemes enable the acquisition of images with lower resolution
in the direction that is parallel to the tag lines. This enables the acquisition time to
be reduced, leading to images that exhibit less motion artifact. However, two sets
of images are then needed to sample the in-plane 2-D motion. Tag displacement
data in three orthogonal directions are required to reconstruct the 3-D trajectory
of material points. A typical 3-D tagging data set consists of two sets of short-axis
images (or one set with a tag grid), one with the tag lines oriented 90◦ from the
other set, and a set of long-axis images with tag planes that are parallel to the
short-axis imaging planes.
?
Strain Rate Analysis
It is also possible with certain imaging modalities to measure directly the rate
of change of strain. As described above, the tracking of material points leads to
the computation of the local Lagrangian strain tensor, which is the description of
motion around a given point in the tissue as it traverses through space and time. An
alternative way to describe the deformation is to consider the relative velocity of
motion at a particular location in space as a function of time. The local gradient of
the velocity field at a given spatial location leads to the computation of the Eulerian
strain rate tensor, which is analogous to the above computation of the strain tensor
from the displacement gradient (78). In 1-D analysis, the velocity information can
also be integrated over time to obtain the trajectory of material points and the local
strain tensor.
Magnetic Resonance Phase-Contrast Imaging MR phase-contrast imaging can
be used to directly measure the velocity of the myocardial tissue on a pixel-by-pixel
basis (79). In a phase-contrast image, the change in phase of the net magnetization
inside each pixel, compared with a reference image, correlates to the velocity of
the underlying tissue in the direction that is parallel to the applied magnetic field
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gradient. This method has the advantage over tagging in that each pixel provides a
unique motion measurement, and MR phase-contrast imaging has great potential
for reconstructing 3-D motion (80). However, current implementation of phasecontrast imaging for 3-D motion measurement is hampered by low SNRs, high
susceptibility to motion artifacts, and, hence, limited accuracy of the reconstructed
velocity profiles.
?
Tissue Doppler Imaging The Doppler shift of the reflected echocardiographic
wave also contains velocity information that is analogous to that obtained with
MR phase-contrast imaging. Doppler ultrasound provides real-time velocity (81)
and velocity gradient (82) information about blood and tissue. The frequency shift
spectrum vs time information, presented as a sonogram, reveals the velocity range
and distribution. The additional motion information from TDI has been shown to
improve, over transthoracic ECG, detection of anomalous conduction pathways
in patients with Wolff-Parkinson-White syndrome (83). However, velocity information is obtained only in the direction parallel to the echo beam and CNR noise
(Doppler speckle), and the number of available viewing angles limit the image
quality. Tessler et al (84), using a calibrated 1-D flow phantom, found that the
Doppler-measured velocity had a baseline error of 6.8 cm/s (9%–17%) for peak
flows that range from 40.5 to 75.3 cm/s. This error was independent of inter- or
intraobserver variability or variability that is attributable to different flow probes
or the flow phantom. Fleming et al (82) also used a test phantom and showed that
3 mm by 3 mm was the smallest region of tissue from which a measurable change
in velocity could be detected with Doppler imaging.
Velocity vector mapping in two and three dimensions is theoretically possible
by using additional ECG receivers or by electronically separating a linear array
receiver into spatially separate subapertures (85, 86). The unidirectional velocity
magnitudes and the angle difference between the subapertures and the source echo
are used to derive the direction and true magnitude of the velocity.
Slice Motion Correction
Accounting for the full 3-D motion of the heart, particularly the motion through
the fixed short-axis image plane locations, is crucial for 3-D deformation analysis. The approaches mentioned above can accommodate this need by acquiring
3-D tagging or velocity data sets. However, alternatives, such as the slice isolation presented by Rogers et al (41), can also be used. A related technique involving subtraction of positive and negative tagged images has been shown by
Fischer et al (87). In another approach, WeDeen et al (88) implemented a motionless movie scheme, in which the same slice was imaged at the same time
in 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 tissue
at a sequence of preceding time increments. From this they were able to compute the 2-D Eulerian strain (or strain rate) at that slice location. Hybrid tagging/
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velocity-encoding methods are inherently difficult because the tagged regions of
tissue contain no velocity information (are a signal void), and the velocity encoding step requires a reference and a phase-encoding image; thus it does not
offer an overall time advantage compared with 3-D tagging or 3-D phase-contrast
imaging.
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Model-Based Deformation Analysis
?
Reconstruction of the 3-D strain field from discrete samples of displacement requires an interpolation scheme to describe the motion between samples in space, to
correct for noise in the sampling, and to compute the local displacement gradients
that are used for strain calculation (unless explicitly stated, considerations for velocity field and strain rate reconstruction can be assumed to be analogous to those
described here for displacement field and strain reconstruction). The interpolation
method usually includes a model of the 3-D displacement field. A priori assumptions of the displacement field can be used to generate a model that contains the
expected modes of motion, and the displacement or velocity samples can be used
to optimize the magnitude and direction of those modes (55).
A more general formulation is to use 3-D basis functions to describe the local
motion within each element of a finite element model of the heart (89), increasing
the number of degrees of freedom in the reconstruction to the number of local
basis functions per element times the number of elements. Taking this globally, a
model containing hundreds of candidate modes can be formulated, and the sampled
motion can be used to solve for the magnitude of those modes over the entire
heart. This removes the requirement for a priori assumptions about the modes
of motion, useful for reconstructing motions in regions of altered mechanical
state, such as sites of ischemia. O’Dell et al (53) use a displacement field fitted
to a polynomial series in prolate spheroidal coordinates (a 3-D analogy to the
2-D surface reconstruction presented earlier) to reconstruct 3-D material point
trajectories from parallel-tag data sets. As shown in Figure 2 (see color insert), the
contribution of each mode to the overall motion of the heart can be quantified and
interpreted independently by using computer models of the heart (90).
Another interesting approach, presented by Denney et al (91), uses samples
of motion along with energy minimization equations that penalize large gradients
in deformation to estimate the motion at each point in a rectangular grid that
encompasses the entire heart. This approach is related to optical-flow techniques
and is a powerful model-free method of computational analysis.
Limitations of the Reconstructions
Ultimately, the resolution and accuracy of the results from a reconstruction scheme
are determined by the deformations of the heart tissue and the density and quality of
original motion sampling. First, if the motion is simple, for example, the translation
of a solid body, only a few simple parameters and a few samples of motions
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Figure 2 Top six deformation modes from high-density healthy human left ventricular data set,
demonstrated on a computer-generated model. λ is the radial coordinate, φ is the longitudinalangle–coordinate, and θ is the circumferential angle. (1) ∂φ = constant; longitudinal contraction of
the base of the heart toward apex. (2) ∂λ = constant; concentric contraction without wall thickening.
(3) ∂θ = cos(φ); clockwise twist of the apex with respect to the base. (4) ∂θ = sin(θ)sin(φ);
circumferential contraction toward lateral wall. (5) ∂φ = cos(φ); longitudinal contraction toward
the equator. (6) ∂λ = sin(φ)cos(θ ); bulging of the lateral free-wall.
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IMAGING 3-D CARDIAC FUNCTION
447
are needed. However, for the complex, 3-D heart wall motion, with high-order
transmural gradients in the displacement field and spatial heterogeneity (i.e. from
septum to free wall and base to apex), many global degrees of freedom are required
to describe the motion around a given material point.
To describe the trajectory and strain environment of a given material point (e.g.
to within 0.3-mm 3-D tracking accuracy) requires many parameters in a local
deformation model or perhaps >100 in a global model. However, the resolution
and accuracy one actually needs for a given purpose may be considerably less
stringent. Models based on a priori assumptions and a few simple expected modes
may give sufficient information in an efficient manner.
Upon successful image segmentation, a typical MRI parallel-tagging data set
generates 3000–10,000 samples of 1-D displacement. Points along tag lines are
obtained typically at 1- or 2-mm intervals. In the clinical setting, the separation
between tags is typically 6–7 mm, the distance between contiguous image slices
is often 7–10 mm, and hence the 3-mm sampling criterion estimated by Douglas
et al (61) is not met in all directions. Experimental conditions, however, can afford
greater image quality and spatial resolution and can overcome these limitations.
?
REGIONAL STRAINS IN DISEASE
The ultimate clinical goal of 3-D cardiac deformation analysis is to quantify and
characterize regions of altered mechanical function. Figure 3 (see color insert)
compares subendocardial and subepicardial circumferential strains at end-systole
(referenced to end-diastole) in a patient with LV anterior-wall dysfunction that
is secondary to ischemia. This region is typically supplied by the LAD coronary
artery; therefore, we can postulate that there is a critical occlusion of that artery.
In the central ischemic zone, the circumferential strain is positive, indicating that
the region is undergoing stretch or bulging in response to the contraction of the
neighboring healthy tissue and the imposed cavity pressure.
For clinical application, the primary concern is whether the tissue is viable. If
the tissue were necrotic, then an aggressive and expensive treatment paradigm,
e.g. open-chest coronary graft surgery, would not be beneficial. However, if it can
be shown that the tissue is yet viable, then restoration of normal circulation will
presumably restore normal cardiac function. The secondary issue is to quantify the
degree of dysfunction. A patient exhibiting only a 20% loss of contractile function can perhaps be treated with a less aggressive, less expensive pharmacologic
regimen, whereas a patient with an 80% loss of regional function will perhaps
need more immediate aggressive therapy, such as balloon angioplasty, to restore
vascular patency.
Dobutamine or adenosine stress testing has been suggested for noninvasive detection of viable but noncontracting (hibernating) myocardium in conjunction with
MRI motion tracking. Croisille et al (92) found improved function in response to
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Figure 3 Three-dimensional rendering of end-systolic circumferential strain derived from magnetic resonance imaging tagging in a patient with left anterior descending coronary arteryassociated ischemia. Sub-endocardial (left) and sub-epicardial (right) strains are shown. Positive
strain (stretching) is indicated by dark blue, and negative strain is rendered in bright yellow. Range,
0.2 to −0.2. MRI data provided by E McVeigh, Johns Hopkins University School of Medicine.
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inotropic stimulation in at-risk regions of canine hearts subject to LAD occlusion and reperfusion. Regions of unchanged function after dobutamine infusion
were shown to correlate with areas of infarction as evidenced by TTC staining.
Hopefully, conclusive clinical test results will soon be forthcoming.
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MEASUREMENT OF THREE-DIMENSIONAL TISSUE
ARCHITECTURE
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The heart has a complex 3-D anatomy that plays a significant role in the generation of 3-D wall deformation (93). There exists a predominant fiber direction
that is nearly completely confined to a circumferential-longitudinal plane, with an
in-plane angle with respect to the heart long-axis that varies nearly linearly with
wall depth. However, conflicting theories remain as to the tertiary structure of the
fibers. The dissections and histological findings of LeGrice et al (94) suggest a
laminar structure of the fiber bundles, with loose collagen connections between
bundles of 4–5 fibrils. They found that the laminar or sheet arrangement is consistent among canine subjects and hypothesized that the sheets facilitate large
wall shears and increased wall thickening during contraction. A dilemma for any
anatomical study is that intervention distorts the underlying 3-D fiber structure,
and, hence, conclusions about the intact structure are suspect. Yet, dissection and
histological sectioning remain the gold standards for elucidating the 3-D fiber
architecture.
Considerable data on fiber structure in canines have been presented by Streeter
& Hanna (93) and LeGrice et al (94), but these findings do not necessarily apply
to the human heart. Owing to difficulties in obtaining suitable human hearts and
in performing the histological sectioning, detailed 3-D fiber structure analysis for
a human heart has yet to be performed.
A recent application of MR phase-sensitive imaging is now finding use for
measurement of myocardial fiber architecture. MR diffusion-sensitive imaging
uses phase-contrast imaging techniques, but these are tailored to motions on the
scale of free-water diffusion. The tissue sample is spatially marked by applying
a magnetic field gradient for a short period of time, creating a linear dispersion
of the phase of the tissue magnetization across the sample along the direction of
the applied gradient field. Nuclei that subsequently move will carry their phase
information to the new location. A refocusing gradient then resets the stationary
spins to their original phase state.
In a population of nuclei, random motion that is parallel to the applied gradient
field will cause a dispersion of phase around the stationary-phase value and a corresponding decrease in pixel intensity that varies exponentially with the square of
the magnitude of the applied gradient (assuming that restricted diffusion effects
can be ignored). The coefficient of that exponential is the diffusion coefficient. The
longer the average displacement of the population, the greater the spread in the
phase, the greater the signal attenuation, and the larger the diffusion coefficient.
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IMAGING 3-D CARDIAC FUNCTION
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For many biological tissues, the diffusion coefficient is different for different directions. In three dimensions, this is described fully by the local diffusion tensor.
Phase dispersion mapping with measured diffusion coefficients in six nonparallel
directions (the diffusion tensor is symmetric) can be used to estimate the local 3-D
diffusion tensor (95).
From a tissue standpoint, the free diffusion of water is hypothesized to occur
more readily in a direction more parallel to the local fibers than perpendicular.
Studies by Hsu et al (96) in dogs and Scollan et al (97) in rabbits have shown that
the principal direction of maximal diffusion is related to the local myocardial fiber
direction, with a 12◦ uncertainty, using histological sectioning as a guide. Scollan
et al (97) go on to describe a qualitative relationship between the laminar fiber
architecture and the remaining diffusion eigen components. Reese et al (98) have
applied such techniques to in vivo canine and human subjects. With this technology,
it should be possible to noninvasively measure the 3-D fiber architecture in the same
hearts that are used for mechanical testing. This will be especially enlightening in
certain disease states where interindividual variation in fiber architecture can be
large and unpredictable.
?
FUTURE DIRECTIONS
The 3-D nature of heart deformation is dependent on the 3-D ventricular geometry,
regional myocardial strain, 3-D fiber tissue architecture, and internal wall stresses.
We have shown examples of promising techniques to independently assess heart
anatomy, regional strains, and fiber architecture. The additional measurements of
myocardial stresses would enable analysis of the myocardial work output, which
relates to the metabolic requirements of the tissue, including oxygen consumption
(99). It is not yet possible to directly measure myocardial stresses in vivo without
destroying the tissue or significantly altering the measurement (100). However,
it has been shown that pulsed Doppler ultrasound (101) can provide an estimate
of tissue stiffness because the speed of propagation (and hence wavelength) of
the ultrasonic beam varies with stiffness. This approach, however, suffers from
the typical limitations of TDI. The promising method of MR elastography, introduced by Muthupillai et al (102), combines ultrasonic oscillating mechanical
surface stress waves (at 10–1100 Hz) with MR phase-sensitive imaging to monitor
the propagation of the ultrasonic beam through tissue, with increased sensitivity
and clarity compared with Doppler ultrasound. These techniques have yet to be
successfully applied to the in vivo heart.
The approach that has seen some success is to estimate the stress-strain behavior
of heart tissue by computational modeling (103). It is conceivable to use an inverse
approach to fit constitutive law parameters from measured strains. Moulton et al
(104) have shown the potential of such an approach by using a simplified constitutive law and finite element modeling of a 2-D cross section of tissue. The finite
element model was loaded with approximated 2-D surface tractions and allowed
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to deform by the laws of equilibrium. The error was computed between the finite
element-predicted strain field and that measured with an MRI tagging grid over that
slice, and the constitutive law parameters were varied to achieve a minimal strain
error. This approach is analogous to that used by Guccione et al (105), who used
an axisymmetric 3-D finite-element model and transversely isotropic constitutive
law to match 3-D strains measured at a single site, using radiopaque markers and
cineradiography. When fully 3-D geometric representations are considered, including fiber anatomy and material anisotropy, compressibility, and heterogeneity,
this approach still involves substantial computational time. It is also conceivable
to design an inverse approach based on matching measured surface tractions and
stress equilibrium constraints (106), but this is highly susceptible to uncertainties
in the strain field and all of the 3-D properties.
Just as new modalities for imaging cardiac structure and function are aiding the
computational estimation of myocardial stress and work, a priori knowledge of
myocardial mechanics can be used to improve image segmentation and analysis.
Duncan et al (107) described the general theory in a recent review, and it could be
applied directly to the finite element-based strain reconstruction methods for MRI
tagging data by Kraitchman & Young (77) and Young & Axel (89).
Apart from improvement in imaging individual components of 3-D cardiac deformation, the assessment of multiple components during a single imaging session
(and within a reasonable time frame) is likely to become of increasing interest.
Very recently, WeDeen et al (108) have shown preliminary data for measuring
both myocardial strains and fiber direction in hearts from human volunteers and
patients using MRI phase-sensitive imaging and MR diffusion tensor imaging.
Despite the capabilities available currently, the use of 3-D cardiac functional
analysis in the clinical setting remains limited. As outlined by the National Institutes of Health Cardiac MRI Work Group (109), the principal reasons for this include long imaging times (compared with single-plane/projection imaging), timeconsuming and labor-intensive post-processing requirements (primarily in image
segmentation), and lack of understanding of benefits by clinicians. To this list can
be added the difficulty in reducing and presenting the resulting voluminous and
complex 3-D data sets into simple, informative parameters that can be readily used
by the clinician. The challenges are for commercial, academic, and government
agencies to improve the efficiency of 3-D image acquisition, to bring near real-time
3-D display of the processed image data into the examination room, and to perform the necessary clinical studies to demonstrate the capabilities of 3-D cardiac
functional imaging.
?
ACKNOWLEDGMENTS
The authors acknowledge the many informative discussions and contributions from
Paul Friedman, Sabrina Au, and Elliot McVeigh, and funding support from the
AHA and NIH grant HL41603. W. G. O. is supported by an American Heart
Association Post-Doctoral Fellowship.
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CONTENTS
PIERRE M. GALLETTI: A Personal Reflection, Robert M. Nerem
1
PHYSICOCHEMICAL FOUNDATIONS AND STRUCTURAL
DESIGN OF HYDROGELS IN MEDICINE AND BIOLOGY, N. A.
Peppas, Y. Huang, M. Torres-Lugo, J. H. Ward, J. Zhang
9
BIOENGINEERING MODELS OF CELL SIGNALING, Anand R.
Asthagiri, Douglas A. Lauffenburger
31
FUNDAMENTALS OF IMPACT BIOMECHANICS: Part I Biomechanics of the Head, Neck, and Thorax, Albert I. King
55
INJURY AND REPAIR OF LIGAMENTS AND TENDONS, Savio L.-Y.
Woo, Richard E. Debski, Jennifer Zeminski, Steven D. Abramowitch,
Serena S. Chan Saw, MS, James A. Fenwick
83
ELECTROPHYSIOLOGICAL MODELING OF CARDIAC
VENTRICULAR FUNCTION: From Cell to Organ, R. L. Winslow, D. F.
Scollan, A. Holmes, C. K. Yung, J. Zhang, M. S. Jafri
119
CRYOSURGERY, Boris Rubinsky
157
CELL MECHANICS: Mechanical Response, Cell Adhesion, and
Molecular Deformation, Cheng Zhu, Gang Bao, Ning Wang
189
MICROENGINEERING OF CELLULAR INTERACTIONS, Albert
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227
QUANTITATIVE MEASUREMENT AND PREDICTION OF
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257
MICROFABRICATED MICRONEEDLES FOR GENE AND DRUG
DELIVERY, Devin V. McAllister, Mark G. Allen, Mark R. Prausnitz
289
CURRENT METHODS IN MEDICAL IMAGE SEGMENTATION,
Dzung L. Pham, Chenyang Xu, Jerry L. Prince
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ANTIBODY ENGINEERING, Jennifer Maynard, George Georgiou
339
NEW CURRENTS IN ELECTRICAL STIMULATION OF EXCITABLE
TISSUES, Peter J. Basser, Bradley J. Roth
377
TWO-PHOTON EXCITATION FLUORESCENCE MICROSCOPY,
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IMAGING THREE-DIMENSIONAL CARDIAC FUNCTION, W. G.
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THREE-DIMENSIONAL ULTRASOUND IMAGING, Aaron Fenster,
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BIOPHYSICAL INJURY MECHANISMS IN ELECTRICAL SHOCK
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WAVELETS IN TEMPORAL AND SPATIAL PROCESSING OF
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MICRODEVICES IN MEDICINE, Dennis L. Polla, Arthur G. Erdman,
William P. Robbins, David T. Markus, Jorge Diaz-Diaz, Raed Rizq,
Yunwoo Nam, Hui Tao Brickner, Amy Wang, Peter Krulevitch
NEUROENGINEERING MODELS OF BRAIN DISEASE, Leif H.
Finkel
EXTRACORPOREAL TISSUE ENGINEERED LIVER-ASSIST
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INTERVENTIONAL AND INTRAOPERATIVE MAGNETIC
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CARTILAGE TISSUE REMODELING IN RESPONSE TO
MECHANICAL FORCES, Alan J. Grodzinsky, Marc E. Levenston,
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IN VIVO NEAR-INFRARED SPECTROSCOPY, Peter Rolfe
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