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1 Department of Cardiovascular
and Thoracic Surgery and Cardiovascular Medicine, Left ventricular
(LV) wall stress is an important element in the assessment of LV
systolic function; however, a reproducible technique to determine
instantaneous local or regional wall stress has not been developed.
Fourteen dogs underwent placement of twenty-six myocardial markers into
the ventricle and septum. One week later, marker images were obtained
using high-speed biplane videofluoroscopy under awake, sedated,
atrially paced baseline conditions and after inotropic stimulation
(calcium). With a model taking into account LV pressure, regional wall
thickness, and meridional and circumferential regional radii of
curvature, we computed average midwall stress for each of nine LV
sites. Regional end-systolic and maximal LV wall stress were
heterogeneous and dependent on latitude (increasing from apex to base,
P < 0.001) and specific wall
(anterior > lateral and posterior wall stresses;
P = 0.002). Multivariate ANOVA
demonstrated only a trend (P = 0.056)
toward increased LV stress after calcium infusion; subsequent
univariate analysis isolated significant increases in end-systolic LV
wall stress with increased inotropic state at all sites except the
equatorial regions. The model used in this analysis incorporates local
geometric factors and provides a reasonable estimate of regional LV
wall stress compared with previous studies. LV wall stress is
heterogeneous and dependent on the particular LV site of interest.
Variation in wall stress may be caused by anatomic differences
and/or extrinsic interactions between LV sites, i.e.,
influences of the papillary muscles and the interventricular septum.
systolic function
LEFT VENTRICULAR (LV) wall
stress is an important determinant of myocardial oxygen consumption
(27), a modulator of ventricular hypertrophy during abnormal loading of
the heart (1), and an important factor in our understanding of LV
mechanics (31). Additionally, determination of regional contractility
(e.g., myocardial stiffness) requires the use of regional analysis of
LV wall stress (22). Despite this fundamental importance, a technique
to determine instantaneous regional LV wall stress at different
locations simultaneously has not been described. Numerous methods were
devised either to measure directly (13, 15) or to approximate (using
geometric models) regional LV stress (8, 10, 21, 26, 29) but typically
only at a single LV wall location. Both these approaches, furthermore,
have limitations that potentially confound data interpretation: direct
measurement of transmural wall stress (with implantable strain gauges)
is hampered by uncertainty in quantifying the degree of coupling
between the transducer and the ventricular wall; geometric modeling
typically relies on an axisymmetric idealized ventricle, thereby
potentially masking regional variations. Although some degree of
geometric modeling is required, the assumption of axisymmetry eliminates the ability to detect circumferential differences. Recent
advances utilizing magnetic resonance imaging (MRI) techniques combined
with finite-element analysis have also been described; these have the
potential of minimizing these geometric assumptions but are limited in
their capability to evaluate multiple different LV regions
simultaneously and cannot be applied for beat-to-beat analyses (3, 4,
9, 18, 19).
In an attempt to minimize the limitations inherent in the direct
measurement and modeling techniques, a combination of myocardial marker
technology and regional (rather than global) modeling assumptions was
used to compute simultaneous regional average wall stresses at multiple
LV locations. A comprehensive LV myocardial marker array permitted
simultaneous wall thickness measurements at nine discrete sites;
geometric assumptions were then introduced to compute local wall
stresses at these nine sites. We hypothesized that the magnitude of
wall stress would vary as a function of both the LV wall site examined
and distance from the base of the heart. We speculate that this
variability may be accounted for by considerations of local geometry.
Surgical Preparation: Placement of LV Myocardial Markers
ABSTRACT
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
INTRODUCTION
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
MATERIALS AND METHODS
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
Experimental Protocol
Approximately 1 wk (9 ± 7 days, mean ± SD; range = 5-34 days) after marker implantation, the animals were taken to the cardiac catheterization laboratory for hemodynamic and videofluoroscopic data acquisition. Diazepam (5 mg iv) and ketamine (5 mg/kg iv) were administered as needed to achieve mild sedation. A micromanometer-tipped catheter (Millar SPC-350) was zeroed in a 37°C water bath and advanced into the LV chamber through a left femoral arterial introducer to measure LV chamber pressure. To minimize reflex sympathetic and parasympathetic responses that can occur in conscious animals, autonomic blockade was achieved with intravenous esmolol (0.25-0.4 mg · kg
1 · min1
infusion, titrated to reduce heart rate to <120 beats/min) and atropine (0.02-0.04 mg/kg). UL-FS49 (Boehringer-Ingelheim,
Ridgefield, CT; highly specific negative chronotropic agent that does
not change Q-T interval, inotropic state, or systolic or diastolic blood pressure; Ref. 28) was administered as necessary to lower heart
rate (average dose = 5.6 ± 1.4 mg). All dogs were atrially paced at
a target rate of 120 beats/min. Baseline hemodynamic and
videofluoroscopic data recordings were obtained during steady-state conditions and then repeated after a bolus of calcium chloride was
administered (250 mg iv). All data acquisition runs containing premature ventricular contractions were discarded, and the run was repeated.
All animals received humane care in compliance with the Principles of Laboratory Animal Care formulated by the National Society for Medical Research and the Guide for the Care and Use of Laboratory Animals prepared by the National Academy of Sciences and published by the National Institutes of Health (NIH) [DHHS Publication (NIH) 85-23, revised 1985]. The study was approved by the Stanford Medical Center Laboratory Research Animal Review Committee and was conducted according to Stanford University policy.
Data Acquisition
All imaging studies were conducted with the animal in the supine position as previously described (6). The 45° RAO and 45° LAO biplane video images were recorded at 60 Hz. The analog LV pressure (LVP) signal was digitized and recorded on each video image, and the peak electrocardiogram (ECG) R wave was used as an end-diastolic timing marker. The two-dimensional coordinates of each marker in each projection were digitized frame by frame using a semiautomated, computerized image processing system developed in our laboratory (23). The RAO and LAO marker coordinates were merged using custom software to yield the three-dimensional (x, y, z) coordinates of each marker every 16.7 ms. With the use of this system, determination of marker position is accurate and reproducible with a mean overall error of 0.1 ± 0.3 mm (5). Although marker displacement (chordal length changes) during the cardiac cycle is dependent on marker location, typical values for anterior regional chord shortening (strain, %) were 6.5 ± 1.9 and 5.6 ± 3.2 for circumferential and longitudinal strains, respectively.Data Analysis
Hemodynamics.
To minimize the effects of intrathoracic pressure variation,
end-expiratory beats were selected for analysis. Instantaneous global
LV volume (based on the epicardial LV markers) was calculated for each
videofluoroscopic frame using a multiple tetrahedral model (6). For
each cardiac cycle, end diastole was defined as the videofluoroscopic
frame that contained the ECG R wave marker; end systole was defined as
the time of the maximum LVP-to-volume ratio (32). Stroke volume was
calculated as SV = EDV 
ESV, where EDV and ESV are LV
end-diastolic and end-systolic volumes, respectively. LV afterload was
estimated as the arterial elastance [Ea = end-systolic pressure (ESP)/SV] (17). For each cardiac cycle the
LVP signal was differentiated with respect to time to determine maximal
rate of increase during systole (LV
dP/dtmax) and
maximal rate of decrease following ejection
(dP/dtmin).
Regional average wall stress.
Determination of LV regional wall stress relied on measurement of
instantaneous LVP, the circumferential
(r
) and
meridional (r
) radii of
curvature, and local wall thickness (Fig.
1). The septum was excluded because of
uncertainty in septal wall thickness measurements caused by
difficulties inherent in implanting the septal markers accurately. The
assumptions used in this analysis were
1) the myocardium was isotropic,
linearly elastic, and homogeneous; 2) distortion of the LV wall
occurred only in the radial direction (thereby ignoring bending moments
and transverse shear stresses); 3)
the meridional midwall radius of curvature could be derived as the
epicardial radius of curvature minus one-half of the wall thickness;
4) the midwall LV wall stress is an
average of the epicardial and endocardial stresses; and
5) the only load on the ventricle
was an internal pressure (i.e., LVP).
|
was determined in the Ant, Lat, and Pos LV walls using techniques
previously described for endocardial r (7).
Epicardial circumferential radii were determined for each of the nine
wall thickness sites by considering each region to be locally
ellipsoidal; r
was then calculated as the chord length from the epicardial marker of
interest to the center of gravity of all markers at the same level
[7 (4 epicardial and 3 endocardial) markers]. From these
two radii and LVP, regional average wall stress (
) was derived by
first calculating "isotropic" wall tension. Assuming the local LV
geometry to be an elliptical cylinder, the isotropic wall tension is
the average of the circumferential and meridional wall tensions
(T and
T; Ref.
25). The isotropy in this context refers not to the
material properties of the myocardium but rather to the fact that under
these assumptions tension is invariant with respect to direction in the
plane perpendicular to both of the radii of curvature at the particular
point of interest. For purposes of clarity, the derived isotropic wall
stress is referred to as the average wall stress. From Laplace's law
and a prolate ellipsoid thick-walled model, isotropic epicardial wall tension (T) is
|
(1) |
is
equivalent to the minor radius (b)
and r is
equivalent to
a2/b.
Tension thus is calculated as
|
(2) |
|
(3) |
|
|
Statistical analysis. All data are reported as means ± SD. Continuous hemodynamic and geometric data before and after inotropic stimulation were compared using Student's t-test for paired observations. Evaluation of midwall average stresses was performed using multivariate ANOVA with the level (AE, EQ, BE), wall (Ant, Lat, Pos), and inotropic state (with and without calcium) coded as independent variables; dog identification was entered as a dummy variable to adjust for between-animal differences. When indicated by a significant F statistic (P < 0.05), regional differences were isolated using post hoc comparisons with the Bonferroni correction.
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RESULTS |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
|
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Postmortem examination of the excised hearts revealed all subendocardial and subepicardial markers to be within 1 mm of the endocardial or epicardial surface, respectively, and the septal markers to be within 2 mm of the right ventricular endocardial surface. No markers were inadvertently placed within either papillary muscle.
Hemodynamics
As expected, calcium infusion significantly increased LV end-systolic pressure, stroke work, Ea, and dP/dtmax. Table 1 summarizes the hemodynamic observations before and after calcium. A single dog had a heart rate of 122 beats/min after receiving esmolol and UL-FS49 and was subsequently studied at a paced rate of 125 beats/min. Despite the use of wall thickness markers to subtract LV wall (or myocardial) volume, the LV volume measurements are still overestimates compared with angiographic values because of the inability to account for papillary muscle mass and LV chamber endocardial trabecular systolic obliteration. This magnification factor leads to an underestimation of LV ejection fraction, similar to those reported by Shintani and Glantz (30) using both conductance catheter and sonomicrometric measurements. Additionally, autonomic blockade may also have contributed to the relatively low calculated ejection fractions observed.
|
Regional LV Wall Geometry
The LV exhibited regional heterogeneity in local LV epicardial longitudinal radius of curvature, a finding similar to that shown previously by our group for endocardial measurements (6). Calcium infusion resulted in significant decreases in end-systolic r, although
not at every location, representing a relative "sphericalization"
(i.e., a decrease in the base-apex dimension) of the ventricle (Table
2). In a similar manner, enhanced inotropic state decreased end-systolic
r in all
regions except the AE sites on the Lat and Pos walls. Calcium did not
significantly increase end-systolic wall thickness uniformly at all
sites; this heterogeneity has been seen in both humans and dogs and is
well described (20).
|
Regional Average Wall Stress
Figure 2 depicts representative tracings (for the anterior wall at 3 levels) of LVP, volume, and wall stress during two beats from a single animal under baseline conditions. Because the pattern of LV wall stress was heterogeneous, a step-by-step description of the changes observed is appropriate. Beginning at end diastole, stress rose rapidly in parallel with the increase in LVP during isovolumic contraction. Subsequently, after reaching peak levels at the beginning of ejection, wall stress declined significantly in all regions except the AE region in the Lat wall (149 ± 82 to 116 ± 44, P = not significant). This fall in stress occurred while LVP remained relatively constant and was therefore presumably a consequence of the dynamic alterations in LV geometry [i.e., changes in circumferential and meridional curvature and wall thickness (decrease in LV volume with a concomitant decrease in r having the largest potential impact)] occurring in systole.
During late systole and isovolumic relaxation, stress again paralleled LVP. Wall stress was relatively static during the first half of diastole and appeared to be independent of LV volume increase. As was
the case during systole, a gradient of wall stress increasing from apex
to base was present during diastole, caused primarily by to the larger
r (compared
with the increase in
r). Table
3 summarizes changes in midwall average
wall stress with calcium.
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|
Multivariate analysis of variance of regional end-systolic wall stresses demonstrated significant regional heterogeneity, with influences from the ventricular level (AE, EQ, or BE; P < 0.001) and the LV meridian (P = 0.002). Included as an independent variable in the multivariate analysis, inotropic state did not have a statistically significant influence (P = 0.056) on regional wall stress. Post hoc comparisons further isolated the differences seen between marker insertion level as AE versus EQ or BE (P < 0.001) and EQ versus BE (P = 0.017). Post hoc comparison of the individual walls isolated a significant difference only between the Ant versus Lat (P = 0.020) or Pos walls (P = 0.003); the Lat versus Pos wall comparison did not reveal any significant differences. It is notable that in the dog some of the anterior wall fibers originate from the septum.
Univariate ANOVA of end-systolic LV wall stress after an increase in inotropic state isolated significant (P < 0.05) increases in stress in all regions except the equatorial sites (Ant-EQ, P = 0.065; Lat-EQ, P = 0.058; Pos-EQ, P = 0.092). Univariate ANOVA using maximal stress as the dependent variable after calcium infusion revealed changes that were less clear-cut; although wall stress increased significantly in all levels of the Pos wall after calcium infusion (P < 0.05), none of the three Lat sites changed significantly. For the Ant wall, the BE site alone did not change significantly (P = 0.114). As noted for the multivariate analysis, there were two distinct gradients of LV wall stress, with stress increasing from apex to base and decreasing from the Ant around to the Pos wall.
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DISCUSSION |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
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LV average wall stress is dependent on wall thickness, local LV geometry, and chamber pressure. Although variations in wall stress occur throughout the cardiac cycle, the magnitudes of regional wall stresses at end diastole and end systole are probably maintained within narrow, well-defined physiological ranges. Perturbations in wall stress would therefore reflect the cumulative effect of alterations in any or all of these variables; the magnitude of the perturbation needed to disrupt normal stress patterns, however, remains unknown. Hood et al. (14) evaluated stress as an "index of the `appropriateness' of the anatomic and functional responses to any given pressure or volume load" without attempting to define the normal range of LV wall stress. In their study, biplane angiocardiographic data were used to derive mean LV wall stress (using an axisymmetric model) in both normal human hearts (n = 6) and hearts with a variety of pathological loading conditions. The authors demonstrated that, compared with normal controls, wall stress was generally in the normal range in patients with mitral stenosis, compensated LV volume overload, primary myocardial disease, and LVP overload. These findings are germane in that in each clinical situation, one or more of the variables that determine LV wall stress are presumably altered, but the myocardium appears to be able to adapt to these pathophysiological conditions. In hearts with hypertrophic myocardial disease, however, wall stress was significantly lower; in mixed pressure volume overload and decompensated LV volume overload, wall stress was significantly increased. The quest of Hood et al. (14) for an "index of appropriateness" in terms of LV wall stress therefore seems sensible; wall stress appears to be altered only when the ventricle is no longer able to compensate for the abnormal pressure or volume loads. Before this index can be implemented, however, the normal distribution of LV wall stress and the assumptions of such estimation should be defined.
In this study, a number of assumptions were made to simplify the analysis and thereby estimate the LV wall stress pattern. These results were not greatly different from those described by other investigators. Segar et al. (29) were able to demonstrate that a regional end-systolic wall stress-velocity of circumferential fiber shortening relationship was preload independent and was able to differentiate between normal, ischemic, and reperfused myocardium. As in the study of Hood et al., mean circumferential wall stress was estimated at a single location on the LV wall (anterolateral equatorial region) using a formula derived from Sandler and Dodge (26); regional circumferential wall stress was estimated using the techniques described by Janz (16). For the normal ventricle, at this location, Segar et al. (29) obtained a mean midwall stress approximately one-half of what we saw in our study (100 vs. 255 kdyn/cm2). This is caused in part by the inclusion of meridional stress in our measurement. On the other hand, Gaynor et al. (10) used methods described by Regen (24) to obtain global values of midwall stress similar to our equatorial values. These studies are summarized in Table 4. Of note in the study by Gaynor and co-workers (10), although end-systolic stress increased during the initial stages of aortic regurgitation, it returned to baseline values after the development of compensatory hypertrophy, a finding similar to that seen by Hood et al.
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The relationship between LV wall stress and wall thickness has been demonstrated to be an index of contractility independent of the size of the ventricle (22), adding to the usefulness of this parameter. This index can presumably be used even when the wall stress has not been altered. As mentioned previously, direct measurement of LV wall stress remains difficult and relies on a priori assumptions of myocardial isotropy and LV chamber geometry. Furthermore, as shown in the results of this current experiment, one cannot generalize an estimate of LV wall stress to encompass the whole ventricle or to serve as an index of global LV wall stress because wall stress varies depending on the particular location of measurement. It is promising that MRI techniques may overcome these limitations in the future; the development and refinement of three-dimensional cine MRI techniques have enabled reconstruction of the ventricle by the interleaving of multiple long- and short-axis images (with transmural tagging to aid in strain analysis). It is anticipated that other hurdles (e.g., direct LVP measurement, increased temporal resolution) will also be overcome.
Traditional axisymmetric models of LV wall stress determine stress at
the equator of a prolate ellipsoid (the site of maximal stress in such
a model). With myocardial marker techniques, we found a gradient of
average stress increasing from the apex toward the base. This is a
result of the larger
r at the base
of the heart despite the concomitant increase in
r. These
gradients are impossible to determine without simultaneous measurement
of wall thickness at different levels of the ventricle. Cine MRI has
demonstrated this longitudinal gradient of LV wall stress (9), although
regional variations between different LV walls cannot be detected.
Likewise, models using axisymmetric idealizations of the ventricle also
preclude the ability to distinguish changes in stress between different
LV walls. Guccione et al. (12) obtained a different distribution of
transmural end-systolic fiber stress, with minimal difference between
the base and equatorial regions and a significant increase in stress
from the midventricle to the apex of the heart. The authors used an
elegant three-dimensional finite-element model using a longitudinal
cross section of an unloaded canine LV free wall. Differences in
results from our study probably reflect in part the difference in
estimating longitudinal versus isotropic stress as well as the use of
an anisotropic model by Guccione et al.
In our study, the significant differences in LV wall stress seen between the Ant wall and the Lat and Pos walls are caused in part by the heterogeneity in curvature among these walls (7). Although the differences between the Lat and Pos walls did not reach statistical significance, it can be appreciated that the Lat wall had the lowest wall stress at any level. This may be caused by the origin of the myocardial fibers constituting the Ant and Pos walls (i.e., septal contributions) as well as the insertions of the papillary muscles in the canine heart. This heterogeneity also implies that the meridional gradient is opposite to that seen with longitudinal torsional deformation (when the base of the heart is used as the frame of reference). One interpretation of this would be that an increase in torsional deformation reduces average wall stress during systole, especially in those regions where a thin wall (small h) might be expected to lead to very high stress levels when LVP is high. This is in agreement with the model of Arts et al. (2), who postulated that LV twist acts to normalize LV wall stress across the LV wall and throughout the ventricle.
Models used in the evaluation of LV wall stress need not be complex. Goldfine et al. (11) used a simple mathematical model to estimate postoperative systolic stress from end-diastolic dimension and ejection fraction. Although the exact values of wall stress in their elegant clinical study could be challenged, their findings of a significant difference in wall stress after mitral valve replacement (with and without chordal preservation) were concordant with echocardiographic data.
Finally, inotropic stimulation generally resulted in significant increases in LV wall stress values, as one would intuitively predict. What was unexpected was the result of the univariate ANOVA analysis with respect to end-systolic stress. Why the equatorial regions would be spared from parallel increases in wall stress with enhanced inotropic state is unclear. These findings may possibly reflect the influences of boundary conditions (i.e., the annulus at the base of the ventricle) or may reflect a limitation of the assumptions of this technique. Likewise, the results for maximal wall stress suggest that anatomic variations may play an important role in determining LV wall stress. The lack of increase in wall stress in the lateral wall after administration of calcium again points to the independence of the free wall from the septum and the papillary muscle insertion sites. Hemodynamic results that demonstrated significant increases in Ea (a measure of global LV afterload) may not be sensitive to local variations in wall stress (or regional LV afterload).
Experimental Limitations
This analysis was based on the assumptions noted in MATERIALS AND METHODS. Additional geometric assumptions are those initially used by Laplace and modified for a thick-walled elliptical cylinder; the stress calculations are therefore most appropriate for the equatorial LV region of an elliptical cylinder. Essentially, we have modeled each marker pair site as representing locally an elliptical cylinder. Because we are able to accurately measure local radii of curvature (in both the longitudinal and meridional planes) using the same assumptions, this model should suffice. Estimation of LV wall stress in areas influenced by anatomically imposed boundary conditions (e.g., the base of the heart vis à vis the mitral and aortic valves) would be less accurately computed by this model. The ventricle is a complex pump that ultimately cannot be modeled as simply as we have attempted in this study. The assumptions of isotropy, linear elasticity, and homogeneity are made only to simplify the estimation of regional wall stress; experimental models with more complexity exist (12) and may ultimately be incorporated in this type of study. Nonetheless, these data should provide a framework for further studies in regional wall stress after intervention and/or development of pathological conditions (i.e., dilated cardiomyopathy). We anticipate that, enfin, three-dimensional MRI and finite-element analysis will be the gold standard for these types of analyses.| |
ACKNOWLEDGEMENTS |
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The authors acknowledge the expert technical assistance of Cynthia E. Handen, Erin K. Schultz, Geraldine C. Derby, Joshua Cohen, Mary K. Zasio, and Carol W. Mead in the performance of this work and Phoebe Taboada for help in preparing the manuscript and figures.
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FOOTNOTES |
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This work was supported by National Heart, Lung, and Blood Institute Grants HL-29589 (D. C. Miller) and HL-48837 (G. T. Daughters II) and the Department of Veterans Affairs Medical Research Service (D. C. Miller). A. DeAnda, Jr., M. Komeda, G. R. Green, and M. R. Moon are Carl and Leah McConnell Cardiovascular Surgical Research Fellows. A. DeAnda, Jr., and M. R. Moon were also supported by Individual National Research Service Awards HL-08928 and HL-08532.
This work was presented in part at the American College of Cardiology 45th Annual Scientific Session, Orlando, FL, in March 1996.
Address for reprint requests: D. Craig Miller, Dept. of Cardiovascular and Thoracic Surgery, Falk Cardiovascular Research Center, Stanford Univ. School of Medicine, Stanford, CA 94305-5247.
Received 9 April 1997; accepted in final form 2 July 1998.
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
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