Vol. 90, Issue 6, 2427-2438, June 2001
Smooth muscle relaxation and local hydraulic
impedance properties of the aorta
Bernard P.
Cholley1,
Roberto M.
Lang1,
Claudia E.
Korcarz1, and
Sanjeev G.
Shroff2
1 Cardiology Section, Department of Medicine, University of
Chicago, Chicago, Illinois 60637; and 2 Department of
Bioengineering, University of Pittsburgh, Pittsburgh, Pennsylvania
15261
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ABSTRACT |
Smooth muscle relaxation is expected to yield
beneficial effects on hydraulic impedance properties of large vessels.
We investigated the effects of intravenous diltiazem infusion on aortic
wall stiffness and local hydraulic impedance properties. In seven
anesthetized, closed-chest dogs, instantaneous cross-sectional area and
pressure of the descending thoracic aorta were measured using
transesophageal echocardiography combined with acoustic quantification
and a micromanometer, respectively. Data were acquired during a vena
caval balloon inflation, both at the control condition and with
diltiazem infusion. At the operating point, diltiazem reduced blood
pressure in all dogs but did not alter aortic dimensions or wall
stiffness. Over the observed pressure range, aortic area-pressure
relationships were linear. Whereas diltiazem affected the slope of this
relationship variably (no change in 3 dogs, increase in 1 dog, decrease
in 3 dogs), the zero-pressure area intercept was significantly
increased in every case such that higher area was observed at any given pressure. When comparisons were made at a common level of wall stress,
wall stiffness was either increased or unchanged during diltiazem
infusion. In contrast, diltiazem decreased wall stiffness in every case
when comparisons were made at a common level of aortic midwall radius.
Aortic characteristic impedance and pulse wave velocity, components of
left ventricular hydraulic load that are determined by aortic elastic
and geometric properties, were affected variably. A comparison of wall
stiffness at matched wall stress appears inappropriate for assessing
changes in smooth muscle tone. Because of the competing effects of
changes in vessel diameter and wall stiffness, smooth muscle relaxation
is not necessarily accompanied by the expected beneficial changes in
local aortic hydraulic impedance. These results can be reconciled by
recognizing that components other than vascular smooth muscle (e.g.,
elastin, collagen) contribute to aortic wall stiffness.
compliance; incremental elastic modulus; characteristic impedance; pulse wave velocity; calcium channel blocker
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INTRODUCTION |
AORTIC ELASTIC
PROPERTIES play a major role in transforming the pulsatile
ejection from the left ventricle (LV) into a continuous flow at the
level of the capillaries and in determining the hydraulic load faced by
the LV during ejection. These properties are altered with aging
(4, 19, 20) or hypertension (4, 17, 21, 26,
44) such that LV afterload is increased, impairing the "ideal" ventriculoarterial coupling (7, 27). Hence, it
has been suggested that the pharmacological therapy of hypertension should not only be aimed at reducing elevated systemic vascular resistance but also at improving the decreased distensibility of large
arteries (26, 36-39).
Calcium channel blockers are used for the treatment of systemic
hypertension. Although it is clear that these agents reduce peripheral
vascular resistance (the steady component of hydraulic load imposed by
the systemic arterial circulation), some studies have demonstrated that
they can also increase large vessel compliance via a reduction in
arterial smooth muscle tone (18, 35, 40, 47, 49).
Consequently, it is logical to expect that calcium channel blockers
will reduce the pulsatile component of systemic arterial hydraulic load
as well. However, experimental data have yielded equivocal results. For
example, the observation of increased global arterial compliance in
hypertensive subjects following acute or chronic administration of
calcium channel antagonist nifedipine supports the above-mentioned
expectation (10, 12, 45). In contrast, nifedipine
administration in these hypertensive subjects did not alter localized
measures of pulsatile arterial load, such as aortic characteristic
impedance, in a consistent manner; the group-averaged values were
unchanged (10, 12, 45). It can be argued, at least on a
theoretical basis, that the interplay between changes in distending
pressure and vessel geometric and elastic properties underlies this
disparity. However, limited in vivo experimental data exist to evaluate
this theoretical argument. Until recently, in vivo evaluation of
regional aortic geometric and elastic properties was limited due to
methodological difficulties encountered in simultaneously acquiring
instantaneous measurements of aortic diameter, wall thickness, and
pressure. New developments in ultrasound technology, such as
transesophageal imaging of the aorta with automated endothelial border
detection, have overcome these limitations by allowing continuous
assessment of aortic dimensions (11, 19).
Accordingly, the purpose of this study was to investigate the acute
effects of smooth muscle relaxation (as produced by intravenous infusion of diltiazem) on geometric and elastic properties of the
aorta. In addition, the consequences of these changes on aortic characteristic impedance and pulse wave velocity, components of LV
hydraulic load that are determined by aortic elastic and geometric properties were evealuated. We wished to test the hypothesis that smooth muscle relaxation always yields beneficial changes in localized aortic hydraulic impedance properties (i.e., reduced aortic
characteristic impedance and pulse wave velocity).
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METHODS |
Surgical preparation and data acquisition.
Seven mongrel dogs (29 ± 3 kg body wt, male) were studied. All
protocols were approved by The University of Chicago Institutional Animal Care and Use Committee and conformed with the National Institutes of Health (NIH) Guide for the Care and Use of
Laboratory Animals (no. 85-23, revised 1996). Animals
received unlimited food and water until 8 h before the study.
Anesthesia was induced using intravenous pentobarbital sodium (30 mg/kg) injected via a peripheral vein and maintained throughout the
experiment using a constant inspired halothane fraction of 1%. Animals
were intubated and mechanically ventilated (respirator model 683, Harvard Apparatus, South Natick, MA) with room air at a frequency of 20 cycles/min. Tidal volume was adjusted to maintain arterial
PCO2 between 30 and 40 Torr.
Electrocardiogram (ECG) was continuously monitored.
The methodology used for data acquisition has been described previously
(11). Briefly, a transesophageal probe (5 MHz, monoplane) connected to an echocardiographic unit (Sonos-1500, Hewlett Packard, Andover, MA) was introduced into the esophagus. The aorta was visualized by rotating the shaft toward the spine of the animal. The
transducer was then positioned immediately distal to the off-take of
the left subclavian artery, and the aorta was imaged in the transverse
plane. Short-axis images of the aorta were optimized by adjusting time-
and lateral-gain compensation settings to improve the visualization of
the aortic-endothelial interface. The backscatter-based endothelial
boundary detection system (31, 32) was then activated, and
gain controls were readjusted to enhance the tracking of the aortic
endothelium-blood interface. A region of interest was traced around the
blood pool cavity. A built-in software package (31, 32)
computed and instantaneously displayed aortic lumen area as a function
of time (Fig. 1). A data port, providing
an electrical analog output of the instantaneous aortic lumen area, was
incorporated into the ultrasound imaging system. Without changing the
position of the transesophageal transducer, end diastolic aortic
diameter and wall thickness were measured from aortic two-dimensional
targeted M mode recordings at the time of the R wave on the ECG.
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Fig. 1.
Two-dimensional image (short-axis view) of the aorta
obtained with transesophageal echocardiography (top). The
aortic endothelium-blood interface (orange line) was identified using
an on-line, automated border detection system. Instantaneous aortic
lumen cross-sectional area (A), aortic pressure (P), and
electrocardiogram (ECG) data were recorded simultaneously
(bottom).
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To measure instantaneous aortic pressure, a 6-Fr catheter with a
micromanometer at the tip (SPC-360, Millar Instruments, Houston, TX)
was introduced retrogradely via a femoral artery and positioned immediately distal to the ultrasonic imaging plane. Instantaneous aortic pressure and area signals were displayed on the monitor of the
echo machine (Fig. 1). An 8-Fr balloon-tipped catheter (balloon
diameter-40 mm; Medi-tech, Watertown, MA) was positioned in the
inferior vena cava (IVC), via a femoral vein, approximately at the
level of the diaphragm. Balloon inflation was used to generate a broad
range of aortic pressures and areas (11).
Experimental design.
Thirty minutes were allowed for stabilization of the preparation before
the initiation of data acquisition. With the respirator turned off,
data were acquired during the initial 30 s of IVC balloon
inflation. Aortic pressure, aortic area, and ECG data were digitized
on-line at 400 Hz and stored on the hard drive of a commercially
available computer. After the completion of baseline recordings
(control), intravenous diltiazem was injected as a bolus (0.2 mg/kg)
followed by a continuous infusion (0.3 mg · kg
1 · h1). Data
acquisition protocol, similar to the control condition, was repeated 15 min after the initiation of the diltiazem infusion.
Determination of aortic elastic and local hydraulic impedance
properties.
Two-dimensional imaging of the aorta was performed at a frame rate of
33 Hz. Because the processing delay of the backscatter algorithm
approximates the duration of one video frame (46), the
digitized aortic area was offset by 30 ms with respect to the pressure
recordings. Data acquired during IVC balloon inflation enabled the
determination of aortic area-pressure relationships over a wide range
of loading conditions. Only peak systolic and minimum diastolic
pressures and the corresponding area values from each cardiac cycle
during balloon inflation were used to construct the area-pressure
relationships. These peak and minimal values correspond to the extremes
of the elliptic area-pressure loops where the contribution of the
viscous properties may be small (19, 29). Aortic
compliance per unit length (CL) was calculated
as the slope of the aortic area-pressure linear regression.
Instantaneous aortic thickness was derived from measurements of
end-diastolic aortic diameter and wall thickness and then used to
compute instantaneous aortic midwall radius and wall stress (see
APPENDIX). From the stress-radius relationship, aortic wall stiffness was quantified in terms of the incremental elastic modulus (Einc) at a given stress or midwall radius
(19).
With the use of the pressure, radius, and thickness data, local
hydraulic impedance properties were quantified in terms of aortic
characteristic impedance (Zc) and aortic pulse wave
velocity (Cph). We calculated Zc and
Cph for any given level of aortic pressure and established
the individual Zc-pressure and Cph-pressure relationships before and after diltiazem infusion. All relevant equations used to compute the derived quantities are presented in the
APPENDIX.
Statistical analysis.
Data were compared using paired t-test (control vs.
diltiazem). The Wilcoxon signed rank test was used when the assumption of normal distribution was violated. Least squares regression analysis
was performed on area-pressure and stress-midwall radius relationships.
The method of excess variance (or extra sum of squares)
(34) was used to compare regression parameters between the
two conditions (i.e., control vs. diltiazem). A P value
<0.05 was considered significant. All results are expressed as
means ± SD.
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RESULTS |
Diltiazem infusion reduced both systolic and diastolic blood
pressures in all dogs without significant changes in heart rate (Table
1); pulse pressure increased by a small
amount (5 ± 3 mmHg). Despite the fall in blood pressure after
infusion of diltiazem, aortic area and change in area during a cardiac
cycle (pulse area) at the operating point (i.e., steady-state value
just before the IVC balloon inflation) did not change (Table 1).
IVC balloon inflation resulted in a progressive decrease in aortic
pressures in all animals, which was accompanied by a reduction in
aortic area. Under control conditions, the ranges of aortic pressure
and area reductions with IVC balloon inflation were 54 ± 9 mmHg
and 0.63 ± 0.18 cm2, respectively. Similar reductions
in pressure and area were noted with IVC balloon inflation during
diltiazem infusion (55 ± 13 mmHg and 0.59 ± 0.20 cm2). All aortic area-pressure relationships were highly
linear (median R2 = 0.961;
range-0.830-0.984), and diltiazem shifted these relationships such
that aortic area for any pressure was higher during diltiazem infusion
in each of the seven dogs (Figs.
2A and
3A).
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Fig. 2.
Aortic lumen area-aortic pressure (A) and
aortic wall stress-midwall radius (B) relationships obtained
by inferior vena caval balloon inflation in a single dog (dog
3) before (control) and during diltiazem infusion (diltiazem).
Solid and dashed lines correspond to the linear (A) and
exponential (B) fit to the measured data (symbols). Solid
symbols in A and B denote the operating point
data (i.e., peak systolic and minimum diastolic pressures and
corresponding area values just before the onset of balloon inflation).
From these data, aortic wall incremental elastic modulus
(Einc)-aortic wall stress (C) and
Einc-midwall radius (D) relationships were
calculated. Although diltiazem shifted the area-pressure relationship
such that aortic area for any pressure was higher, the slope of this
relationship (i.e., compliance per unit length) was unaffected in this
example.
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Fig. 3.
Aortic lumen area-aortic pressure (A) and
aortic wall stress-midwall radius (B) relationships obtained
by inferior vena caval balloon inflation in a single dog (dog
2) before (control) and during diltiazem infusion (diltiazem).
Aortic wall Einc-wall stress (C) and
Einc-midwall radius (D) relationships were
calculated. Similar to the data in Fig. 2, diltiazem shifted the
area-pressure relationship such that aortic area for any pressure was
higher. However, unlike Fig. 2, the slope of this relationship (i.e.,
compliance per unit length) was increased.
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The excess variance analysis indicated that diltiazem infusion did not
change the slope of the area-pressure relationship (i.e.,
CL) in three dogs (dogs 1,
3, and 4; Fig. 2A); the remaining four
dogs had a statistically significant change of +21% in dog
2 (Fig. 3A), 
24% in dog 5, 39% in
dog 6, and 16% in dog 7. In contrast, the
zero-pressure-area intercept was increased significantly in each of the
seven dogs (group averages, 0.09 ± 0.27 vs. 0.41 ± 0.24 cm2). Although the linear extrapolation of the
area-pressure relationship to zero pressure may be questionable, these
data do indicate that diltiazem infusion shifted the aortic
area-pressure relationship leftward over the observed pressure range
(i.e., larger area for a given pressure).
Stress-midwall radius relationships were nonlinear (Figs. 2B
and 3B) and fitted well (median
R2 = 0.985; range-0.934-0.994) by an
exponential function (see APPENDIX). In response to
diltiazem infusion, stress-midwall radius relationships were shifted to
the right in all dogs such that, for a given wall stress, midwall
radius (Figs. 2B and 3B) was greater following smooth muscle relaxation. Aortic wall stiffness for a given wall stress
was either greater (dogs 1, 3, 5,
6, and 7; Fig. 2C) or unchanged
(dogs 2 and 4; Fig. 2D). In contrast,
Einc at a given midwall radius was lower during diltiazem
infusion in every dog (Figs. 2D and 3D). At the
operating point, however, aortic dimensions and wall stiffness were not
different between control and diltiazem (Table 1).
The effects of changes in aortic elastic and geometric properties on
local hydraulic impedance properties were quantified in terms of aortic
Zc and Cph. Diltiazem infusion resulted in variable qualitative and quantitative changes in Zc (Fig.
4); Zc decreased in 4 dogs
(dogs 1, 2, 3, and 4) and
increased in 2 dogs (dogs 6 and 7) over the
entire pressure range, whereas it had a mixed effect in the remaining
dog (dog 5, Zc-pressure relationships
intersected). Despite a beneficial reduction in Zc in four
dogs, none of the dogs exhibited a reduction in Cph following diltiazem (i.e., reduced Cph at a given
pressure). In fact, increased Cph at a given pressure was
noted in 4 dogs (dogs 1, 3, 5, and
6; Fig. 5), whereas the
Cph-pressure relationship was unaltered in the remaining
three dogs (dogs 2, 4, and 7; Fig. 5).
At the operating point, the mean Zc and Cph
values (i.e., averaged over all 7 dogs) were not different before or
after diltiazem (Table 1).
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Fig. 4.
Individual relationships between aortic characteristic
impedance (Zc) and aortic pressure at control condition and
during diltiazem infusion for dogs 1-7.
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Fig. 5.
Individual relationships between aortic pulse wave
velocity (Cph) and aortic pressure at control condition and
during diltiazem infusion for dogs 1-7.
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DISCUSSION |
In addition to methodological considerations, the following
discussion focuses on the two main observations of the study. 1) Inferences regarding diltiazem-induced changes in aortic
wall stiffness depend on the method of comparison (i.e., common level of wall stress vs. common level of midwall radius). 2)
Smooth muscle relaxation does not necessarily yield the expected
beneficial changes in local hydraulic impedance of the aorta in
normotensive, anesthetized dogs.
Methodological considerations.
The use of transesophageal echocardiography together with the automated
border detection to assess regional elastic properties of the
descending thoracic aorta has been previously validated in both human
and animal studies (11, 19). Before the availability of
this technique, instantaneous aortic dimension measurements could only
be obtained in opened-chest or chronically instrumented animals using
invasive devices such as sonomicrometers or electromechanical calipers.
Recently, investigators were able to obtain measurements of aortic
diameter or volume without opening the chest using ultrasonic dimension
(40, 42) or impedance catheters (16).
Transesophageal echocardiography allows measurements of instantaneous
lumen area and aortic thickness, variables necessary for the
computation of instantaneous aortic wall stress and Einc.
Consequently, we were able to obtain in vivo measurements of
Einc, a measure of aortic wall stiffness independent of
vessel geometry, and to compare aortic elastic properties at matched
levels of aortic wall stress or midwall radius.
Although the analog signals for pressure and area were digitized at 400 Hz (or sampling interval of 2.5 ms), the true temporal resolution for
the area measurement was limited by the imaging frame rate (33-Hz or
30-ms sampling interval). In other words, the area information for time
intervals shorter than 30 ms was generated by interpolating actual
measurements obtained at 30-ms intervals (digital-to-analog conversion
and low-pass filtering incorporated within the automatic boundary
detection system). This would be inadequate for examining aortic
properties that critically depend on the temporal synchrony between
pressure and area measurements (e.g., viscous and inertial properties).
However, the temporal fidelity requirements for quantifying elastic
properties are less stringent, especially when one uses only the peak
systolic and minimum diastolic pressure points in analysis. Because the rates of area change are small around these points, errors in area
measurement due to coarse temporal sampling are expected to be small.
Inflation of a balloon in the IVC was used to construct aortic
area-pressure relationships over a wide range of pressures. Nicolosi
and Pieper (23, 24) have shown that acute reductions in
venous return affect aortic pressure-diameter relationships via reflex
changes in sympathetic input to the aorta. The effects on aortic
pressure-diameter relationships in their study were measured at
30-45 s after the reduction in venous return. More importantly,
these investigators also reported that aortic pressure oscillations
with magnitude of ~60 mmHg (a value similar to pressure changes in
the present study) and cycle length of 4 s do not invoke reflex
responses in anesthetized dogs (23). Thus it appears that
the reflex mechanisms do not respond too rapidly. During the first
10-15 s after the onset of balloon inflation in our studies, no
increase in heart rate was noted despite a significant drop in aortic
pressure. In addition, anesthesia is known to depress smooth muscle
responsiveness (1, 28). Taken together, these observations
suggest that the sympathetic reflex activation during the initial phase
of balloon inflation was probably small. Consequently, the observed
alterations in midwall radius, Einc, Zc, and
Cph during balloon inflation most likely reflect the
passive changes in regional aortic elastic mechanical properties caused
by pressure alterations. Finally, as long as balloon inflation-mediated
reflex changes are similar between control and diltiazem conditions, these changes are unlikely to be a confounding factor.
Two pairs of area-pressure data points per cardiac cycle (i.e., peak
systolic and minimum diastolic pressures and corresponding area values)
were used to generate aortic area-pressure relationships. These
discrete points were chosen because they correspond to the extremes of
the elliptic area-pressure loop, where the contribution of viscous
phenomena may be negligible (19). Thus the area-pressure relationship obtained most likely represents the static elastic behavior of the vessel (29).
The small number of experimental animals (7 dogs) does not negate the
main finding of the study that smooth muscle relaxation does not
necessarily yield the expected beneficial changes in local hydraulic
impedance properties of the aorta; individual animal responses are
quite variable. For an individual animal, area and pressure
measurements were obtained over a broad range of pressures. These
area-pressure relationships (as well as stress-radius relationships)
before and after smooth muscle relaxation were compared using least
square regression analysis and the method of excess variance. Thus the
effects of smooth muscle relaxation in an individual animal are
supported by appropriate and robust (i.e., with adequate statistical
power and significance) statistical testing. It is true that additional
experimental animals would have yielded better statistical power for
comparing the group-averaged responses (control vs. diltiazem; Table
1). However, this does not have any impact on the statistical validity
of individual responses and, consequently, the main finding of this study.
Comparisons of aortic wall elastic properties.
When comparisons were made at a common level of wall stress, we did not
observe a decrease in Einc; in fact, it increased in five
of seven dogs. We hypothesize that this "paradoxical" stiffening of
the arterial wall during smooth muscle relaxation is due to the
stretching/recruiting of passive elastic elements of the aortic wall as
the vessel circumference increases (6, 14, 48). In other
words, diltiazem-induced smooth muscle relaxation caused redistribution
of stress among the various components of aortic wall such that, for a
given total wall stress, the stresses borne by elastin and collagen
were higher, resulting in a net increase in Einc. This
hypothesis is further supported by the result that diltiazem decreased
Einc in every case when comparisons were made at a common
level of midwall radius (i.e., comparable strain). Thus the observation
that diltiazem did not alter aortic dimension and/or wall stiffness at
the operating point can be reconciled on the basis of the offsetting
effects of reduced distending pressure and reduced smooth muscle tone.
Although changes in Einc are typically compared at a common
level of wall stress, comparisons made at common midwall radius were
more consistent with the expected changes in the smooth muscle tone.
This observation suggests that the comparison of Einc at matched wall stress is inappropriate for assessing changes in smooth
muscle tone. This conclusion is in agreement with earlier observations
of Dobrin and Rovick (14) and Barra et al.
(6).
Aortic area-pressure relationships.
The dose of diltiazem used in this study is comparable to that used in
humans. This dose produced an average of 13% reduction in mean blood
pressure (106 ± 15 to 92 ± 18 mmHg; P = 0.01) without inducing a simultaneous change in aortic cross-sectional
area. The drop in distending pressure was expected to reduce passively aortic short-axis area, but this was not observed because the "active" drug-induced relaxation of aortic smooth muscle tone counterbalanced this effect. Other investigators conducting comparable studies noted either no change (18, 47) or a decrease
(47, 49) in aortic dimensions following infusion of a
calcium channel blocker. These differences underscore the variable
balance occurring between the active and passive phenomena in different
experimental protocols.
We observed highly linear aortic area-pressure relationships, both
under control conditions and during diltiazem infusion, implying that
CL was constant over the range of pressure studied. These findings are consistent with some of the previous reports (5, 33). However, other investigators, using
aortic constriction to produce very high pressures, were able to
demonstrate nonlinearities in aortic pressure-diameter relationships
(3, 18, 49).
Although diltiazem increased aortic area at any given pressure in all
dogs, no significant changes in local compliance (i.e., slope of the
area-pressure relationship) were noted. The two independent determinants of CL are vessel geometry [mostly
diameter because length is relatively fixed (30)] and
wall stiffness. With diltiazem, neither the aortic short-axis area nor
incremental elastic modulus was altered significantly at the operating
point, and, consequently, compliance per unit length was unchanged.
However, the leftward shift of the area-pressure relationship [i.e., a larger area at a common level of pressure (Figs. 2A and
3A)] clearly indicates a physical alteration in the vessel
mechanical characteristics following diltiazem administration.
In anesthetized dogs, two studies using comparable doses of
diltiazem reported increases in local compliance of the thoracic aorta as quantified by the ratio of the change in lumen diameter to the
change in pressure (47, 49). However, these
diltiazem-induced changes were quite small (~5%) and therefore do
not contradict the present observations. In contrast, diltiazem
significantly increased (~50%) the aortic distensibility index in
awake normotensive and hypertensive humans (40). For the
sake of comparison, we computed the same distensibility index
(Eq. 10 in APPENDIX) from our data and found no
difference before or after diltiazem at operating points (0.0044 ± 0.0013 vs. 0.0047 ± 0.0017 mmHg1, respectively).
Anesthesia is known to depress the smooth muscle responsiveness
(1, 28); this may account for the difference observed
between anesthetized animals and awake humans. Furthermore, we examined
the effects of smooth muscle relaxation at a single dose of diltiazem.
The variability of responses in local hydraulic impedance properties
may be less at other (higher) doses. Therefore, our data should not be
interpreted to imply anything about the clinical efficacy of diltiazem;
clearly, this evaluation would depend on the experimental conditions
(e.g., drug dose, anesthetized vs. awake state, normotension vs.
hypertension, normal vs. diseased vessels). Other pharmacological
treatments [e.g., angiotensin I-converting enzyme (ACE) inhibitors or
ACE inhibitors in combination with calcium antagonists] have been
found to have beneficial effects on aortic elastic and local hydraulic
impedance properties in hypertensive patients (8, 9).
Similarly, nifedipine, a calcium channel antagonist, has been reported
to significantly increase the distensibility index in both the
ascending aorta of human subjects (41) and the descending
thoracic aorta of dogs (18). Thus our results with
diltiazem should not be taken as representative of other vasodilators
that affect smooth muscle by different mechanisms. Instead, we wish to
focus on the message that smooth muscle relaxation does not necessarily
yield the desired reduction in wall stiffness and local hydraulic
impedance (i.e., simultaneous decrease in Zc and
Cph) and discuss the reasons for this observation.
Relationship to systemic arterial hydraulic load.
From the perspective of the LV and mechanical function of the coupled
LV-arterial system, only alterations in hydraulic load are relevant. LV
hydraulic load consists of two components: 1) a steady
component, determined by arteriolar properties and quantified by the
systemic vascular resistance (SVR), and 2) a pulsatile component, mostly determined by the vascular viscoelastic properties and the distributed vascular architecture that gives rise to wave propagation and reflections. Our laboratory (12) and other
workers (10, 45) have shown that nifedipine reduces SVR.
Thus it is likely that diltiazem reduces SVR as well, although we did
not experimentally evaluate this component of LV load in the present study (cardiac output was not measured). Changes in the regional aortic
elastic and geometric properties determine two aspects of the pulsatile
component of LV hydraulic load: Zc, which represents the
hydraulic load due to the aorta itself and plays an important role in
determining the pulsatility of aortic pressure and flow, and
Cph, which is important in determining the characteristics of pressure- and flow-wave propagation and reflections. Reductions in
Zc and Cph would lower LV hydraulic load and
are considered to be beneficial changes. Although both Zc
and Cph are equally sensitive to changes in wall stiffness
(
E
), their respective sensitivities to
geometric properties [e.g., internal radius
(Ri)] are quite different (Eqs. 8 and 9 in APPENDIX): Zc
~R
and Cph
~R
. Therefore, according to the
relative changes in Ri and Einc
following the diltiazem-induced pressure drop in each animal,
Zc and Cph for a given aortic pressure could
either decrease, increase, or remain unchanged. Over comparable ranges
of pressure, our Zc-pressure relationships are similar to
those described by Stone and Dujardin (43). These authors
found that smooth muscle activation elicited by hemorrhage consistently
resulted in increased Zc at matched distending pressure,
mainly as a consequence of aortic diameter reduction and some degree of
wall stiffening (15, 43). Unlike hemorrhage, wherein both
geometric and elastic properties change so as to increase
Zc (reduced radius and increased Einc),
diltiazem-induced changes had competing effects on Zc
(increased radius and Einc for a given pressure). This
resulted in the variability of the absolute magnitude of Zc
response. On the basis of the leftward shift of the area-pressure
relationship, it is clear that diltiazem induced smooth muscle
relaxation in every dog. However, this smooth muscle relaxation caused
the expected reduction in Zc in only four of seven dogs,
and the expected reduction in Cph was never observed (Fig.
5). In fact, four of seven dogs had increased Cph following
diltiazem infusion. Thus diltiazem-induced smooth muscle relaxation
does not necessarily yield the expected beneficial effects on local
hydraulic impedance in anesthetized dogs with normal vessels.
Components other than vascular smooth muscle (e.g., elastin, collagen)
contribute to aortic wall stiffness. Collagen is significantly stiffer
than the other two components, and its relative contribution increases
with increments in aortic radius (strain). Thus the smooth muscle
relaxation-induced decrease in wall stiffness may be offset by the
increased contribution of collagen that is associated with increased
radius. A theoretical analysis was performed to further explore this
possibility. A mathematical model of aortic elastic behavior was
formulated (see APPENDIX for details). Smooth muscle
relaxation was simulated by reducing the relative smooth muscle tone
from 0.50 (control condition) to 0.34; other parameter values were
unchanged (APPENDIX). Results of these simulations are presented in Fig. 6. Over the
experimentally observed ranges of aortic pressure (demarcated by the
solid symbols in Fig. 6), simulated smooth muscle relaxation affected
area-pressure (Fig. 6A vs. Fig. 2A), wall
stress-midwall radius (Fig. 6B vs. Fig. 2B),
Einc-wall stress (Fig. 6C vs. Fig.
2C), Einc-midwall radius (Fig. 6D vs. Fig. 2D), Zc-pressure (Fig. 6E vs.
Fig. 4, dog 3), and Cph-pressure (Fig.
6F vs. Fig. 5, dog 3) relationships in a manner
identical to the effects of diltiazem observed in the experiment.
Significant nonlinearity in the area-pressure relationship was observed
in the simulation study; however, this occurred at pressures greater than 130 mmHg. Certain differences between experimental and simulation results were noted [e.g., more pronounced nonlinearity and
minima for Zc-pressure relationships in the
simulation study (Fig. 6E vs. Fig. 4, dog 3) and
nonlinear Einc-wall stress relationships in the simulation
study (Fig. 6C vs. Fig. 2C)]. Despite these differences, simulation results clearly support the main observation of
the present study: smooth muscle relaxation does not necessarily yield
the expected beneficial changes in local hydraulic impedance of the
aorta. After a reduction in smooth muscle tone, wall stress and
Einc at a common level of pressure (100 mmHg) increased by 12.4 and 57.3%, respectively. The relative contributions of collagen to wall stress and Einc increased as well [from 0.2%
(control) to 1.4% (
tone) for wall stress and from 2.9% (control)
to 15.0% (reduced tone) for Einc]. Thus simulation-based
results clearly demonstrate that a reduction in smooth muscle tone can
alter relative contributions of vessel wall components; this
redistribution can explain our experimental observations.
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|
Fig. 6.
Results from a mathematical simulation study. Reduced
smooth muscle tone ( Tone) was simulated by altering the tone
parameter; all other parameters were held constant at control values
(see APPENDIX). The responses following a reduction of
smooth muscle tone are identical to those seen following diltiazem
infusion in 1 of the experiments (dog 3): Compare
A-D with Fig. 2, E with Fig. 4 (dog
3), and F with Fig. 5 (dog 3). Solid symbols
demarcate the pressure ranges over which data were collected from the 2 experimental conditions ( , control;  ,
diltiazem) (dog 3).
|
|
Although results of the simulation study are consistent with our
experimental data, they do not identify specific reasons for the
observed interanimal variability of responses. Although all dogs were
male and normotensive, there could have been differences in age and
life history, leading to interanimal differences in vessel wall
composition, smooth muscle tone under control condition, and the extent
of smooth muscle relaxation. Because no independent measurements of
these factors were made in the present study, we cannot examine the
determinants of the interanimal variability of responses. Further
studies are necessary to address this important issue.
We have evaluated impedance properties at a single location in the
cardiovascular system (i.e., at the point of pressure and area
measurements in the descending thoracic aorta). Clearly, other parts of
the systemic arterial circulation contribute to the overall pulsatile
load as seen by the LV. Because vessel wall composition (especially,
the smooth muscle content) and geometric properties vary, other parts
of the arterial circulation may respond to smooth muscle relaxation
differently from that observed for the aorta. This, in part, may
explain our previous observations regarding the disparity in responses
of global arterial compliance (AC) and Zc to vasoactive
drugs: both nifedipine and ramipril (ACE inhibitor) consistently
increased AC in hypertensive subjects but left Zc
unaffected (12). In agreement with the AC response, both
the first and the second harmonic of the input impedance spectrum were
reduced with nifedipine or ramipril (12). Whereas Zc is determined exclusively by the localized aortic
geometric and wall elastic properties, AC is determined by the entire
systemic circulation. Although it would be useful to examine the
responses to smooth muscle relaxation of vessels other than the aorta,
our data are still relevant to the main message of the study that smooth muscle relaxation does not necessarily yield the desired reduction in wall stiffness and local hydraulic impedance (i.e., simultaneous decreases in Zc and Cph).
A direct extrapolation of our observations derived from normotensive
animals with normal vessels to hypertensive animals with remodeled
vessels may be questionable. The responses in the latter case would
depend on the baseline smooth muscle tone and the interplay among
changes in smooth muscle tone, distending pressure, and vessel elastic
and geometric properties. It is encouraging, however, to note that
nifedipine did not reduce aortic Zc in hypertensive human
subjects (10, 12, 45), a result consistent with our present observations.
Acute reduction of smooth muscle tone after intravenous administration
of diltiazem in anesthetized, normotensive dogs shifts the aortic
area-pressure relationship leftward without a significant change in
aortic distensibility (CL). Inferences regarding the effects of diltiazem on aortic wall stiffness depend on whether the
comparisons are made at matched wall stress (increased or unchanged
stiffness) or matched midwall radius (decreased stiffness). Our data
support the notion that a comparison of wall stiffness at matched wall
stress is inappropriate for assessing changes in smooth muscle tone.
Finally, diltiazem affects the aortic contribution to LV hydraulic load
(i.e., Zc and Cph) in a variable manner because of the competing effects of changes in vessel diameter and wall stiffness. This underscores the difficulty in predicting the in vivo
effects of a vasoactive agent on large vessel hydraulic impedance properties based solely on the knowledge of its in vitro smooth muscle
relaxation properties.
| |
APPENDIX |
Calculations of Aortic Wall Stress and Local Hydraulic Impedance
Properties
Measurements of end-diastolic aortic diameter (D) and
wall thickness (h) were used to calculate the
"muscle" area (Am) surrounding the vessel
lumen using the following formula
|
(1)
|
Assuming an incompressible aortic wall and negligible
longitudinal shortening (i.e., constant Am
throughout the cardiac cycle), instantaneous aortic wall thickness
[h(t)] was calculated from measured
instantaneous aortic lumen area [A(t)] as
|
(2)
|
Instantaneous aortic internal
[Ri(t)], external
[Ro(t)], and midwall
[Rm(t)] radii were computed as
|
(3)
|
|
(4)
|
|
(5)
|
Instantaneous aortic wall stress [
(t)] was
calculated from measured instantaneous aortic pressure
[P(t)] using the following formula (28)
![&sfgr;(t)=2P(<IT>t</IT>)<IT>×</IT><FENCE><FR><NU><IT>R</IT><SUB>i</SUB>(<IT>t</IT>)<IT>×R</IT><SUB>o</SUB>(<IT>t</IT>)</NU><DE><IT>R</IT><SUB>m</SUB>(<IT>t</IT>)</DE></FR></FENCE><SUP><IT>2</IT></SUP><IT>×</IT>[<IT>R</IT><SUP><IT>2</IT></SUP><SUB>o</SUB>(<IT>t</IT>)<IT>−R</IT><SUP><IT>2</IT></SUP><SUB>i</SUB>(<IT>t</IT>)]<SUP><IT>−1</IT></SUP>](/content/vol90/issue6/fulltext/2427/img009.gif)
|
(6)
|
After the -Rm relationship was fitted
by an exponential function ( = 
e
Rm, where and
are constants), Einc for a given was calculated as
(28)
|
(7)
|
Zc and Cph were calculated according to
the following formulas (
: blood density) (22, 25)
|
(8)
|
|
(9)
|
Aortic distensibility index was calculated as
|
(10)
|
where subscripts S and D refer to maximum systolic and minimum
diastolic values, respectively.
Mathematical Model of Aortic Elastic Behavior
The model formulation is based on the conceptual framework
originally proposed by Cox (13) and subsequently extended
by Armentano and colleagues (2, 3, 6) to include the
smooth muscle component. Briefly, aortic wall was represented as a
parallel combination of three compartments (elastin, collagen, and
smooth muscle), each having a specified -strain (
) relationship
(subscripts e, c, and sm denote elastin, collagen, and smooth muscle,
respectively). A linear - relationship was assumed for elastin
|
(11)
|
|
(12)
|
where Einc,e is the incremental elastic modulus of
elastin, and a1 and a2
are parameters. The elastic behavior of collagen was simulated using
the concept of strain-dependent recruitment of collagen (2, 3,
13). A sigmoidally shaped recruitment function
(fr) was used, which varied from a value of 0 at
low strains to a value of 1 at high strains (Eq. 13). The
incremental elastic modulus of collagen (Einc,c) was
modulated by fr, such that it asymptotically
rose to a maximum value at high strains (parameter
a5 in Eq. 14).
![f<SUB>r</SUB><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>1+</IT>exp[−<IT>a<SUB>3</SUB></IT>(<IT>&egr;−a<SUB>4</SUB></IT>)]</DE></FR>](/content/vol90/issue6/fulltext/2427/img016.gif)
|
(13)
|
|
(14)
|
![&sfgr;<SUB>c</SUB><IT>=</IT><LIM><OP>∫</OP><LL><IT>0</IT></LL><UL><IT>&egr;</IT></UL></LIM> E<SUB>inc,c</SUB><IT>d&egr;=</IT><FR><NU><IT>a<SUB>5</SUB></IT></NU><DE><IT>a<SUB>3</SUB></IT></DE></FR> log<FENCE><FENCE><FR><NU><IT>1+</IT>exp[−<IT>a<SUB>3</SUB></IT>(<IT>&egr;−a<SUB>4</SUB></IT>)]</NU><DE>exp[−<IT>a<SUB>3</SUB></IT>(<IT>&egr;−a<SUB>4</SUB></IT>)]</DE></FR></FENCE><FENCE><FR><NU>exp[<IT>a<SUB>3</SUB>a<SUB>4</SUB></IT>]</NU><DE><IT>1+</IT>exp[<IT>a<SUB>3</SUB>a<SUB>4</SUB></IT>]</DE></FR></FENCE></FENCE>](/content/vol90/issue6/fulltext/2427/img018.gif)
|
(15)
|
where a3-a5
are parameters. The elastic behavior of smooth muscle was simulated
using a strain-dependent activation function, fa
(2). A modified Lorentzian function was used to
represent fa, which is a skewed unimodal
function of strain (2)
|
(16)
|
![<FR><NU>d<IT>f</IT><SUB>a</SUB></NU><DE>d<IT>&egr;</IT></DE></FR><IT>=</IT><FR><NU><IT>a<SUB>6</SUB>a<SUB>8</SUB>+a<SUB>6</SUB>a<SUB>9</SUB></IT>(<IT>&egr;−a<SUB>10</SUB></IT>)<SUP><IT>2</IT></SUP><IT>−2a<SUB>9</SUB></IT>(<IT>a<SUB>6</SUB>&egr;+a<SUB>7</SUB></IT>)(<IT>&egr;−a<SUB>10</SUB></IT>)</NU><DE>[<IT>a<SUB>8</SUB>+a<SUB>9</SUB></IT>(<IT>&egr;−a<SUB>10</SUB></IT>)<SUP><IT>2</IT></SUP>]<SUP><IT>2</IT></SUP></DE></FR>](/content/vol90/issue6/fulltext/2427/img020.gif)
|
(17)
|
|
(18)
|
|
(19)
|
where Einc,sm is the incremental elastic modulus of
smooth muscle,
a6-a11 are
parameters, and Tsm is the user-specified value of relative
smooth muscle tone (range: 0 to 1).
For given values of smooth muscle tone and parameters
a1-a11, one can
calculate the three stresses (e, c,
sm; Eqs. 11, 15, and
18) and three incremental elastic moduli
(Einc,e, Einc,c, Einc,sm; Eqs. 12, 14, and 19) corresponding to
any strain. and Einc were calculated using the three
individual component values and the relative amounts of elastin
(We), collagen (Wc), and smooth muscle (Wsm) in the aortic wall
|
(20)
|
|
(21)
|
Given values of unstressed midwall radius
(Rmo) and cross-sectional
Am, Rm,
Ri, and Ro for any strain
were calculated as
|
(22)
|
|
(23)
|
|
(24)
|
Once , Einc, Rm,
Ri, and Ro were known for
a given strain, aortic P, Zc, and Cph were
calculated using Eqs. 6, 8, and 9, respectively. The following parameter values were used for the simulation: a1 = 2.7 × 106 dyn/cm2, a2 = 0.9, a3 = 30, a4 = 1.4, a5 = 1.0 × 109 dyn/cm2,
a6 = 71.23,
a7 = 93.45, a8 = 0.49, a9 = 997.98, a10 = 1.337, a11 = 4.0 × 106
dyn/cm2; We = 0.31, Wc = 0.21, Wsm, = 0.48, Rmo = 0.682 cm, and Am = 0.9 cm2. These
values were chosen based on the present data and published information
(2, 3, 6, 13, 22) with some modifications to fit our
control data for dog 3. To simulate smooth muscle
relaxation, only the relative smooth muscle tone was reduced (smooth
muscle tone = 0.5 for control, and 0.34 for reduced tone); all
other parameters were held constant.
| |
ACKNOWLEDGEMENTS |
We thank Dr. Theodore Karrison for his help with the statistical
analysis and associated discussion.
| |
FOOTNOTES |
This study was supported in part by National Institute on Aging Grant
R01-AG-13920 to S. G. Shroff and a French Ministère des
Affaires Etrangères (Fondation Lavoisier) grant to B. P. Cholley.
Present address of B. P. Cholley: Anesthesiology and Intensive Care
Dept., Hôpital Lariboisière, Paris, France.
Address for reprint requests and other correspondence: S. G. Shroff, Dept. of Bioengineering, Univ. of Pittsburgh, 749 Benedum Hall, Pittsburgh, PA 15261 (E-mail: sshroff{at}pitt.edu).
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.
Received 23 May 2000; accepted in final form 4 January 2001.
| |
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ABSTRACT
INTRODUCTION
