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Abstract
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.
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.
Materials and Methods
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.
a, Schematic equatorial section showing sites of radiopaque marker columns in anterior left ventricle (LV) and interventricular septum. RV indicates right ventricle. b, Diagrams showing finite elements fitted to columns of markers at end diastole (ED) and end systole (ES) (shaded lines). Transmural distribution of strain is calculated from deformation of the element from ED to ES. Alternatively, changes in length of the sides of tetrahedrons formed from four markers (dark lines) can be used to calculate local strain with the “homogeneous-strain” method.
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 (×20) 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.
Schematic diagrams showing methods for measuring laminar morphology and for comparing orientation of myocardial laminae and strain (E). a, Local cardiac coordinate system. b, Tissue block sectioned parallel to the epicardium. c through e, Measurement of angles in circumferential-longitudinal (1-2), circumferential-radial (1-3), and longitudinal-radial (2-3) planes, respectively. Angles represent local tangents to the cleavage planes. f, Schematic diagrams of the normal and shear strain orientations. g, Principal strain orientations at a representative subendocardial site. h, Planes of maximum relative sliding (diagonals). i, Normals to the planes (S1 and S2). j, Scalar products calculated to obtain the angle between each of S1 and S2 and the morphology vector M. For further explanation, refer to text.
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 mm×3 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[M×S1]) (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.
Results
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.
Graphs showing transmural distribution of wall thickening strain (E33) from outer surface (0% depth) to left ventricular (LV) endocardial surface (LV En, 100% depth) and the accompanying longitudinal-radial shear strain (E23). The data are from anterior LV and septum in one heart, showing increasing strain from outer to inner wall and the opposite direction of E23 accompanying wall thickening at the two sites. Comparison of finite-element with homogeneous-strain results shows close agreement between the two approaches. EDP indicates end-diastolic pressure.
Normal and Shear Strains (Finite-Element Method) for Outer Wall (0% to 33%), Midwall (34% to 66%), and Inner Wall (67% to 100%) at Anterior Left Ventricular and Septal Sites
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.
Schematic diagrams (top) and photomicrographs (bottom) of subendocardial cleavage planes shown in longitudinal-radial (2-3) plane in anterior left ventricle (LV) and septum. RV indicates right ventricle. Angles are measured relative to the local outer surface tangent. Myocardial laminae approach the LV endocardium from opposite directions at the two sites. Subendocardial cleavage plane angle is steeper in anterior LV (−67±11°) compared with septum (44±12°) (P<.0005 by paired t test for absolute magnitude of angle).
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.
a, Bar graphs showing end-systolic wall thickening strain (E33) and longitudinal-radial shear strain (E23) in the subendocardium of left ventricular (LV) free wall (solid bars) and septum (hatched bars) of seven hearts. Wall thickening (positive E33) is accompanied by positive E23 in the free wall and negative E23 in the septum. b, Bar graph showing subendocardial cleavage-plane orientation in the longitudinal-radial (2-3) plane of the LV free wall and septum in eight hearts. Values are mean±SD, and P values are for paired t test comparisons between anterior LV and septum.
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.
Left, Graphs showing transmural distribution of cleavage-plane angles in the circumferential-longitudinal (1-2, ▵), 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 ≈2-mm diameter of the surface beads. Ep indicates epicardium; En, endocardium; and RV, right ventricle. Middle, Schematic examples of 1-3 and 2-3 sections showing cleavage planes and coordinate axes with direction of positive and negative angles. Epi indicates epicardium. Right, Schematic three-dimensional representation of a block of myocardium from which the LV sections were cut, with exploded view illustrating each of the measured angles.
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).
Angle between myocardial laminae (or cleavage planes) and planes of maximum sliding from strain analysis. Top left, Plot showing all angles fulfilling morphological acceptance criteria for anterior left ventricle (LV) and septum. Each heart is represented by a different symbol. Top right, Bar graph showing mean angle data (±SD) for outer wall, midwall, and inner wall (divisions indicated by dashed lines in top left panel). Bottom panel, Bar graph (left) showing mean angle data (±SD) divided into anterior LV and septum with accompanying ANOVA data (right). Near the LV endocardium (LV En), the angle becomes small, indicating that maximum shearing in the wall occurs by means of myocardial laminae sliding relative to each other. See text for further details.
Number of Data Points Fulfilling Morphological Selection Criteria and Mean Angles for Maximum Shear Analysis at Different Depths in Each Heart (Combined Anterior Left Ventricular and Septal Data)
Discussion
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.
Possible mechanism of systolic wall thickening for the inner third of the ventricular wall. a, Schematic diagram of anterior left ventricular (LV) apex-base section in longitudinal-radial (2-3) plane showing that myocardial laminae and intervening cleavage planes approach the endocardium obliquely. Subject to measured positive 2-3 shear strain, myocardial laminae (shaded) slide relative to each other and change orientation from end diastole (b) to end systole (c), resulting in displacement of the endocardium inward and subsequent wall thickening, which can be 40% in the subendocardial region. Increases in myocyte diameter during contraction also contribute to systolic wall thickening.
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 (β), given an initial angle (α). 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 (β) in the 2-3 plane resulting from the given finite strains is given by the following formula36 : 
For our two inner wall sites, this angle is near 12°. We see that the thickening ratios calculated by this simple mechanism are consistent with the thickening strains we have measured, and when we add a further small amount for cell diameter increases, the calculated values are still within 1 SD of measured wall thickening. Note that although the finite-strain E33 is not exactly equivalent to a simple linear thickening ratio (ΔT/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.)
Schematic diagram showing that wall thickening resulting from shearing of myocardial laminae through a given angle (β) depends on the initial cleavage-plane orientation (α). In panels a and b, the magnitude of the initial angle is 67° and 44°, respectively; a 12° angle change in each case results in greater displacement of the tip (wall thickening) in panel a than in panel b. In panel c, we have plotted the thickening ratio function (ΔT/To, given by the formula at bottom) for different values of α and β. Illustrated angles correspond to mean data for anterior left ventricular (LV) and septal (S) sites.
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 (M×S1 or M×S2) 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.
Appendix A1
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 m1×m2=0.91, m1×m3=0.90, and m1×m2=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 M×S1=0.000 and M×S2=−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).
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.
- Received June 3, 1994.
- Accepted March 29, 1995.
- © 1995 American Heart Association, Inc.
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