Cardiovascular Research 37 Ž1998. 636–645
Flow–function relations during graded coronary occlusions in the dog:
effects of transmural location and segment orientation
Andrew D. McCulloch
a
a,)
, Derrick Sung a , James M. Wilson a , Richard S. Pavelec b,
Jeffrey H. Omens b
Department of Bioengineering, UniÕersity of California San Diego, 9500 Gilman DriÕe, La Jolla, California 92093-0412, USA
b
Department of Medicine, UniÕersity of California San Diego, La Jolla, California, USA
Received 13 June 1997; accepted 14 October 1997
Abstract
Objective: The sensitive relationship between regional myocardial perfusion and local systolic deformation during acute myocardial
ischemia is not independent of the transmural location or segment orientation. The aim of this study was to determine the effects of fiber
orientation and transmural location on the relationships between regional myocardial flow and three-dimensional systolic wall strain
during graded coronary artery occlusions. Methods: Transmural distributions of three-dimensional strain Žby biplane radiography of
implanted radiopaque markers. and myocardial blood flows Žusing fluorescent microspheres. were measured in the ischemic region
during graded left anterior descending ŽLAD. coronary artery occlusions in 12 anesthetized dogs. Results: Occlusion of the coronary
artery did not significantly alter mean heart rate or end-systolic pressure. As flow decreased during graded occlusions, ischemia
significantly changed systolic circumferential, longitudinal, radial, fiber and cross-fiber strains Ž p - 0.004.. There was a significant effect
of transmural position on circumferential, cross-fiber and radial strains, but not on fiber or longitudinal strains. Ischemia significantly
altered all normal strains: circumferential, longitudinal, fiber, cross-fiber and radial. There was a strong interaction effect between
transmural location and blood flow for circumferential, cross-fiber and radial strains, but not fiber or longitudinal strains. Conclusion:
During non-transmural ischemia, there is evidence of strong transmural tethering in the cross-fiber direction, whereas the fiber-strain flow
relation is independent of transmural position. Thus, whether the relationship between local myocardial bloodflow and systolic strain
during acute ischemia is dependent on transmural location, depends on segment orientation. q 1998 Elsevier Science B.V.
Keywords: Heart; Blood flow; Fluorescent microspheres; Systolic strain; Regional function; Dog
1. Introduction
There is sensitive relationship between regional myocardial perfusion and local systolic segment deformation
during acute myocardial ischemia w1–3x. However, the
flow–function relation is not independent of the transmural
location or orientation of the myocardial segment being
used to measure local function. For example, Vatner w1x
found that a 70% reduction in subendocardial flow caused
a 50% loss of subendocardial fiber shortening, whereas
Prinzen and colleagues w4x reported that reducing subepicardial perfusion by only 32% decreased systolic fiber
strain on the epicardium by 60%. On the other hand,
Weintraub and co-workers w5x reported that longitudinal
shortening was completely eliminated at the subepicardium
while local perfusion was reduced by less than 50%.
A similar disparity has been reported in the relationship
between regional myocardial flow and systolic wall thickening. Significantly impaired transmural and subepicardial
systolic wall thickening have been observed during partial
coronary artery occlusions in the dog despite no significant
reduction of subepicardial perfusion w3,6x. Consequently,
these investigators found that epicardial segment function
correlates more strongly with endocardial flow and endocardial function than with epicardial flow. This has lead to
the hypothesis that epicardial motion is ‘tethered’ or ‘coupled’ to endocardial deformation w3–5x.
)
Corresponding author. Tel.: q1 Ž619. 534-2547; fax: q1 Ž619.
534-5722; E-mail: [email protected]
0008-6363r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
PII S 0 0 0 8 - 6 3 6 3 Ž 9 7 . 0 0 2 9 0 - 3
Time for primary review 26 days.
A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
Contrary to the coupling hypothesis, Torry and colleagues w7x reported that the degree of local segment
dysfunction closely paralleled the pattern of regional perfusion through the thickness of the ventricular wall. Thus,
they concluded that perfusion, rather than transmural interaction, largely determined subepicardial function in nontransmural ischemia.
Bertha and Folts w8x also dismissed the tethering hypothesis in their assessment of the relationship between
subendocardial and subepicardial fiber shortening during
gradual coronary flow reductions. They observed that at
the lowest flow levels, active fiber shortening was still
maintained in the subepicardium even though simultaneous
severe bulging was observed in the subendocardium. During partial coronary artery occlusion with normal subepicardial blood flow, Gallagher and co-workers w9x found
that circumferential subepicardial and subendocardial
shortening were eliminated whereas subepicardial shortening in the direction of the myofibers remained normal.
This result pointed to the importance of accounting for
segment orientation in relation to myofiber architecture
when assessing regional flow–function relations.
Using biplane radiography of an array of implanted
myocardial markers, it is possible to measure the transmural distribution of the systolic strain tensor, and the alterations associated with acute regional ischemia w10x. This
provides a complete three-dimensional measure of local
myocardial segment function, which can also be related to
the local myofiber structure w11x. Therefore, we used this
approach to identify the effects of fiber orientation and
transmural location on three-dimensional flow–function
relations during graded coronary artery occlusions in anesthetized dogs. The analysis showed that whether the relationship between local myocardial bloodflow and systolic
strain during acute ischemia is dependent on transmural
location depends on segment orientation. In particular,
there is evidence of strong tethering in the cross-fiber
direction, whereas the fiber-strain flow relation was independent of transmural position.
2. Methods
Transmural distributions of three-dimensional strain and
myocardial blood flows were measured in the ischemic
region during graded left anterior descending ŽLAD. coronary artery occlusions in anesthetized dogs. The University
of California, San Diego ŽUCSD. is accredited by the
American Association for Accreditation of Laboratory Animal Care. All animal protocols were approved by the
UCSD Animal Subjects Committee and conducted in accordance with the Institute of Laboratory Resources’ Guide
for the Care and Use of Laboratory Animals published by
the National Research Council ŽWashington DC, 1996..
Twelve random-sourced dogs weighing from 24 to 33
kg were anesthetized with pentobarbital Ž30 mgrkg. and
637
maintained at a surgical plane with supplemented doses.
The animals were intubated and ventilated with room air
using a Harvard respiratory pump. Care was taken to
ensure full lung expansion throughout the experiment.
Blood gases were monitored intermittently, and blood pH
was maintained between 7.36 and 7.45. Hemodynamic
conditions were observed and kept stable throughout each
experiment. End-diastolic pressure ŽEDP. was raised and
lowered by intravenous dextran infusion Ž70% in 0.9%
NaCl. and blood withdrawal. The class I A antiarrhythmic
agent procainamide was given via intermittent intravenous
administration over several minutes Ž200–400 mg total.
before the first coronary ligation. There were no lasting
changes in heart rate, peak systolic pressure or QRS
interval after the procainamide infusion. Intravenous lidocaine Ž2 mgrkg. was also administered as needed to
control arrhythmias.
The heart was exposed through a median sternotomy
and left lateral thoracotomy at the fifth intercostal space
and supported by a pericardial cradle. A section of the
LAD coronary artery distal to the first or second diagonal
branch was dissected free for placement of a mechanical
occluder. A micromanometer ŽKonigsberg Instruments Inc.,
Pasadena, CA. was inserted into the left ventricle ŽLV.
through the left atrial appendage and was calibrated with a
fluid-filled catheter introduced from the femoral artery into
the left ventricle. Once the LV pressures were matched,
the fluid-filled catheter was withdrawn into the aortic root
to monitor aortic pressure. Limb leads were placed for an
electrocardiogram.
To measure transmural distributions of systolic deformation in the ischemic region, 3 columns Ž; 10 mm
separation. of 4–6 radiopaque beads Ž1.0–1.2 mm diameter. were implanted in the LV anterior free wall in the area
perfused by the LAD ŽFig. 1.. Five additional beads
Ž2-mm diameter. were sutured to the epicardial surface at
the apex, base, and above each column of beads. The
anterior–posterior and lateral axes of the X-ray machine
were adjusted so that the radiopaque markers were all
visible in both imaging planes, and synchronized fluoroscopic video images were recorded on two VHS videocassette recorders ŽPanasonic AG6300. with dubbed time
codes. Biplane video and hemodynamics were recorded at
baseline and during successive graded occlusions of the
LAD coronary artery using the mechanical occluder, with
end-diastolic pressures maintained relatively constant. Finally, bead positions in a geometric phantom were recorded
and used to reconstruct three-dimensional coordinates from
the two-dimensional images w12x.
Fluorescent microspheres 15 mm in diameter ŽMolecular Probes Inc., Eugene, OR. were used to measure myocardial perfusion immediately after each video-recording
period.
Microspheres labeled with 7 different fluorochromes
were available with the following emission wavelengths:
blue, 420 nm; blue-green, 457 nm; green, 488 nm;
638
A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
Fig. 1. Approximate location of the transmural bead set and ischemic
zone relative to occlusion site of the left anterior descending coronary
artery. The 3 epicardial beads for each of the 3 columns are depicted,
along with apex and base beads used to define the cardiac coordinate
system shown in the inset.
yellow-green, 506 nm; orange, 530 nm; red, 565 nm;
crimson, 635 nm. Each vial of microspheres was sonicated
and placed in a vortex agitator for 3 min to ensure proper
mixing before injection. Ten million microspheres were
injected into the left atrium through a catheter and flushed
with 10 ml of room temperature saline. A reference blood
sample was collected in a heparinized glass syringe at a
constant rate of 10 mlrmin Žusing a dual-piston Harvard
withdrawal pump. through a catheter placed in the femoral
artery beginning 5 s before the injection and ending 60 s
afterwards.
At the end of the protocols, the dog was sacrificed by
an overdose of sodium pentobarbital. A plastic catheter
was tied into the LAD coronary artery for injection of a
monastral blue B suspension to demarcate the ischemic
region. The heart was then excised; tissue which contained
all of the radiopaque beads was carefully cut out. Tissue
blocks from the ischemic zone were cut from tissue adjacent to the bead set Žfrom 2–15 mm from the edges of the
bead array.. Nonischemic tissue blocks were also obtained.
All of the tissue blocks were divided into epicardial,
midwall, and endocardial blocks Ž; 1-g pieces. for regional blood-flow measurements.
The fluorescence of each tissue block and the reference
blood flow samples were determined following the method
described by Glenny and co-workers w13x. Tissue and
blood samples were digested with 4 M and 16 M KOH,
respectively, filtered through 10-mm polycarbonate filters,
washed with aqueous tween and isopropanol and allowed
to dry overnight. The spheres were dissolved in xylene and
fluorescence spectra of dyersolvent were measured with a
fluorometer ŽPerkin-Elmer LS-50B, Norwalk, CT.. A linear curve of fluorescent intensity vs. microsphere concentration was then fitted by least squares for each fluorochrome from successive dilutions of defined standards
and used to calibrate sphere concentration from the measured fluorescence intensity. The slopes and intercepts for
these linear curves ranged from 29 to 966 spheresrmlrIU
and y196 to 74 spheresrml, respectively, with all r 2
values greater than or equal to 0.985. Samples from tissue
were diluted so that the measurements would fall on the
linear portion of the calibration curves.
Blood flows were calculated using the equation Qm s
Ž Cm = Qr .rCr where Qr is the withdrawal rate of the
reference sample Žmlrmin., Cm is the myocardial microsphere concentration, and Cr was the reference blood
sample microsphere concentration.
For two experiments, the method for microsphere processing was modified slightly so that the polycarbonate
filters were not needed w14x thereby reducing the risk of
microsphere loss during processing. The tissue blocks and
blood samples were initially digested in 2 M ethanolic
KOH, centrifuged and the supernatant removed. The samples were washed in tween, and then washed twice in
100% ethanol. After ample time for the ethanol to evaporate, xylene was added to each sample to dissolve the
polystyrene microspheres, leaving the fluorescent label.
Before using this new method, we processed multiple
calibration samples with both methods, and found the
accuracy to be equal in either case Žresults from calibration
samples were within 5% of each other.. Myocardial blood
flows were then determined as described above.
The techniques for measuring fiber angles have been
described previously w15x. A transmural block of tissue
containing the bead array was excised and fixed by immersion in 10% formalin phosphate buffer for at least 24 h. A
sample of the fixed tissue cut adjacent to the beads was
dehydrated through graded ethanol treatments and embedded in paraffin. Sections 10 mm thick were cut parallel to
the epicardium at 9–10 transmural locations, stained with
picrosirius red, and viewed under low-power Ž=20. light
microscopy. The fiber angle was then measured with respect to the circumferential axis by digital image analysis
as a function of depth through the ventricular wall.
The three-dimensional coordinates of the beads were
reconstructed from biplane images at end-diastole and
end-systole, determined from the time of the peak R-wave,
and 40 ms before peak negative d Prdt w16x, respectively.
The epicardial reference beads were used to transform the
A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
three-dimensional bead coordinates into a right-handed
orthogonal system of ‘cardiac’ coordinates w17x defined by
local circumferential, longitudinal, and radial axes ŽFig. 1..
A finite element method was used to compute continuous transmural distributions of three-dimensional strain at
end-systole Žwith respected to an undeformed reference
state at end-diastole. w18,19x. At 10% increments of relative wall depth, the six components of the strain tensor
were computed in cardiac coordinates: the three normal
strains, representing circumferential, longitudinal, and radial segment length change, with positive strain indicating
segment lengthening and negative strain corresponding to
shortening. In addition shear strains are found, which
reflect angle changes during deformation between originally orthogonal pairs of coordinate axes. The torsional,
axial and azimuthal shear strains represent shearing in the
circumferential–longitudinal, circumferential–radial and
longitudinal–radial reference coordinate planes, respectively.
For the description of flow–function relations, strains
are reported at three depths: 20% Žsubepicardial., 50%
Žmidwall., and 80% Žsubendocardial. of wall depth. Since
the local myofiber angles were measured and fitted by a
linear function of wall depth, the strain tensor was also
rotated into a ‘fiber’ coordinate system giving local fiber
and cross-fiber in-plane strains, leaving the radial strain
component unchanged.
639
Table 1
Values are means"SD averaged over 11 dogs. P-values examine statistical differences between the baseline and total coronary occlusion states
and were obtained using a paired t-test
Heart rate Žbeatsrmin.
ESP Žmm Hg.
EDP Žmm Hg.
Baseline
Total occlusion
p-value
105.4"18.6
120.9"20.1
9.1"2.2
109.6"17.0
116.4"22.1
12.6"5.2
0.0642
0.5861
0.0110
Statistical significance was taken as pF 0.05. ESP, end-systolic pressure;
EDP, end-diastolic pressure.
ence blood sample was started late, two because arrhythmias occurred during the data acquisition, and one because
the video recordings were not synchronized. Endocardial
strains interpolated at a transmural depth of 80% of wall
thickness were excluded from 4 dogs in which the average
relative wall depth of the three deepest beads was less than
80%.
3.2. Hemodynamics
Average left ventricular weight was 129 " 27 g Žmean
" SD.. Hemodynamic data are summarized in Table 1.
2.1. Statistical analysis
Differences in pressures and heart rate between the
baseline and ischemic conditions were compared using a
paired t-test. Blood flow comparisons between baseline
and ischemic states were performed with a non-parametric
Wilcoxon signed rank test while transmural distributions
of blood flow were analyzed using a non-parametric Friedman test. Variations in strain as a function of wall depth
were analyzed using two-way repeated-measures analysis
of variance ŽANOVA. with transmural location as the
within factor and occlusion state as the between factor.
Strains were analyzed using two-factor ANOVA with blood
flow group and transmural location as nominal factors.
Statistical significance was accepted at the 95% confidence
level Ž p - 0.05..
3. Results
3.1. Exclusions
Data from one dog were excluded from analysis because of a large error in the three-dimensional reconstruction of the bead coordinates, possibly due to movement of
the X-ray tubes or image intensifiers. Of the 57 runs
recorded in the other 11 dogs, five were excluded for the
following reasons: two because withdrawal of the refer-
Fig. 2. End-systolic normal strains Žtop 3 panels. at graded blood flows
shown as a function of wall depth Žepicardium s 0%.. Blood flows at
20%, 50%, and 80% depth are shown in the bottom panel for each of the
5 mean transmural blood flows. Average transmural blood flows are
listed for each run. Data shown are from one animal.
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A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
Occlusion of the coronary artery did not significantly alter
mean heart rate or end-systolic pressure. A small increase
in mean end-diastolic pressure Ž3.5 mmHg. occurred between baseline and total coronary artery occlusion.
Since the distribution of measured regional blood flows
was not Gaussian, non-parametric statistics were used. In
the ischemic region, median transmural myocardial blood
flow was 1.01 mlrminrg and it was reduced to 0.13
mlrminrg at total occlusion. At all three transmural depths
in the ischemic region, there was a significant decrease in
blood flow during total coronary occlusion Ž p - 0.03.. In
the non-ischemic region, median transmural myocardial
flow was 1.29 mlrminrg at baseline and 1.38 mlrminrg
at total occlusion, and did not change significantly during
total LAD occlusion at any wall depth.
3.3. Transmural strain distributions
Negative circumferential and longitudinal strains, indicating in-plane shortening, and positive radial wall thicken-
ing all increased in magnitude from epicardium to endocardium during baseline, as seen in the representative
measurements from one animal ŽFig. 2.. As flow decreased
during graded occlusions, shortening gradually gave way
to lengthening Žpositive strains. and systolic wall thickening was replaced by thinning Žnegative strain..
The transmural gradients of strain tended to decrease
with progressive ischemia so that the loss of circumferential, longitudinal and radial strain was largest at the subendocardium and smallest at the epicardium as seen for the
mean results for baseline and total occlusion runs ŽFig. 3..
Mean longitudinal–radial Žazimuthal. transverse shears
were small and positive at baseline but changed sign
during total occlusion. By two-way analysis of variance
comparing baseline and total occlusion runs only, ischemia
significantly changed all three normal strains Ž p - 0.002.,
and the longitudinal–radial transverse shear strain Ž p s
0.0096., but not the other two shear strain components.
There was a significant effect of transmural position on
circumferential strain Ž p s 0.0001., radial strain Ž p s
Fig. 3. Average Ž"standard deviation. end-systolic normal and shear strains in cardiac coordinates shown as a function of wall depth Žepicardium s 0%.
for baseline and total LAD occlusion. Data points, except those denoted by an asterisk, are an average from all 11 animals. Asterisks denote a sample size
of ns 7.
A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
Fig. 4. Average Ž"standard deviation. end-systolic fiber and cross-fiber
strains plotted as a function of wall depth Žepicardium s 0%. for baseline
and total LAD occlusion. Data points, except those denoted by an
asterisk, are an average from all 11 animals. Asterisks denote a sample
size of ns 7.
641
Fig. 5. Average Ž"standard error. endocardial to epicardial blood flow
ratios for each run grouped according to mean transmural blood flow.
Mean transmural blood flows for each run are a weighted average of the
local flows at the epicardium, midwall, and endocardium.
0.2, 0.2–0.5, 0.5–0.8, 0.8–1.2, and 1.2–2.0 mlrminrg. At
high transmural blood flows, the average ratio of regional
endocardial to epicardial flow in the ischemic region was
0.004., and both transverse shears Ž p s 0.012 and p s
0.040.. From the interaction effects, ischemia significantly
altered the transmural variations of circumferential, longitudinal, and radial strains Ž p s 0.0001 for all. but not the
shears.
End-systolic strains were also computed with respect to
fiber and cross-fiber coordinates ŽFig. 4.. Mean fiber strains
were negative at baseline and positive during total occlusion tending to increase slightly in magnitude across the
ventricular wall. By two-way analysis of variance comparing baseline and total occlusion runs only, ischemia significantly changed fiber and crossfiber strains Ž p s 0.004 and
p s 0.0001, respectively.. There was a significant effect of
transmural position on crossfiber strain Ž p s 0.001. but
not fiber strain Ž p s 0.7.. Negative strains in the cross-fiber
direction at baseline had a significant transmural variation
increasing markedly toward the endocardium Ž p s 0.0001..
After LAD occlusion, systolic fiber and cross-fiber strains
changed significantly and on average were positive
Žlengthening. and transmurally uniform. From the interaction effects, ischemia significantly altered the transmural
variations of fiber and crossfiber strains Ž p s 0.0001 for
both.. Radial strains in the fiber coordinate system are the
same as those in cardiac coordinates.
3.4. Transmural myocardial flow
The effect of transmural depth on blood flow in the
ischemic region was not statistically significant during
either baseline or total occlusion. Fig. 5 shows endocardial
to epicardial blood flow ratios according to the overall
transmural blood flow grouped as follows: 0.0–0.1, 0.1–
Fig. 6. Average Ž"standard error. end-systolic normal strains in cardiac
coordinates as grouped by their corresponding levels of local blood flow.
Each bar represents the average of all strain data in the corresponding
local blood flow group at the specified transmural location.
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A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
greater than unity. However, as transmural flow decreased,
the ratio tended to decrease such that at the lowest transmural blood flows, flow to the endocardium was about
70% of that of the epicardium. For comparison, at baseline
endocardialrepicardial flow ratios were 1.22 " 0.16 Žmean
" 1SE. compared with 0.86 " 0.18 Žmean " 1SE. at total
occlusion Ž p s NS..
In the nonischemic region, endocardialrepicardial flow
ratios were 1.29 " 0.22 Žmean " 1SE. at baseline and 1.18
" 0.16 Žmean " 1SE. at total occlusion, and were not
significantly different from each other. There was no significant effect of transmural depth on non-ischemic zone
perfusion during baseline or total LAD artery occlusion.
For the six flow groups in Fig. 5, the corresponding
median transmural blood flows relative to the median
baseline flows were 6%, 11%, 32%, 61%, 92% and 147%
Žfrom the 0.0–0.1 to 1.2–2.0 groups, respectively.. The
relative flows for each of the 3 transmural layers were
similar to the these transmural values. The baseline flows
were not normally distributed, so the mean relative flows
were lower than the median values but the trends between
groups were the same.
Fig. 7. Average Ž"standard error. end-systolic fiber and cross-fiber
strains as grouped by their corresponding levels of local blood flow. Each
bar represents the average of all strain data in the corresponding local
blood flow group at the specified transmural location. Radial strains are
the same as those shown in Fig. 6.
3.5. Flow–function relations
Fig. 6 shows the relationship between average transmural strain components and local myocardial flow. The
strains were grouped according to tissue blood flows using
the same intervals as used in Fig. 5. Average circumferential strains had positive or small negative values in the low
flow groups. As local blood flow increased, circumferential strains tended to become more negative throughout the
wall. Average longitudinal strains were all positive in the
low blood flow groups and tended to become small or
negative at high blood flows. Average radial strains were
negative during the low flow group and tended to become
positive at high blood flows.
The results of a two-way analysis of variance for both
the normal and shear strains in cardiac coordinates are
summarized in Table 2. Mean-squared values indicate the
strength of an effect, without taking into account the
residual error sum of squares; the p-values indicate the
significance of each effect. The analysis indicated a significant effect of blood flow on all of the normal strain
components as well as the longitudinal–radial transverse
shear component. There was also a significant effect of
transmural location on the circumferential and radial strains
and on the circumferential–radial transverse shear. In the
circumferential direction, there was a significant interaction effect between transmural location and blood flow,
indicating a dependence of the circumferential strain–blood
flow relation on wall depth. Conversely, there was no
significant interaction between the longitudinal strain–flow
relation and location.
Fig. 7 plots the average strain components referred to
fiber coordinates grouped according to local blood flow.
Fiber strains were positive in the low-flow groups and
became negative at high blood flows. Similarly, average
midwall and endocardial strains in the cross-fiber direction
Table 2
Results from the two-way analysis of variance of the normal and shear strain data in cardiac coordinates, with transmural location and blood flow group as
the nominal factors
Strain orientation
Circumferential
Longitudinal
Radial
Circumferential–longitudinal
Circumferential–radial
Longitudinal–radial
Transmural location
Blood flow
Location)Blood flow interaction
mean square
p-value
mean square
p-value
mean square
p-value
0.0574
0.0001
0.0638
0.0008
0.0133
0.0014
0.0010
0.9810
0.0246
0.5653
0.0001
0.4333
0.0426
0.0142
0.1066
0.0022
0.0014
0.0078
0.0001
0.0447
0.0001
0.2009
0.3350
0.0008
0.0090
0.0081
0.0265
0.0026
0.0016
0.0025
0.0391
0.2095
0.1188
0.0788
0.2432
0.1518
Mean square values indicate the strength of the given effect on the strain, while p-values indicate the significance of the effect.
A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
643
Table 3
Results from the two-way analysis of variance of strain data in fiber coordinates
Strain orientation
Fiber
Cross-fiber
Radial
Transmural location
Blood flow
Location)Blood flow interaction
mean square
p-value
mean square
p-value
mean square
p-value
0.0024
0.0744
0.0638
0.6542
0.0001
0.0246
0.0222
0.0294
0.1066
0.0029
0.0001
0.0001
0.0066
0.0094
0.0265
0.3315
0.0463
0.1188
Mean square values indicate the strength of the given effect on the strain, while p-values indicate the significance of the effect.
tended to become more negative as the blood flow was
increased; however, epicardial cross-fiber strains did not
appear to follow this same trend.
Two-way analysis of variance of the fiber strain components and blood flow groups are shown in Table 3. There
was a highly significant effect of local blood flow on both
fiber and cross-fiber strains. Transmural location had a
significant effect on cross-fiber strains but not on fiber
strains. In the cross-fiber direction, the ANOVA indicated
a significant interaction effect between transmural location
and blood flow; such an effect was not present in the fiber
direction. Thus, the relationship between blood flow and
cross-fiber strain appears to be dependent upon wall depth
whereas the relationship between blood flow and fiber
strain appears to be unique and independent of transmural
location. Results in the radial direction are the same as
those previously discussed in cardiac coordinates.
There were no significant differences between the normal cardiac and fiberrcross-fiber strains in the highest
flow group Ž1.2–2.0 mlrminrg. compared with those
measured during baseline conditions.
4. Discussion
In this study, regional ischemic systolic function in the
left ventricular wall was assessed from the transmural
distributions of three-dimensional finite strains during
graded left anterior descending coronary artery occlusions.
We examined the relationship between regional myocardial blood flow and regional systolic function, and found a
dependence of this relationship on transmural location,
segment orientation, and fiber architecture.
4.1. Effects of ischemia on 3D mechanics
Reductions in blood flow had a significant effect on
three-dimensional systolic segment function. Circumferential, longitudinal, radial, fiber, and cross-fiber strains were
all significantly altered as a result of the graded LAD
occlusions. However, of the shear strains, only the longitudinal–radial transverse shear was significantly affected by
ischemia. These results are in general agreement with a
previous study by Villarreal and colleagues w10x in which
three-dimensional finite strains were computed in much
the same manner as our study. Villarreal and co-workers
also observed that the transmural gradient of the circumferential strains at baseline tended to be lost in ischemia. In
the present study, we noted a similar trend not only for the
circumferential strains, but also for the radial and crossfiber strains. The transmural distributions of the longitudinal, fiber, and shear strains appeared more uniform than
the other components, and remained so after total occlusion.
4.2. Flow–function relationship depends on transmural
location and orientation
As reported by others w3,5,6x, the flow–function relationship was not, in general, independent of transmural
position. This finding is consistent with the hypothesis that
mechanical interaction results in a tethering between the
endocardium and epicardium w5,20x.
However, our study also indicated for the first time that
the degree of mechanical interaction was highly dependent
on segment orientation, i.e. the orientation in which function is measured. Specifically, for segments parallel to the
plane of the wall, the interaction was highest and highly
significant for cross-fiber and circumferential shortening,
but lower and not statistically significant in the fiber and
longitudinal directions. Although the radial strain did not
show a statistically significant interaction, it did show the
greatest strength of the effect of the interaction on strain,
suggesting that the flow–function interaction for this strain
component is dependent on position. This evidence supports the conclusion that transmural interactions are minimized for myocardial strain in the fiber direction and
emphasizes the importance of accounting for segment orientation with respect to fiber anatomy as suggested by
Gallagher and colleagues w9x. Thus, we conclude that there
appears to be a unique relationship between local myocardial blood flow and function, independent of transmural
location, in the fiber direction; however, such a unique
relationship does not exist in cross-fiber directions, due to
an effect of transmural tethering.
4.3. Regional wall thickening
In their review of systolic wall thickening, Hexeberg
and colleagues w20x conclude that thickening of a discrete
myocardial layer is not independent of the surrounding
644
A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
layers and that it is not appropriate to relate a change in
local thickening to a change in local blood flow.
We found that in the radial direction, the dependence of
the flow–function relationship on transmural position was,
in fact, the strongest of all the directions as indicated by
the mean square value of the ANOVA ŽTables 2 and 3..
For example, as shown in Fig. 6, positive radial strains
Žwall thickening. became zero or less at the epicardium
when flow was reduced to the 0.2–0.5 mlrminrg range.
However, midwall radial strains did not give way to
thinning until the local blood flow fell to the 0.1–0.2
mlrminrg range, and endocardial wall thinning did not
begin until the myocardial blood flow fell below 0.1
mlrminrg. These data suggest that radial function is
tethered in some fashion between layers of myocardium,
hence this local function is not uniquely determined by
local perfusion.
Edwards and co-workers w6x also found evidence of
tethering as measured in the radial direction when they
noted that subepicardial thickening correlated most closely
with subendocardial blood flow. Although we found a
large transmural interaction in the radial direction Žmeansquared value., the smaller marker separation in the radial
direction Žcompared with the column separation. resulted
in larger variations in the radial strains, and thus the
interaction that we observed did not achieve statistical
significance.
Torry and colleagues w7x found that, under conditions of
non-transmural ischemia, the increasing degree of radial
dysfunction from subepicardium to subendocardium paralleled the increased loss of blood flow through the wall.
Thus, they concluded that perfusion, rather than tethering,
was the primary determinant of subepicardial function
under conditions of non-transmural ischemia.
In our study, during the high levels of mean transmural
blood flow, the local epicardial to endocardial flow ratio
was close to 1, indicating relatively uniform transmural
flow during the baseline conditions. However, during the
baseline conditions, we observed a significant transmural
gradient of radial strain, with maximum wall thickening
occurring at the endocardium as expected w11x. The graded
LAD occlusions produced a non-uniform transmural pattern of perfusion in which the average epicardial to endocardial flow ratio increased as mean transmural flow was
reduced. Yet, at total LAD occlusion, we observed that the
transmural gradient in radial strain had markedly diminished. This observation supports the notion that perfusion
may not be as important a determinant as mechanical
tethering in contributing to radial dysfunction.
4.4. Limitations
Several limitations of the present study should be noted.
The main determinant of the strain measurement is the
resolution of the radiographic images used to compute the
three-dimensional coordinates of the implanted beads, and
hence the accuracy in locating the actual bead coordinates.
The error in finding the centroid of the beads was estimated to be 0.2–0.3 mm by Waldman and colleagues w11x.
Using the finite element fitting technique, this corresponds
to a practical resolution of about "0.02 in the strains w21x,
although due to the bead spacing, radial components may
have greater resolution. Local injury due to the implantation of the bead set, differences in the location of the bead
set, and differences in heart sizes are also possible sources
of variation for strains among the animals.
Other limitations to this study result from the resolution
and accuracy of the blood flow measurements. The fluorescent microsphere technique itself correlates well with
results for regional blood flow using radioactive microspheres w22,23x. Even though our measurements of transmural flow are close to several previously reported values,
the endocardialrepicardial flow ratio did not decrease as
much as previously reported. For example, Edwards et al.
w6x report a baseline endocardialrepicardial flow ratio of
0.82, reduced to 0.43 after partial LAD stenosis. Torry and
colleagues w7x give a baseline ratio of 0.81 and then 0.58
during partial coronary occlusion. In the present study, our
mean ratios were 1.22 and 1.29 in the ischemic and
non-ischemic zones at baseline, and 0.86 and 1.18 in these
same zones during maximum occlusion. Thus, the baseline
ratios in this study may be somewhat higher than normal
and the decrease with occlusion may not be as great as
expected.
There are local variations in myocardial perfusion especially during ischemia. Blood flows were found in close
proximity to the location of the mechanical measurements
Žwithin 2 cm., but blood flow could be different at the
center of the transmural radiopaque marker set. The transmural location of the blood flow measurement may not
exactly match the transmural locations of the strain measures. Loss of microspheres during tissue digestion, filtering of the samples, or sample handling is one probable
source of error. Although care was taken, the addition of
unequal volumes of solvent to each sample would have
also affected the total microsphere count. Inconsistencies
in the measurements of the fluorescence of each sample
could have resulted in additional errors. There is also
‘spillover’ from each color band to adjacent color bands,
which will decrease the accuracy of the fluorescent microsphere method. Glenny et al. w13x report fairly large
spillovers from blue-green, green and yellow-green into
the adjacent color bands Žup to 18% of the correct color
band emission.. We calculated the spillover from these
three colors on our fluorometer to compare with the Glenny
values. We found that our maximum value was about
one-half that given by Glenny: the spillovers from bluegreen, green and yellow-green to the two adjacent colors
were: 2.7 and 6.8; 7.1 and 0.2; 0.1 and 0.1 respectively.
Overall, the spillovers for all seven colors are comparable
to the corresponding values given by Glenny. But nevertheless, there is some spillover which we do not correct
A.D. McCulloch et al.r CardioÕascular Research 37 (1998) 636–645
for, and acknowledge this as a limitation of the microsphere technique. These limitations of the fluorescent microsphere technique may have contributed to an increase in
the variation observed in the blood flow data, and precluded the determination of more accurate distributions of
strain–flow relationships.
w5x
w6x
w7x
5. Conclusion
In summary, using three-dimensional strain distributions as an index of myocardial systolic function, we found
that the uniqueness of the local blood flow–function relationship is largely dependent on segment orientation. The
relationship appeared to be unique and independent of
transmural location in the fiber direction but not in the
cross-fiber or radial directions. The apparent dependence
of the flow–function relationship on wall depth in the
cross-fiber and radial directions supports the conclusion
that a mechanical tethering occurs between the transmural
layers of the myocardium, and this tethering most strongly
affects cross-fiber, rather than fiber function. This is also
consistent with the hypothesis that perfusion directly governs myocardial fiber tension development which in turn
influences fiber shortening.
w8x
w9x
w10x
w11x
w12x
w13x
w14x
Acknowledgements
w15x
The authors gratefully acknowledge the assistance of
Monica Adams and Babak Fazeli with the experimental
procedures and the assistance of Daren Deffenbaugh with
the data analysis. We also acknowledge Dr. Dan McKirnan
for technical advice and assistance, and Dr. James Covell
for the generous use of his laboratory. This research was
supported by National Heart, Lung and Blod Institute
grants HL-41603 and HL-32583.
w16x
w17x
w18x
w19x
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