Vol. 275, Issue 6, H2308-H2318, December 1998
Histological validation of myocardial microstructure obtained
from diffusion tensor magnetic resonance imaging
D. F.
Scollan1,
Alex
Holmes1,
Raimond
Winslow1, and
John
Forder2
1 Department of Biomedical
Engineering and Center for Computational Medicine and Biology, and
2 Department of Radiology, Johns
Hopkins University School of Medicine, Baltimore, Maryland 21205
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ABSTRACT |
Diffusion tensor magnetic resonance imaging
(MRI) is a possible new means of elucidating the anatomic structure of
the myocardium. It enjoys several advantages over traditional
histological approaches, including the ability to rapidly measure fiber
organization in isolated, perfused, arrested hearts, thereby avoiding
fixation and sectioning of artifacts. However, quantitative validation of this MRI method has been lacking. Here, fiber orientations estimated
in the same locations in the same heart using both diffusion tensor MRI
and histology are compared in a total of two perfused rabbit hearts.
Fiber orientations were statistically similar for both methods and
differed on average by 12° at any single location. This is similar
to the 10° uncertainty in fiber orientation achieved with
histology. In addition, imaging studies performed in a total of seven
hearts support a level of organization beyond the myofiber, the
recently described laminar organization of the ventricular myocardium.
myocardial fiber architecture; fast spin echo
| |
INTRODUCTION |
IT IS WELL KNOWN that the myofiber structure of the
heart plays a critical role in electrical propagation and force
production. Myocardial electrical propagation is anisotropic, with the
spread of current greatest in the direction of the long axis of the
fiber (21, 28, 36, 43, 44). Fiber orientation is also an important determinant of myocardial stress and strain (24, 31, 47) and,
therefore, of cardiac perfusion and oxygen consumption (8) and
structural adaptation (1). Furthermore, fiber organization is thought
to play a role in arrhythmogenesis (5, 20, 32), and fiber architecture
is known to be altered in some cardiac disease states, such as ischemic
heart disease (48) and ventricular hypertrophy (22, 37, 45). Therefore,
a detailed knowledge of fiber microstructure in normal and diseased
hearts will contribute significantly to an understanding of normal and
abnormal cardiac electromechanics. Determination of fiber
microstructure in large numbers of hearts in various disease states is
not yet feasible, because current histological methods of
reconstruction of myocyte microstructure are complex and labor
intensive (29). Reconstruction of the entire ventricular fiber
microstructure can take several weeks per heart, and few laboratories
have the expertise to do this. Furthermore, reconstruction can only be
performed on fixed hearts, and fixation may alter the architecture from
the normal, viable state.
Recently, a number of studies (3, 11, 14, 34, 46) have indicated that
diffusion-weighted magnetic resonance imaging (MRI) may be used to
determine the muscle fiber orientation of tissues. Diffusion of water
within a tissue in the presence of a magnetic field gradient causes MRI
signal attenuation. In one approach, known as diffusion tensor magnetic
resonance imaging (DTMRI), this fact is used to estimate a
voxel-averaged diffusion tensor specifying diffusivity in each of three
principal coordinate directions at each voxel of the tissue image. The
eigenvector corresponds to the maximum eigenvalue of the diffusion
tensor points in the direction of the maximum rate of diffusion. It
appears that water, being unrestricted by membrane, preferentially
diffuses in the direction of the long axis of a cylindrical fiber. This observation has been used to map fiber orientation of the myocardium (11, 34) and white matter (7, 9, 19, 27, 33). However, quantitative
histological verification of this apparent correlation has been
lacking. Recently, the study by Hsu et al. (15) provided the first
quantitative correlation of DTMRI and histology fiber angles, albeit in
an excised portion of the right ventricle (RV). The long imaging times
required to reconstruct the architecture of the intact ventricular
myocardium will require perfusion to avoid ischemia, which can
corrupt DTMRI estimates; indeed, it is the effect of ischemia
on diffusion that makes diffusion MRI a promising new modality for
detection of strokes.
Here, we will show that DTMRI estimates of fiber orientation obtained
from perfused, nonbeating rabbit hearts accurately reproduce histological measurements of this orientation made at the same locations in the same heart. Specifically, quantitative agreement will
be shown between transmural sequences of fiber angles, obtained by
histology and DTMRI. Agreement will be found to hold for DTMRI estimates based on a spin-echo or a fast spin-echo pulse protocol. The
latter reduces image acquisition time by a factor of eight. Furthermore, DTMRI estimates will be shown to provide evidence of a
level of organization of the myocardium beyond that of the fibers. This
organization appears consistent with the controversial laminar
architecture described recently (23, 24) and, because it is from
viable, intact hearts, is not liable to the same criticism of artifact
(25, 39) as in previous studies.
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THEORY |
Basser et al. (3), building on the work of Skejskal and Tanner (38),
have shown that the diffusion tensor can be calculated from knowledge
of signal attenuation and magnetic gradient strengths applied during a
diffusion-weighted spin-echo experiment (Fig. 1A)
using the equation
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(1)
|
where
A(bij)
is the voxel-attenuated signal (echo) intensity recorded in the
presence of gradients, A(0) is the
gradient-free, unattenuated echo intensity,
Dij is the
(symmetrical, positive definite, 3 × 3) diffusion tensor, and
(bij) is a
matrix specified by the magnetic field gradients applied during the
spin echo. This so-called b matrix has
the form
|
(2)
|
where the superscript T denotes the transpose operator;
F(t) = 
G(t') dt',
where
G(t) = [Gx(t),
Gy(t),
Gz(t)]T
is the applied magnetic gradient vector; and
f = F(TE/2), with
H(t')
as the unit Heaviside function, TE as the echo time, and 
as the
gyromagnetic ratio of protons. Although the gradient vector
G(t)
includes imaging and diffusion-weighting gradients, the imaging
gradients are typically negligible relative to the diffusion gradients.
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Fig. 1.
A: spin-echo pulse sequence with
addition of half-sine diffusion gradients of duration  .
Gslice,
Gread, and
Gpe represent slice, read-out, and
phase-encoding gradients, respectively. Half-sine crushers are played
on either side of slice-selective 180° radiofrequency (RF) pulse to
reduce artifacts from stimulated echoes.
B: fast spin-echo pulse sequence with
addition of bipolar half-sine diffusion gradients of lobe width and
lobe separation  . The first diffusion-encoded echo is formed after
slice-selective 90° and 180° RF pulses, with crushers applied
immediately before and after the latter. Phase encoding is applied to
subsequent echoes in the train, which are obtained by repeated
refocusing with slice-selective 180° RF pulses. The first echoes of
each train are used to fill the center of
k space. TE, echo time.
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Equation 1 is a linear relationship
between the signal intensities
A(bij)
and the components of the b matrix,
(bij). The six
unique elements of the diffusion tensor
Dij can thus be
calculated using multilinear regression. To do this, measurements of ln
A(bij)
are made at n different gradient
strengths in m noncolinear directions.
These mn observations of ln
A(bij) are stored in an mn × 1 column
vector, x. The corresponding (bij) are
stored in an mn × 7 matrix
B, and the parameters to be estimated
[the six unique
Dij and, in
addition, ln A(0)] in a 7 × 1 column vector 
, such that
x = B is the linear system to be fit.
Application of a least-squares error approach yields the optimal
parameters opt = (BT
1B)1(BT1)x,
where 1
is the diagonal covariance matrix of weights. For each voxel in the
two-dimensional MR images, the
Dij are calculated, and from them, the tensor eigenvalues and eigenvectors are
calculated. The primary eigenvector yields the direction of maximal
water diffusion in the tissue.
Although Eqs. 1 and 2 were originally developed for
spin-echo DTMRI, they were also used to determine the diffusion tensors from a fast spin-echo pulse sequence (Fig.
1B). Their applicability to fast
spin-echo DTMRI is only approximate, however, because each echo in the
train is exposed to different imaging gradients and therefore has a
unique b matrix. Once again, the
contribution of the relatively small imaging gradients to the
b matrix is negligible compared with
the contribution of the much larger diffusion gradients. The effect of
any diffusion weighting caused by imaging gradients can be reduced
further by keeping the echo trains short (
8 echoes) and using the
initial echoes of each train to fill the center of
k space and thus set image contrast (4). This was the approach we used.
| |
MATERIALS AND METHODS |
Heart extraction and perfusion.
New Zealand White male rabbits (2-4 kg) were anesthetized using
ketamine (2 mg/kg iv) followed by heparin (1,000 U/kg iv) and were then
exsanguinated. The heart and lungs were excised rapidly and were placed
in a bath of cold (4°C) cardioplegic solution (described below).
The aorta was cannulated, the lungs were ligated and removed, and the
hearts were perfused retrogradely using an MR-compatible Langendorff
apparatus as described previously (2). The initial perfusate was a
modified Krebs-Henseleit buffer containing (in mM) 118.0 NaCl, 25.0 NaHCO3, 5.0 dextrose, 4.6 KCl, 2.5 CaCl2, 1.2 KH2PO4,
and 1.0 MgSO4. To avoid excess
hydrostatic pressure accumulation and distension of the left ventricle
(LV) resulting from thebesian drainage or aortic valvular
insufficiency, a thin (1-mm OD) polyethylene tube was inserted into the
LV through the mitral valve to serve as a vent. The heart was allowed
to beat several times to provide proper seating of the valves. Before imaging, the heart was arrested because of the sensitivity of diffusion-weighted MR images to bulk motion. Cardiac arrest was induced
and maintained by perfusing with a cardioplegic solution [modified St. Thomas' Hospital solution (50)] that
consisted of (in mM) 110.0 NaCl, 16.0 MgCl2, 16.0 KCl, 10.0 NaHCO3, 5.0 dextrose, and 1.2 CaCl2. BSA (3% wt/vol) was added
to both perfusates to minimize formation of interstitial edema. Both
perfusates were continually equilibrated with a 95%
O2-5%
CO2 gas mixture, resulting in
partial pressures of O2 in excess
of 600 mmHg and a pH of 7.4. All perfusion was conducted at room
temperature (18°C) to help maintain cellular viability.
Two sets of fiducial markers (made of fluid-filled Tygon tubing) were
sutured onto the ventricular epicardium for correlation of the MR
images with the histology (described in detail in
Histological determination of fiber inclination
angles). Hearts were then suspended in a
closed-end acrylic cylinder (31-mm diameter) that served as a bathing
chamber for the heart and around which a loop-gap radio frequency (RF)
coil was wound.
Magnetic resonance imaging.
Studies were performed on a 4.7-T MR spectrometer/imager (GE Omega,
Fremont, CA). Once inside the imager, the coil (31-mm diameter) was
tuned to proton resonance and magnetic field homogeneity was optimized
with the water proton signal. Proton diffusion images were then
obtained using either a standard spin-echo technique or a fast
spin-echo technique, followed by two-dimensional Fourier transform.
Diffusion weighting was provided by half-sine magnetic gradient pulses
that were 10 ms in duration and unipolar (spin echo) or 8 ms in
duration and bipolar, with 1-ms lobe separation (fast spin echo). The
gradients were applied sequentially in six noncolinear directions,
taking on the values 4, 6, 8, and 10 Gauss/cm (spin echo) or 4, 
4, 14, and 14 Gauss/cm (fast spin echo). These values
correspond to "b factors" as defined by others (4, 11) of 3.2 × 103, 1.3 × 104, 2.9 × 104, and 5.2 × 104 (spin echo) or 2.6 × 104 and 3.2 × 105 (fast spin echo). Thus a total
of 24 images were obtained per slice, each with 128 phase-encoding
steps and 256 frequency-encoding steps, providing an in-plane
resolution of 156 × 313 µm and a slice thickness of 2 mm. For
each image, two signal averages were performed and a repetition time of
2 s was used, resulting in an image time of 8 min 32 s per image for
spin echo. The fast spin-echo protocol used an echo train of eight,
resulting in an image time of 1 min 4 s. In addition to the imaging and
diffusion gradients, unipolar half-sine crushers were applied around
each 180° RF pulse in the slice direction, with duration of 2 ms
and amplitudes of 4 Gauss/cm. Their amplitudes were doubled for the first echo in the fast spin-echo sequence to further reduce
stimulated-echo artifacts; despite this, calculations showed that they
still imparted negligible diffusion weighting.
Determination of diffusion tensor, eigensystem, and orientation
angles.
The voxel components of the diffusion tensor were determined by
multilinear regression (3), and determination of the eigensystem of the
diffusion tensor was performed in MATLAB (MathSoft, Cambridge, MA).
Orientation of eigenvectors is defined by two angles, as shown in Fig.
2. The "inclination angle" was
defined as the angle the eigenvectors make with the transverse (image)
plane in a plane parallel to the epicardial tangent plane. We seek to
show that, for the primary eigenvector, this angle is equivalent to the
inclination angle (also called the fiber angle or helix angle)
determined from histology, as it is usually defined (42). The
"transverse angle" is the angle the eigenvectors make with the
circumferential direction in the image plane. It represents the
transmural component of the eigenvector orientation.
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Fig. 2.
Definition of the 2 angles necessary to determine orientation of
eigenvectors and fibers first requires determination of a tangent
plane. A point on the epicardial surface is referred to as the
epicardial tangent plane. For all points along a normal directed inward
from that point, a tangent plane is defined as the plane parallel to
the epicardial tangent plane. The inclination angle () is then the
angle between the image plane and the projection of an eigenvector (or
fiber) onto the tangent plane. We define this angle to best correspond
with the manner in which it is calculated using the histological
approach, that is, in sectioned planes parallel to the epicardium of
the sample. The transverse angle ( ) is the angle between the tangent
plane and the projection of the eigenvector onto the image plane.
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Histological determination of fiber inclination angles.
Immediately after MR imaging, hearts were removed from the perfusion
chamber and placed in a bath of isotonic 3% formaldehyde in phosphate
buffer. One-half liter of this solution was fed through the aortic
cannula to perfuse the coronary circulation over a period of ~30 min.
On the following day, the heart was sectioned and histological samples
were obtained. Two pieces of Tygon tubing sutured to the epicardial
surfaces of the LV and RV in the shape of the letter "N" (upright
in the basal-apical direction) enabled accurate correlation of MR and
histological sample locations. In the short-axis view, three cross
sections of tubing were evident for each N. The set of distances
between the cross sections on the MR image was measured. A set of three
points on each piece of the tubing of the actual heart whose distances
corresponded to those of the image was determined. These two sets of
points on opposite sides of the heart uniquely define the imaging
plane. Repeated measurements showed that the set of points defining the imaging plane on the heart varied by <1 mm out of plane. Because the
MR image slice thickness was 2 mm, histological samples 1 mm above and
below the imaging plane were obtained. To this end, the heart was
sectioned parallel to and 1 mm above the imaging plane and parallel to
and 5 mm below it. Although the tissue beyond 1 mm below the plane was
superfluous, the added thickness made the tissue easier to cut and
process. A transmural slab, with edges cut perpendicular to the
epicardium, was then removed from the transverse section for
histological processing. With the use of the tubing as markers, the
boundaries of this slab could easily be determined on the MR images.
The tissue was embedded in Historesin (Cambridge Instrument's brand of
glycol methacrylate) according to the manufacturer's instructions. The
slab was then sectioned in planes parallel to the epicardium, inward
from the epicardium at 50-µm increments, with tissue retained every
250 µm for hematoxylin and eosin staining. The stained slides were
photographed at ×4 magnification and digitized at 1,200 dpi
resolution. The digitized slides were imported into NIH Image (version
1.61, Wayne Rasband, National Institutes of Health). At five locations
at 1-mm increments along the circumferential direction, fiber
inclination angles were measured relative to the cut top surface of the
tissue. At each transmural depth, measurements were made at the basal
edge and at 1 and 2 mm below the surface and averaged. This was
repeated for each slide, resulting in five sets of average inclination
angle versus transmural depth. For later comparison to DTMRI estimates
in the perfused heart, these estimates of inclination angle were
retabulated with respect to percent distance through the wall, thus
accounting for tissue shrinkage that occurs with fixation.
The histological measurements of fiber inclination angle were found to
be reproducible to within ±10°, similar to the precision of
Streeter et al. (40). All sample locations that yielded measurable inclination angles were included in the comparison with the DTMRI results. For some histological sample locations (<18%), no
measurements were possible because of tissue fragmentation incurred
during slicing or because of the presence of large vascular spaces.
Statistical analysis.
Each of the five transmural histological samples was compared with a
DTMRI transmural sample at the same location in the LV, ~5 mm from
the base. The DTMRI sampling of fiber inclination angle versus
transmural depth was obtained by defining a transmural line
perpendicular to the epicardium, extending to the endocardium, with
these boundaries defined by an edge-detection algorithm implemented in
MATLAB. For each heart, five of these lines were constructed, each
aligned to one of the five sets of transmural histological measurements, using the fiducial markers as reference points. Calculations of inclination angle versus percent distance along the
line were then generated. Thus a total of 10 pairs of samples was
obtained for comparison: five histology versus spin-echo DTMRI pairs
from one heart, and five histology versus fast spin-echo DTMRI pairs
from the second heart.
The statistical tests used to examine the correspondence between the
histology and DTMRI fiber angle estimates are those of Hsu et al. (15).
To examine the differences between the estimates of inclination angle
obtained by DTMRI (MRI) and
histology (Hist) at each
voxel, histograms of Hist MRI were constructed. A difference in mean near zero indicates minimal systematic error between
the two estimation procedures, and a small standard deviation of the
distribution further indicates a minimal random error. In addition, for
each of the 10 sites, curves of fiber inclination angle versus percent
transmural depth were constructed. At each site, the shape of the
curves obtained by DTMRI and histology were compared by determining the
Pearson correlation coefficients between the angles obtained by each
method at the same transmural depth. In addition, the probability that
each observed correlation coefficient had occurred by chance alone,
Pr, was
calculated as by Hsu et al. Although a correlation coefficient close to
unity would imply that the shape of the curves for angle versus depth are similar for the two methods, it would not imply that at each voxel
the inclination angles are close; indeed, adding a constant to each
DTMRI angle estimate would not change the correlation, and multiplying
each DTMRI angle by some constant would not change the correlation.
Such effects would be manifest in a large mean or standard deviation of
the distribution of Hist MRI for a set of
transmural samples. To detect a shift or a scaling of the set of DTMRI
curves compared with the set of histology curves, the mean and standard
deviation of the inclination angles were determined for each curve.
These data were then averaged among all measurement sites and compared
using paired Student's t-test, with
P < 0.05 considered significant
(15).
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RESULTS |
Myocardial anisotropy.
Diffusion tensor MRI experiments have been performed in a total of
seven hearts, two of which had additional histology performed on them
for correlation with DTMRI fiber inclination angles. In each of these
hearts, water diffusion within the vast majority of the myocardium is
highly anisotropic: the primary voxel diffusion tensor eigenvalue is
generally much larger than the secondary and tertiary eigenvalue
throughout the myocardium. To quantify the degree of anisotropic
diffusion, an anisotropy index is defined as the ratio of the voxel
diffusion tensor primary and tertiary eigenvalues. The image in Fig.
3 (left)
is a map of the anisotropy index in one heart. The anisotropy index is
seen to be nonuniform, taking on values >1 within the myocardium. In
contrast, the ratio is uniform and near 1 for perfusate within the
ventricular chambers and external to the heart. Furthermore, in the
hearts studied, the myocardium tends to be fully anisotropic, with
statistically significant differences between the eigenvalues. This is
particularly true for the septum and LV free wall, as can be seen in
Fig. 3 (right), which is a map of
the ratio of the secondary to tertiary eigenvalues. Figure 3,
inset A, shows that the primary,
secondary, and tertiary eigenvalues are all statistically distinct
along the line segment labeled A in the LV free wall. In parts of the RV free wall, and near the junction of the RV free wall with the septum, however, the map shows that the secondary and tertiary eigenvalues are much less distinct, because their ratio approaches unity in some areas. For example, in the region covered by the line
labeled B, the secondary and tertiary eigenvalues are not statistically
different (Fig. 3, inset B),
suggesting that the myocardium approaches transverse isotropy in this
region. Four hearts displayed this pattern of anisotropy, two others
displayed a more random distribution of anisotropy, and one other was
found to have greater anisotropy in the free walls.
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Fig. 3.
Maps of the ratio of primary to tertiary eigenvalues
(left; also called anisotropy index)
and of secondary to tertiary (right)
eigenvalues for a short-axis (horizontal) image of 1 perfused rabbit
heart. Left: red, anisotropic
myocardium is generally well contrasted with blue, isotropic perfusate
that surrounds it. In addition to the thin right ventricle (RV) and
thick, circular septum/left ventricle (LV), 2 papillary muscles can be
observed within the LV. Asterisk indicates a flow artifact, which leads
to an anomalous reading of high anisotropy in the RV.
Right: ratio of secondary to tertiary
eigenvectors is seen to be especially large in midseptum and lateral
LV. Inset A shows that along
line A in lateral LV, differences in
eigenvalues are generally statistically distinct (error bars denote 2 SE); here, the myocardium is fully anisotropic. In anterior and
posterior LV, differences in secondary and tertiary eigenvalues are
less significant as is evident from inset
B, which plots eigenvalues for voxels along
line B. Here, the myocardium
approaches transverse isotropy.
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Primary eigenvectors and fiber orientation.
If the direction of the maximum rate of diffusion, given by the primary
eigenvector, is oriented in the same direction as the myofiber long
axis, then the inclination and transverse angles of the primary
eigenvectors should be comparable to those of the myofibers obtained
from histology. The left panel of Fig.
4 shows a map of the
inclination angle of the primary eigenvector; the middle panel shows an
interpolated version of this raw data. The spatial variation of the
angle is qualitatively consistent with the well-known transmural
variation of the inclination angle obtained from histology by others
(11, 13, 29, 40, 42, 45); for comparison, the interpolated (and
therefore smoothed) inclination angles of a transverse section of
canine heart from the histological reconstruction of Nielsen et al.
(29) are shown in the right panel of Fig. 4. Note that for
both versions, large negative angles are common on the LV and RV free
walls and on the RV septal endocardium but are uncommon near the
junction of the two ventricles.
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Fig. 4.
Left: raw inclination angle estimates
of primary eigenvector obtained from a horizontal image slice of 1 rabbit heart. Middle: same estimates
smoothed with a median filter. Right:
horizontal slice of histological reconstruction of canine heart
performed by Nielsen et al. (29) on which fiber inclination angle
values are plotted. These measurements are
stored in the form of a finite element model, and therefore are
heavily interpolated.
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Figure 5A
plots primary eigenvector inclination angles estimated using spin-echo
DTMRI. These inclination angles were computed along five different
transmural line segments through the LV free wall of one rabbit
heart. Fiber angles estimated at corresponding transmural
locations using histological techniques are also shown. The transmural
variation of fiber angles determined by both methods appears similar;
this is supported by an average voxel error of 12°, which is close
to the measurement uncertainty of 10° for determination of the
fiber angles by histology. The Pearson correlation coefficients for
each of the five sets of inclination angles are given in Table
1 and have an average of 0.95 ± 0.15. The significance coefficients,
Pr, are also
shown and have an average of 0.0002 ± 0.0002. Figure
5B shows similar data obtained at five
transmural locations in a different heart, with the exception that
inclination angle was estimated using the fast spin-echo diffusion
sequence. As was the case for the spin-echo data of Fig.
5A, the DTMRI estimates obtained using
fast spin-echo agree well with the histological measurements. Again,
the mean voxel inclination angle error is 12°. The Pearson
correlation coefficients and significance coefficients are given in
Table 2 and have average values of 0.86 ± 0.05 and 0.005 ± 0.006, respectively. The average means of the individual DTMRI and histology fiber inclination angle curves are 21.2 ± 2.6° and 18.2 ± 2.1° (average ± standard error,
P = 0.15), and their average standard
deviations are 26.5 ± 0.8° and 26.4 ± 1.3° (P = 0.93). The extent to which the
DTMRI and histological data agree is further quantified in Fig. 5,
C and
D, which show the distribution of
voxel inclination angle differences between the two methods. For spin
echo, the distribution mean was 4.9 ± 1.7° (mean ± SE,
P < 0.01 by Student's
t-test to the zero-mean null hypothesis), and the standard deviation was 14.6°. For fast spin echo, the distribution mean was 0.42 ± 1.9°, which was not
significantly different from zero. The standard deviation of the
distribution was 15.2°.
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Fig. 5.
A: fiber inclination angle
measurements ( ) and primary eigenvector inclination angle estimates
( ) obtained from a spin-echo pulse sequence for a total of 5 transmural locations in 1 heart. B:
same as A but for measurements
obtained in another heart using a fast spin-echo pulse sequence.
C: distribution of differences in
fiber inclination angle at each voxel obtained using histology
(Hist) and spin-echo DTMRI
(MRI).
D: constructed similar to
C but for fast spin-echo heart.
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To ascertain the accuracy of the alignment of the MRI and histology
sample sites, we examined the correlation between the fast spin-echo
DTMRI inclination angles at one site with the inclination angles
determined from histology at each of the other sites. Table 3 shows that the best correlation occurs when the
DTMRI and histology estimates are compared at the same site
or at immediately adjacent sites. The correlation rapidly declines as
the DTMRI estimates are compared with increasingly remote sites,
suggesting that the alignment of MRI and histology sample sites is
accurate to ~1 mm in plane.
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Table 3.
Dependence of goodness of fit as fast spin-echo DTMRI fiber angles are
compared with histology fiber angles at increasingly remote sample
sites
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To fully define the orientation of the primary eigenvectors and
myofibers, the transverse angle must also be specified. The transverse
angles of the primary eigenvectors in the LV free wall were found to
average 7.9°, with a standard deviation of 1.2°, suggesting
that the fibers tend to run in planes roughly parallel to the
epicardium. The average value obtained here compares well with
previously reported values of this angle, namely, 7.3 ± 0.9° in
bovine myocardium and 4.64 ± 0.76° in canine myocardium (39, 41).
Eigenvectors and laminar structure.
As with the primary eigenvector, there is a systematic pattern to the
orientations of the secondary and tertiary eigenvectors. Figure 6 shows the eigenvectors computed at
endocardial (A), midwall (B), and epicardial
(C) locations in the LV free wall.
To aid orientation, the longitudinal (i.e.,
apical-basal)-circumferential plane is shaded. The transmural rotation
of the primary eigenvector as it follows the rotation of the myofibers
is evident. The secondary eigenvector at each location points
predominantly in the transmural direction. Thus the primary and
secondary eigenvectors form a sheet that is nearly horizontal at the
midwall and warped in opposite directions at the endocardial and
epicardial surfaces. The tertiary eigenvector is the local normal to
this sheet. Figure 6D shows a cartoon
representation of a sheet, with primary, secondary, and tertiary
eigenvectors represented by single, double, and triple arrowheads,
respectively.
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Fig. 6.
Orientation of eigenvectors at 3 transmural locations in LV free wall
of 1 heart. Primary eigenvector points along fiber direction. Its
rotation from oblique with positive inclination angle (endocardial;
A), to horizontal (midwall;
B), to oblique with negative
inclination angle (epicardial; C) is
evident. Rather than being randomly oriented from voxel to voxel, the
secondary and tertiary eigenvectors have systematic orientations as
well. The secondary eigenvector is found to consistently point in the
transmural (radial) direction, whereas the tertiary eigenvector is
found to lie, along with the primary eigenvector, in a plane roughly
parallel to the epicardial tangent plane (shaded plane).
D: cartoon representation of a sheet
formed by the primary (single arrowhead) and secondary (double
arrowhead) eigenvectors. The tertiary eigenvector (triple arrowhead) is
everywhere normal to the sheet.
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This systematic variation of the eigenvectors appears to be quite
consistent throughout the slice. The left panel of Fig. 7 is a color map of the
inclination angle of the tertiary eigenvector, and the middle panel is
an interpolated version of this raw data. The inclination angle of the
sheet normal rotates from being roughly horizontal at the epicardial
surface, to vertical near the midwall, and back toward the horizontal
near the endocardium. The apparent sheet structure formed by the
eigenvectors is consistent with anatomic laminae recently described by
LeGrice et al. (23) in the canine ventricles. For comparison, the
interpolated inclination angles of the normals to the laminae
determined by LeGrice et al. in canine ventricle are shown for a
transverse slice in the right panel of Fig. 7. The qualitative
correlation between the inclination angles of the tertiary eigenvector
and laminae normals is striking, despite not only being from different
hearts but also different species. We also note that near the junctions
of the RV and LV, there appears to be an increased variance in
neighboring inclination angles: they appear to vary less smoothly. This
is especially evident in the unsmoothed mapping (Fig. 7,
left). Regions such as this were
evident in each of the heart slices studied and appeared to be
correlated with regions in which transverse isotropy was approached.
Four of these hearts exhibited such variation in regions near the
intersection of the LV and RV, whereas one other exhibited it in the LV
free wall. For the remaining two hearts, a clear pattern was not
evident.
View larger version (36K):
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|
Fig. 7.
Left: map of inclination angles (see
Fig. 2) of the tertiary eigenvector for a horizontal section of a
perfused rabbit heart. Middle: map at
left smoothed with a median filter.
Right: horizontal section from a
histological reconstruction of a canine heart accomplished by LeGrice
et al. (23) showing interpolated inclination angles of normals to the
laminae they describe.
|
|
| |
DISCUSSION |
Fiber orientation.
Previous studies have observed qualitative agreement of diffusion
anisotropy with fiber orientation in the heart (11, 34), skeletal
muscle (3, 6, 46), and other tissues (7, 9, 19, 27, 33, 49). In a
recent study, quantitative agreement was shown between the principal
eigenvector and the orientation of the long axis of myofibers in an
excised slab of the RV of a rabbit (15). The results reported here
extend that study by showing quantitative agreement in the LV in
perfused hearts, arguably a situation somewhat closer to the in vivo
case. Furthermore, the results appear to hold both for spin-echo
imaging and for fast spin-echo imaging, a technique that provided an
eightfold reduction in imaging time. The good quantitative
correspondence between the inclination angle of the principal
eigenvector and that of the fiber suggested by Fig. 5,
A and
B, is echoed by the statistical tests.
The correlation coefficients for the comparison of histology and
spin-echo DTMRI were exceptionally good for biologic data, with an
average of 0.95. Those for the comparison of the fast spin-echo DTMRI
and histology inclination angles were somewhat lower, with an average
of 0.86, which is still quite good for biologic data. These results
suggest that the shapes of the curves for inclination angle versus
transmural depth obtained by both DTMRI and histology are similar.
However, this excellent correlation does not imply that at each voxel
the inclination angles are close; indeed, adding a constant to each
DTMRI angle estimate will not change the correlation, and scaling the
DTMRI data by some constant factor will not change the correlation.
However, the similar means of these curves suggest that no significant
lead or lag exists between the transmural sequence of inclination
angles derived from DTMRI or histology. Furthermore, the similar
standard deviations imply that a scaling bias was not present. The mean
voxel errors of 12° for the DTMRI estimates also imply good
correspondence at each voxel; indeed, it would be difficult to achieve
an average voxel error smaller than this, because it approaches our
histology measurement uncertainty of 10°, similar to what others
have achieved (40). In addition, the distributions of voxel differences
in DTMRI and histology angles had means that were both near zero, implying negligible systematic differences between the measurement methods. Although the distribution mean for that of the differences between spin echo and histology estimates is significant, it is nevertheless small. This small mean difference could be caused by a
number of factors, with the most likely being tissue shrinkage and
distortion during histological processing or small errors in alignment
of the DTMRI and histology sample sites. We note, finally, that the
average transmural gradient of inclination angle in each of the hearts
of 1.1 ± 0.1° and 1.6 ± 0.3° per percent transmural
depth is consistent with values of 1.4 ± 0.4° (39) and 1 ± 0.3° per percent transmural depth (34) reported
elsewhere. In summary, DTMRI performed in perfused,
nonbeating hearts appears to be able to provide fiber orientation data
very much in agreement with data obtained from traditional histological methods.
The histological verification of fiber orientation extraction using
DTMRI was attempted at high resolution, comparing inclination angles in
156 µm × 312 µm × 2-mm voxels with histological
measurements at what were intended to be the same locations. Evidence
that accurate alignment of the histological and DTMRI sample sites was
achieved is shown in Table 3. Here, the correlation between the
inclination angles calculated using fast spin-echo DTMRI at site 1 with the inclination angles
obtained from histology at each of the other sites is reported. As
increasingly distant sites are compared, there is a loss of
correlation, providing evidence that the sample locations were indeed
close and that the correlations reported here are not merely trivial.
Also, the fall in the correlation coefficients for sites >1 mm away
is consistent with our estimated alignment uncertainty of 1 mm in the
image plane.
Anisotropy.
The eigenvalue and eigenvector DTMRI estimates reported here extend
those of earlier studies, showing for the first time quantitative correspondence between the primary eigenvectors and local fiber orientation in perfused, nonbeating hearts. In accordance with a
previous study in the perfused heart (11), the primary eigenvalue estimates obtained here show that water diffusion approaches that of
free water along the fiber axis. Although the reported primary eigenvalues of Garrido et al. (11) for a population of voxels in the
rat midwall of 3.29 (±0.57 SD) is larger than ours, this difference
may be attributed to the higher experimental temperature of 37°C.
At higher temperatures, the maximum rate of diffusion, and thus the
primary eigenvalues, representing least restricted diffusion, will be
greater. Our results are also consistent with previously reported
findings in the myocardium (11, 34) of a preferential direction of
diffusion orthogonal to the fiber axis, with the secondary and tertiary
eigenvalues typically quite different throughout much of the myocardium.
Laminar structure.
Although others have observed that the secondary and tertiary
eigenvalues are significantly different in much of the myocardium, no
mention has been made of the systematic orientations of their corresponding eigenvectors. The hearts we have imaged have exhibited a
nonrandom, systematic variation of the secondary and tertiary eigenvectors, as well as that of the primary, throughout much of the
myocardium. The primary eigenvectors follow the local fiber orientation, and the additional finding that the secondary and tertiary
eigenvectors are also nonrandomly oriented suggests a further level of
anatomic organization, such as fiber bundles or laminae, to which they
may be linked.
The existence of myocardial laminae or fiber bundles, separable by
distinct anatomic cleavage planes, has been a controversial subject for
years and remains so today (23, 39, 41). Earlier studies purporting to
find myocardial cleavage planes separating laminae or bundles of
myocytes (26, 35) have later been dismissed by some as resulting from
dissection artifact (25, 39), and several recent authors have
reasserted the view of the myocardium as a continuous three-dimensional
syncytium of cells (10, 39, 42). LeGrice et al. (23), however, have
recently challenged this idea with their comprehensive, detailed
measurements of canine ventricular macrostructure and microstructure.
They have reported that the myofibers are arranged into distinct
myocardial laminae, about four myocytes thick, separated from adjacent
laminae by the extracellular collagen network. The myocytes are tightly
coupled within the laminae but sparsely coupled between adjacent
laminae. The planes of the laminae are defined locally by the long axis of the myofibers and the transmural direction. Thus the laminae are
approximately radially oriented, nearly horizontal at the midwall, and
pitched about the radial axis in opposite directions near the
myocardial surfaces. Figure 12 in LeGrice et al. (23) is a cartoon
depiction of this laminar architecture. LeGrice et al.
cite a number of studies that support their view of the existence of
laminae, but the possibility still remains that the apparent cleavage
planes were introduced artifactually because of the fixation and
processing of the tissue.
In our perfused hearts, the voxel primary eigenvector (directed along
the fiber long axis) and the secondary eigenvectors (directed
predominately radially) form planes, which vary continuously in
orientation as the fiber orientation changes across the wall; the
planes are nearly horizontal at midwall and then pitch about the radial
axis in opposite directions as the myocardial surfaces are approached.
Together, the planes form a radial sheet qualitatively similar in
morphology to the laminae described by LeGrice et al. (compare our Fig.
6D with Fig. 12 in Ref. 23). Indeed,
Fig. 7 shows a qualitative correspondence between the inclination
angles of the normals to the anatomically defined sheets, taken from the quantitative reconstruction of LeGrice et al. (Fig. 7,
right), and the DTMRI estimates of
the tertiary eigenvector, which is normal to the plane formed by the
primary and secondary [Fig. 7,
left (raw) and
middle (smoothed)]. In both
cases, the normals are nearly vertical at the midwall and rotate in
opposite directions as the myocardial surfaces are approached. We have
seen this qualitative behavior of the secondary and tertiary
eigenvalues in all seven hearts studied.
The structure of the laminae as described by LeGrice et al. (23) could
account for the consistent orientation of the secondary and tertiary
eigenvectors in at least three ways. To see this, first note that a
decreased diffusivity implies that water molecules encounter barriers
that prohibit them from attaining their mean free path, the average
distance a water molecule would diffuse without restriction. This path
length, x, can be found from
Einstein's equation, x = (2 · D · T)1/2,
where D is the unrestricted
diffusivity and T is the diffusion time. For our studies, the mean path length was about 8 µm,
approximately the radius of a myocyte, much less than the typical
myocyte length of 100 µm. The finding that water diffusion is
greatest along the fiber direction, but still less than that of free
water, implies that there are some barriers that restrict diffusion in
this direction. These barriers are probably subcellular structures
(organelles, structural proteins, myofilaments, etc.), rather than the
membranes at the ends of the cell, because the mean free path is so
much less than the cell length. The even more attenuated diffusion in
the cross-fiber directions implies further restrictions. Here, the mean
free path is similar to the radius of the cell, and therefore the
cellular membrane may play a role in restriction. Greater cell-to-cell
coupling within laminae and extensive branching of cells within laminae
as found by LeGrice et al. (23) may mitigate membrane restriction
relative to the direction normal to the laminae. As a result, the most
attenuated diffusion would be normal to the laminae.
A second way that the architecture described by LeGrice et al. (23)
could explain our findings can be seen by considering extracellular
water in the spaces between the laminae. It may be that water molecules
attempting to diffuse in the direction normal to the laminae would
encounter the lamellar surface, attenuating diffusion in this
direction. Conversely, diffusion between and parallel to the laminae
would be unrestricted. Thus one would expect to see the tertiary
eigenvectors, representing the most restricted diffusion, oriented
normal to the laminae, with the secondary and primary eigenvectors
lying within the local plane of the laminae. However, the surfaces of
the laminae would be a significant barrier to extracellular water
diffusion only if their spacing approached that of the diffusion mean
free path length of water under the conditions of our experiments.
LeGrice et al. do not report measurements of the separations between
laminae, although their depictions of processed specimens indicate that separations of approximately two or three times the free path length
are not uncommon. However, as LeGrice et al. point out, processing accentuates these separations. In addition, extracellular matrix fibers may further reduce the effective separations between laminae and thus provide a physical basis for the apparent restriction of diffusion.
A third possibility, not dependent on laminar architecture, is that
perfusion of water within the vascular system is the cause of
preferential radial diffusion in the cross-fiber plane. Large vessels
penetrate the epicardium and dive radially through the wall as they
course toward the endocardium, giving off capillaries that run parallel
to the fibers (18, 23). It is possible that water flowing in these
large vessels could produce an apparent increased diffusivity in the
radial direction, resulting in the observed cross-fiber anisotropy and
sheet structure. However, because the voxels are small, it is unlikely
that all or even the majority would contain a section of these large
vessels. This is inconsistent with the observations that most voxels
show a significant anisotropy normal to the fiber, and the sheet
structure appears to vary smoothly over most of the voxels (e.g., see
Fig. 7, left). Clearly, however, a
quantitative validation of the correspondence between the sheet
structure obtained from DTMRI and the laminar architecture found using
histological methods should be a goal of future studies.
The existence of a hierarchical structure for the myocardium, with the
extracellular fibers matrix separating laminae or bundles of highly
connected myocytes, would have a number of important implications, as
LeGrice et al. (23) point out. The variations in cellular coupling
between laminae could give rise to a preferential direction of
conduction orthogonal to the maximal conduction that occurs along the
fiber axis (17). Inclusion of this information in three-dimensional
models of cardiac depolarization, which currently assume equal
conductivity in all directions orthogonal to the fiber axis, could
improve their accuracy; there is already some evidence to this effect
(12). The existence of laminae and a hierarchically organized
extracellular connective tissue matrix would also impact our current
understanding of cardiac mechanics. The matrix itself is well known to
be an important determinant of ventricular mechanical properties, and
the laminar muscular organization it imparts may be important in the
normal changes in transmural thickness that occur during the cardiac
cycle (24) and in the wall thinning that occurs after myocardial
infarction (30). Furthermore, the extracellular skeleton appears to be remodeled in a number of important disease states (22, 37, 45, 48),
leading to impaired mechanical function and increased risk of abnormal
electrical behavior. DTMRI measurements of myocardial microstructure
may thus enable the creation of more anatomically based electrical and
mechanical models of the ventricles and aid in understanding the
anatomic changes that occur in some disease states.
In the future, in vivo imaging of microstructure using DTMRI could
potentially provide a noninvasive means of clinical cardiac assessment.
Diffusion MRI is now becoming widely used in hospitals to detect
cerebrovascular ischemia earlier than was previously possible.
Recent work in the isolated rabbit heart has verified that myocardial
ischemia results in a reduction of tissue diffusivity, although
with a different time course than in the brain (16). DTMRI may be
clinically useful in locating areas of fiber disarray that occur in
some disease states, such as after myocardial infarctions and in
hypertrophic cardiomyopathy. This may be of use in determining the
extent of disease or in following over time the development of
myocardial maladaptation or its remission by various therapies. However, it is unlikely that in vivo studies could be carried out at
very high resolution, because of both the necessary imaging time and,
more formidably, the motion of the heart. Even with very precise
gating, it is unlikely that a given voxel will correspond to the same
region of the heart in the multiple images required for the analysis,
although there are techniques that may improve correspondence (31). The
degree of resolution that would afford useful in vivo studies is not
currently known.
In the results presented here, image slices have come from near the
base of the ventricles. An immediate goal is to reconstruct the fibrous
architecture of the entire ventricles of a heart. This presents no
theoretical difficulty, only practical ones. As the apex is approached,
the curvature of the ventricle increases. If the slice thickness used
in this study (2 mm in the apical-basal direction) were used for slices
near the apex, two problems would arise. First, the large surface
curvature would result in significant partial voluming (a possibly
large fraction of each voxel would contain signal from the perfusate
surrounding the heart, rather than the myocardium). The isotropic
diffusion of the perfusate would tend to bias the diffusion tensor
estimates for these voxels. Second, a 2-mm slice thickness would likely
not be able to capture the rapidly changing orientations in this
region. To circumvent these problems, thinner slices will be necessary,
with the corresponding cost of increased imaging time to maintain the
same amount of signal to achieve similar precision. For example, a
halving of the slice thickness will require a doubling of the imaging
time to maintain the same signal intensity. Fast imaging techniques, such as the fast spin-echo sequence used here, will be necessary to
make this practical.
| |
ACKNOWLEDGEMENTS |
The help of Rong Xue in preparation of the perfusion experiments
was greatly appreciated, as was the assistance of Prasad Gharpure and
Jiangyang Zhang in manipulation of the MRI data files. We also thank
Scott Reeder and Ed Hsu for useful suggestions in the development of
the fast spin-echo pulse sequence, and Missy Leppo was instrumental in
the histological processing of the specimens.
| |
FOOTNOTES |
This work was funded by National Heart, Lung, and Blood Institute Grant
R01-HL-60133-01 and Physiome Sciences, Incorporated (to R. Winslow) and
the Whitaker Foundation (to R. Winslow and J. Forder). D. F. Scollan is
supported by a Medical Scientist Training Program fellowship.
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests: D. F. Scollan, 410 Traylor Bldg., 720 Rutland Ave., Johns Hopkins Univ. School of Medicine, Baltimore, MD
21205-2195.
Received 10 February 1998; accepted in final form 31 August 1998.
| |
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Abstract
Introduction
