Vol. 277, Issue 3, H901-H910, September 1999
Regional assessment of wall curvature and wall stress in left
ventricle with magnetic resonance imaging
Philippe
Balzer1,
Alain
Furber2,
Stéphane
Delépine2,
Frédéric
Rouleau2,
Franck
Lethimonnier1,
Olivier
Morel1,
André
Tadéi2,
Pierre
Jallet1,
Philippe
Geslin2, and
Jean-Jacques
le
Jeune1
Departments of 1 Biophysics and
2 Cardiology, University
Hospital of Angers, 49033 Angers Cedex 01, France
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ABSTRACT |
Left ventricular functional abnormalities are
associated with regional increases of wall stress and modifications of
wall curvature. This study describes the integration of the short-axis and long-axis wall curvatures for determining peak systolic wall stress. Quantification was realized with cine magnetic resonance imaging (MRI) from the location of the endocardial and epicardial borders of the left ventricle on pairs of consecutive short-axis sections. Fifteen normal volunteers were subjected to cine MRI, and
different methods of calculating peak systolic wall stress were
compared. A short-axis analysis showed a 55 ± 13% increase of the
circumferential mean of the peak systolic wall stress between apical
and basal sections. Regarding the curvature, no significant increase of
wall stress was observed except on the septal wall (31 ± 18%).
Short-axis studies proved to be insufficient for determining the
regional variations of left ventricular wall stress and for providing
normal reference values for the location of abnormal regions in patients.
myocardial function; systolic wall stress; wall thickening; cine
magnetic resonance imaging
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INTRODUCTION |
MONITORING OF LEFT VENTRICULAR diseases requires
accurate evaluation of anatomic parameters (volume, mass, wall
thickness) and functional parameters (ejection fraction, wall
thickening, endocardial motion, wall stress, etc.). However,
identification and assessment of abnormalities of the left ventricular
structures and contractility require knowledge of normal references as
well as regional measurements.
The spatial and temporal resolution of the images, the contrast between
tissues and blood, the absence of geometric assumptions, and the
precise definition of the endocardial and epicardial borders justify
the use of short-axis magnetic resonance imaging (MRI) for following up
the cardiac remodeling induced by myocardial infarction or
hypertension. Previous works established the reliability of a
noninvasive functional study of the left ventricle with MRI in
comparison with echocardiography (7, 19, 29), ventriculography (18),
angiography (32), and indicator-dilution methods (10). Mass assessment,
which requires location of the endocardial and epicardial borders, is
well correlated with ex vivo measurements (33). The association of MRI
with an automated image processing software ensures the adequacy of
this examination with regard to clinical routine (17), and
interobserver variability is compatible with observation of the
expected functional modifications caused by cardiac disease (9, 11).
In comparison with long-axis studies (20), sets of short-axis sections
are independent of geometric assumptions and minimize the partial
volume effects. However, a short-axis section toward the apex of the
left ventricle is no longer perpendicular to the wall. A planar
short-axis analysis of the left ventricular structures consequently
leads to erroneous estimation of the radius and the wall thickness.
These errors are proportional to the curvature of the wall.
The heterogeneity of left ventricular function between the apex and the
base, as well as between the endocardial and epicardial borders, was
studied by echocardiography (3, 35) and, more recently, by tagging of
magnetic resonance images (12, 37). These observations are in agreement
with physiological works in which authors observed regional variations
in the morphology and orientation of the myocardial fibers (21). The
internal structure of the myocardium affects ventricular contractility
and the equilibrium between wall resistance and blood pressure. This
aspect of left ventricular function is demonstrated by the peak
systolic wall stress given by the product of the peak systolic blood
pressure with a geometric factor (1, 22, 26). In previous studies, the
systolic wall stress was mostly determined by contrast ventriculography or echocardiography. However, the technical limitations of these methods do not permit precise regional measurements of radius and wall
thickness as functions of the three-dimensional wall curvature.
The aim of this study was to assess the regional variations of wall
stress in the normal left ventricle when the wall curvature is taken
into account. This curvature was assessed in the short-axis plane as
well as in the long-axis plane.
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MATERIALS AND METHODS |
Study Group
The study population used to define normal left ventricular function
consisted of 15 healthy volunteer subjects (6 women and 9 men) with no
history or physical finding of cardiac or pulmonary disease. All
subjects gave informed consent. General data concerning this population
are given in Table 1. Five noninvasive
measurements of systolic and diastolic blood pressures were recorded
and averaged at the time of the MRI examination.
Imaging Technique
All volunteers were studied with a 1.5-T imager (Signa Horizon release
5.7, GE Medical Systems, Milwaukee, WI). The subjects were placed in a
supine position with a phased-array coil (Torso coil). A fast-gradient
echo segmented k-space sequence with radio frequency phase spoiling was
used with electrocardiogram gating. Scout transversal and sagittal
views ensured correct determination of the short-axis plane of the left
ventricle. Each section was then acquired in a single breath hold
(20-25 s) with 9-21 temporal phases per heartbeat using view
sharing and uniform repetition time radio frequency excitation.
Interleaved images were obtained in 8-12 planes from the apex to
the base with the following parameters: 10-mm section thickness, no gap
between sections, 320-mm field of view, partial echo, echo time 2.7 ms,
repetition time 10.2 ms, receiver bandwidth 15.6 kHz, flip angle
30°, eight views per segment, 256 × 128 matrix, and one
excitation. The total study time averaged 30 min.
Image Analysis
For analysis and computation, the magnetic resonance images were
transferred to a multimodality station (HP 715-50,
Hewlett-Packard, Palo Alto, CA) with a UNIX environment. Endocardial
and epicardial borders of the left ventricle were drawn with an
automatic segmentation method previously validated in animal subjects
and patients (4). In brief, this technique is an integrated approach to
segmentation by region growing, edge detection, and adaptative
thresholding. The main steps are 1)
a thresholding to isolate the blood pools; 2) a region-growing process to
approximate the surface of the left ventricular wall;
3) construction of the epicardial
borders with a gradient map and a set of a priori information; and
4) refinement of the contours in
areas of slow blood flow or papillary muscles with an adaptative thresholding.
The tracing of the left ventricular borders was then controlled and
possibly modified by a trained clinical observer through an interactive
interface. For measurement of the wall thickness and radius of the
ventricular cavity, the papillary muscles were smoothed out of the
endocardial contour.
Computation of Regional Left Ventricular Function
The multisection images at the diastolic and systolic phases were
determined by locating the largest and smallest areas of the left
ventricular cavity on a midventricular short-axis plane. On all
sections, the centroid of the left ventricle was located as the mass
center of the median line between the endocardial and epicardial
borders. Each short-axis section was centered on the mean position of
the ventricular centroid during the cardiac cycle. The parameters of
the regional left ventricular function (wall thickening, endocardial
motion, peak systolic wall stress) were studied on a set of five
contiguous short-axis planes (Fig. 1). For
all volunteers, the set encompassed sections with closed and clearly
defined endocardial and epicardial borders. Apical planes with no
ventricular cavity and valvular planes with an open chamber were
consequently excluded from the analysis.
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Fig. 1.
Set of 5 adjacent short-axis magnetic resonance images of left
ventricle at diastolic (top) and
systolic (bottom) phases. For
functional study of each subject, set was centered on midventricular
plane (section 3), which was defined
as level of papillary muscle insertions. From
left to
right,
sections 1 and
2 were short-axis planes located 2 and
1 cm away from section 3 toward apex, respectively, and
sections 4 and
5 were 1 and 2 cm away from
section 3 toward base, respectively.
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Calculation of the wall curvature relies on a polar transformation of
the image. This process has been widely used for segmentation algorithms (15), and it allows a radial study of the left ventricle. With a centerline approach (34), the wall curvature from base to apex
is assessed on 128 radii and the left ventricular radius and wall
thickness are deduced from the geometry of the ventricle on two
consecutive short-axis sections (Ref. 5; Fig.
2). The main steps of the method are
summarized in the APPENDIX. Wall
thickening and peak systolic wall stress were subsequently measured on
four adjacent levels and were averaged in the anterior, lateral,
inferior, and septal sectors (Fig. 3).
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Fig. 2.
Curvature directions inside left ventricle.
A: schematic short-axis view of left
ventricle.  , Curvature angle in short-axis plane;
R and
T, radius of blood pool and wall
thickness, respectively, along radial lines emanating from center of
mass (O) of ventricle; 2 DR, 2 DT,
and O', radius of blood pool, wall thickness, and center of
mass, respectively, in direction perpendicular to middle line between
endocardial and epicardial borders. B:
schematic long-axis view of left ventricle.  , Curvature angle in
long-axis plane; 3DR and 3DT, radius of blood pool and wall thickness,
respectively, accounting for 3-dimensional curvature.
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Fig. 3.
Sectorial analysis of left ventricular wall at end diastole. Images
were centered on center of mass of middle line between endocardial and
epicardial contours. Regional functional parameters were determined for
16 sectors of ventricle and were then averaged for anterior, lateral,
inferior, and septal walls.
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For each subject, the complete analysis, including edge detection and
quantitative analysis, required 15 ± 5 min.
Regional ejection fraction.
Diastolic volume and systolic volume were measured inside the anterior,
lateral, inferior, and septal sectors. Regional ejection fractions were
derived from the corresponding volumes.
Regional wall thickening and endocardial motion.
Wall thickening (WT) was calculated at each level and for each sector
with the following formula
where EST
and EDT are WT at end systole and end diastole, respectively.
Three-dimensional wall thickening was given by the same ratio when the
wall thickness accounted for spatial curvature. Endocardial motion was
defined as the variation in millimeters of the radius of the left
ventricular cavity during the cardiac cycle.
Regional peak systolic wall stress.
The wall stress is given by the equilibrium of forces between the left
ventricular cavity and the wall. The regional peak systolic wall stress
(WS) is determined, following Grossman (see Refs. 22, 28, 32), from
knowledge of the inner radius (R) and wall thickness (T) at end
systole
where
SP is peak systolic ventricular blood pressure in millimeters of
mercury. In this study, SP was assessed by the systolic noninvasive
blood pressure (31); 0.133 is a conversion factor to express the final
results in 103
N/m2. Peak systolic wall stress
was also calculated with the radius and the wall thickness defined with
the three-dimensional curvature.
Other studies (13, 16) of left ventricular wall stress in the
short-axis plane with MRI or echocardiography were based on the Janz
method of wall stress assessment (26). This approach relies on the
measurement of the areas
Ac and
Aw of the blood pool and the ventricular wall, respectively. The peak systolic wall
stress (AWS) in 103
N/m2 was given by
Data Processing and Statistical Analysis
Automatic drawing of the ventricular borders was independently
supervised and corrected by three observers to assess the interobserver variability of the functional and anatomic measurements (mass, diastolic volume, systolic volume, ejection fraction, diastolic thickness, wall thickening, endocardial motion, and wall stress). The
optimal evaluation of the parameters was taken as the mean of the
values obtained with the three observers. For determination of
intraobserver variability, one of the observers controlled the tracing
on two occasions, 1 mo apart. Intra- and interobserver variabilities
were quantified by linear regression analysis and calculation of the
standard error of estimation (SEE).
The mean value of the wall stress for each short-axis level and each
sector was determined with the different formulations given in
Regional peak systolic wall
stress. The significance of differences
between short-axis levels and sectors was evaluated first by analysis
of variance. If there was a significant interaction (P < 0.05) between multiple
measurements, further examination of selected pairwise comparisons was
undertaken. The gradient of the wall stress from the apex to the base
was assessed for each formulation by applying a paired Student's
t-test between adjacent levels.
Two-dimensional and three-dimensional evaluations of the wall stress
were compared with a paired Student's
t-test, SEE, and the confidence
interval of the difference between two methods of evaluation.
A similar study was realized for wall thickening calculated in the
short-axis plane and in the direction of the three-dimensional curvature. Linear regression analysis was used to define the
relationship between the different formulations of peak systolic wall
stress and wall thickening.
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RESULTS |
Global Left Ventricular Function
Global values of the functional and anatomic parameters of left
ventricular function are given in Table 2.
A good interobserver variability was observed for the anatomic
parameters (mass and volumes) as well as the mean assessments of
functional parameters. The interobserver variability of the wall stress
measurement was given by a correlation coefficient
(r = 0.94) and SEE = 1 g. The wall
stress measurements of all observers were highly correlated (r = 0.93). The ratio between SEE (1 g) and the mean was 11%.
Evolution of Peak Systolic Wall Stress From Apex to Base
The circumferential values of the wall stress are given in Fig. 3 to
highlight the regional variations of the left ventricular function and
in Table 3 to correlate the results
obtained with a short-axis analysis and with the calculation of the
three-dimensional wall curvature.
A study of the peak systolic wall stress in the short-axis plane
revealed a significant gradient between all adjacent levels from the
apex to the base (Fig. 4,
A and
B). Wall thickness and radius of the
cavity were first measured in the direction originating from the
ventricular centroid. The wall stress (WS) calculated with these data
was closely correlated with the wall stress (AWS) assessed with area
measurements. The correlation coefficient between WS and AWS was
r = 0.99. In the short-axis
plane, the curvature of the two-dimensional middle line averaged 0.10 ± 0.07 rad. The planar wall stress (2DWS) accounting for this
two-dimensional curvature was not significantly different from WS.
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Fig. 4.
Evolution of peak systolic wall stress from apex to base of left
ventricle in normal subjects. A: estimation of wall stress
WS in short-axis radial direction from center of mass of ventricle.
B: estimation of wall stress AWS from measurements of areas
of wall and blood pool. C: estimation of wall stress 3DWS
accounting for 3-dimensional curvature of wall. Values are means ± SD. P, 2-tailed significance of paired differences. N.S., not
significant.
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When wall thickness and radius of the cavity were calculated in the
spatial direction perpendicular to the wall, the gradient of the wall
stress (3DWS) from the apex to the base was no longer observed (Fig.
4C). The difference between 2DWS and
3DWS was reduced at the more basal level (Table 3), when the curvature
in the long-axis plane was lower. The ratio between the radius and the wall thickness was highly correlated with 3DWS
(r = 0.98).
Evolution of Wall Thickening and Endocardial Motion From Apex to
Base
The wall thickening (WT) determined along the short-axis radial line
from the centroid of the left ventricle was constant on the three more
apical levels and significantly decreased near the base (Fig.
5A).
This evolution was not modified when the wall thickening (3DWT) was
given in the direction perpendicular to the wall (Fig.
5B). The comparison between 3DWT and
a two-dimensional assessment of the wall thickening (2DWT) accounting
for the curvature in the short-axis plane did not reveal significant
differences at apical or basal sections (Table
4). The correlation between wall stress and
wall thickening in the short-axis plane
(r = 
0.58 between WS and WT)
was similar to the correlation obtained with data accounting for the
three dimensional curvature (r = 0.58 between 3DWS and 3DWT). No significant evolution of the
endocardial motion was observed from the apex to the base. This result
was obtained in a short-axis view (mean endocardial motion on 4 sections 12 ± 2 mm) as well as in the direction perpendicular to
the wall (13 ± 4 mm). There was no significant difference between
methods of calculation.
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Fig. 5.
Evolution of wall thickening from apex to base of left ventricle in
normal subjects. A: estimation of wall
thickening WT in short-axis radial direction from center of mass of
ventricle. B: estimation of wall
thickening 3DWT accounting for 3-dimensional curvature of wall. Values
are means ± SD. P, 2-tailed significance of paired
differences.
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Regional Quantification of Peak Systolic Wall Stress
No significant variations between the sectorial ejection fraction
measurements were observed. They ranged from 58 ± 9 (lateral wall)
to 63 ± 11% (septum) and were similar to the global ejection fraction (61 ± 10%).
The gradient of the wall stress for the anterior, lateral, inferior,
and septal sectors from the apex to the base are given in Fig.
6. A gradient of 3DWS was observed on the
septal wall between sections
1 and
4 (P = 0.01). No gradient of
3DWS was observed on the other sectors. With a short-axis analysis, the
mean wall stress on the lateral sector was significantly higher than
the wall stress on the septal sector regardless of the method of
calculation. When the three-dimensional curvature was considered, the
difference between septal and lateral walls was smaller toward the apex
and was not significant on section
1. The mean radius of curvature in the
short-axis plane ranged from 0.06 ± 0.05 rad on the septal wall to
0.16 ± 0.09 rad. The mean difference between the sectorial evaluations of WS and 3DWS was 3.1 ± 1.8 × 103
N/m2. The ratio (3DWS WS)/3DWS averaged 36 ± 10% (Fig. 7).
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Fig. 6.
Regional peak systolic wall stress in short-axis radial direction
(A), with measurements of areas of
wall and blood pool (B), and in
direction perpendicular to wall (C).
Values are means ± SD. * Opposite walls that are
significantly different from each other
(P < 0.005).
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Fig. 7.
Sectorial means of wall stress. Range of normal values (means ± SD) is calculated in short-axis radial direction (black
lines) and in direction perpendicular to wall (gray lines), and these
values (scale from 0 to 16 × 103
N/m2) are shown. Circular
representation allows a direct correlation between wall stress
magnitude and orientation from long axis of left ventricle (central
point of axes).
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Regional Quantification of Wall Thickening
The method of evaluation of the wall thickening did not affect the
regional variations of this parameter (Fig.
8). When the three-dimensional curvature
was considered, the difference of wall thickening between lateral and
septal walls was 30% for all section levels, 18% for
section
1 (apex), 41% for
section
2, 39% for
section
3, and 23% for
section
4 (base). The endocardial motion in
the direction perpendicular to the wall averaged 15 ± 5 mm in the
anterior sector, 12 ± 4 mm in the lateral sector, 15 ± 5 mm in
the inferior sector, and 13 ± 5 mm in the septal sector. No
significant differences were recorded between sectors.
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Fig. 8.
Regional peak systolic wall thickening in short-axis radial direction
(A) and in direction perpendicular
to wall (B). Values are means ± SD. * Opposite walls that are significantly different from each
other (P < 0.005).
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DISCUSSION |
This work describes the normal regional variations of peak systolic
wall stress with a three-dimensional approach provided by breath-hold
fast-gradient echo MRI. An extensive analysis of different magnetic
resonance methodologies for the assessment of peak systolic wall stress
was carried out to define the most reliable calculation.
Methodology for Measurement of Peak Systolic Wall Stress
Angiography has been widely used for the assessment of peak systolic
wall stress. With left ventriculography in the right oblique
projection, normal peak systolic wall stress appeared to be greater in
basal inferior segments than in anterior segments (23, 30). However,
angiography is invasive and requires injection of a contrast agent, the
viscosity of which may alter the left ventricular geometry, blood
volumes, and wall stress. Additionally, inferior segments of the
epicardial borders are not accurately located for all patients. The
wall stress values obtained with angiography and transthoracic
echocardiography proved to be well correlated (31). Echocardiography is
a simpler and widely available examination, but it relies on geometric
assumptions. Moreover, the difficulty in acquiring parallel tomographic
views implies that the wall stress estimations are provided only at the
level of papillary muscle insertions or at the level of the tips of mitral valve leaflets (13). With an ultrafast scanner and a contrast
agent, Feiring and Rumberger (14) described an increase of the wall
stress from the apex to the base. These results were confirmed by other
works based on the two-dimensional analysis of magnetic resonance
images (16). The resolution and contrast of magnetic resonance images
allows local measurements of wall stress without any geometric assumptions.
Our short-axis analysis of the magnetic resonance images did not reveal
any significant differences between the methods of Grossman (see Refs.
22, 28, 32) and Janz (26) for the wall stress calculation.
Pouleur et al. (30) previously suggested that the accuracy of Janz's
formulation was inversely proportional to the ventricular area. Lessick
et al. (27) compared the methods of Grossman and Janz for determination
of the meridional wall stress in patients with aneurysm. Significant
differences between results were observed, but the qualitative
conclusions were similar.
New Data on Regional Peak Systolic Wall Stress
Our bidimensional study of the short-axis sections indicates that the
meridional wall stress increases from apex to base along the long axis
of the left ventricle. However, few studies are available to support
these observations, and direct measurements of wall stress are poorly
related to short-axis calculations (36). Fujita et al. (16) reported
lower values of circumferential peak systolic wall stress than in the
present study or in the echocardiographic data given by Douglas et al.
(13). This difference with the same method of wall stress calculation
may be explained by the fact that we used the peak systolic arterial
pressure, which is more similar to the peak left ventricular systolic
pressure used by Douglas et al. than to the left ventricular peak
systolic pressure estimated by Fujita et al. Janicki et al. (25)
observed that the average ratio of radius to wall thickness
(R/T)
was homogeneous over the basal half of the left ventricle and was more
variable at the lower ventricular levels. This variability was
attributed to possible inclusions of extraneous papillary muscles, thus
increasing apparent wall thickness. In contrast, we excluded all
visible papillary muscles and still found similar variations of
R/T.
Peak systolic wall stress is related to wall curvature by the Laplace
equation: a large radius of curvature implies a large wall stress and
prevents fiber shortening. This further justifies the integration of
the curvature in the wall stress calculation. The long-axis curvature
averaged 0.55 ± 0.12 rad on the apical level 2 cm away from the
midventricular plane. The wall curvature was important enough to cause
a significant underestimation of the wall stress when
R/T
was measured in a short-axis direction. The conclusion concerning the
axial evolution of the wall stress was consequently modified. The
increase of the wall stress observed from the apex to the base with a
short-axis analysis was no longer significant when the curvature of the
wall was taken into account. In this case, a regional analysis of the
images revealed that the peak systolic wall stress increased on the
septal wall only (28% between
sections
1 and
4). Beyar et al. (6) also noticed in
dogs that the gradient of
R/T
between apex and base was smaller when the transversal curvature was
considered. However, a short-axis analysis did not induce any errors on
the regional wall thickening measurements for all short-axis levels.
Limitations of Study
Wall stress is the product of the ventricular peak systolic blood
pressure and a geometric factor. An invasive measurement or an indirect
calculation of the blood pressure only provides a global value for the
whole ventricle. Consequently, regional variations of the wall stress
are induced by those of the geometric factor but do not integrate the
local changes in pressure. Moreover, the systolic blood pressure was
150 mmHg for two subjects participating in this study, and the
subsequent mean value (130 ± 10 mmHg) was higher than in other
studies (31). In one patient, only nine temporal phases per heartbeat
were obtained.
Moreover, the evaluation of the wall curvature implies the location of
the endocardial and epicardial borders on two consecutive short-axis
sections. The reliability of the wall stress measurement depends on the
accuracy of the short-axis orientation, the section thickness, and the
gap between sections. Two preacquisitions in the transversal and
sagittal planes were used to precisely define the short-axis view. Each
section was then acquired in one breath hold. The limitation of
movements between two breath holds was easier to obtain with normal
volunteers than with patients. The effect of the axial twist on the
determination of the wall stress between two adjacent sections was
minimized by averaging the measurements for sectors encompassing
22°. This approach also reduced the influence of the axial rotation
during the cardiac cycle on the value of the wall thickening. Moreover,
previous studies (see Ref. 8) showed that the axial twist was maximal
toward the apex and more negligible at the midventricular and basal levels.
Regional differences in cardiac twist suggest heterogeneous shear
forces (24). Peak systolic wall stress may consequently be subjected to
longitudinal and shear deformations as well as through-plane motion and
cardiac shortening. The identification of anatomic features such as
papillary muscles allowed supervision of the pairing of the sections at
end diastole and end systole.
Clinical Applications
Knowledge of normal values of regional peak systolic wall stress in the
left ventricle allows identification and follow-up of local functional
abnormalities. Peak systolic wall stress is one of the primary
determinants of myocardial oxygen consumption. This parameter is higher
in ischemic areas, and the changes in its regional variations are
proportional to the ventricular remodeling after myocardial infarction
(30). In the case of a dilated cardiomyopathy, the wall stress is
correlated with the myocardial lesions (23, 32). Wall stress has also
been studied in patients with valvulopathy and volume overload.
Auffermann et al. (2) described a link between global wall stress
increase and the degree of regurgitation. Disproportionately high
systolic wall stress relative to regurgitant volume indicates the
presence of myocardial disease, and wall stress assessment is useful in
timing valve replacement in patients with regurgitant lesions.
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APPENDIX |
Determination of Radius and Wall Thickness in Direction Perpendicular
to Left Ventricular Wall
Short-axis curvature.
On all short-axis sections, a set of N
lines Rn originating from the
centroid of the left ventricle was expressed by
where
n is the angular direction and
is the distance from the centroid. In our study
N = 128, so that the difference between two directions n and
n + 1 was 2.8.
For each value of n, the
radius Rn of the
left ventricular cavity and the wall thickness
Tn were
measured. With plane geometry, the curvature
n of the middle line of the
wall in the direction n (Fig.
2A) is given by
where
(xn 
1,
yn 1)
and
(xn + 1,
yn + 1) are the coordinates of the points of the middle line along the direction
n 1
and
n + 1.
To reduce the sensitivity of the calculation to local artifacts, the
left ventricle was divided into 16 sectors in which the measurements of
the radius of the blood pool, the wall thickness and the short-axis
curvature were averaged. In the middle of each sector
S, the radius of the blood pool
2DRS and the wall thickness
2DTS in the direction of the
short-axis curvature S were
either measured on the image or deduced by geometry
where
RS and
TS are the mean
radius of the blood pool and the mean wall thickness in
sector
S along the radial lines originating from the centroid of the left ventricle.
The values of 2DRS and
2DTS obtained by direct
measurements and those given by the previous formulas were closely
related; the choice of method did not significantly affect the
following results.
Long-axis curvature.
In the median plane between two adjacent short-axis sections, the
curvature S in the long-axis
direction for sector S is determined from
where
Th is the thickness of the short-axis sections and
drS is given by
where
R1S,
T1S,
and 1S
are the radius of the blood pool, the wall thickness, and the
short-axis curvature of sector
S in
image
1 (Fig.
2B).
R2S,
T2S, and 2S
are the corresponding data for the adjacent
image 2.
The radius of the blood pool
(3DRS) and the wall thickness
(3DTS) along the direction
perpendicular to the ventricular wall were deduced by the same
reasoning as for the short-axis curvature (Fig.
2B)
The
values of RS,
TS,
3DRS, and
3DTS were determined at end
diastole and end systole for each
sector
S.
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FOOTNOTES |
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. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: A. Furber, Dept. of Cardiology, University Hospital of Angers, 4 rue
Larrey, 49033 Angers Cedex 01, France (E-mail:
apfurber{at}chu_angers.fr).
Received 29 September 1998; accepted in final form 24 March 1999.
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Auffermann, W.,
S. Wagner,
and
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Am J Physiol Heart Circ Physiol 277(3):H901-H910
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ABSTRACT
INTRODUCTION
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