Vol. 276, Issue 2, H595-H607, February 1999
Laminar fiber architecture and three-dimensional systolic
mechanics in canine ventricular myocardium
Kevin D.
Costa1,
Yasuo
Takayama2,
Andrew D.
McCulloch3, and
James W.
Covell4
1 Department of Biomedical
Engineering, Washington University, St. Louis, Missouri 63110;
2 Department of Internal Medicine,
Kansai Medical University, Kyoto, Japan; and Departments of
3 Bioengineering and
4 Medicine, University of
California, San Diego, La Jolla, California 92093
 |
ABSTRACT |
Previous studies suggest that the laminar
architecture of left ventricular myocardium may be critical for normal
ventricular mechanics. However, systolic three-dimensional deformation
of the laminae has never been measured. Therefore, end-systolic finite strains relative to end diastole, from biplane radiography of transmural markers near the apex and base of the anesthetized open-chest canine anterior left ventricular free wall
(n = 6), were referred to
three-dimensional laminar microstructural axes reconstructed from
histology. Whereas fiber shortening was uniform [
0.07 ± 0.04 (SD)], radial wall thickening increased from base (0.10 ± 0.09) to apex (0.14 ± 0.13). Extension of the laminae transverse to the muscle fibers also increased from base (0.08 ± 0.07) to apex (0.11 ± 0.08), and interlaminar shear changed sign
[0.05 ± 0.07 (base) and 0.07 ± 0.09 (apex)],
reflecting variations in laminar architecture. Nevertheless, the apex
and base were similar in that at each site laminar extension and shear contributed ~60 and 40%, respectively, of mean transmural
thickening. Kinematic considerations suggest that these dual
wall-thickening mechanisms may have distinct ultrastructural origins.
cleavage planes; cardiac mechanics; finite strain; wall thickening; regional
| |
INTRODUCTION |
MORPHOLOGICAL STUDIES of ventricular myocardium reveal
a syncytium of myocytes organized into branching laminar
"sheets," which are approximately four cells thick and roughly
stacked from apex to base (19, 34). A network of extracellular collagen fibers appears to provide tight coupling of myocytes within the sheet
and looser coupling between adjacent sheets (5, 19). Potential spaces
between the laminae give rise to "cleavage planes" in long- and
short-axis sections of the mammalian heart (11, 16, 18, 35), and these
exhibit substantial transmural and regional variations in orientation
(19, 20).
The functional significance of this laminar architecture is not well
understood. However, recent work from this laboratory by LeGrice and
co-workers (20) indicates that a primary role may be to allow
rearrangement of myofiber bundles by sliding along cleavage planes
during the cardiac cycle. This may arise from reorientation of cleavage
planes toward the radial direction with increased wall thickness, as
observed in contracted (11, 18) and passively unloaded (35) ventricles.
Such rearrangement is also consistent with an increased number of
myocytes spanning the ventricular wall thickness (17, 35) and with
transverse shear deformations measured in dogs (10, 29, 39, 40) and humans (4, 43) during systole. LeGrice and co-workers also showed that
reorientation of longitudinal-radial (i.e., long-axis) cleavage planes
due to transverse shear could account for the majority of end-systolic
wall-thickening strain in the inner one-third of the canine midanterior
left ventricular (LV) free wall and septum. However, the source of the
remaining thickening in the subendocardium and outer two-thirds of the
LV wall and the role of circumferential-radial (i.e., short-axis)
cleavage planes and transverse shears were not explained.
Systolic radial thickening is of particular interest as a functional
measure because of its significant contribution to stroke volume (8,
15) and its sensitivity to local changes in perfusion (13) and
metabolism (31). Although myofiber contraction is the basis of
ventricular function, several studies point out that the increase in
myocyte diameter due to fiber shortening accounts for only a small
fraction of systolic wall thickening (20, 32, 35). Furthermore, whereas
fiber shortening is similar at the epicardium and endocardium (21, 32,
40) and also from apex to base (32), local wall thickening increases
significantly from subepicardium to subendocardium (14, 32, 33, 40) and
may also be greater at the apex and midventricle than at the base (3,
32, 38). In fact, Rademakers and co-workers (32), using magnetic
resonance image (MRI) tagging in the closed-chest dog, showed no
correlation between fiber strain and wall thickening. On the other
hand, they found a significant correlation between regional thickening
and endocardial cross-fiber shortening. Rearrangement of laminar
myocardium has also been suggested to explain the paradoxically large
cross-fiber shortening (21, 32, 40), but the specific mechanisms remain unclear.
To fully comprehend the functional role of laminar myocardium, an
analysis of the three-dimensional (3-D) mechanics of the laminae is
required. However, no studies have actually measured systolic
deformations of myocardial laminae. We hypothesize that, in addition to
sliding of adjacent sheets due to interlaminar shear, sheets of
myocardium are dynamic structures that deform (i.e., extend
and/or shorten) during systole and that both mechanisms are
important for normal regional ventricular function. Measurements of
transmural end-systolic finite strains were referred to 3-D sheet
microstructural axes reconstructed from histology near the apex and
base of the canine anterior LV free wall. These two regions have
distinct cleavage-plane anatomy (19) and differences in wall thickening
(3, 32) but similar in-plane mechanics in terms of principal strain (2)
and fiber shortening (32) and thus provide a unique opportunity to test
our hypothesis. The findings revealed that the transverse shear
associated with reorientation of sheets around the local fiber axis, as
opposed to reorientation of long- or short-axis cleavage planes,
contributes to LV wall thickening and cross-fiber shortening strains.
In addition, we found substantial laminar extension transverse to the
muscle fibers that varied transmurally and regionally and was the
dominant source of radial thickening across the wall, which has not
previously been shown. Kinematic considerations suggest that sheet
extension and shear may have distinct ultrastructural origins
critically dependent on the hierarchical organization of the collagen
extracellular matrix.
| |
METHODS |
All animal studies were performed according to National Institutes of
Health guidelines for the care and use of laboratory animals in
research. All protocols were approved by the Animal Subjects Committee
of the University of California, San Diego, which is accredited by the
American Association for Accreditation of Laboratory Animal Care.
Surgical preparation.
Six adult mongrel dogs (19-27 kg) were anesthetized to a surgical
plane with pentobarbital sodium (25 mg/kg, with additional 50-100
mg/h), intubated, and ventilated with room air. The heart was exposed
via median sternotomy and left fourth intercostal space thoracotomy and
suspended in a pericardial cradle. A limb-lead electrocardiogram (ECG)
was continuously recorded. Aortic pressure was monitored with a
fluid-filled 120-cm 7-F pigtail catheter inserted into the right
femoral artery and connected to a gauge (model P23XL,
Spectramed-Statham). LV pressure was recorded with a micromanometer
(model P6, Konigsberg) inserted through a stab wound in the apex, and
the recorded pressure was matched with that from the pigtail catheter
advanced into the LV.
To measure 3-D myocardial deformation in each heart, the LV long axis
was defined using 1.6-mm-diameter lead beads sutured to the epicardium
at the origin of the left main coronary artery and the apical dimple.
Marker implantation sites were selected approximately one-fourth (basal
site) and three-fourths (apical site) of the distance from base to apex
measured along the LV long axis in a region midway between the left
anterior papillary muscle and the anterior interventricular sulcus
(Fig.
1A).
Each marker array, or "bead set," consisted of three transmural
columns of four to six 1-mm-diameter gold beads implanted using a
stainless steel trocar, as described previously (39), with a 1.6-mm
lead marker sewn to the epicardium above each column. For each of the two bead sets, the three epicardial surface markers and two long-axis markers were used to define a system of local "cardiac
coordinates" {X1, X2, X3}
aligned with the circumferential, longitudinal, and radial axes of
the LV wall (25), respectively, as determined separately at the basal
and apical measurement sites. Because these coordinate systems are
defined by the local epicardial-tangent plane, curvature of the LV wall
is accounted for.
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Fig. 1.
Method for defining fiber-sheet coordinate system.
A: epicardial markers used to define
cardiac coordinates aligned with local circumferential
(X1),
longitudinal
(X2), and
radial (X3)
axes of left ventricle (LV) at apical and basal measurement sites.
B: excised block of tissue containing
bead set and used to measure transmural laminar morphology. Fiber angle
( ) is measured from serial sections cut parallel to (1-2) plane.
Cleavage-plane angles ( ' and  ) are measured from
transverse sections (dashed lines) cut parallel to (2-3) and (1-3)
planes, respectively. C: at a given
transmural depth, measured angles are used to compute sheet angle
(), which together with defines local "fiber-sheet
coordinates" consisting of fiber axis
(Xf), sheet
axis perpendicular to
Xf within sheet
plane (Xs), and
axis normal to sheet plane
(Xn).
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Experimental protocol.
The animal was positioned in a biplane X-ray system with image planes
adjusted so all radiopaque markers were visible in both views.
End-diastolic pressure was adjusted to 8-10 mmHg by inferior vena
cava occlusion or infusion of warm saline via a catheter in the right
femoral vein as needed. With the respirator turned off at end
expiration, biplane images were recorded for several heartbeats using
high-speed asynchronous cineradiography (16-mm film, 120 frames/s).
During each run, ECG, aortic pressure, LV pressure, and camera shutter
pulses were recorded on an eight-channel chart recorder
(Brush-Clevelite, model 2000, Gould). At the end of the experiment,
snares were placed around lung hila and inflow and outflow vessels from
the heart. An overdose of pentobarbital sodium was administered, and
the heart was brought to anoxic arrest by tightening the ligatures
around the inflow vessels. Pressure in the LV was adjusted to 8-10
mmHg by injection of saline into the LV cavity, the right ventricle was
vented, and the heart was fixed by retrograde aortic perfusion with
buffered glutaraldehyde (2.5%) (41). The heart was excised and stored
in 10% buffered Formalin for 24-48 h. Finally, with the positions
of the X-ray tubes and image intensifiers unchanged, a geometric
phantom was recorded and later used to compute perspective
transformations so that 3-D coordinates of myocardial markers could be
reconstructed from the biplane images (22).
Histology.
To avoid the distortional effects of dehydration and shrinkage
associated with embedding, histological measurements were obtained using freshly fixed heart tissue. The initial gross-sectioning procedure followed that of LeGrice et al. (20). A transmural rectangular block of tissue containing the implanted marker columns was
carefully removed from the ventricular wall at the apical and basal
measurement sites, with the edges of the block cut parallel to the
local circumferential, longitudinal, and radial axes of the LV as
determined from the same epicardial markers used for the strain
analysis. The transmural thickness of the block was measured. With a
Plexiglas template to guide the blade, two 1-mm-thick transmural slices
were cut from the block: one parallel to the longitudinal-radial (2-3)
surface and one parallel to the circumferential-radial (1-3) surface
(Fig. 1B). These thick slices, which
revealed laminar tissue structures separated by gaps, or cleavage
planes, were further sectioned for quantitative histology,
as described below.
To measure transmural variations in the orientation of laminar
structures in the longitudinal-radial plane, the 1-mm thick transmural
slice from the (2-3) surface was mounted on an anodized aluminum block
with a cyanoacrylate-based specimen adhesive. The aluminum block was
secured in the specimen vice of a vibrating microtome (Vibratome 1000, Technical Products International), and transmural sections 50-100
µm thick were obtained with high-amplitude, slow-advance settings
with use of a single-edge Teflon-coated razor blade held at a
presentation angle of 20°. The specimen was carefully transferred
to a glass slide and allowed to dry partially at room temperature for
~20 min. With use of a video camera (model DXC-151, Sony) mounted on
a light microscope (Optiphot-2, Nikon), video images of the tissue
section at low-power (×30) magnification were acquired onto a
microcomputer (Macintosh Quadra 900, Apple) with image-processing
software (NIH Image 1.47), yielding an image resolution of 78 pixels/mm
in the transmural direction. The dimensions of the wall thickness
generally exceeded the field of view, so two separate images of each
tissue section were acquired. The software allowed accurate
registration and combination of the two images. Myocardial laminae and
the cleavage planes separating them were visible with no further
enhancement of the digital montage (Fig.
2). At each 1-mm increment across the wall
thickness from epicardium to endocardium (including the trabeculate
layer), a mean cleavage-plane orientation (') was calculated
from five angle measurements on the image within a 1.5-mm band along
one edge of the tissue section; an angle of 0° was defined as
parallel to the
X3 axis, and a
counterclockwise rotation was represented by a positive angle. The
process was repeated using the 1-mm-thick transmural tissue slice from
the (1-3) plane to obtain the transmural distribution of the
circumferential-radial cleavage-plane angle () along the
adjacent edge of the tissue section (Fig.
1B).
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Fig. 2.
Images of laminar cleavage planes in longitudinal-radial
(A) and circumferential-radial
(B) tissue sections from basal and
apical measurement sites in anterior LV free wall. Each image is a
montage of 2 video micrographs acquired under ×30 magnification.
Orientation of specimen is indicated by cardiac coordinate axes
X1,
X2, and
X3, with
endocardium to left and epicardium to
right. Study
AF3; LV pressure during fixation, 8 mmHg; section
thickness, 50 µm; scale bar, 1 mm.
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The remainder of the original transmural block of tissue was sliced
into 1-mm-thick sections parallel to the circumferential-longitudinal (1-2) plane, forming a series from epicardium to endocardium used to
measure the fiber-angle variation through the wall. Digitized video
micrographs of each section were acquired as described above but under
reflected light from an external source. The angle between the local
muscle fiber axis and the circumferential edge of the tissue section
was measured at nine sites on each image in the corner of the tissue
section, and the mean fiber angle () was calculated at each
transmural depth. The
X1 axis
represented 0°, with a positive fiber angle representing a
counterclockwise rotation. By making measurements along a single edge
of the tissue block (Fig. 1B),
corresponding fiber- and cleavage-plane angle data at a given depth
represented the laminar architecture in ~5
mm3 of myocardium, sampled from
the same region where strains were measured.
Strain analysis.
Data from a single heartbeat were selected for each animal so that
end-diastolic pressure closely matched (within about ±1 mmHg) LV
pressure during perfusion fixation of the heart. At each apical and
basal measurement site, 3-D coordinates of the implanted markers in
their end-diastolic and end-systolic configurations were computed from
biplane X-ray images of the two-dimensional bead projections (22). End
diastole and end systole were defined by the X-ray frames closest in
time to the peak of the R wave of the ECG and the nadir of the dicrotic
notch in the aortic pressure signal, respectively. With the 3-D marker
coordinates at each site, a least-squares quadratic finite-element
analysis was used to compute continuous transmural distributions of 3-D
Lagrangian finite strains (7, 24), which describe the myocardial
deformation at end systole with respect to an undeformed reference
state defined to be end diastole. In cardiac coordinates
{X1, X2, X3},
the three normal strain components measure myocardial stretch or
shortening along the circumferential
(E11),
longitudinal
(E22), and
radial (E33)
cardiac axes. The three shear strains
(E12,
E13, and
E23) represent
angle changes between pairs of the initially orthogonal coordinate
axes. The strains were interpolated along the centroid of the deformed
finite element at 10% increments of relative wall depth from the
epicardium at each measurement site, and strains were not extrapolated
beyond the depth of the most subendocardial beads.
The following model of the 3-D laminar architecture of ventricular
myocardium has been described in detail elsewhere (7, 19, 20). To
investigate the kinematic consequences of assuming this architecture,
end-systolic strains at a given point in the LV wall were related to
the local 3-D structural axes of the myocardial laminae. This was
accomplished using a previously described method (7) to construct a
system of local "fiber-sheet coordinates" {Xf, Xs, Xn}
defining the muscle fiber axis
(Xf), the sheet
axis (Xs),
which lies within the sheet plane and is perpendicular to Xf, and the
orthogonal Xn
axis oriented normal to the sheet plane (Fig.
1C). Briefly, a continuous
transmural fiber-angle distribution was obtained from a linear
least-squares fit to the measured fiber angles (). Then each
cleavage-plane angle measurement (' and ), together
with interpolated at a matching wall depth, was used compute a
sheet angle () at that depth from one of the following equations
|
(1a)
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|
(1b)
|
resulting
in two separate distributions of . The final transmural distribution
of was estimated from a weighted quadratic least-squares fit to the
two sets of data obtained from Eq. 1, a and
b, with residuals weighted by the sine
or cosine of to account for the effect of the fiber orientation on
the theoretical accuracy of the cleavage-plane angle measurement (7).
With values of and at a given depth obtained from the fitted
transmural distributions, 3-D end-systolic strains
(E) were transformed from cardiac
coordinates to fiber-sheet coordinates by using the following equation
(12)
|
(2)
|
where
MT is the
transpose of the 3 × 3 coordinate transformation matrix given by
M = [cos ,
sin , 0; sin sin ,
cos sin , cos ;
sin cos ,
cos cos , sin ]. The
resulting "fiber-sheet strains" include stretch or shortening along the fiber
(Eff), sheet
(Ess), and
normal (Enn)
directions and the three shear strains
(Efs,
Efn, and
Esn,
respectively). Whereas
Efs describes
shearing within the sheet plane, the other two shear strains may arise
from a relative sliding of adjacent myocardial laminae parallel to the
fiber axis
(Efn) or
transverse to the fiber axis
(Esn). It
follows that Ssheet = 
represents shear in the direction of maximum interlaminar sliding. The
overall maximum shear strain
(Smax) at any point equals
one-half of the difference between the maximum and minimum principal
strains (12). Comparison of Ssheet
and Smax allows assessment of the contribution of interlaminar sliding to overall systolic shear strain.
Contributions of fiber-sheet strain to wall thickening.
To examine the contributions of laminar deformation to systolic cardiac
strains, the components of
E(cardiac) may be
solved in terms of E(fiber
sheet) by inverting Eq. 2. In general, all six sheet strain components and the
fiber and sheet angle may be involved in these relations. However, as
the following equation reveals
|
(3)
|
the
radial wall-thickening strain
(E33) depends
only on and the fiber-sheet components of strain in the
(Xs, Xn)
plane perpendicular to the local fiber axis, namely
Ess,
Enn, and
Esn. The
contribution of each term on the right-hand side of
Eq. 3 is investigated to assess the
fiber-sheet strain determinants of systolic wall thickening.
Statistical analysis.
Values are means ± SD unless otherwise specified. The effects of
region (apex vs. base) and wall depth on each strain component were
determined by two-factor ANOVA. The two-tailed
t-test was used to compare each strain
component at each region with a hypothesized mean value of zero. The
effects of region and depth on the correlation between
Smax and
Ssheet were tested by two-way
analysis of covariance. Statistics were performed using SuperANOVA
version 1.11 and StatView version 4.01 software (both by Abacus
Concepts, Berkeley, CA). Statistical significance was accepted at
P < 0.05.
| |
RESULTS |
Mean hemodynamic parameters were as follows: heart rate 100 ± 11 beats/min, LV end-diastolic pressure 9 ± 2 mmHg, and LV
end-systolic pressure 117 ± 34 mmHg. Mean LV pressure during
glutaraldehyde fixation (9 ± 1 mmHg) was not significantly
different from end-diastolic pressure. Therefore, the fiber- and
cleavage-plane orientations measured in the fixed hearts were assumed
to represent accurately the laminar tissue structure in the
end-diastolic reference configuration. The basal and apical measurement
sites were located 23 ± 6 and 80 ± 11%, respectively, of the
distance from base to apex along the LV long axis, in a region of the
anterior LV free wall ~2-4 cm septal of the anterior papillary
muscle. Mean wall thickness was 12 ± 3 mm at the base and 10 ± 2 mm at the apex.
Fiber and sheet orientation.
Figure 3 illustrates the transmural
variations of the measured , ', and , which were
very consistent from heart to heart at a given site but showed
considerable regional variation from apex to base. At both sites, spanned an ~120° range from epicardium to endocardium (Fig. 3,
A and B,
top), but the distribution was more symmetrical at
the base, where circumferential fibers ( = 0°) were located near
midwall compared with ~20% depth at the apex. The orientation of
(2-3) cleavage planes (') at the apex decreased from nearly
radial (' = 0°) at the epicardium to nearly longitudinal
(' = 90°) at the endocardium, whereas ' at
the base increased from about 45° at the epicardium to
45° in the midwall and endocardium (Fig. 3,
A and B,
middle). The opposite orientation of (2-3) cleavage
planes between apex and base is clearly illustrated in Fig.
2A. The (1-3) angle ()
crossed 90° near midwall at the two sites but again had opposite
transmural gradients (Fig. 3, A and
B, bottom) corresponding to a
chevron pattern of the cleavage planes that fanned out from a
circumferential orientation and was oppositely oriented at the apex
compared with the base (Fig. 2B). In
three hearts at the base and one at the apex, an abrupt change in sheet
orientation at the compacta-trabeculata interface was indicated by a
rapid change in ' or near the inner one-fourth of
the wall. Such a transition is observed in Fig. 2B,
bottom.
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Fig. 3.
Measured distributions of , ', and vs. relative
wall depth from all hearts at apical
(A) and basal
(B) sites. Each point represents
average of several measurements at a given depth (,
n = 9; ' and ,
n = 5).
AF3-7 and
AF9, study designations; epi,
epicardium; endo, endocardium.
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Fitted sheet-angle distributions at the apex and base of each heart are
shown in Fig. 4. The average
root-mean-squared error in the fit to was 18.4 ± 8.2°,
which was comparable to the variability of cleavage-plane angle
measurements (~20°) and was not significantly improved by
increasing the order of the fitted polynomial from quadratic to cubic.
The sheet angle changed sign from negative at the apex to mainly
positive at the base, but the magnitude of ' did not usually
exceed 45° in either region, indicating that the 3-D orientation of
the myocardial sheet axis was predominantly radial.
Systolic strains in cardiac coordinates.
Mean end-systolic strains referred to cardiac coordinates are shown in
Fig. 5. Because not all bead sets spanned
the entire wall thickness, mean values at the subendocardial depths
were obtained from a reduced sample size. At the apex, mean
circumferential shortening strain
(E11) exceeded
longitudinal shortening
(E22), whereas
E11 and
E22 were
comparable at the base. At both regions, radial thickening
(E33) was
consistently the largest strain component in magnitude and gradient.
The torsional shear strain
(E12) was uniform and positive. The circumferential-radial transverse shear strain (E13)
changed sign from apex to base. The mean longitudinal-radial transverse
shear strain
(E23) was
negative at the epicardium and positive in the subendocardium at both
regions. All three cardiac shear strains were small (less than
±0.04) compared with the normal strain components, but only the
mean value of E23
at the base was not significantly different from zero
(P = 0.09).
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Fig. 5.
Cardiac strain transmural distributions of mean end-systolic finite
strains referred to local circumferential, longitudinal, and radial
coordinates (X1,
X2, and
X3),
respectively, at apical (A) and
basal (B) sites. Error bars, SD
(n = 6, except as noted). Note
different scales for shear and normal strains.
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All six cardiac strain components exhibited a significant effect of
region (base vs. apex), and all except
E12 and
E13 had a
significant wall depth effect. The only significant interaction between
region and depth was for
E11, which was
more uniform at the base than at the apex. There were no significant
effects of region or depth (P > 0.3)
on the determinant of the deformation gradient tensor
(detF), which averaged 0.95 ± 0.06 (data not shown), indicating a 5% overall mean loss in tissue
volume from end diastole to end systole.
Systolic strains in fiber-sheet coordinates.
Mean end-systolic strains referred to fiber-sheet coordinates are shown
in Fig. 6. Fiber strain
(Eff) was
significant (P < 0.0001) and
indicated a transmurally and regionally homogeneous 5-8% fiber
shortening during systole. Similarly, negative
Enn indicated
small but significant (P < 0.0005)
shortening normal to the fiber-sheet plane, possibly reflecting
thinning of the laminae. In contrast, the sheet strain
(Ess) was
positive and increased transmurally from zero at the epicardium,
indicating substantial (10-20%) extension of the sheet plane
transverse to the muscle fiber axis. Shear strain within the sheet
plane (Efs) was
not significantly different from zero at the apex or base (P > 0.25). A small negative
Efn at the apex
suggested some relative sliding of adjacent myocardial laminae parallel
to the fiber axis, but mean
Efn was not
significant at the base (P = 0.31).
Far greater sliding transverse to the fiber axis was indicated by the
dominant Esn
component, particularly in the inner one-half of the wall where the
magnitude of Esn
was ~0.10 at the base and 0.15 at the apex, similar to
Ess. Also, the
sign of Esn
changed from positive at the base to negative at the apex, similar to
. Statistically, only
Ess,
Esn, and
Efn differed in
magnitude from apex to base (all were greater at the apex), there were
no significant interactions between the effects of region and depth,
and the depth effect was not significant for
Eff
(P = 0.13) or
Efs
(P = 0.058).
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Fig. 6.
Fiber-sheet strain transmural distributions of mean end-systolic finite
strains referred to local fiber, sheet, and normal coordinates
(Xf,
Xs, and
Xn),
respectively, at apical (A) and
basal (B) sites. Note large sheet
extension (Ess)
and sheet-normal shear
(Esn), which
changes sign from apex to base. Same format as Fig. 5.
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Maximum end-systolic shear strain.
Ssheet and
Smax exhibited a significant
effect of depth (P = 0.0001),
increasing from epicardium to endocardium (data not shown). However,
the regional variation was not significant. Two-way analysis of
covariance revealed a strong dependence of
Smax on Ssheet
(P < 0.0001), with no significant
interaction of region (P = 0.077) or
depth (P = 0.9). Post hoc
regression by using data from both regions and all depths (Fig.
7) had a slope of 1.00 ± 0.05 (SE), a
small but significant intercept of 0.05 ± 0.005 (SE;
P < 0.0001), and a correlation
coefficient
(r2) of 0.81. The overall mean value of Ssheet
was 0.08 ± 0.06 (n = 109),
or ~60% of the overall mean value of
Smax (0.13 ± 0.07).
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Fig. 7.
Linear regression (solid line, with equation and correlation
coefficient) indicates strong dependence of overall maximum shear
strain (Smax) on maximum shear
between adjacent myocardial sheets
(Ssheet). Dashed line, unity
slope with zero intercept. Data from all depths at apical and basal
regions are represented (n = 109).
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Contributions of fiber-sheet strain to wall thickening.
Considering the shear term in Eq. 3,
positive values of
Esnsin cos act to increase
E33 and negative
values decrease
E33. Therefore,
because the sheet angle was in the range 90° < < 90°, Esn must
have the same sign as for
Esnsin cos to augment wall thickening. Figure 8
indicates that this was a consistent trend at the apex and base
[data labeled "midanterior" and "septum" were derived
from a previous study (20); see
DISCUSSION]. Data from the
apical region were concentrated in the quadrant where Esn and are
negative; basal data fell primarily in the quadrant where
Esn and are
positive. Linear regression indicated a significant correlation between
shear strain and (P < 0.0001, r2 = 0.47).
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Fig. 8.
Scatterplot of
Esn vs.
reconstructed from all depths at 4 regions of canine LV. Apex and
base data from present study; midanterior and septum data from LeGrice
et al. (20). Note globally consistent trend for
Esn and to
have same sign, and || < 45°.
|
|
To assess the contributions of fiber-sheet strains to systolic wall
thickening, the mean transmural distribution of each of the three terms
on the right-hand side of Eq. 3 was
plotted along with mean
E33 from the apex
and base (Fig. 9). At both sites the "Ennsin2"
term was nearly zero across the wall, whereas the
"Esscos2"
and
"2Esnsin cos "
terms increased strongly with depth and were nearly equivalent in the
inner one-half of the LV wall. Table 1
indicates the average transmural fractional contribution of the three
terms to E33. The
shear term accounted for almost one-half of the radial strain at the
apex and base. The remainder of
E33 was due
primarily to the sheet extension
(Ess) term,
indicating that stretching of myocardial laminae transverse to the
fiber axis is also an important mechanism for systolic wall thickening. These results were consistent between the apex and base despite regional differences in mean
E33
(P = 0.04).
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Fig. 9.
Average transmural distributions, at basal
(A) and apical
(B) sites, of 3 fiber-sheet terms
that contribute to radial thickening strain according to
E33 = Esscos2 + Ennsin2 + 2Esnsin cos .
Ess,
Enn, and
Esn, systolic
strains in sheet-normal transverse plane.
|
|
| |
DISCUSSION |
The objective of this study was to test the hypothesis that relative
sliding of adjacent sheets of myocardium and deformations along sheet
structural axes are each important mechanisms for normal regional
ventricular function. Measurements indicated laminar deformations that
have not previously been documented; these include sheet thinning and
substantial laminar extension transverse to the muscle fibers, which
varied transmurally and regionally. Also, there were large interlaminar
transverse shear strains that changed sign from base to apex. Sheet
extension and shear were the primary determinants of wall thickening
strain, and their relative contributions were regionally consistent
despite significant variations in radial thickening and laminar
architecture. The ultrastructural basis of these findings and their
functional implications are discussed below.
Fiber and sheet orientation.
Our fiber-angle measurements indicated circumferential fibers located
near midwall at the base but substantially closer to the epicardium
(~20% wall depth) at the apex. Although such a nonsymmetrical
transmural distribution of apical fiber orientation is not well
recognized, it is not entirely new. For example, although Streeter and
colleagues (36, 37) emphasized that circumferential fibers occur midway
between epicardium and endocardium throughout the entire LV wall, some
of their classic work shows circumferential fibers at ~35% depth
from the epicardium near the apex compared with 55% depth near the
base (see Fig. 7C in Ref. 37). The
comprehensive 3-D ventricular model of Nielsen et al. (27) also
indicates considerable regional variability in fiber-angle orientation, although a trend toward apical asymmetry is not clear. On the other
hand, LeGrice and co-workers from the same laboratory presented full
longitudinal sections of LV myocardium showing subepicardial fiber
angles that were much smaller in magnitude at the apex than at the
midventricle and base (see Fig. 2B in
Ref. 19), indicative of increasing transmural asymmetry toward the
apex. Several previous studies from our laboratory (7, 23, 28, 40), in
canine LV free wall locations between midventricle and apex, reported negative epicardial fiber angles of approximately one-half the magnitude of the positive endocardial angles, yielding circumferential fibers at ~30-40% wall depth. Therefore, there are substantial data consistent with an increasingly nonsymmetrical transmural distribution of fiber orientation from base to apex in the dog heart.
Published data on cleavage-plane orientations are far more limited.
However, our transmural distributions of cleavage-plane angles
(' and ) at the apex were very consistent with
corresponding data in the midanterior LV free wall of a dog heart fixed
at similar inflation pressure (see Fig.
6A in Ref. 20) and with our previous data in stress-free myocardium (7). Regional apex-base variations in
' were also similar to data reported by LeGrice and co-workers from the posterior LV free wall of two dog hearts fixed at zero transmural pressure (see Fig. 4A in
Ref. 19). The roughly 30° offset in angle values between that study
and ours may be an effect of inflation pressure or circumferential
location. The chevron patterns observed in the circumferential-radial
plane have also been previously described (16, 18, 20), and our data
indicate a reversal of the chevron orientation from apex to base.
These histological measurements were used to reconstruct the 3-D
orientation of myocardial laminae across the LV wall. Our approach
differs from that of LeGrice et al. (20) in that the reliability of the
computed sheet angle was incorporated into the reconstruction algorithm
to account for expected discrepancies between ' and
. The theoretical basis for this analysis and examples of
the resulting model fits have been given previously (7).
Regional heterogeneity in fiber and cleavage-plane orientations
resulted in that tended to be negative in the apical region and
positive in the basal region. Nevertheless, typically did not
exceed ±45°, similar to our previous data in stress-free
midanterior LV myocardium (7). Therefore, although the fiber and
cleavage-plane angles may vary by 90-120° through the wall,
the sheet angle is more consistent such that myocardial laminae are
predominantly radial in orientation at end diastole. Differences
between the actual 3-D sheet orientation and the "projected"
two-dimensional cleavage-plane orientations have important implications
for some proposed mechanisms of ventricular wall thickening (20, 35;
see below).
Although cleavage-plane orientations generally varied smoothly from
epicardium to endocardium, in several instances there was an abrupt
change associated with the trabeculata-compacta interface (Fig. 3).
Unfortunately, possible differences in mechanics between the compacta
and trabeculata could not be specifically studied because of an
insufficient number of markers for strain analysis within the
trabeculate layer.
End-systolic strains.
End-systolic finite strains in cardiac coordinates agreed with previous
data from our laboratory (20, 39, 40) and others (4, 9, 26, 43).
Nevertheless, all six cardiac strain components exhibited significant
regional differences between apical and basal measurement sites. The
decreased magnitude and gradient of circumferential shortening from
apex to base has previously been shown using MRI tissue tagging in
humans (6, 30). Waldman et al. (39) reported instances where
longitudinal and circumferential shortening were comparable in
magnitude, which we found to be a consistent trend at the base but not
at the apex. Radial strain indicated greater wall thickening at the
apex than at the base, consistent with recent 3-D MRI tagging studies
in the closed-chest dog heart (3, 32). The circumferential-radial shear
strain changed sign (but not magnitude) from apex to base, as predicted by Young et al. (42) on the basis of measurements of short-axis rotational displacements with use of MRI tagging in humans, possibly reflecting the opposite orientation of short-axis cleavage planes between the two sites. However, this contrasts with behavior in the
long-axis plane where subendocardial ' changed sign from apex
to base, but the longitudinal-radial shear strain remained positive.
Consequently, models of ventricular wall thickening based on
reorientation of long-axis cleavage planes (20, 35) would predict
subendocardial systolic wall thinning at the base, which is
inconsistent with our data.
When strain components were referred to local fiber-sheet coordinates
aligned with 3-D microstructural axes of myocardial laminae, much of
the regional apex-base variation disappeared. In particular, fiber
shortening
(Eff) was
homogeneous transmurally and regionally, supporting some theoretical
models of LV mechanics (1). Consequently,
E33 was poorly
correlated with
Eff across the
wall (r2 = 0.20),
which has previously been shown at the endocardium and epicardium only
(32). Other studies have shown similarity between inner- and outer-wall
fiber shortening in dogs (32, 40) and humans (21), and Rademakers et
al. (32) also found homogeneity of
Eff from apex to
base, although there was significant variability around the LV circumference.
The data indicate that myocardial laminae also undergo substantial
systolic deformations transverse to the fiber axis. Somewhat unexpectedly, Enn
was small but consistently negative, indicating shortening normal to
the sheet plane (i.e., sheet thinning). Moreover, strain along the
sheet axis
(Ess) indicated
large extension of the laminae transverse to the muscle fibers. Another
striking feature was the large sheet-normal shear strain
(Esn), which
changed sign from apex to base concomitant with . Of the three
fiber-sheet strain components that exhibited significant regional
effects, only Ess
and Esn were
strongly correlated with
E33
(r2 = 0.80, 0.77, and 0.12 for Ess,
|Esn|,
and Efn,
respectively). These findings are not easily explained by a simple
increase in the diameter of myocytes within the sheet due to systolic
fiber shortening. Alternative mechanisms based on the hierarchical
organization of the collagen extracellular matrix are considered at the
end of the DISCUSSION.
End-systolic shear strains.
A recent study from this laboratory (20) concluded that relative
sliding of adjacent myocardial laminae occurs primarily in the
subendocardium, where the direction of maximum systolic shear is
closely aligned with the local 3-D sheet orientation. However,
substantial "slippage" of sheets might also be expected in the
midwall where the transmural interlaminar branching density reaches a
minimum (19). In the present study, we computed interlaminar shear
(Ssheet) directly from the
fiber-sheet strain data
(Efn and
Esn) and found
a strong and consistent correlation between Ssheet and
Smax that was statistically
independent of wall depth. Specifically,
Ssheet and
Smax decreased in magnitude from
endocardium to epicardium, which may reflect an increased interlaminar
coupling in the subepicardium (19). However,
Smax was always slightly greater
than Ssheet, which contributed to
the nonzero intercept in our regression analysis. Therefore, the
relative contribution of Ssheet to
Smax decreased from endocardium to
epicardium, consistent with the maximum shear vector diverging from the
sheet-normal vector, as reported previously (20). Nevertheless,
although interlaminar shear (like most other systolic strain
components) was largest in the subendocardium, it was also present in
the midwall and subepicardium, indicating systolic slippage of the sheets across the entire LV wall.
In our correlation analysis, the small intercept may partially
represent other noninterlaminar shear contributions to
Smax, such as in-plane torsional
shearing. In addition, because no shear strain can exceed
Smax, any errors in
Ssheet (i.e., in
Efn and Esn) will skew
the intercept away from zero. Consequently, the unity slope of the
correlation suggests that Ssheet
may actually represent a substantially greater percentage of
Smax than the 60% overall mean contribution.
Contributions of sheet strain to wall thickening.
Transverse shear (i.e., relative sliding) of myocardial laminae has
previously been proposed as a mechanism for generating large changes in
wall thickness during the cardiac cycle (20, 35). Our analysis reveals
that it is the transverse shear associated with sliding of sheets
lateral to the local fiber axis
(Esn), as
opposed to the reorientation of long- or short-axis cleavage planes
(E23 or
E13,
respectively), that contributes to radial wall thickening strain
(E33). In
addition, E33
also depends on , as well as changes in sheet length and thickness
due to Ess and
Enn,
respectively. Figure 10, which represents
a region of laminar myocardium viewed in the plane perpendicular to the
local fiber axis, helps visualize how each of these factors can locally alter wall thickness. We found that the relationship between
Esn and was
consistent with reorientation of myocardial laminae toward the radial
direction during systole. Sheet extension lateral to the myofiber axis
(Ess) was also
important, which has not previously been shown. At the apex and base,
sheet extension and shear each contributed ~50% of
E33 in the inner
one-half of the wall, whereas sheet extension was the dominant
mechanism in the outer wall.
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Fig. 10.
Small region of myocardium viewed in sheet-normal
(Xs, Xn)
plane perpendicular to local fiber axis based on mean data from apical
region at 60% wall depth.
X3 axis points
from endocardium to epicardium. A:
myocardial sheets at end diastole have negative sheet angle ( < 0)
and are 4 cell diameters thick, and cells have circular cross section.
B: at end systole,
Esn < 0 causes
reorientation of sheets toward radial direction, one sheet slides
relative to the other, and local wall thickness (T) increases by  T
from initial value of T0.
C: wall thickness also increases,
because end-systolic sheets are thinner
(Enn < 0) and longer
(Ess > 0) than
at end diastole (dotted rectangle indicates end-diastolic dimensions).
Myocytes have increased cross-sectional area because of fiber
shortening. If myocytes do not rearrange, cell cross sections become
elliptical (top sheet). If cells
remain circular, average number of cells per sheet thickness decreases
and cell count along sheet length increases reciprocally, indicating
rearrangement of myocytes within sheet (bottom
sheet).
|
|
To further test these mechanisms for wall thickening, the methods of
the present investigation were used to reanalyze the tissue morphology
and LV marker displacements measured by LeGrice et al. (20) from the
canine midanterior LV free wall and septum. We have included these data
in Fig. 8 and Table 1. The relationship between
Esn and at
these sites was consistent with our findings, with the midanterior wall
being similar to the apex, whereas the septum was more like the base
(Fig. 8). In terms of fractional contributions to
E33 (Table 1),
the midanterior results were similar to the apex and base: interlaminar
shear was an important mechanism for wall thickening, but the
contribution of sheet extension accounted for the majority of
E33. These
findings indicate a highly consistent mechanism for systolic wall
thickening in the LV free wall despite a twofold variation in mean
E33. Because of
the more extensive surgical preparation in Ref. 20, the large
midanterior thickening may not be simply a regional effect,
particularly because greater wall thickening at the midventricle than
at the apex is not consistent with recent MRI tagging studies (3, 32).
In the septum, there was a reduced contribution from
Ess, compensated by a positive Enn
term, which accounted for 13% of
E33 on average. This apparent regional difference in the wall-thickening mechanism may
be a consequence of the unique functional role of the interventricular septum, where the "outer wall" is actually the pressure-loaded right ventricular subendocardium, or it may reflect the antisymmetrical mechanical behavior of the anterior-posterior and septal-lateral walls
described by Azhari et al. (2).
A similar approach can be used to determine the fiber-sheet strain
contributions to the paradoxically large systolic cross-fiber shortening strains,
Ecc < 0, reported by several investigators (21, 32, 40). Similar to
Eq. 2, the transformation equation relating fiber-sheet strains to fiber-cross-fiber strains yields the following relation
|
(4)
|
where
the shear term is identical in magnitude to the shear term in
Eq. 3 and accounted for >75% of
Ecc on average at
the four measurement sites at which we have data.
Therefore, the strong correlation between endocardial
Ecc and
E33
described by Rademakers and co-workers (32) probably arises from
the fact that the same interlaminar shear mechanism contributes
substantially to radial thickening and cross-fiber shortening.
Ultrastructural basis for the observed fiber-sheet strains.
Our analysis averages the deformations determined from radiographic
bead coordinate data and the corresponding histological measurements
over several cubic millimeters. Unfortunately, it is not yet possible
to directly measure the motion of myocardial laminae. However, because
pathological processes may act to alter ventricular function by
affecting laminar mechanics, it is interesting to speculate on the role
of various laminar structures.
Shear within the sheet plane
(Efs) was not
significant, suggesting that adjacent muscle fibers remain essentially
parallel to one another during systole and do not slide along the fiber axis. This may reflect mechanical restriction by the extensive endomysial collagen network connecting myocytes within the laminar fiber bundles (5, 19, 34). In contrast, sheet-normal shear (Esn) indicates
a 10-20° change of myocardial sheet orientation in the
subendocardium, which is within the range of longitudinal-radial cleavage-plane reorientation observed by Spotnitz et al. (35) during
passive inflation of the rat LV. If a typical sheet is four myocytes
thick at end diastole (19), this angle change is equivalent to a
lateral displacement of 0.7-1.5 cell diameters per sheet thickness
(Fig. 10B). Such motions would most
likely be accommodated by the longer perimysial collagen strands
connecting adjacent laminar cell bundles (5, 19). This assumes that Esn is due to a
gradient along the normal axis of deformation in the sheet direction
(i.e.,
xs/Xn).
Alternatively,
Esn could arise
from a gradient along the sheet axis of deformation in the normal
direction (i.e.,
xn/Xs).
However, this would require parallel sheets of myocardium to become
skewed. It is unlikely that this would occur, since the myocardial
laminae in fresh tissue are tightly packed, and interlaminar gaps arise
primarily from tissue shrinkage due to dehydration (19). Therefore,
sliding of adjacent myocardial sheets along cleavage planes probably
accounts for the consistently large sheet-normal shear strain and
similarly for the smaller fiber-normal shear
(Efn).
We also measured significant shortening and extension of the myocardial
laminae. If it is assumed that myocytes have a circular cross section
(17, 18), the sheet is four cells thick at end diastole (19),
individual cells are incompressible, and the number of cells within the
sheet is constant, we calculated the change in cell cross-sectional
shape or the cell rearrangement within the sheet that was consistent
with the measured strains (Fig.
10C). If myocytes within the sheet
do not rearrange during systole, then subepicardial cells could remain
essentially circular, with a major-to-minor axis ratio (ellipticity)
<1.1. However, in the subendocardium, sheet thinning
(Enn < 0) and
lateral extension (Ess > 0) would
require myocyte cross sections to become distorted (ellipticity
~1.3). This is not consistent with measurements of cell
cross-sectional shape in the canine LV midwall, which showed <5%
change in myocyte ellipticity in contracted vs. dilated hearts (18).
Alternatively, if cell cross sections remain circular during systole,
then sheet extension would require rearrangement of myocytes within the
sheet, e.g., interdigitation. Specifically, an increase in cell
diameter due to fiber shortening
(Eff < 0), combined with the observed sheet thinning
(Enn < 0),
would lead to a decrease in the number of cells across the sheet
thickness from 4 at end diastole to ~3.8 in the subepicardium and 3.5 in the subendocardium at end systole. There would also be a reciprocal increase in the number of cells along the sheet length of 5% in the
subepicardium and 14% in the subendocardium, which, combined with the
increased end-systolic cell diameter (3-4%), closely matches the
measured sheet extension based on
Ess. It is
unclear whether apparent slackening of intermyocyte struts during
systole (5) would allow such cellular rearrangement within the sheet plane. However, together with the reorientation of sheets toward the
radial direction due to
Esn, this method
of sheet extension is qualitatively consistent with published increases
in transmural cell number and center-to-center distance with increasing
ventricular wall thickness (17, 35).
Thus the two mechanisms that contribute most to systolic wall
thickening may depend on different components of the hierarchical collagen extracellular matrix, with sheet extension regulated by the
endomysial intralaminar network and interlaminar shear associated with
the perimysial connections between adjacent sheets of myocardium.
In conclusion, we have demonstrated that normal LV mechanics involve
considerable deformation of laminar sheets of myocardium. In the
anterior LV free wall, the sheets become thinner from end diastole to
end systole, and there is substantial sheet extension transverse to the
muscle fibers that varies transmurally and regionally. Also, the
laminae become more radially oriented because of interlaminar transverse shear strains, which represent the majority of overall systolic shear, and change sign from base to apex, reflecting regional
differences in the underlying 3-D laminar architecture. Sheet extension
and shear accounted for 60 and 40% of radial wall thickening strain,
respectively, and also explained the transmural and regional variations
in radial strain, which was poorly correlated with uniform systolic
fiber shortening. The specific mechanisms by which myocyte contraction
is converted to sheet extension and interlaminar shear remain to be
identified. However, kinematic considerations suggest that sliding of
adjacent myocardial sheets and rearrangement of myocytes within the
laminae may be two cellular mechanisms responsible for the sheet
strains that contribute to large ventricular wall thickening at end
systole. The apparently distinct ultrastructural origins of sheet
extension and shear may provide redundant mechanisms for sustaining LV
function during pathological alterations of the collagen extracellular matrix.
| |
ACKNOWLEDGEMENTS |
We thank Rish Pavelec and Dr. Jeff Holmes for assistance with the
experiments and Dr. Lewis Waldman for many stimulating and fruitful
discussions. We are indebted to Dr. Ian LeGrice for sharing expertise
and insight about the laminar structure of the myocardium and for
generously providing raw histology and bead coordinate data from the
midanterior and septal regions of the LV.
| |
FOOTNOTES |
This research was supported by National Heart, Lung, and Blood
Institute Grants HL-32583 (J. W. Covell) and HL-41603 (A. D. McCulloch)
and National Science Foundation Grant BES-9634974. K. D. Costa was
supported by National Heart, Lung, and Blood Institute Predoctoral
Training Grant HL-07089 (S. Chien).
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: J. W. Covell, UCSD School of Medicine,
Dept. of Cardiology, 9500 Gilman Dr., Mail Code 0613J, La Jolla, CA
92093.
Received 11 May 1998; accepted in final form 15 October 1998.
| |
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Top
Abstract
Introduction
