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1Department of Cardiovascular and Thoracic Surgery, Stanford University School of Medicine, Stanford; 3Laboratory of Cardiovascular Physiology and Biophysics, Research Institute of The Palo Alto Medical Foundation, Palo Alto, California; and 2Department of Biomedical Engineering, Texas A & M University, College Station, Texas
Submitted 7 February 2005 ; accepted in final form 26 April 2005
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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wall thickening; myocardium; systolic function
This finding that contracting LV myofibers need not develop a significant transmural systolic wall thickening gradient challenges some fundamental concepts about how the ventricular wall works. Thus we thought it important to delve more deeply into these experimental data in an attempt to provide a possible mechanistic interpretation.
The analytic technique in the present study employs a laminar sheet anatomic model for the LV wall. Spotnitz et al. (16) first suggested that reorientation of transmural sheets of fibers could provide a basis for wall thickness changes. LeGrice et al. (13, 14) subsequently showed that ventricular fibers were arrayed in stacked laminar sheets, three to four cells thick, and demonstrated that longitudinal-radial shear of these sheets was likely to be an important mechanism underlying systolic wall thickening. Costa et al. (6) extended this work, showing that systolic sheet extension and sheet-normal shear were the primary determinants of systolic wall thickening. The analytic approach of Costa et al. was used in the present study.
Our previous analysis of these data expressed transmural strains in terms of circumferential, longitudinal, and radial coordinates (4). Employing quantitative histological techniques to directly measure fiber and sheet angles (11), we converted these circumferential-longitudinal-radial strains into fiber-sheet-normal coordinates using the transformation derived by Costa et al. (6). We then employed a relation derived from this transformation (6) to express the contributions of sheet extension, sheet thickening, and sheet shear to the increase in transmural systolic wall thickness.
This analysis showed that 1) sheets are oriented in a transmural pleated geometry in this lateral equatorial LV location, confirming a recent finding from another study in our laboratory (11), 2) systolic wall thickening involved a different "mix" of sheet mechanisms at different transmural depths, 3) subepicardial sheet strains were selectively increased from 1 to 8 wk after surgery, and 4) the greatest contributors to the increase in subepicardial systolic wall thickening from 1 to 8 wk after surgery (the primary factor underlying abolition of the transmural thickening gradient at 8 wk) were sheet extension and sheet-normal shear. A mechanistic model was proposed to relate sheet geometry, sheet dynamics, and wall thickening in an attempt to further understand these results.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Surgical preparation and marker data acquisition. The surgical preparation and marker data acquisition methods for these experiments have been described in detail in our previous publication (4) and, therefore, are only outlined here. Through a left thoracotomy, 13 subepicardial radiopaque markers were surgically implanted into 7 sheep to silhouette the LV chamber (Fig. 1A). Epicardial echocardiography was used to identify and measure the wall depth of a free segment of the midlateral equatorial LV wall between papillary muscle insertions, and three transmural columns of beads (4 beads each, evenly spaced from endocardium to epicardium, 10-mm intercolumn distance; Fig. 1A) were then implanted into this region using a bead-insertion trochar oriented normal to the regional epicardial tangent plane. The chest was closed, and the sheep were resuscitated. At 1 and 8 wk postoperatively, each animal was taken to the cardiac catheterization laboratory, sedated with ketamine (25 mg/kg im), intubated, and mechanically ventilated, and anesthesia was maintained with inhalational isoflurane (1–2.5%). Simultaneous biplane videofluoroscopy (60 Hz), ECG, and LV and aortic pressures were recorded during steady-state baseline conditions with the heart in normal sinus rhythm, and ventilation was arrested at end expiration. Data from the two radiographic views were subsequently digitized and merged to yield three-dimensional (3D) coordinates for each radiopaque marker every 16.7 ms. After the 8-wk study, conventional 3.0-mm perfusion balloon catheters were placed into the proximal circumflex and left anterior descending coronary arteries. The animals were then euthanized by sodium pentothal administration (1 g iv) followed by an intravenous bolus of potassium chloride (80 meq) to arrest the hearts at end diastole (ED). After adjustment of LV pressure by blood withdrawal to match previous in vivo LV ED pressure, simultaneous infusions of 300 ml of buffered glutaraldehyde (5%) were employed to fix the hearts in situ. The hearts were then explanted and stored in 10% formalin for later histological examination.
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(positive as illustrated in Fig. 1C) between the local muscle fiber axis (F; Fig. 1C) and the circumferential axis (X1, Fig. 1C) was measured at five sites on each image using image-processing software (SPOT Advanced version 4.0.1, Diagnostic Instruments, Sterling Heights, MI). Mean was used to characterize the fiber angle at each transmural depth. Two parallel cuts separated by 
1 mm were then made normal to the fiber axis in each of these transmural sections. The sheet (S)-normal (N) faces of these cuts at 20%, 50%, and 80% depths are schematically depicted in Fig. 1B; the S-N face at 80% depth, identified as "section 
to F," is further delineated in Fig. 1C. The samples were kept moist with a 30% sucrose solution to avoid the distortional effects of dehydration and to minimize freezing artifact during direct histological measurements of sheet angle 
from the S-N plane (positive is shown in Fig. 1C). The fiber-normal slices were placed in 15 x 15 x 5 mm plastic molds (Tissue-Tek, Cryomold Intermediate, Miles, Elkhart, IN), embedded in OCT compound (Tissue-Tek, Sakura Finetek, Torrance, CA), frozen over dry ice, and then stored for 2–4 days in a –80°C freezer. They were cut into 8- to 10-µm-thick sections using a cryostat (Jung Frigocut 2800 N, Leica) and transferred to a glass slide, where they were imaged immediately with a digital camera (RT Color, 1X HRD 100-NIK, Diagnostic Instruments) mounted on a light microscope (type 301-371.010, Leica) at x25 magnification. Myolaminae coursing in the direction noted from the frozen specimen were observed (Fig. 1B and Fig. 1C, "sheets"), and, over a 1-min period, gaps between the cleavage planes appeared between the myolaminae (Fig. 2). Image-processing software was used to measure five values between sheet orientations (Xs) and X3 normal to the endocardial face, over the length of the specimen (Fig. 2 illustrates negative ). Mean was used to characterize at each transmural depth.
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Cardiac finite strains. Cardiac finite strains have been described in detail previously (4). Strains are reported at 20%, 50%, and 80% depths from the epicardium, with ED as the reference configuration and ES as the deformed configuration.
Sheet finite strains.
The method of Costa et al. (6) for three consecutive beats and at each transmural depth in each heart was used to transform cardiac finite strains (i.e., relative to X1, X2, and X3; Fig. 1C) at that depth into sheet strains at that depth oriented along the fiber (f), sheet (s), and sheet-normal (n) axes (Fig. 1C) by application of and in that heart at that depth as follows
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ED and ES sheet remodeling strains. ED sheet remodeling strains were obtained for each heart by comparison of bead positions at ED in sheet coordinates from the 1-wk study (reference configuration) with the positions of these same beads in the same heart at ED in sheet coordinates from the 8-wk study (deformed configuration). ES remodeling sheet strains were obtained for each heart by comparison of bead positions at ES in sheet coordinates from the 1-wk study (reference configuration) with the positions of these same beads in the same heart at ES in sheet coordinates from the 8-wk study (deformed configuration).
Statistical analysis. Values are means ± SD, unless otherwise stated. Sheet strains were compared using two-way repeated-measures ANOVA with Student-Newman-Keuls pairwise multiple comparisons (Sigmastat 2.03, SPSS, Chicago, IL). ED and ES strains were compared with zero using a one-sample t-test. P < 0.05 was considered statistically significant.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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and measured for each of the seven hearts in this study at 20%, 50%, and 80% wall depth from the epicardium. Fiber angles varied almost linearly with depth: was nearly circumferential in the midwall; exhibited a pleated-sheet behavior and alternating sign between 20%, 50%, and 80% depths. This fiber and sheet geometry is illustrated schematically in Fig. 1B.
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(thereby contributing to wall thickening) at each wall depth.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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The analytic approach of Costa et al. (6) was used to obtain these findings. Beginning with regional transmural strains defined in local "cardiac" coordinates (in the circumferential, longitudinal, and radial directions), quantitative histological measurements of fiber and sheet geometry were obtained as a function of transmural depth in the region under study. The fiber-sheet data in Eq. 1 were used to transform cardiac strains into "sheet" strains (fiber, sheet, and sheet-normal coordinates). Although Costa et al. studied the anterior wall of open-chest dogs and we studied the lateral wall of closed-chest sheep, we discuss our findings in relation to their pioneering work, inasmuch as theirs is the only study to our knowledge with the required spatial resolution across the wall for comparison. The same strain tensor definition and timing reference states of Costa et al. were used for direct comparison.
Cardiac strains. The lateral wall systolic cardiac strains for these hearts were reported in our previous publication (4). These strains [ES (deformed state) and ED (reference state)] were similar to those measured by Costa et al. (6), except we observed 1) smaller longitudinal strains (E22) in the midwall and subendocardium, 2) abolition of the transmural radial wall thickening gradient (E33) 8 wk after surgery, 3) circumferential-radial shear (E13) of opposite sign, and 4) greater longitudinal-radial shear (E23) in the midwall and subepicardium.
Sheet geometry.
Distribution of for these hearts (Table 1) was virtually indistinguishable from that observed in the canine basal anterior wall (6), but distributions of were distinctly different. Costa et al. (6), with indirect measurements, reported mean basal anterior wall values of 0° at 20% depth to 20° at 50% and 80% depths from the epicardium, i.e., near-radial sheets. We found, by direct measurement (11), much greater magnitudes of in a pleated- pattern, ranging from a mean of +37° at 20% depth to –37° at 50% depth and then back to 62° at 80% depth (Table 1).
Sheet strains.
In these ovine hearts, systolic fiber shortening (Eff) was 5–12% (Table 2) and did not exhibit a transmural gradient, consistent with the predictions of Arts et al. (1) and the observations of Costa et al. (6). Sheet extension (Ess), however, although large and positive, decreased with depth in our study, most prominently at 8 wk after surgery, in contrast to the increase with depth observed in the canine hearts (6). The most profound difference between our findings and those of Costa et al., however, was our positive Enn during systole (i.e., sheet thickening) and their small and consistently negative (sheet thinning) Enn at their basal and apical anterior sites. Sheet thickening has a straightforward explanation; sheet thinning is more difficult to explain, potentially requiring cellular interdigitation (6). It is possible that the thinning they observed could result, in part, from the very small measured by their indirect histological approach in the canine studies; we measured much larger values with our direct histological approach applied to the anterior basal region of the ovine heart (11).
In contrast to canine hearts, where fiber-sheet shear (Efs) was essentially zero (6), Efs in these ovine hearts exhibited a significant systolic transmural gradient, ranging from negative in the subepicardium to positive in the subendocardium (Table 2). Significant Efs suggests considerable sliding of fibers with respect to one another within the sheets during systole. Also, in contrast to canine hearts, where sheet-normal shear (Esn) was positive and increased with depth (6), Esn, in concert with , alternated sign at increasing transmural depth (Table 2).
Contributions of sheet strain to wall thickening. Computed from Eq. 2 (Table 5, Fig. 3), Ess and Esn contributions to radial wall thickening (E33) were dominant at 20% depth, with little contribution from Enn. At 50% depth, however, Ess, Enn, and Esn contributed importantly to E33. At 80% depth, Enn and Esn dominated, with little contribution from Ess. These findings differ from those reported by Costa et al. (6), where the contribution of Enn to E33 was almost zero at all depths, and sheet extension (Ess) and shear (Esn) each contributed about half of E33 in the inner half of the wall, and sheet extension was the dominant mechanism in the outer wall.
Costa et al. (6) pointed out that Esn must have the same sign as for Esnsincos to augment wall thickening. They found large positive Esn at all depths, but negative at 20% depth; hence, Esn contributed to subepicardial wall thinning in their study. In contrast, Esn and always had the same sign in the present study; thus, as illustrated in Fig. 3, Esn contributed significantly to +E33 at all transmural depths.
Spotnitz et al. (16) and then LeGrice et al. (14) suggested that reorientation of transmural laminar structures by E23 might underlie LV wall thickness changes. Costa et al. (6) found this model to be only partially true, in that they found basal-site E23 and to be positive at 50% and 80% depths, which, according to this model, incorrectly predicted wall thinning. They pointed out that "it is the transverse shear associated with sliding of sheets lateral to the local fiber axis (Esn), as opposed to the reorientation of long- or short-axis cleavage planes (E23 or E13, respectively), that contributes to radial wall thickening strain (E33)." We support this conclusion, in that E23 and E33 were positive at all transmural depths in these ovine hearts, yet was negative in the midwall, again incorrectly predicting midwall thinning. We add, however, that the pleated- sheet configuration we measured, indicated by the alternating signs of from subepicardium to midwall to subendocardium (Table 1), allows wall thickness changes with less total transmural E23 than would be required in the presence of a single transmural sheet from epicardium to endocardium. Furthermore, this pleated sheet structure provides a mechanism for radial wall thickening from sheets confined to very compact X1-X2 spaces.
The most powerful approach to studying sheet dynamics is undoubtedly through the use of MRI techniques, inasmuch as MRI studies are noninvasive and allow assessment of the entire LV, rather than just a few specific regions. Using diffusion MRI to obtain sheet structure and phase-contrast MRI to obtain strain rate, Dou et al. (8) recently reported midsystolic sheet dynamics at the equatorial LV level in normal human subjects and found, as we found in the present study, substantial contributions of Ess, Esn, and Enn to E33 in the lateral free wall. Their study, however, reported average contributions over the entire transmural thickness at each LV site. The present study suggests that considerable transmural sheet geometry and strain fine structure remain to be revealed by MRI as its spatial resolution increases.
Dou et al. (8) found considerable intersubject variability, and this also characterized our findings. We typically observed characteristic sheet "fingerprint" strain patterns, which exhibited beat-to-beat repeatability in each heart but were quite variable from heart to heart. The ubiquity of the Esn contribution to E33 in dogs, sheep, and humans and at various transmural depths, however, suggests that Esn is a highly conserved mechanism for altering ventricular wall thickness.
As in the canine (6) and human (8) studies, Esn in these ovine hearts greatly exceeded Efn (Table 2). Dou et al. (8) advanced the reasonable proposition that this preference for sheets sliding relative to one another along the sheet direction, rather than along the fiber direction, may reflect the specifics of 3D sheet packing.
Wall thickening mechanism.
Figure 4 illustrates our mechanistic speculation concerning sheet geometry, sheet dynamics, and wall thickening. This model proposes, along with LeGrice et al. (13, 14), Costa et al. (6), and Dou et al. (8), that systolic LV wall thickening arises from extension, thickening, and shear of laminar myofiber sheets, each three to four cells thick, with cleavage planes sliding radially with wall thickening (6, 9, 12, 16). We assume tight coupling of myocytes by the extensive endomysial collagen network within the sheets (3, 6, 13), with looser coupling between adjacent sheets (3, 13), such that Eff, Ess, and Efs are strains primarily within the sheets and Efn and Esn are strains primarily between adjacent sheets, possibly accommodated by the perimysial collagen strands connecting adjacent laminar cell bundles (3, 6, 13). In this model, positive Enn (thickening) could be accommodated by an increase in the gap between the sheets, as suggested by Dou et al., an increase in the thickness of the sheets themselves, or both. Although the model applies generally, for geometric simplicity we have selected a midwall location for this illustration, because fibers are roughly circumferential in the midwall ( 
0°); thus the long axes of the fibers in Fig. 4 are shown oriented normal to the page. Fiber force and shortening during systole, therefore, are oriented normal to the page. Because fibers encircle the LV, however, such normal fiber force is converted to radial force (F3, the basis of pressure generation) directed, as shown, toward the interior of the LV chamber. F3, in turn, can be expressed in terms of components aligned with the sheet and normal axes, Fs and Fn, respectively. Force in the sheet direction, Fs, tends to extend the sheets (+Ess), lengthening the elastic matrix (elastic constant Ks) connecting the fibers within each sheet. Force in the normal direction, Fn, tends to thicken and/or separate the sheets (+Enn), lengthening the elastic matrix (elastic constant Kn) within/between the sheets. However, Fn also tends to rotate the sheet axis toward the radial (X3) axis, which results in sheet-normal shear (–Esn) as tends toward zero (i.e., radial). All this, of course, takes place within tethering constraints imposed by adjacent structures, here represented by generic elastic elements with elastic constants K2 and K3, oriented in the longitudinal (X2) and radial (X3) directions, respectively. Note that this interpretation assumes that Esn (and possibly Enn) primarily affects energy storage in the elastic elements Kn between the sheets during systole, rather than in those within the stiff sheets themselves (Ks), a reasonable, but as yet untested, assumption.
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is positive at both of these depths (Table 1), E33 appears to be generated by different mechanisms in the subepicardium and subendocardium (Table 5, Fig. 3). In light of the above-described sheet-model interpretation, this mix of sheet mechanisms for converting fiber shortening to systolic radial wall thickening at different wall depths suggests the presence of transmural gradients of Ks and Kn, with Ks increasing and Kn decreasing from subepicardium to subendocardium. Among other mechanisms, such gradients could be brought about by transmural gradients of collagen type and/or cross-linking in the LV wall. To hypothesize the existence of such gradients is not unreasonable, inasmuch as transmural gradients have been documented in titin (10), sarco(endo)plasmic reticulum Ca2+-ATPase (5), myosin regulatory light chain phosphorylation (7), and connexin43 (15) across the LV wall. Changes from 1 to 8 wk after marker implantation. For the group, fiber length was not significantly altered from 1 to 8 wk after marker implantation at ED or ES (Eff; Tables 3 and 4), yet subepicardial systolic fiber contraction increased in six of seven hearts (Eff, 20% depth; Table 2). This could reflect a selective increase in the force-generating capability of the subepicardial fibers as well as a selective decrease in Ks (Fig. 4) of the elastic matrix within the subepicardial sheets. We cannot distinguish between these possibilities with the present data, and indeed both may have occurred, but the fact that subepicardial Ess and Efs increased significantly lends some support to the latter possibility. A selective decrease in subepicardial Ks could present a reduced load on the fibers (thereby allowing increased Eff), and the greater matrix elasticity within the sheets could allow greater Efs shear as well as greater sheet extension (Ess).
The magnitude of subepicardial shear (Esn, 20% depth; Table 2) increased in all seven hearts from 1 to 8 wk after marker implantation. This change did not achieve statistical significance, however, because one heart (heart 3, Table 1) exhibited a transition from positive to negative in the vicinity of the 20% depth, and strict adherence to our 20% depth selection requirement dictated that we select the negative value. Thus Esn was negative at 1 wk and became more negative at 8 wk, and although Esn magnitude always increased, statistical significance was lost for the grouped data. As seen below in our discussion of the components of wall thickening, however, this is a case where functional significance trumps statistical significance. We interpret the increase in subepicardial Esn magnitude in all seven hearts as indicating a decrease in Kn, as well as Ks, from 1 to 8 wk after marker implantation. Thus a selective increase in the dynamics within and between the subepicardial sheets appears to be a likely factor in the abolishment of the systolic wall thickening gradient from 1 to 8 wk after marker implantation.
Systolic radial wall thickening of the subepicardium more than doubled from 1 to 8 wk (E33; Table 5). Application of Eq. 2, which allows assignment of the sheet strain components of this thickening, demonstrated that from 1 to 8 wk the magnitudes of the sheet extension contribution (E20ssc) and sheet-normal shear contribution (E20snc) increased significantly (Table 5, Fig. 3). At both times, roughly half of systolic radial wall thickening of the subepicardium arose from Esnc and the other half from Essc. In contrast to subendocardial dynamics, where Ennc was an important component of thickening, subepicardial Ennc did not participate in subepicardial thickening. Note that the change in Esnc was statistically significant here (Table 5), because negative Esn paired with negative contributes to positive E33, as does positive Esn paired with positive .
Thus, from combination of these considerations with those discussed in our previous study (4), our current working hypothesis as to why subepicardial E33 more than doubled from 1 to 8 wk after marker implantation invokes selective, heterogeneous changes in the subepicardial intercellular matrix. We postulate an abnormally stiff subepicardial Ks at 1 wk that becomes considerably more elastic at 8 wk, thereby allowing increased subepicardial systolic fiber shortening (Eff) and markedly increased subepicardial sheet extension (E20ssc), coupled with an abnormally stiff subepicardial (increased) Kn at 1 wk that becomes considerably more elastic at 8 wk, thereby allowing a significant increase in subepicardial sheet-normal shear (E20snc).
Limitations. Caution is always warranted before extrapolation of the results from animal studies to the human heart; in this case, however, the convergence of a number of findings from the studies of normal human hearts by Dou et al. (8), those of canine hearts by Costa et al. (6), and the present study of ovine hearts is encouraging, in that applicable data were obtained, despite the surgery, anesthesia, and marker implantation in these animal studies.
It should be emphasized that the analytic approach used in the present study is based on the validity of the fiber-sheet model developed by LeGrice et al. (13, 14). Although much evidence supports this model, much more remains to be understood about myocardial structure; thus the findings of the present study must be considered provisional.
Although measurements are relatively straightforward and reproducible, measurements are much more difficult and subjective. Myocardial laminae in fresh tissue are tightly packed, and interlaminar gaps are thought to arise primarily from tissue shrinkage due to dehydration (6, 13). Thus the gaps in Fig. 2 are presumed to be interlaminar, but it is apparent that a range of values can be observed. This requires measurement of many values in each section and then derivation of a composite mean for the section as reported in Table 1. However, Fig. 2 is a fairly unambiguous illustration; many sections are more difficult to interpret. The situation becomes increasingly difficult in the subendocardium, where two or more populations may be present. It is not appropriate to average these populations, because they are often of opposite sign and could average, inappropriately, to zero. Our approach in the present study, as in those of Costa et al. (6) and Ashikaga et al. (2), was to employ the dominant population in our analysis, which is usually fairly evident, but much future work needs to be done to understand the functional importance of regions with multiple populations. A further difficulty is that can change sign abruptly in a few millimeters. Costa et al. reported encountering discontinuities in the subendocardial trabeculata-compacta interface, and we encountered such discontinuities from 20% to 50% depth and again from 50% to 80% depth in the transmural pleated- configuration, as well as in samples from nearby longitudinal or circumferential sites. We were concerned that this could be a source of error, because, for technical reasons, our tissue blocks were taken immediately basal to the marker columns, and if sheet angles changed abruptly in a few millimeters, these populations might not represent those present in the region spanned by the columns. This appears not to be a major problem at this location, however, because tissue blocks from all studies, including these seven hearts and five additional hearts (11) taken a statistical population of sites in this lateral equatorial region and measured by independent observers unaware of the findings of others, have yielded the same transmural pleated- sheet configuration. Thus the sheet geometry in the lateral equatorial region of the ovine heart appears to be fairly independent of longitudinal or circumferential shifts of 1 cm, so we felt justified in using these values in our cardiac-to-sheet strain transformations.
Finally, it should be emphasized that we did not measure the collagen content or elasticity of the intracellular matrix in this study. Our mechanistic model helped us conceptualize a working hypothesis for future experiments to test whether a selective decrease in subepicardial intercellular matrix stiffness is responsible for elimination of the transmural wall thickening gradient from 1 to 8 wk after surgery. We should also emphasize, as did Costa et al. (6), that deformations measured from bead columns or MRI techniques average the deformations of large numbers of sheets, and we cannot yet measure the dynamics of individual sheets. Thus all inferences regarding the dynamics of individual sheets must remain speculative.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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) and transmural equatorial lateral wall beads (
). Shaded box is location of transmural tissue block taken from lateral equatorial wall for histological examination. B: fiber and sheet geometry at 3 transmural levels from histological examination of transmural tissue block. Dark shaded planes are sections perpendicular to the local fiber axis. Black bands illustrate sheet orientations at each depth. Fiber orientation is illustrated on the rightmost surface of the subblock at each depth. C: subblock of tissue at 80% depth. Dark shaded plane is section perpendicular to the local fiber axis. Black bands illustrate sheet orientation. Fiber orientation is identified on the rightmost surface. Cardiac coordinates X1 (circumferential), X2 (longitudinal), and X3 (radial) are shown, along with sheet coordinates F (fiber), S (sheet), and N (normal). Fiber angle (
