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Am J Physiol Heart Circ Physiol 284: H475–H479, 2003;
10.1152/ajpheart.00360.2002.
Border zone geometry increases wall stress after myocardial
infarction: contrast echocardiographic assessment
BENJAMIN M. JACKSON,1 JOSEPH H. GORMAN III,1 IVAN S. SALGO,3
SINA L. MOAINIE,1 THEODORE PLAPPERT,2 MARTIN ST. JOHN-SUTTON,2
L. HENRY EDMUNDS, JR.,1 AND ROBERT C. GORMAN1
1
Department of Surgery and the Harrison Department of Surgical Research and
2
Division of Cardiology, Department of Medicine, Hospital of the University of
Pennsylvania, Philadelphia, Pennsylvania 19104; and 3Philips Medical Systems,
Andover, Massachusetts 01810
Jackson, Benjamin M., Joseph H. Gorman III, Ivan S.
Salgo, Sina L. Moainie, Theodore Plappert, Martin St.
John-Sutton, L. Henry Edmunds, Jr., and Robert C.
Gorman. Border zone geometry increases wall stress after
myocardial infarction: contrast echocardiographic assessment. Am J Physiol Heart Circ Physiol 284: H475–H479,
2003;;10.1152/ajpheart.00360.2002.—After myocardial infarction (MI), the border zone expands chronically, causing
ventricular dilatation and congestive heart failure (CHF). In
an ovine model (n ⫽ 4) of anteroapical MI that results in
CHF, contrast echocardiography was used to image shortaxis left ventricular (LV) cross sections and identify border
zone myocardium before and after coronary artery ligation.
In the border zone at end systole, the LV endocardial curvature (K) decreased from 0.86 ⫾ 0.33 cm⫺1 at baseline to
0.35 ⫾ 0.19 cm⫺1 at 1 h (P ⬍ 0.05), corresponding to a mean
decrease of 55%. Also in the border zone, the wall thickness
(h) decreased from 1.14 ⫾ 0.26 cm at baseline to 1.01 ⫾ 0.25
cm at 1 h (P ⬍ 0.05), corresponding to a mean decrease of
11%. By Laplace’s law, wall stress is inversely proportional to
the product K 䡠 h. Therefore, a 55% decrease in K results in a
122% increase in circumferential stress; a 11% decrease in h
results in a 12% increase in circumferential stress. These
findings indicate that after MI, geometric changes cause
increased dynamic wall stress, which likely contributes to
border zone expansion and remodeling.
congestive heart failure; remodeled myocardium; coronary
artery disease; perfusion echocardiography
(CAD) is the most common
cause of congestive heart failure (CHF) in the United
States (4). The mechanism of CHF due to CAD is
complex and multifactorial. In addition to irreversibly
damaged (infarcted) myocardium, the ischemic syndromes of myocardial stunning (2) and hibernating
myocardium (13) contribute to the manifestations and
progression of CHF in some patients with left ventricular (LV) dysfunction secondary to CAD. However, in
many patients, myocardial infarction (MI) insidiously
leads to CHF in the absence of ongoing ischemia or
CORONARY ARTERY DISEASE
Address for reprint requests and other correspondence: R. C. Gorman,
Silverstein Pavilion, Hospital of the Univ. of Pennsylvania, 6th floor, 3400
Spruce St., Philadelphia, PA 19104 (E-mail: [email protected]).
http://www.ajpheart.org
recurrent infarction. Loss of contractile function in this
later group is attributed to postinfarction LV remodeling (15). Remodeled myocardium has recently been
defined clinically and experimentally as a unique form
of dysfunctional myocardium adjacent to an infarct
that is normally perfused but hypocontractile. The
postinfarction remodeling process causes this region of
hypocontractility to extend to involve progressively
more normally perfused myocardium, resulting in ventricular dilatation and CHF (7, 12). The term border
zone myocardium (BZM) has also been used in experimental and clinical studies to describe this phenomenon (3, 6, 10, 14) and is probably the better term when
dealing with changes immediately after infarction.
A recent experimental finite element stress analysis
in an ovine model of fully developed LV aneurysm
suggested that the mechanism underlying mechanical
dysfunction in remodeled myocardium is primarily the
result of an intrinsic abnormality of the myocardium
rather than increased wall stress. The study, however,
did not assess BZM stress in the early postinfarction
period (5). The cause of these intrinsic myocardial
changes has been difficult to determine given the complexity of the finite element stress calculations and the
difficulty in identifying the area of remodeled myocardium over time. The latter requires serial registration
of regional function and perfusion to adequately differentiate infarction from remodeled myocardium.
In this study, we test the hypothesis that regional
geometric changes consistent with increased BZM
stress occur immediately after infarction. The term
border zone will be used in preference to remodeled
myocardium because of the time frame of the study
(i.e., within 1 h of acute infarction). We employ an
ovine model of anteroapical MI, a modified form of
Laplace’s law, perfusion echocardiography (to precisely
define BZM), and the assumption that the material
properties of the BZM are unchanged immediately
after infarction.
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.
0363-6135/03 $5.00 Copyright © 2003 the American Physiological Society
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Submitted 8 May 2002; accepted in final form 7 October 2002
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ALTERED BORDER ZONE GEOMETRY INCREASES WALL STRESS
METHODS
Fig. 1. Method of measuring endocardial radius of curvature (R). Left, baseline (without
contrast); right, postinfarction. PPM, posterior papillary muscle; APM, anterior papillary muscle; RV, right ventricular cavity.
point 1, septal border of the infarct; point 2,
posterior border or observed flattening; point
3, midpoints of points 1 and 2. In all sheep,
there was a sharp demarcation of the infarct
at its septal border. The line of demarcation
was decidedly distinct on cine echocardiogram; reference to the video allowed precise
location of the infarct line (in yellow) in the
still images.
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Surgical protocol. Four Dorsett hybrid sheep were induced
with thiopental sodium (10–15 mg/kg), intubated, anesthetized with isofluorane (1.5–2%), and ventilated with oxygen
(Drager anesthesia monitor, North American Drager; Telford, PA). All animals received glycopyrrolate (0.4 mg iv) and
cefazolin (1 g iv both before and after operation). Animals
were treated in compliance with National Institutes of
Health Guide for the Care and Use of Laboratory Animals
(NIH Publication No. 85-23, Revised 1985). The surface ECG
and arterial blood pressure were continuously monitored
(Sonometrics; London, Ontario, Canada).
With the use of sterile surgical techniques, a left anterolateral thoracotomy was performed in the fifth interspace.
Polypropylene snares were placed around the left anterior
descending artery and second diagonal coronary arteries
(⬃40% from the apex) (11). The animal was allowed to recover.
Infarction. After 10–14 days, the sheep were again anesthetized and placed supine. An arterial catheter (model Spc350, Millar Instruments; Houston, TX) was positioned with
its tip in the LV cavity. Baseline echocardiographic images
were recorded as described below, without injection of contrast. The exteriorized subcutaneous snares were tightened.
Once the animal stabilized (⬃1 h), experimental measurements were made.
Echocardiographic data collection. Subdiaphragmatic
echocardiographic images were obtained through a sterile
midline laparotomy as previously described (8). Real-time
contrast echocardiography was performed with a second harmonic technique (Sonos 5500, Hewlett-Packard). For each
recording of perfusion and wall motion, 0.1 ml of albumen
with octafluoropropane gas echo contrast agent (Optison,
Mallinckrodt) was injected directly into the left coronary
ostium. Short-axis cross-sectional images at the level of the
papillary muscle bases were recorded continuously during
the injection of contrast.
Data analysis. In all sheep, there was a sharp demarcation
of the infarct at its septal border (Fig. 1). The line of demarcation was decidedly distinct on cine echocardiogram; reference to the video allowed the precise location of the infarct
line in the still images derived directly from the cine recording. The superiority of cine ultrasound for recognition and
identification of cardiac structures and features is well recognized (1, 17). For acoustic reasons, the lateral border of the
infarction was not as clearly demarcated with contrast;
therefore, no measurements were performed at that border.
All measurements were made at end systole, identified as the
frame at which LV cavity area was smallest. The endocardial
and epicardial contours were traced by an echocardiography
technician who was unaware of the hypotheses of the study.
In all sheep, the endocardial contour anterior to the infarct
demarcation was observed to have flattened with infarction
(in the short-axis plane). All measurements are presented as
means ⫾ SD.
Measurement of radius of curvature. As demonstrated in
Fig. 1, three points were identified along the endocardial
contour: the septal border of the infarct (point 1), the posterior border of the observed flattening (point 2), and their
midpoint (point 3). After superposition of the baseline and
postinfarction images such that both the posterior and anterior papillary muscles coincided, three analogous points were
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ALTERED BORDER ZONE GEOMETRY INCREASES WALL STRESS
a force. Because the wall stress in this case acts on all four
sides of the square, the force opposing P is 4 䡠 ␴p 䡠 Rd␪ 䡠 h,
where h is the thickness of the shell.
Therefore
P 䡠 R2 䡠 d2␪ ⫽ 4 䡠 ␴ 䡠
d␪
䡠 Rd␪ 䡠 h
2
And ␴ is
␴⫽
PR
2h
RESULTS
identified along the endocardial contour of each baseline
echocardiographic study. For each contour, the three points
allowed the calculation of the endocardial radius of curvature
(R) and of its inverse (the curvature K). The coordinates
(pixels) represented by points 1 and 2 were connected by a
line segment and the bisector to this line segment was calculated; the same was done for points 2 and 3. The distance
from the origins of the bisectors to their intersection was then
taken to be R.
Measurement of wall thickness. Myocardial wall thickness
was determined in the border zone region by measuring, for
each of the aforementioned three endocardial points, the
distance to the closest point along the epicardial contour
(again, at end systole). Border zone wall thickness was then
calculated as the mean of these three measurements.
Measurement of circumferential extent of endocardial flattening. The geometric center of the curve comprising the
endocardial contour was taken to be the geometric center of
the LV cavity. The angle subtended by points 1 and 2 around
this center was measured to be the circumferential extent of
the observed phenomenon.
Mechanics model. Laplace’s law is applicable to differential areas of a three-dimensional shell under a pressure load.
This can be demonstrated using a spherical balloon inflated
to pressure P, as in Fig. 2. The force on a differential squareshaped piece of the surface of the sphere, as depicted, is
P 䡠 R2 䡠 d2␪, where d␪ is the differential sphere surface. As d␪
approaches zero, the component of wall stress ␴p in the
direction of this force is
␴ p ⫽ ␴ 䡠 sin
d␪
d␪
⫽␴䡠
2
2
where ␴ is wall stress. Stress has the same units as pressure
and must be multiplied by the area over which it acts to find
AJP-Heart Circ Physiol • VOL
Fig. 3. Endocardial contours (K) from a single animal at baseline
(blue) and after infarction overlayed. The region of the infarct (red)
can be seen to “billow,” as reflected in an increased K. As a result, the
adjacent endocardium (green) necessarily demonstrates decreased K
compared with baseline.
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Fig. 2. Laplace’s law as applied to a differential area of a threedimensional shell under a pressure load. ␴, Wall stress; ␴P, component of wall stress; A, surface area; A⬘, surface area upon which ␴
acts; d␪, differential sphere surface; P, pressure.
In the border zone, K decreased from 0.86 ⫾ 0.33
cm⫺1 at baseline to 0.35 ⫾ 0.19 cm⫺1 at 1 h (P ⬍ 0.05),
corresponding to a mean decrease of 55%. Note that the
ventricles were all approximately the same size, with a
mean radius of 2.4 ⫾ 0.3 cm. The area of decreased K
extended 42° ⫾ 10° circumferentially from the infarct
in the direction of preserved perfusion. Also in the
border zone, h decreased from 1.14 ⫾ 0.26 cm at baseline to 1.01 ⫾ 0.25 cm at 1 h (P ⬍ 0.05), corresponding
to a mean decrease of 11%.
According to Laplace’s law, ␴ is inversely proportional to the product K 䡠 h in a differential segment of
the LV wall. Therefore, a 55% decrease in K results in
a 122% increase in circumferential ␴. To demonstrate
this, assume that c is a constant, that ␴⬘ is the new
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ALTERED BORDER ZONE GEOMETRY INCREASES WALL STRESS
circumferential stress, and that the new curvature
K⬘ ⫽ 0.45 䡠 K. Then
␴⬘ ⫽
c
c
c
⫽
⫽ 2.22 ⫽ 2.22␴
K⬘ 0.45 䡠 K
K
Similarly, a 11% decrease in h results in a 12% increase in circumferential ␴.
The final determinant of wall stress with the use of a
Laplace’s law formulation is cavity pressure. In these
experiments, the mean LV systolic pressure (LVP) did
not change with infarction. At baseline, the LVP was
114 ⫾ 6 mmHg, and in the infarcted ventricles the LVP
was 116 ⫾ 10 mmHg.
DISCUSSION
AJP-Heart Circ Physiol • VOL
This work was supported by National Heart, Lung, and Blood
Institute Grants HL-36308 and HL-63594, the Mary L. Smith Char-
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This study uses an ovine model of acute anteroapical
MI that undergoes early expansion and real-time contrast echocardiography to study myocardial mechanics
in BZM. According to the straightforward mechanics
model (based on Laplace’s law for a differential segment of a thin-walled vessel) used in this study, the
two determinants of wall stress are wall thickness and
endocardial curvature. The results provide evidence
that myocardial wall stress is increased in BZM immediately after MI and that this increase is primarily due
to reduced endocardial curvature, with a more limited
contribution from myocardial wall thinning.
This study marks the first attempt to demonstrate
altered border zone geometry after acute MI by using
methods that allow definitive identification of BZM.
Picard et al. (16) demonstrated the existence of a border zone 6 wk after MI in sheep, but evaluated wall
motion abnormalities, not geometric changes. The
present study demonstrates acute geometrical changes
in the BZM adjacent to an expanding MI. Given the
stable hemodynamic loading conditions before and after infarction, and by making the reasonable assumption that there is no significant acute change in local
material properties during the first hour after MI,
these geometric distortions are consistent with increased wall stress in this region of the left ventricle.
These results suggest that in BZM the primary etiology
of increased stress immediately after MI is early geometric change.
These distortions in the border zone are likely due to
the geometric boundary conditions imposed on the border zone by the adjacent infarct. The infarct expands
and thins and is displaced radially outward from the
center of the ventricle; to accommodate this distortion
in the infarcted region, the adjacent myocardium is
forced to curve outward, decreasing the local K, as
indicated in Fig. 3.
With the use of sonomicrometry array localization,
serial microsphere injections, and this ovine model of
anteroapical infarction, our laboratory has recently
shown that an initially small area of normally perfused
but hypocontractile BZM extends over weeks to involve
progressively more normally perfused myocardium, resulting in ventricular dilatation and CHF (7). We have
proposed that this enlarging area of dysfunctional but
normally perfused myocardium is responsible for the
CHF associated with postinfarction remodeling (7).
Our findings confirm the results of Kramer and colleagues (9) demonstrating progressive BZM contractile
dysfunction in this model up to 6 mo after infarction.
Guccione and colleagues (5), using an elegant finiteelement stress analysis of this model, have suggested
that the contractile dysfunction seen in the BZM 8 wk
after infarction is due to intrinsic changes in the myocardium and not to increased stress. The results of our
study suggest that, in contrast, early acute geometric
changes in BZM lead to increased stress and as a result
loss of contractility. We hypothesize that this early
increase in stress causes the progressive and chronic
intrinsic changes in BZM demonstrated by Guccione et
al. (5). While remodeling progresses, these intrinsic
changes in BZM become dominant to those related to
the mechanical disadvantage associated with increased regional stress.
The present study was limited in that two-dimensional echocardiograms were used to make conclusions
about a three-dimensional ventricle. Two-dimensional
endocardial curvature was measured; implications
about myocardial wall stress were then inferred. Given
the three-dimensional nature of the LV, three-dimensional contrast echocardiography would provide more
comprehensive data and a more rigorous analysis.
However, the two-dimensional (short axis) nature of
this study is not necessarily a substantial limitation
because the curvature in the orthogonal direction along
the wall is less (the ventricle being longer in that
direction), it is unlikely that a significant fraction of
the pressure is opposed by stresses in the longitudinal
(base-to-apex or long axis) direction. In addition, it is
expected that a smaller fractional change in R is experienced in the long axis or meridional direction than in
the short axis or hoop direction.
The mechanics model utilized is of limited applicability: Laplace’s law is a first approximation for the
determination of wall stress. In a thick-walled chamber with heterogeneous material properties, the approximation must be used with care and conclusions
thereof must be considered preliminary. A more comprehensive model of myocardial mechanics, incorporating local endocardial curvature measured in two orthogonal directions (and incorporating three-dimensional
data), a more rigorous theoretical treatment of thickwalled structures under load, and myocardial material
properties, would clearly be more exact. However, the
conclusions are still valid, given that 1) the acute
change in local material properties in a normally perfused region of myocardium are likely minimal, and 2)
the differential (in the radial direction) circumferential
expansion of the border zone under the loads imposed
during systole are likely not appreciably different than
those endured by the normal myocardium in the uninfarcted ventricle.
ALTERED BORDER ZONE GEOMETRY INCREASES WALL STRESS
itable Trust (Chester, PA), and the W. W. Smith Charitable Trust
(Chester, PA).
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