© 1995 American Heart Association, Inc.
Articles |
Transverse Shear Along Myocardial Cleavage Planes Provides a Mechanism for Normal Systolic Wall Thickening
From the Division of Cardiology, Department of Medicine, University of California, San Diego (La Jolla).
Correspondence to James W Covell, MD, BSB 2004-0613J, UC San Diego, 9500 Gilman Dr, La Jolla, CA 92093.
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Abstract Recent studies in humans and other species show that there is substantial transverse shear strain in the left ventricular myocardium, and others have shown transverse myocardial laminae separated by cleavage planes. We proposed that cellular rearrangement based on shearing along myocardial cleavage planes could account for >50% of normal systolic wall thickening, since <50% can be explained by increases in myocyte diameter. To test this hypothesis, we measured strains at two sites with different cleavage-plane anatomy in eight open-chest dogs. Columns of radiopaque markers were implanted in the left ventricular anterior free wall and septum. Markers were tracked with biplane cineradiography, and strains were quantified by using finite deformation techniques. Hearts were perfusion-fixed with glutaraldehyde, and cleavage-plane orientations at the bead sites were measured in three orthogonal planes. At subendocardial sites of the anterior left ventricular wall, where the cleavage planes approach the endocardium obliquely from the apical side of the surface normal in the longitudinal-radial plane (-67±11°), systolic longitudinal-radial transverse shear (E23) was positive (0.14±0.08). At the septal sites where the subendocardial cleavage planes approach the endocardium obliquely from above the surface normal (44±12°), E23 was negative (-0.12±0.08). The differences in cleavage-plane angle and E23 at the two sites were each highly significant (P<.0005). At both sites, the transverse shear strain accompanied substantial systolic wall thickening at the subendocardium (anterior, E33=0.44±0.16; septum, E33=0.22±0.14). These data are not representative of the behavior in midwall and outer wall sites, where cleavage-plane orientation was not consistently different between anterior left ventricle and septum. Our data indicate that rearrangement of myocytes by slippage along myocardial cleavage planes is in the correct direction and of sufficient magnitude in the subendocardium (inner third) to account for a substantial proportion (>50%) of systolic wall thickening. Furthermore, three-dimensional reconstruction of the myocardial laminae and local comparison with maximum strain vectors indicate that for the inner third of the ventricular wall the maximum shear deformation is a result of relative sliding between myocardial laminae.
Key Words: laminar myocardium • myocardial mechanics
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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Ventricular wall thickening is an important mechanism for systolic ejection. Previous studies have shown that left ventricular (LV) wall thickening strain between end diastole and end systole is near 0.1 to 0.2 in the anesthetized animal,1 2 3 much of which is due to large radial strains (0.4) in the inner wall.4 5 Simple calculations based on the conservation of individual myocyte volume lead to the conclusion that the increase in cell diameter as myocytes shorten maximally would contribute only about one fifth of the local thickening at the inner wall (0.08); thus, other mechanisms must account for the large wall thickening strains at this site. It has been suggested that cellular rearrangement may contribute to changes in wall thickness during both diastole6 and systole,4 and reports of significant shearing deformation in transmural planes2 4 5 7 8 9 seem to support this idea.
Furthermore, recent descriptions of the laminar organization of myocardium10 11 12 have provided a possible structural link between transmural shear and wall thickening. Those previous studies have shown myocardium to be laminar in nature, with laminae or sheets of myocytes (on average, four cells thick) connected by a loose collagen network that spans the cleavage planes between the sheets. There are significant regional variations in the organization of the laminae, the differences being particularly marked between the subendocardial regions of the anterior LV and the interventricular septum of the canine heart. In the anterior LV, the cleavage planes curve steeply in a basal direction as they approach the endocardium, whereas in the septum, they approach the endocardium obliquely from the opposite direction. Implicit in suggestions of a link between cellular rearrangement and changes in wall thickness was the notion that transmural shearing deformation must occur.4 6
It was our aim to determine whether the laminar structure of myocardium provides the basis for this cellular rearrangement and whether transmural shearing deformation contributes significantly to systolic wall thickening (wall thickening hypothesis). We exploited the difference in laminar morphology between the anterior LV and septum to investigate this question, determining whether the shearing deformation at each site was of appropriate magnitude and direction to explain the observed local systolic wall thickening. A second hypothesis (maximum shear hypothesis) that followed from this analysis was that a primary function of the laminar myocardial structure is to allow adjacent sheets to slide relative to one another. Consequently, the maximum shearing deformation would be oriented such that planes of maximum relative sliding determined by strain analysis would coincide with the local myocardial laminae. In the present study, we analyzed strain and myocardial morphology across the ventricular wall and found that planes of maximum relative sliding were closely aligned with the myocardial laminae toward the endocardium. This suggests that transverse shearing deformation along myocardial cleavage planes is an important component of normal subendocardial function.
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Materials and Methods |
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The University of California, San Diego, is accredited by the American Association for Accreditation of Laboratory Animal Care (AAALAC); all experiments were conducted according to AAALAC guidelines for the use of animals in research and were approved by the local faculty animal-use committee.
Ten adult mongrel dogs (20 to 25 kg) were anesthetized with
pentobarbital (25 mg/kg), intubated, and ventilated on room air
(Narkovet 2 ventilator). Throughout the experiment additional
pentobarbital was administered at a rate of 50 to 100 mg/h. The heart
was exposed through a median sternotomy and right lateral thoracotomy
and supported in a pericardial cradle. A limb-lead ECG was continuously
recorded, and arterial pressure was monitored with a pigtail catheter
inserted in the right femoral artery and connected to a
Spectramed-Statham P23xl gauge. LV pressure was recorded with a
Konigsberg micromanometer (model P6), which was inserted through a stab
wound in the apex and matched with the pigtail catheter advanced into
the LV before recordings. As illustrated in Fig 1
, three
columns of four to six gold beads (diameter, 1 mm) were inserted in the
anterior LV wall by using techniques similar to those described
previously.8 Briefly, a Plexiglas template was sutured to
the epicardium, and the three holes drilled in the template at the
corners of an equilateral triangle (sides, 10 mm) acted as guides for
the bead insertion trocar. Once the bead insertion was complete, the
platform was removed, and lead beads were then sewn onto the epicardial
surface above each column. Further beads were attached at the apex and
base (bifurcation of left main coronary artery) of the heart to provide
markers for a longitudinal cardiac axis.
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To insert columns of markers into the interventricular septum, it was necessary to perform a right-heart bypass.13 To isolate the right heart, the superior and inferior venae cavae were cannulated (through the azygos vein and right atrial appendage, respectively). The cannulas were connected to tubing (Bentley medical tubing; outer diameter, 9.5 mm) that drained into a 5-L reservoir suspended below the table. Blood from the reservoir was returned to the main pulmonary artery through a cannula connected to a roller pump (Sarns-Travenol, model 3500). A second pump was connected to a small suction cannula inserted through the right atrium and was used to return coronary sinus and thebesian flow to the reservoir. Heparinized donor dog blood (1 to 2 L) was used to prime the pump and reservoir system. Once the bypass was initiated, a diagonal incision 50 to 60 mm long was made through the right ventricular (RV) wall approximately perpendicular to the long axis of the pulmonary outflow tract, exposing the septal surface just anterior to the anterior papillary muscle. The bead implantation procedure was repeated in the septum, but because of the limited space available, the platform was not used, and sites for column insertion were judged by eye. The RV incision was repaired, and the dog was weaned off the bypass. Finally, a short fluid-filled polyvinyl tube connected to a second Gould-Statham gauge was inserted through the RV wall and used to monitor RV pressure.
Avoiding overlap of the myocardial markers, we positioned the dog in the biplane x-ray system, and high-speed cineradiography (16 mm, 120 frames per second) was performed with respiration suspended at end expiration. ECG, LV pressure, RV pressure, aortic pressure, and camera shutter pulses were recorded on an eight-channel chart recorder (Brush-Clevelite, model 2000, Gould) during the cineradiography runs. Data were recorded for LV end-diastolic pressures (LVEDPs) ranging from 5 to 20 mm Hg in steps of 5 mm Hg. LVEDP was increased by volume expansion and reduced by inferior vena caval constriction.
At the end of the experiment, snares were placed around lung hila and the inflow and outflow vessels from the heart, and the left anterior descending and circumflex coronary arteries were then isolated and cannulated. An overdose of pentobarbital was administered, and the heart was brought to anoxic arrest by first tightening the snares about the inflow vessels. Pressure in the LV was adjusted to 5 to 10 mm Hg by injection of saline into the LV cavity, the RV was vented, and the heart was fixed by infusing buffered glutaraldehyde (10%) through the coronary cannulas.
At the end of the study, a calibration phantom was positioned in the x-ray field, and biplane x-ray images were recorded for use in reconstructing the three-dimensional (3-D) coordinates of the bead locations after the method of MacKay et al.14
Strain Analysis
The 3-D coordinates of the implanted anterior LV and septal
beads were reconstructed from the biplane images at end diastole (ECG,
R wave) and end systole (dichrotic notch). These coordinates were then
used to calculate transmural 3-D finite strains at each site; both
homogeneous-strain and finite-element techniques were used. The
homogeneous-strain technique has been described in detail
elsewhere.4 5 8 Briefly, sets of four noncoplanar markers
were used to form tetrahedrons, the six edges of which each provided a
length and orientation at end diastole and end systole (Fig 1
). From
these data, it is possible to calculate the finite strain components
(normal and shear strain) in reference to a local cardiac coordinate
system that uses the three surface beads at each site. Normal strains
describe length changes in the circumferential direction
(E11), in the longitudinal direction (E22), and
in the radial direction (E33) normal to the epicardium.
Shear strains describe angle changes in planes parallel to the
epicardium (E12), in the longitudinal-radial plane
(E23), and in the circumferential-radial plane
(E13). The finite-element technique used in this laboratory
to calculate finite strains has also been described
previously.15 16 In this method, a finite element is
fitted to the three columns of markers at end diastole and end systole,
and continuous transmural profiles of wall strain can be computed from
the two fitted elements (Fig 1).
Morphological Studies: Wall Thickening Hypothesis
Blocks of fixed tissue containing the columns of beads were
removed from the anterior LV and septal sites. The blocks were cut so
that their sides aligned with the local cardiac coordinate system,
which was used for strain analysis (Fig 2a). To
ensure that the blocks were cut along the known axis system, the fixed
heart was held in a cutting jig by a rod inserted along the apex-base
axis. Slices 1 mm thick were then removed from one side of the block in
the longitudinal-radial (2-3) plane (Fig 2e). This cut was made by
holding the tissue block in a small Plexiglas vice with 1 mm thickness
exposed past the front face and running a sharp razor down the face of
the vice. On the cut surface of the thick section, myocardial cleavage
planes are visible when reflected light with a low-power (x20) light
microscope is used. Images of the sections were acquired into
image-processing software (NIH Image 1.47) via a video camera (Sony
DXC-151) mounted on the microscope (Nikon Optiphot-2), and orientations
of cleavage planes could be measured and referenced to depth from the
epicardium. For measurement of cleavage-plane angles in the 2-3 plane,
the section was aligned with the epicardium parallel to the 2-axis and
with the 3-axis (surface normal) representing 0°. When
looking in the positive 1-axis direction, angles clockwise from the
3-axis are recorded as negative (Fig 2e). A series of 
100
measurements were recorded in a 5-mm-wide strip across the section from
epicardium to endocardium. These angles were then averaged in 1-mm
steps across the wall. For the wall thickening hypothesis, we only
required the mean cleavage-plane orientation (in the 2-3 plane) for the
inner third of the wall. These angles were calculated for LV free wall
and septum in each heart from the transmural data described above.
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Morphological Studies: Maximum Shear Hypothesis
For the maximum shear hypothesis, we needed to locally
reconstruct the topology of the myocardial laminae. Since we measure
the local topology in adjacent 1-mm-thick sections, we must assume that
the topology is homogeneous over the measurement volume. For this
reconstruction, it was necessary to measure the cleavage-plane
orientations across the wall in at least two noncoplanar sections. In
fact, we chose to make these measurements in three planes defined by
the orthogonal cardiac coordinate system (2-3, circumferential-radial
[1-3], and circumferential-longitudinal [1-2] planes). The use of
angles in three rather than two planes provided us with a method for
checking our assumption that the topology was homogeneous. For the
measurement of angles in the 1-3 plane, a 1-mm-thick slice was removed
from the bottom (or top) of the block (Fig 2d). We have described
measurement of angles in the 2-3 plane in the previous section; an
identical approach was used for recording angles in the 1-3 plane,
although in this case, the 3-axis corresponded to 0°, and when viewed
in the negative 2-axis direction, counterclockwise rotations
represented positive angles (Fig 2d). As in the 2-3 plane,
a series of 100 measurements were recorded in the 1-3 plane in a
5-mm-wide strip across the section from epicardium to endocardium.
These angles were then averaged in 1-mm steps across the wall. The
remainder of the original block was finally cut into 1-mm-thick slices
in planes parallel with the epicardium, the 1-2 planes (Fig 2b). For
angles in this plane (conventional "muscle fiber angles"), the
tissue section was aligned with the lateral edge parallel to the 2-axis
and with the 1-axis (circumferential) representing an angle of
0°. When viewed in the negative 3-axis direction, counterclockwise
angles are recorded as positive, in accordance with the convention of
Streeter et al17 (Fig 2c). The surface of each slice
represented a known transmural depth, and in each case nine
measurements were made in a 3 mmx3 mm square area in the center of the
slide; the mean of these measurements provided the 1-2 plane angle
(fiber angle) for that depth.
It is possible to determine the local 3-D orientation of the myocardial
laminae from the cleavage-plane orientations measured above. Since each
of the angles can be described as a vector in the local cardiac
coordinate (1, 2, 3) system and since each of these vectors lies in the
laminar plane, it follows that a cross product between any two of these
"angle vectors" will be normal to the local myocardial laminae.
In practice, at each depth we calculated normalized vector products
between pairs of angle vectors, resulting in three unit vectors normal
to the local sheet plane (m1,
m2, and m3), which
should all be parallel if the angle data from the three sections were
self consistent. Only if these unit vectors were, on average, within
25° of each other (mean scalar product of all vector pairs was
>0.91) was that data point accepted for further analysis, as
described below. For data points included in the analysis, a mean
sheet- normal unit vector (M; see Fig 2) was then calculated
from the components of the three vectors m1,
m2, and m3. The rather strict criterion
we have used to eliminate data from our analysis was deemed
necessary because of problems inherent in reconstructing 3-D sheet
orientations from angles measured in three different tissue sections.
It was evident from examination of the tissue that the 3-D structure
can change quite dramatically over small distances and that cleavage
planes observed in the three sections may not come from the same group
of laminae. Only when all three cleavage-plane measurements produce
self-consistent results can we reliably assume that the reconstructed
sheet orientations accurately represent the laminar structure
of the myocardium where strains were measured. This strict criterion
resulted in the elimination of 35% of the calculation points from the
anterior LV analysis and 56% from the septal analysis,
although this only applied to the maximum shear hypothesis, where 3-D
reconstruction of the sheets was required.
Relation Between Morphology and Maximum Shear Strain
We proposed in the introduction that the myocardial laminae and
the cleavage planes between them were important for normal myocardial
function by allowing shearing deformation, and we expected the planes
of maximum sliding from the strain analysis to be coplanar with
myocardial laminae. Our technique for testing this hypothesis is
described below. From the normal and shear strains at any given site in
the wall (Fig 2f), it is possible to calculate the directions
(eigenvectors v1, v2, and v3) and
magnitudes (eigenvalues) of the three principal strains
(E1, E2, and E3) as
described by Villarreal et al5 (Fig 2g). It is further
possible to calculate the magnitude and orientation of the maximum
shear strain, which occurs in-plane with the eigenvectors for the
largest negative (E1) and largest positive (E3)
principal strains.18 Although the maximum shear is
represented by a change in shape of the top and bottom
faces of the block in Fig 2h, we may imagine that this deformation
arises from the relative sliding motion between planes diagonally
bisecting the block. These "planes of maximum relative sliding"
have two possible orientations designated by their unit normal vectors
S1 and S2 (Fig 2i), which may be computed from
the normalized sum and difference of the eigenvectors v1
and v3. We tested our maximum shear hypothesis by comparing
the vectors normal to the planes of maximum sliding (S1 and
S2) with the morphological sheet normal M described above.
We compared the vector M with each of S1 and S2
by calculating the scalar product and considering the greater absolute
value; the closer the scalar product was to unity, the nearer the two
vectors were to being colinear. The scalar product was converted to an
angle by taking the inverse cosine (eg,
angle=acos[MxS1]) (Fig 2j). We have provided an example
set of the above calculations by using data from a subendocardial site
in the anterior LV of one heart as an appendix.
Statistical Analysis
Data are presented as mean±SD, and where comparisons are
made between anterior LV and septum, paired t tests are
used. In all cases a value of P<.05 was considered to
indicate statistical significance.
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Data from eight of the 10 dogs studied are presented. In one of the remaining two animals, the surface marker above one of the septal bead columns came loose before the cineradiographic recordings, and we were unable to establish a reliable local cardiac coordinate system for that bead set. The second dog sustained visible myocardial damage over the anterior LV bead set during repeated defibrillation shocks and never recovered significant function.
Hemodynamics
The average hemodynamic parameters were as follows: peak LV
pressure, 110±8 mm Hg; peak RV pressure, 33±6 mm Hg; LVEDP, 7±2
mm Hg; and heart rate, 115±31 beats per minute. LV filling pressure
at the time of fixation averaged 8±1 mm Hg.
Strain Analysis
In all cases, systolic normal and transverse shear strains tended
to increase from the outer wall (epicardium in the case of the anterior
LV and RV septal endocardium in the case of the septum) to the LV
endocardium. Positive radial (ie, wall thickening) strain
(E33) increased substantially from outer to inner LV
myocardium both in the free wall and septum, as shown for one typical
animal in Fig 3 (top). However, whereas the transverse
shear strain in the longitudinal-radial plane (E23) was
mainly positive and increased from epicardium to endocardium in the
anterior LV, it was mainly negative and became more negative toward the
LV endocardium in the septum (Fig 3, bottom). Both the
homogeneous-strain and finite-element techniques were used in this (Fig 3) and subsequent analysis, with very similar results; for
simplicity, we will present only results from the finite-element
method. Table 1 summarizes the normal and shear strains
from all hearts. Data are divided into the outer wall (0% to 33%),
midwall (33% to 66%), and inner wall (67% to 100%) and
presented as the mean strain magnitude for each of these sites. In
one heart, beads were not implanted deep enough to provide strain data
deeper than 67% in either the anterior LV or septum; thus, only seven
hearts are represented in the inner wall summary data. Wall
thickening strain at midwall and endocardium was significantly greater
in the anterior LV (E33=0.32±0.17 and 0.44±0.16,
respectively) than in the septum (E33=0.15±0.07 and
0.22±0.14, respectively) by paired t test
(P<.03). Transverse shear strain was also significantly
different at these two depths: positive in the anterior LV
(E23=0.07±0.04 and 0.14±0.08, respectively) and negative
in the septum (E23=-0.08±0.05 and -0.12±0.08,
respectively) (P<.0005). In all cases, inner wall
E23 was positive in the anterior LV (range, 0.03 to 0.25)
and negative in the septum (range, -0.05 to -0.28). There was,
however, no significant difference between the absolute magnitudes of
E23 in the anterior LV wall and septum.
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Laminar Morphology: 2-3 Plane (Wall Thickening Hypothesis)
A consistent observation for measurements in the 2-3 plane was
that in the anterior LV the cleavage planes approached the LV
endocardium obliquely from the apical direction, becoming nearly
parallel to the endocardial surface (large negative angle), and in the
septum the angle was positive and smaller (Fig 4). In
Fig 4, we present photomicrographs of the subendocardial cleavage
planes and myocardial laminae as seen in the 2-3 plane in septum and
anterior LV, with accompanying schematics to illustrate this point. In
the anterior LV, the mean subendocardial (inner third) 2-3 angle for
all eight hearts was -67±11°; in the septum, this angle was
44±12°. Paired t tests of either the signed or absolute
values of the mean inner wall angles both show highly significant
(P<.0005) differences in orientation between septum and
anterior LV.
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Wall Thickening Hypothesis: Relation Between Morphology and
Strain
In Fig 5, we have summarized the inner wall strains
(E33 and E23) and cleavage-plane orientations
in the 2-3 plane for anterior LV and septum. As mentioned above, the
positive E33 (wall thickening) was accompanied by positive
inner wall E23 in the anterior LV and negative
E23 in the septum. These differences in shear directions
were accompanied by opposite subendocardial cleavage-plane orientations
in the 2-3 plane.
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Laminar Morphology: 3-D Reconstruction (Maximum Shear
Hypothesis)
In Fig 6, transmural plots of cleavage-plane (or
myocardial sheet) orientation as seen in the three measurement planes
from anterior LV and septum of a single heart are presented. The
depths of bead centroids in the three columns are also shown; these
provided us with registration between deformation and morphological
measurements. In the middle panel are schematics of the 1-3 and 2-3
plane views with the approximate axis of the 5-mm strip in which the
angles were measured; on the far right is a schematic 3-D
representation of a block of myocardium from which the sections
were cut. Note that these sections have been rotated about the
endocardial edge by comparison with Fig 2 so that the orientation is
consistent with the graph axes. At both sites, the 1-2 (fiber) angle
varies across the wall from negative angles on the outer surface to
near-longitudinal positive angles at the LV endocardium, consistent
with past studies of fiber orientation.17 In the 1-3 view,
the cleavage planes formed a curving chevron pattern across the wall in
this example (in some cases the subepicardial angles did not follow
this arrangement, sweeping across from the inner wall in a sigmoid
pattern and resulting in the subepicardial planes being parallel with
the subendocardial ones). Whereas the subendocardial 1-3 cleavage
planes in the anterior LV approached 0° predominantly from positive
angles, in the septum they approached from negative angles. In most
sections, it was possible to identify two cleavage-plane directions in
localized sites in the 1-3 plane, particularly near the inner and outer
walls, where at times the smooth angle change pattern ended abruptly
and a sudden change in orientation was encountered (see Fig 6, top left
and schematic diagrams). We chose at these sites to measure only the
predominant orientation, consistent with a smooth variation in angle
across the wall. In the 2-3 plane, there was again some variability in
the transmural patterns seen from heart to heart, particularly in the
outer wall. However, there was a consistent pattern at the
subendocardium at each site in the 2-3 plane, as detailed above for the
wall thickening hypothesis.
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), circumferential-radial (1-3, 
), and longitudinal-radial
(2-3, 
) planes for anterior left ventricle (LV) and septum from
one heart (mean±SD). Error bars are for data binned in 1-mm steps
across the section for 1-3 and 2-3 planes and for measurements on one
section in the 1-2 plane (six to nine measurements per step). Heavy
circles show transmural location of radiopaque beads. Note that the
surface bead is centered beyond the outer surface; this is a
consequence of the
Maximum Shear Hypothesis
The results of the comparison between the orientations of the
local myocardial sheets and planes of maximum sliding are shown in Fig 7. In the top left panel, all angles fulfilling our
morphological acceptance criteria are displayed for the anterior LV and
septum. Calculation points are the finite-element output points shown
in Fig 3 for each dog. For the inner wall, in all but one point the
cleavage planes were, at most, 30° out of alignment with the planes
of maximum sliding from the strain analysis, and in the majority
they were closer than 20° (Fig 7, top left). Moving toward the outer
wall, the minimum angle between the morphological and deformation
planes increased, indicating that the maximum shear hypothesis does not
hold in these regions. We calculated the mean angle for each dog and
the overall mean angle for outer wall, midwall, and inner wall (Fig 7,
right panels, and Table 2). In Table 2, we have also
detailed the number of data points available from each heart in each
region. The septum and anterior LV data were grouped for this
analysis. For the outer wall and midwall regions, all eight hearts
are represented (with self-consistent morphology), and for
the inner third, there were data from five hearts. Comparing the outer
wall (43±13) with the inner wall (21±10), there are significant
differences in the angles at these two sites (P=.005,
unpaired t test). In the bottom left panel of Fig 7, we have
presented the mean angle data in each of the three regions for
anterior LV and septum separately. When divided in this way, some
regions had data points from few of the hearts; the worst case was for
the inner wall region of the septum, where only two hearts were
represented. ANOVA was carried with the general linear
models procedure (SAS Institute Inc) using the type III sum of squares
to allow for the missing data. This analysis demonstrates that
there is a significant transmural variation in the angle between local
myocardial sheets and planes of maximum sliding (P=.0001).
Reference to each of the graphs in Fig 7 shows clearly that the trend
is for the angle to become small near the endocardium. Although there
is no significant difference in mean angle between LV and septum
(P=.0706), the rate of change of angle across the wall is
different at the two sites (P=.0424).
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Discussion |
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Early views of the relation between myocardial structure and mechanical function were based on the description of the heart as being made up of discrete muscle bundles19 20 that acted like skeletal muscles but with their long axes spiraling around to form the heart chambers. On the basis of this description, it has been argued in anatomy textbooks for many years that the heart expels blood in a wringing motion.21 22 Implied in this mechanism of ejection is that as the spirally oriented muscles contract, they decrease the diameter of the cavity they enclose, thereby ejecting blood from the chamber within. However, a very important mechanism of ejection is ignored in this simple analysis, namely, ventricular wall thickening.
In more recent times, a variety of techniques of measuring cardiac deformation have revealed that the ventricular wall undergoes considerable thickening during systole,1 8 23 24 25 26 and it has been estimated that systolic wall thickening can account for 25% to 50% of stroke volume.27 28 29 More detailed knowledge of myocardial fiber structure, particularly the transmural gradient of fiber direction,17 and methods of measuring local deformation at different sites across the wall8 allow us to inquire about the relation between local myocardial structure and local myocardial function and perhaps to gain insight into the mechanism of systolic wall thickening. A focus of work on structure and function has been the relation between the local fiber orientation and the direction of the maximum shortening deformation.4 A major finding of that previous study was that the principal shortening direction and fiber direction were almost parallel in the outer wall but perpendicular in the inner wall, where shortening was greatest near the circumferential direction; this shortening was accompanied by substantial wall thickening. It was concluded that some form of geometric rearrangement of myocytes was necessary for this deformation to occur.
The work of Spotnitz et al6 suggests a possible mechanism
of this rearrangement. They showed that wall thinning during passive
filling at increasing pressures in rat hearts was associated with a
reorientation of layers of myocytes, which apparently slid along
transmurally oriented cleavage planes between the layers. Although
ventricular myocardium is widely viewed as a continuous structure that
functions as an electrical and mechanical syncytium, this view is not
consistent with some morphological observations. Sections cut from the
ventricles reveal extensive extracellular gaps, particularly in the
midwall region.6 30 31 32 33 34 It was evident to
Feneis31 that this laminar organization allowed sliding
between adjacent bundles of cells. The laminar organization of
myocardium has more recently been characterized in
detail.10 11 12 This work shows myocardium to be a branching
sheet structure, with the myocardial laminae being four to six cells
thick. This arrangement can be seen most clearly in Figs 6 to
8 from the work of LeGrice et al.10 The
arrangement of sheets is quite complex, but in simple terms they are
"stacked" on top of each other from apex to base. The sheets
branch and twist so that there is a transition in orientation from
endocardium to epicardium when looking in a longitudinal cross section
(Fig 8a). There is also marked regional variation in the organization
of myocardial laminae. This structure provides the morphological basis
for a hypothesis involving systolic wall thickening, which we have
tested in the present study.
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Wall Thickening Hypothesis
In Fig 8, we propose a mechanism of systolic wall thickening
operating in the inner third of the ventricular wall. On the right is a
schematic longitudinal-radial section (2-3 plane) from apex to base of
the LV free wall with cleavage planes following characteristic curved
radial patterns. At the inner wall, these layers curve steeply toward
the endocardium, becoming nearly parallel with the endocardial surface
as shown in Fig 8a. (The myocytes in this region are oriented obliquely
to the plane of section, hence the oval profiles.) One mode of
deformation at this site during systole may be a movement of the
endocardium downward relative to the inner wall regions, giving rise to
a positive E23 shearing deformation as measured in our
cardiac coordinate system (relative upward movement of the endocardium
would be a negative E23). If we also assume that the
myocardial laminae are stiff relative to the shearing stiffness of the
space between them (not unreasonable in systole), then they will tend
to slide relative to one another, causing the endocardial surface to
displace into the LV cavity as it moves down in systole (Fig 8c),
contributing to local wall thickening. This mechanism of systolic wall
thickening is supplemented to a small degree by increases in myocyte
diameter as they shorten along their axis. In fact, significant
positive E23 in the LV free wall has been a consistent
observation in past studies of regional mechanics in normal
myocardium.2 4 5 7 8 35 Furthermore, in studies of
regional mechanics in acutely ischemic myocardium, significant
systolic wall thickening changed to thinning, and this was accompanied
by a marked reduction2 or reversal5 of
E23. These results further support the idea that there is a
direct link between systolic wall thickening and transmural shearing
deformation.
Differences in the laminar organization between the LV free wall and
interventricular septum provide an opportunity for testing this
hypothesis further. In longitudinal-radial (2-3) sections of the
interventricular septum, cleavage planes curve toward the LV
endocardium from the basal direction rather than from the apical
direction, as is the case in the LV free wall (Fig 4). In the septum,
our hypothesis would require that wall thickening be accompanied by an
upward movement of the endocardium relative to the midwall (negative
E23). Our data reveal that these requirements are indeed
satisfied (Table 1 and Fig 5). For the inner third, wall thickening
(positive E33) is accompanied by positive E23
in the anterior LV and negative E23 in the septum. Of note
also is that although E23 is the same magnitude at these
sites (although opposite in sign), E33 is significantly
greater in the anterior LV. The analysis in Fig 9
provides a possible explanation of this apparent anomaly. Here, we show
a simple formula for the thickening associated with a given shear or
angle change (ß), given an initial angle (
). The function for a
range of initial angles is presented on the left. In Fig 4, we
presented the results of cleavage-plane orientation measurements in
the 2-3 plane for the inner third of the wall at septal and anterior LV
sites, showing a significant difference in absolute magnitude of the
angles at these sites. In the anterior LV, the mean angle was -67°,
whereas in the anterior septal region (where we implanted our bead
columns), it was +44°. We can plot the absolute values of these
angles at interpolated points on the graph in Fig 9, which shows quite
clearly that we can expect more thickening in the anterior LV compared
with the septum, given the same amount of shear. The angle change (ß)
in the 2-3 plane resulting from the given finite strains is given by
the following formula36 :
 |
T/To, as used in Fig 9), they are
directly related, and nonlinear analysis does not alter this
conclusion. The data from a single heart shown in Fig 3 does not
reflect exactly the mean data of Table 1, in that the wall thickening
strains for the subendocardium are equal. However, this result is
consistent with the above mechanism, because in this case the magnitude
of E23 is greater in the septum; thus, we could expect to
see greater wall thickening at this site, approaching that in the
anterior LV. (The subendocardial 2-3 angles are 70° for the anterior
LV and 50° for the septum, similar to the average data.)
|
One might expect to find this mechanism for wall thickening occurring
in the 1-3 plane. However, since the myocardial laminae approach the
endocardium at angles near 0° in this plane, it follows that the
mechanism described for the 2-3 plane will produce little change in
wall thickness. It is interesting to speculate that the relatively
small magnitude of E13 (Table 1) relates to the fact that
it would not achieve wall thickening. A similar proposal may be made
for the midwall laminae in the 2-3 plane. At this site, the cleavage
planes are near radial (2-3 angle near 0°); hence, the mechanism
would have little effect on wall thickening at this site. Near the
epicardium, all strains are small, and this mechanism probably has no
role.
Maximum Shear Hypothesis
Implicit in our proposed mechanism of subendocardial rearrangement
is a sliding motion between myocardial laminae; they must slide
relative to one another for the tissue model to deform as we
hypothesize. The laminar myocardial structure with sheets of myocytes
separated by cleavage planes seems to be designed for such a
deformation. One might expect that the maximum relative sliding
occurring in the myocardium is therefore coplanar with the myocardial
sheets, and what is observed in the 2-3 plane is simply a projection of
that maximum sliding. The results in Fig 7 show that for the inner
third of both anterior LV and septum, this indeed appears to be the
case. There is a clear trend for the angle between the local myocardial
laminae and the planes of maximum relative sliding from the strain
analysis to approach 0° near the endocardium. In most cases, the
angle is <20°, which is within experimental error for this rather
difficult assessment. This analysis suggests that toward the
endocardium the shearing forces and myocardial laminae come into
alignment such that there is maximum relative sliding between
myocardial laminae, producing significant wall thickening through the
mechanism proposed above and illustrated in Figs 8 and 9. The
difference in the slope of the transmural trend between anterior LV and
septum revealed by ANOVA may relate to the fact that the outer wall of
the interventricular septum is itself endocardium. We suspect that
cleavage planes and maximum shearing planes may tend to align again
near this surface. Our data do not provide strong evidence for this
view; such a hypothesis would require more work specifically focused on
this question and may not prove fruitful, because the corresponding RV
endocardial zone is likely to be narrow and there are probably
conflicting mechanisms in the tissue that is involved in the function
of both ventricles.
It should be noted that for the data points shown in Fig 7, it is not
possible to get an angle <0° from our method of calculation; hence,
any errors will result in positive angles, thus skewing the results
away from zero. The larger of the two scalar products
(MxS1 or MxS2) defines whether the
morphological sheets are coplanar with the planes of maximum sliding
from the strain analysis. As this value approaches 1.0, the smaller
scalar product approaches zero, since the two sets of planes of maximum
relative sliding are orthogonal to each other (Fig 2h). We have noted
that there are areas in the thick sections where there seem to be two
distinct cleavage-plane orientations, which would imply two coexisting
sets of intersecting sheets at these sites (see schematic diagrams in
Fig 6). It is possible that this second orientation coincides with the
second orientation of planes of maximum relative sliding in the strain
analysis (Fig 2j). We have not tested this hypothesis because these
areas appear to be small patches in most cases, and finding
corresponding patches at corresponding depths in each section seemed
unlikely.
Origin of Transmural Shear
The work presented here does not explain how shear between
cell layers in the subendocardium is generated. We have simply
presented data suggesting that relative sliding occurs between the
myocardial laminae in the subendocardium, and we have shown a simple
model to illustrate how this shearing might result in local wall
thickening. It is interesting to speculate on the cause of this
shearing deformation. A first simple hypothesis relates to the fact
that the LV is a thick-walled chamber, the diameter of which decreases
during systole. This change in global geometry results in the
endocardial tissue being compressed into a smaller space. Since the
tissue being compressed is laminar in nature, it is likely that the
structure will deform along lines of least resistance, ie, the cleavage
planes between the myocardial sheets. The sheets will slide relative to
one another. This deformation is shear.
A second possibility is that the inner wall shearing is a direct result of the transmural variation in fiber direction and the connective tissue coupling between groups of cells across the wall. It is possible that during systole the combination of myocytes shortening along their varying axes and the particular connective tissue coupling between cells across the wall results directly in shearing forces being established in the subendocardium. Such a model implies that the detailed organization of myocytes and connective tissue is very important in ventricular function and that disruption of such organization will result in impaired function.
A third possibility is that the sequence of electrical activation plays a major role in establishing transmural shear in the inner wall. There are at least two aspects to this argument. First, since our proposed mechanism requires that the subendocardial sheets of tissue are stiff relative to the coupling between them, the myocytes must be contracting for this to be the case, and it follows that early endocardial activation is essential if the mechanism is to work effectively. This is needed for the wall thickening hypothesis, although not necessarily for the origin of inner wall E23. Second, it is possible that the wave of activation spreading from endocardium to epicardium through a fiber field with changing axis is necessary to establish the transmural shearing forces. Early this century, it was suggested that abnormal activation sequences result in impaired ventricular function.37 Subsequent studies of hearts paced from ventricular sites varied in their conclusions about whether the impaired function was a result of abnormal atrioventricular coupling or abnormal activation sequence.38 39 40 41 42 More recently, results from an investigation of local transmural deformation during ventricular pacing have shown significant differences between beats initiated in the atria or ventricles, implying that ventricular activation sequence does indeed play an important role.35 That study revealed a reduction of inner wall systolic wall thickening when compared with normal beats, and this was accompanied by reversal (from positive to negative) of E23. The important issue here may not be the direction of the activation sequence but its duration; normal activation via the rapid conduction tissue is almost instantaneous relative to the mechanical events, but full activation of the ventricles takes significantly longer when initiated from an epicardial site,43 and this may lead to asynchrony in the mechanical events that alter the forces developed in the myocardium.
In light of the requirement for stiff myocardial laminae in our model, it is interesting to look at deformation in the diastolic heart. Omens et al16 measured transmural finite strains in the anterior LV wall of passively inflated canine hearts and showed wall thinning associated with negative E23. Although this combination of strains is consistent with our hypothesis for systolic deformation, E23 did not become more negative in parallel with increased wall thinning as the heart was inflated to higher volumes. It is likely that for the passive heart (when the stiffness of the sheets approaches that of the gaps between) this mechanism becomes less effective in generating wall thickness changes.
Limitations
Limitations and sources of error of the methods used to measure
and analyze deformation have been discussed
previously.8 15 The experimental procedure involved
considerable surgical intervention. Incision and repair of the RV free
wall could potentially alter septal function; however, RV and LV
pressures were normal, and there was no other evidence that RV function
was impaired. Furthermore, although the general level of cardiac
function may have been depressed, as is normal in such preparations,
this would not influence our conclusions, which derive from a
comparison of structure and function at two sites in the same heart. As
we pointed out in "Materials and Methods," measurement of the
angles used to define the 3-D sheet morphology is subject to a number
of difficulties. There is some uncertainty about aligning the section
for measurement in terms of the surface tangent orientation and zero
depth, particularly in the septal sections, where the outer surface is
actually the (irregular) endocardial surface on the right side of the
septum. Furthermore, measuring a representative angle for the
curving cleavage planes has an associated error of 10°. (We should
note here that by using our gross sectioning technique we eliminate the
well-established distortion problems related to dehydration and
embedding for microtome sectioning.) A further problem is the
variability of cleavage-plane morphology, as illustrated to the right
in Fig 6, where there are two distinct patterns in the septal 2-3
section; in this case, the site of measurement is critical. It has
already been noted that there can be marked variability in these
patterns from site to site, and preliminary results of further work in
our laboratory show that there is also regional variation in the
relationship between wall thickening and transmural shear. Because of
the relatively large size of the blocks of tissue used, we were likely
to find variability in structure from one section to the other. It was
for this reason that we established strict criteria for accepting a
data point for the 3-D analysis of the sheet orientations, as
described in "Materials and Methods." In cases in which there was
a discontinuity between the sections measured, it was not useful to
take a "mean" sheet orientation, because this would not
represent the structure on either side of the discontinuity.
Our criterion resulted in the elimination of 35% of anterior LV data
and 56% of the points from the septum, the more difficult of the
sites. It should be noted that it is necessary to have a description of
all three angles across the wall to define the sheets with any
certainty, because at certain sites two of the angles may become
parallel, and the sheet normal from the vector product becomes very
unreliable or indeterminate. For example, near the endocardium, both
the 1-2 and 2-3 cleavage-plane orientations are near 90°, and in the
midwall the 1-2 angle is near 0° and the 1-3 angle is near 90°. In
each case, the two vectors representing these angles are nearly
parallel; thus, the third vector is needed to define the sheet. It may
be argued that one should simply use the 1-2 and 1-3 angles at the
endocardium and the 1-2 and 2-3 angles at midwall, and this is
certainly an alternative approach that can be used. We have plotted our
data by use of this technique, and the results are essentially the
same. However, this approach does not eliminate the problems of rapid
changes in morphology; thus, it was considered safer only to use data
in which all three angles were consistent with a single 3-D
cleavage-plane orientation. Furthermore, because there is marked
regional variability in myocardial laminar organization, we have not
attempted to calculate mean orientations across our set of hearts. It
is possible to improve the morphological techniques to some extent:
first, by cutting the 1-3 and 2-3 sections nearer the center of the
bead sets and taking the generally less variable 1-2 (fiber angle) data
from adjacent tissue; second, by creating a stained track at an
accurately known depth in the tissue block before cutting (this would
provide an accurate reference for aligning sections). If even more
accuracy in determining 3-D morphology is required, then confocal
microscopy techniques that enable one to image tissue deep to the
surface plane (optical sectioning) may be necessary.
In conclusion, we have shown that when viewed in the longitudinal-radial plane, the orientation of the cleavage planes in the subendocardium and the direction of the related shear at the two sites studied in the present work are consistent with a hypothesis of systolic wall thickening based on rearrangement of inner wall myocardial laminae. The proposed mechanism may help explain the larger ventricular ejection fractions than those that can be obtained from myocyte thickening alone. Longitudinal-radial shear is of comparable magnitude (though opposite in sign) in the LV free wall and septum, whereas systolic thickening is greater in the LV free wall. The steeper subendocardial 2-3 cleavage-plane angle in the LV free wall provides a possible explanation for the difference in systolic wall thickening. Furthermore, the shearing deformation seen in the longitudinal-radial plane is a "projection" of the local maximum shear vector, and in the subendocardium (though not at outer wall sites), the maximum shearing occurs by sliding of myocardial laminae relative to each other. This mechanism may help explain reduced cardiac performance as a result of endocardial fibrosis or abnormal electrical activation.
|
Acknowledgments |
|---|
This study was supported in part by National Heart, Lung, and Blood Institute grant HL-32583. Dr LeGrice was supported by the Health Research Council of New Zealand. The authors wish to acknowledge the valuable technical assistance of Richard Pavelec and Monica Adams.
|
Appendix 1 |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
|---|
Sample Calculation for the Maximum Shear Hypothesis
At a sample subendocardial site in the anterior LV of one heart, the eigenvectors for principal strains E1 and E3 (referred to local cardiac coordinates) are as follows: v1={0.945, -0.272, 0.181} and v3={-0.095, 0.301, 0.949}, respectively. From the sum and difference of these two vectors, we can calculate the unit normal vectors to the "planes of maximum relative sliding"; in our example, these are as follows: S1={0.601, 0.021, 0.799} and S2={-0.735, 0.405, 0.543} referred to cardiac coordinates (Fig 2i
). The morphological angles at our example site are
as follows: 1-2 angle=78°, 1-3 angle=45°, and 2-3 angle=-60°.
These correspond to unit "angle vectors" {0.208, 0.978,
0.000}, {0.707, 0.000, 0.707}, and {0.000, -0.866, 0.500},
respectively (in cardiac coordinates). Vector products between pairs of
these three angle vectors (scaled to unit length) result in
m1={0.699, -0.149, -0.180}, m2={0.920,
-0.196, -0.339}, and m3={0.655, -0.378, -0.655}.
Scalar products between pairs of these three vectors have values of
m1xm2=0.91,
m1xm3=0.90, and
m1xm2=0.97, the mean of which is 0.93; hence,
these vectors are all nearly colinear, and the morphology is accepted
as reliable. The components of the mean morphology unit vector are
M={0.777, -0.247, -0.578}. Comparing vector M with each of
S1 and S2 by calculating the scalar product
(Fig 2j), we get for our example site MxS1=0.000 and
MxS2=-0.985, showing that the sheets here lie at an angle
of 9.9° to one of the planes of maximum sliding (and consequently
perpendicular to the other). Received June 3, 1994; accepted March 29, 1995.
|
References |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
|---|
1. Feigl EO, Fry DL. Myocardial mural thickness during the cardiac cycle. Circ Res. 1964;14:541-545.
2.
Osakada G, Sasayama S, Kawai C, Hirakawa A, Kemper WS,
Franklin D, Ross J Jr. The analysis of left ventricular wall
thickness and shear by an ultrasonic triangulation technique in the
dog. Circ Res. 1980;47:173-181.
3. Zhu W, Myers ML, Hartley CJ, Roberts R, Bolli R. Validation of a single crystal for measurement of transmural and epicardial thickening. Am J Physiol. 1986;251:H1045-H1055.
4.
Waldman LK, Nossan D, Villarreal F, Covell JW.
Relation between transmural deformation and local myofiber
direction in canine left ventricle. Circ
Res. 1988;63:550-562.
5.
Villarreal FJ, Lew WYW, Waldman LK, Covell JW.
Transmural myocardial deformation in the ischemic canine
left ventricle. Circ Res. 1991;68:368-381.
6. Spotnitz HM, Spotnitz WD, Cottrell TS, Spiro D, Sonnenblick EH. Cellular basis for volume related wall thickness changes in the rat left ventricle. J Mol Cell Cardiol. 1974;6:317-331. [Medline] [Order article via Infotrieve]
7.
Feigl EO, Fry DL. Intramural myocardial shear
during the cardiac cycle. Circ Res. 1964;14:536-540.
8.
Waldman LK, Fung YC, Covell JW.
Transmural myocardial deformation in the canine left ventricle:
normal in vivo three-dimensional finite strains.
Circ Res. 1985;57:152-163.
9.
Young AA, Kramer CM, Ferrari VA, Axel L, Reichek R.
Three-dimensional left ventricular deformation in hypertrophic
cardiomyopathy.
Circulation. 1994;90:854-867.
10. LeGrice IJ, Smaill BH, Chai LZ, Edgar SG, Gavin JB, Hunter PJ. Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol. In press.
11. Smaill B, Hunter P. Structure and function of the diastolic heart: material properties of passive myocardium. In: Glass L, Hunter P, McCulloch A, eds. Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. New York, NY: Springer-Verlag; 1991:1-29.
12. Hunter PJ, Nielsen PMF, Smaill BH, LeGrice IJ, Hunter IW. An anatomical heart model with applications to myocardial activation and ventricular mechanics. In: Pilkington TC, Loftis B, Thompson JF, Woo SL-Y, Palmer TC, Budinger TF, eds. High Performance Computing in Biomedical Research. Boca Raton, Fla: CRC Press; 1993:3-26.
13.
Covell JW, Ross J Jr, Taylor R, Sonnenblick EH,
Braunwald E. Effects of increasing frequency of contraction on
the force velocity relation of left ventricle. Cardiovasc
Res. 1967;1:2-8.
14. MacKay SA, Potel MJ, Rubin JM. Graphics methods for tracking three-dimensional heart wall motion. Comput Biomed Res. 1982;15:455-473. [Medline] [Order article via Infotrieve]
15. McCulloch AD, Omens JH. Non-homogeneous analysis of three-dimensional transmural finite deformation in canine ventricular myocardium. J Biomech. 1991;24:539-548. [Medline] [Order article via Infotrieve]
16.
Omens JH, May KD, McCulloch AD. Transmural
distribution of three-dimensional strain in the isolated arrested
canine left ventricle. Am J Physiol. 1991;261:H918-H928.
17.
Streeter DD Jr, Spotnitz HM, Patel DP, Ross J Jr,
Sonnenblick EH. Fiber orientation in the canine left ventricle
during diastole and systole. Circ Res. 1969;24:339-347.
18. Fung YC. A First Course in Continuum Mechanics. Englewood Cliffs, NJ: Prentice-Hall; 1977:91-112, 134.
19. MacCallum JB. On the muscular architecture and growth of the ventricles of the heart. Johns Hopkins Hosp Rep. 1900;9:307-335.
20. Mall FP. On the muscular architecture of the ventricles of the human heart. Am J Anat. 1911;11:211-266.
21. Schaeffer JP, ed. Morris' Human Anatomy: A Complete Systematic Treatise. New York, NY: McGraw-Hill Book Co; 1953:622-627.
22. Basmajian JV, Slonecker CE. Grant's Method of Anatomy: A Clinical Problem-Solving Approach. Baltimore, Md: Williams & Wilkins; 1989:100-101.
23.
Sjögren A-L, Hytönen I, Frick MH.
Ultrasonic measurements of left ventricular wall
thickness. Chest. 1970;57:37-40.
24.
Troy BL, Pombo J, Rackley CE. Measurement of
left ventricular wall thickness and mass by echocardiography.
Circulation. 1972;45:602-611.
25. Fenton TR, Cherry JM, Klassen GA. Transmural myocardial deformation in the canine left ventricular wall. Am J Physiol. 1978;235:H523-H530.
26.
Olsen CO, Rankin JS, Arentzen CE, Ring WS, McHale PA,
Anderson RW. The deformational characteristics of the left
ventricle in the conscious dog. Circ Res. 1981;49:843-855.
27. Dodge HT, Frimer M, Stewart DK. Functional evaluation of the hypertrophied heart in man. Circ Res. 1974;34(suppl II):II-122-II-127.
28. Gould KL, Kennedy JW, Frimer M, Pollack GH, Dodge HT. Analysis of wall dynamics and directional components of left ventricular contraction in man. Am J Cardiol. 1976;38:322-331. [Medline] [Order article via Infotrieve]
29.
Dumesnil JG, Shoucri RM. Quantitative
relationships between left ventricular ejection and wall thickening and
geometry. J Appl Physiol. 1991;70:48-54.
30. Robb JS, Robb RC. The normal heart: anatomy and physiology of the structural units. Am Heart J. 1942;23:455-467.
31. Feneis H. Das Gefüge des Herzmuskels bei Systole und Diastole. Morphologisches Jahrbuch. 1943;89:371-406.
32. Weitz G. Über das unterschiedliche Verhalten der Lage der Herzmuskelfasern in kontrahiertem und dilatierem Zustand. Med Klin. 1951;46:1031-1032.
33. Hort W. Mikrometrische Untersuchungen an verschieden weiten Meerschweinchenherzen. Verh Dtsch Ges Kreislaufforsch. 1957;23:343-346. [Medline] [Order article via Infotrieve]
34. Hort W. Makroskopische und mikrometrische Untersuchungen am Myokard verschieden stark gefüllter linker Kammern. Virchows Arch A Pathol Anat Histopathol. 1960;333:523-564.
35.
Waldman LK, Covell JW. Effects of ventricular
pacing on finite deformation in canine left ventricles.
Am J Physiol. 1987;252:H1023-H1030.
36. Fung YC. Foundations of Solid Mechanics. Englewood Cliffs, NJ: Prentice-Hall; 1965:98.
37. Wiggers CJ. The muscular reactions of the mammalian ventricles to artificial surface stimuli. Am J Physiol. 1925;73:346-378.
38. Levy JM, Mesel E, Rudolph AM. Unequal right and left ventricular ejection with ectopic beats. Am J Physiol. 1962;203:1141-1144.
39. Lister JW, Klotz DH, Jomain SL, Stuckey JH, Hoffman BF. Effect of pacemaker site on cardiac output and ventricular activation in dogs with complete heart block. Am J Cardiol. 1964;14:494-503. [Medline] [Order article via Infotrieve]
40. Finney JO. Hemodynamic alterations in left ventricular function consequent to ventricular pacing. Am J Physiol. 1965;208:275-282.
41. Samet P, Castillo C, Bernstein WH. Hemodynamic consequences of sequential atrioventricular pacing. Am J Cardiol. 1968;21:207-212. [Medline] [Order article via Infotrieve]
42. Tyers GFO, Waldhausen JA. Effect of site of synchronous unipolar ventricular stimulation and volume loading on cardiac function. J Surg Res. 1973;15:271-284. [Medline] [Order article via Infotrieve]
43.
Arisi G, Macchi E, Corradi C, Lux RL, Taccardi B.
Epicardial excitation during ventricular pacing: relative
independence of breakthrough sites from excitation sequence in canine
right ventricle. Circ Res. 1992;71:840-849.
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C. Coghlan and J. Hoffman Leonardo da Vinci's flights of the mind must continue: cardiac architecture and the fundamental relation of form and function revisited Eur. J. Cardiothorac. Surg., April 1, 2006; 29(Suppl_1): S4 - S17. [Abstract] [Full Text] [PDF]
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M. J. Kocica, A. F. Corno, F. Carreras-Costa, M. Ballester-Rodes, M. C. Moghbel, C. N.C. Cueva, V. Lackovic, V. I. Kanjuh, and F. Torrent-Guasp The helical ventricular myocardial band: global, three-dimensional, functional architecture of the ventricular myocardium Eur. J. Cardiothorac. Surg., April 1, 2006; 29(Suppl_1): S21 - S40. [Abstract] [Full Text] [PDF]
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G. D. Buckberg, M. Castella, M. Gharib, and S. Saleh Structure/function interface with sequential shortening of basal and apical components of the myocardial band Eur. J. Cardiothorac. Surg., April 1, 2006; 29(Suppl_1): S75 - S97. [Abstract] [Full Text] [PDF]
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G. D. Buckberg, M. Castella, M. Gharib, and S. Saleh Active myocyte shortening during the 'isovolumetric relaxation' phase of diastole is responsible for ventricular suction; 'systolic ventricular filling' Eur. J. Cardiothorac. Surg., April 1, 2006; 29(Suppl_1): S98 - S106. [Abstract] [Full Text] [PDF]
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M. Ballester-Rodes, A. Flotats, F. Torrent-Guasp, I. Carrio-Gasset, M. Ballester-Alomar, F. Carreras, A. Ferreira, and J. Narula The sequence of regional ventricular motion Eur. J. Cardiothorac. Surg., April 1, 2006; 29(Suppl_1): S139 - S144. [Abstract] [Full Text] [PDF]
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 |
|
 M. L. Trew, B. J. Caldwell, G. B. Sands, D. A. Hooks, D. C.-S. Tai, T. M. Austin, I. J. LeGrice, A. J. Pullan, and B. H. Smaill Cardiac electrophysiology and tissue structure: bridging the scale gap with a joint measurement and modelling paradigm Exp Physiol, March 1, 2006; 91(2): 355 - 370. [Abstract] [Full Text] [PDF]
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 |
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 A. D. McCulloch and J. H. Omens Myocyte Shearing, Myocardial Sheets, and Microtubules Circ. Res., January 6, 2006; 98(1): 1 - 3. [Full Text] [PDF]
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S. Nishimura, S. Nagai, M. Katoh, H. Yamashita, Y. Saeki, J.-i. Okada, T. Hisada, R. Nagai, and S. Sugiura Microtubules Modulate the Stiffness of Cardiomyocytes Against Shear Stress Circ. Res., January 6, 2006; 98(1): 81 - 87. [Abstract] [Full Text] [PDF]
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J. Chen, W. Liu, H. Zhang, L. Lacy, X. Yang, S.-K. Song, S. A. Wickline, and X. Yu Regional ventricular wall thickening reflects changes in cardiac fiber and sheet structure during contraction: quantification with diffusion tensor MRI Am J Physiol Heart Circ Physiol, November 1, 2005; 289(5): H1898 - H1907. [Abstract] [Full Text] [PDF]
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A. Cheng, F. Langer, F. Rodriguez, J. C. Criscione, G. T. Daughters, D. C. Miller, and N. B. Ingels Jr. Transmural sheet strains in the lateral wall of the ovine left ventricle Am J Physiol Heart Circ Physiol, September 1, 2005; 289(3): H1234 - H1241. [Abstract] [Full Text] [PDF]
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A. Cheng, F. Langer, F. Rodriguez, J. C. Criscione, G. T. Daughters, D. C. Miller, and N. B. Ingels Jr. Transmural cardiac strains in the lateral wall of the ovine left ventricle Am J Physiol Heart Circ Physiol, April 1, 2005; 288(4): H1546 - H1556. [Abstract] [Full Text] [PDF]
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K. B. Harrington, F. Rodriguez, A. Cheng, F. Langer, H. Ashikaga, G. T. Daughters, J. C. Criscione, N. B. Ingels, and D. C. Miller Direct measurement of transmural laminar architecture in the anterolateral wall of the ovine left ventricle: new implications for wall thickening mechanics Am J Physiol Heart Circ Physiol, March 1, 2005; 288(3): H1324 - H1330. [Abstract] [Full Text] [PDF]
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F. Torrent-Guasp, M. J. Kocica, A. F. Corno, M. Komeda, F. Carreras-Costa, A. Flotats, J. Cosin-Aguillar, and H. Wen Towards new understanding of the heart structure and function Eur. J. Cardiothorac. Surg., February 1, 2005; 27(2): 191 - 201. [Abstract] [Full Text] [PDF]
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 U. Rueckschloss and G. Isenberg Contraction augments L-type Ca2+ currents in adherent guinea-pig cardiomyocytes J. Physiol., October 15, 2004; 560(2): 403 - 411. [Abstract] [Full Text] [PDF]
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G. D. Buckberg, M. L. Weisfeldt, M. Ballester, R. Beyar, D. Burkhoff, H. C. Coghlan, M. Doyle, N. D. Epstein, M. Gharib, R. E. Ideker, et al. Left Ventricular Form and Function: Scientific Priorities and Strategic Planning for Development of New Views of Disease Circulation, October 5, 2004; 110(14): e333 - e336. [Full Text] [PDF]
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H. Ashikaga, J. H. Omens, N. B. Ingels Jr., and J. W. Covell Transmural mechanics at left ventricular epicardial pacing site Am J Physiol Heart Circ Physiol, June 1, 2004; 286(6): H2401 - H2407. [Abstract] [Full Text] [PDF]
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|
 F. Yalcin, H. Muderrisoglu, M. E. Korkmaz, B. Ozin, M. Baltali, and F. Yigit The Effect of Dobutamine Stress on Left Ventricular Outflow Tract Gradients in Hypertensive Patients with Basal Septal Hypertrophy Angiology, May 1, 2004; 55(3): 295 - 301. [Abstract] [PDF]
|
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|
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F. Torrent-Guasp, M. J. Kocica, A. Corno, M. Komeda, J. Cox, A. Flotats, M. Ballester-Rodes, and F. Carreras-Costa Systolic ventricular filling Eur. J. Cardiothorac. Surg., March 1, 2004; 25(3): 376 - 386. [Abstract] [Full Text] [PDF]
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H. Ashikaga, J. C. Criscione, J. H. Omens, J. W. Covell, and N. B. Ingels Jr. Transmural left ventricular mechanics underlying torsional recoil during relaxation Am J Physiol Heart Circ Physiol, February 1, 2004; 286(2): H640 - H647. [Abstract] [Full Text] [PDF]
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|
|
|
|
S. Dokos, B. H. Smaill, A. A. Young, and I. J. LeGrice Shear properties of passive ventricular myocardium Am J Physiol Heart Circ Physiol, December 1, 2002; 283(6): H2650 - H2659. [Abstract] [Full Text] [PDF]
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|
|
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M. A. Sussman, A. McCulloch, and T. K. Borg Dance Band on the Titanic: Biomechanical Signaling in Cardiac Hypertrophy Circ. Res., November 15, 2002; 91(10): 888 - 898. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
A. J. Sinusas, X. Papademetris, R. T. Constable, D. P. Dione, M. D. Slade, P. Shi, and J. S. Duncan Quantification of 3-D regional myocardial deformation: shape-based analysis of magnetic resonance images Am J Physiol Heart Circ Physiol, August 1, 2001; 281(2): H698 - H714. [Abstract] [Full Text] [PDF]
|
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|
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R. Mazhari, J. H. Omens, R. S. Pavelec, J. W. Covell, and A. D. McCulloch Transmural Distribution of Three-Dimensional Systolic Strains in Stunned Myocardium Circulation, July 17, 2001; 104(3): 336 - 341. [Abstract] [Full Text] [PDF]
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T. Arts, K. D. Costa, J. W. Covell, and A. D. McCulloch Relating myocardial laminar architecture to shear strain and muscle fiber orientation Am J Physiol Heart Circ Physiol, May 1, 2001; 280(5): H2222 - H2229. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
R. M. Shoucri Active and passive stresses in the myocardium Am J Physiol Heart Circ Physiol, November 1, 2000; 279(5): H2519 - H2528. [Abstract] [Full Text] [PDF]
|
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|
|
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K. Tobita and B. B. Keller Right and left ventricular wall deformation patterns in normal and left heart hypoplasia chick embryos Am J Physiol Heart Circ Physiol, September 1, 2000; 279(3): H959 - H969. [Abstract] [Full Text] [PDF]
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|
|
 |
|
 R. Mazhari, J. H Omens, J. W Covell, and A. D McCulloch Structural basis of regional dysfunction in acutely ischemic myocardium Cardiovasc Res, August 1, 2000; 47(2): 284 - 293. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 W.-Y. I. Tseng, T. G. Reese, R. M. Weisskoff, T. J. Brady, and V. J. Wedeen Myocardial Fiber Shortening in Humans: Initial Results of MR Imaging Radiology, July 1, 2000; 216(1): 128 - 139. [Abstract] [Full Text]
|
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|
|
|
|
J. Bogaert, H. Bosmans, A. Maes, P. Suetens, G. Marchal, and F. E. Rademakers Remote myocardial dysfunction after acute anterior myocardial infarction: impact of left ventricular shape on regional function: A magnetic resonance myocardial tagging study J. Am. Coll. Cardiol., May 1, 2000; 35(6): 1525 - 1534. [Abstract] [Full Text] [PDF]
|
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|
|
|
|
S.-J. Dong, P. S. Hees, W.-M. Huang, S. A. Buffer Jr., J. L. Weiss, and E. P. Shapiro Independent effects of preload, afterload, and contractility on left ventricular torsion Am J Physiol Heart Circ Physiol, September 1, 1999; 277(3): H1053 - H1060. [Abstract] [Full Text] [PDF]
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|
|
K. D. Costa, Y. Takayama, A. D. McCulloch, and J. W. Covell Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium Am J Physiol Heart Circ Physiol, February 1, 1999; 276(2): H595 - H607. [Abstract] [Full Text] [PDF]
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|
|
|
D. F. Scollan, A. Holmes, R. Winslow, and J. Forder Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging Am J Physiol Heart Circ Physiol, December 1, 1998; 275(6): H2308 - H2318. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
E. W. Hsu, A. L. Muzikant, S. A. Matulevicius, R. C. Penland, and C. S. Henriquez Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation Am J Physiol Heart Circ Physiol, May 1, 1998; 274(5): H1627 - H1634. [Abstract] [Full Text] [PDF]
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|
|
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K. D. Costa, K. May-Newman, D. Farr, W. G. O'Dell, A. D. McCulloch, and J. H. Omens Three-dimensional residual strain in midanterior canine left ventricle Am J Physiol Heart Circ Physiol, October 1, 1997; 273(4): H1968 - H1976. [Abstract] [Full Text] [PDF]
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|
|
|
G. A. MacGowan, E. P. Shapiro, H. Azhari, C. O. Siu, P. S. Hees, G. M. Hutchins, J. L. Weiss, and F. E. Rademakers Noninvasive Measurement of Shortening in the Fiber and Cross-Fiber Directions in the Normal Human Left Ventricle and in Idiopathic Dilated Cardiomyopathy Circulation, July 15, 1997; 96(2): 535 - 541. [Abstract] [Full Text]
|
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Y. Takayama, K. D. Costa, and J. W. Covell Contribution of laminar myofiber architecture to load-dependent changes in mechanics of LV myocardium Am J Physiol Heart Circ Physiol, April 1, 2002; 282(4): H1510 - H1520. [Abstract] [Full Text] [PDF]
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J. H. Omens, T. P. Usyk, Z. Li, and A. D. McCulloch Muscle LIM protein deficiency leads to alterations in passive ventricular mechanics Am J Physiol Heart Circ Physiol, February 1, 2002; 282(2): H680 - H687. [Abstract] [Full Text] [PDF]
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