Vol. 277, Issue 2, H481-H487, August 1999
Late systolic pressure augmentation: role of left ventricular
outflow patterns
Mustafa
Karamanoglu and
Michael P.
Feneley
Cardiology Department and Victor Chang Cardiac Research
Institute, St. Vincent's Hospital, Sydney, New South Wales 2010, Australia
 |
ABSTRACT |
Late systolic augmentation of the ascending
aortic pressure waveform is believed to be caused by particular
impedance patterns but also could be caused by particular left
ventricular outflow patterns. Using a linear mathematical model of the
entire human arterial tree, we derived realistic impedance patterns by
altering 1) Young's modulus of the
arterial wall of the individual branches, 2) peripheral reflection
coefficients, and 3) distal
compliances at the terminations. These calculated impedance patterns
were then coupled to realistic left ventricular outflow patterns
determined by unique 1)
end-diastolic and end-systolic pressure-volume relationships, 2) preload-recruitable stroke work
relationships, and 3) shortening paths simulated by altered aortic flow contours. As determined by the
ratio of the individual parameter coefficient of determination (r2) to the
overall model r2,
late systolic pressure augmentation was more strongly determined by
left ventricular outflow patterns than by arterial impedance parameters
(r2 ratio: 53%
vs. 33%). Thus left ventricular outflow patterns are at least as
important as impedance parameters in determining late systolic pressure
augmentation in this model.
arterial model; hemodynamics; ventricular function; hypertension
| |
INTRODUCTION |
ONE OF THE PROMINENT features of the
ascending aortic pressure waveform in elderly humans is the presence of
a late systolic peak (11, 15). This late systolic peak is regarded as
detrimental to left ventricular energetics because it increases the
myocardial oxygen demand-to-supply ratio via increased late systolic
load and decreased pressure during diastole (18). It is considered also
as a major factor in the development and progression of left ventricular hypertrophy, an independent risk factor for cardiovascular mortality (8).
The relationship between the late systolic peak and ascending aortic
impedance patterns was first demonstrated by Murgo et al. (15). It was
suggested that increased reflected pressure waves from the periphery,
as evidenced from altered ascending aortic impedance patterns, summed
with the forward-going pressure waves during late systole (15, 16).
Subsequent studies showed that various drugs alter the modulus of zero
and first harmonic components of the arterial impedance while
simultaneously altering the late systolic pressure peak amplitude (10,
19, 25). Further studies also found that the late systolic pressure
peak increased with age (11), shorter body length (14), and increased arterial stiffness (19). Because pulse wave velocity, characteristic impedance, and zero crossing of the impedance phase were associated with the timing of reflected waves and distal arterial compliance and
resistance were associated with the intensity of reflected waves, these
observations on the amplitude of the late systolic peak were explained
as manifestations of altered timing and intensity of reflected pressure
waves (17).
By definition, however, the aortic pressure waveform is a function not
only of the load (i.e., arterial impedance) but also of the pump, the
left ventricle. One would anticipate, therefore, that the contractile
behavior of the left ventricle might be an important factor in
explaining pressure wave augmentation. Pioneering studies that formed
the basis for establishing the link between the late systolic pressure
peak and reflected waves, however, assumed that the contractile
behavior of the left ventricle remained unchanged across individuals
(11, 15, 18). As a consequence of this assumption, alterations in
outflow patterns of left ventricles were not analyzed to determine
their relationship to the late systolic pressure peak.
The purpose of the present study was to quantify the relative
importance of the left ventricular outflow patterns and arterial impedance in determining late systolic pressure augmentation. We used a
mathematical model of the entire human arterial tree (9) to compute a
range of realistic arterial input impedance patterns. As input to these
ascending aortic impedances, we synthesized different left ventricular
outflow patterns by altering the point, integral, and path descriptors
of the left ventricular contraction behavior. From the computed aortic
pressure waveforms, late systolic pressure peaks were identified and analyzed.
| |
METHODS |
Synthesis of ascending aortic impedance patterns.
Multibranched models that use realistic anatomic and physical
parameters can reproduce all the features of the human arterial impedance patterns. Simpler arterial models based on a few elements, such as asymmetric T tubes and modified three- or four-element windkessels, cannot achieve the same sophistication. In this study, we
used a previously described multibranched mathematical model of the
human arterial system (2) that was subsequently modified to simulate
increased wave velocity with aging and the presence of distal arterial
compliances (9). These modifications yielded realistic impedance
patterns in good agreement with the previously published data. Both the
age-related changes (rightward shift of first zero crossing of the
phase angle, increased first minimum of impedance moduli, and increased
characteristic impedance) and altered distal compliances and reflected
waves were reproduced (9, 17) (Fig.
1B).
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Fig. 1.
Schematic representation of synthesized flow
(A) and arterial impedance
(B) patterns and analyzed aortic
pressure patterns (C). Synthesized
flow waveform patterns contained 3 features that were individually
altered. To obtain arterial impedances with different patterns, 3 features were individually altered: moduli at lower (<1 Hz), middle
(1-3 Hz), and higher (>3 Hz) frequencies were modulated with
reflection coefficient ( 0),
time constant of terminal windkessel elements ( ), and arterial wall
elastance (E), respectively.
T1, time to peak
velocity; T2,
time to shoulder of flow deceleration phase; FSI, flow shoulder index;
PT1 and
PT2, aortic
pressure waveforms corresponding to timing of peak flow and reflected
waves; PTf,
pressure at wave foot.
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|
These changes included the nonuniform increase of the Young's modulus
(E) of the individual branches to
simulate age-related increases in wave velocity from 20 to 60 yr and
the precise description of the frequency-domain characteristics of
terminal mismatches: the resistive component of the terminal mismatches
(0), and the windkessel time
constant (). These changes in E,
, and 0 modified the moduli
of impedance spectrum at higher (>3 Hz), middle (1-3 Hz), and
lower (<1 Hz) harmonics, respectively. Table
1 documents the simulated ranges. As
explained earlier, changes made to E were nonuniform because of variation in the distribution of pulse wave
velocities (a measure of stiffening) of large arteries with aging (3):
the ascending aortic wall elasticity increased from 5.28 to 11.30 × 106 dyn/cm2,
while brachial artery wall elastance increased from 9.56 to 13.62 × 106 dyn/cm2.
To simulate conditions ranging from total vasodilation to total vasoconstriction, we altered 0
from 0.0 to 1.00 in steps of 0.1. Increased distal compliance was
simulated by altering from 0.0 to 0.5 s in steps of 0.1 s.
Because the mathematical assumptions used in this model become less
valid at the capillary level, the multibranched model could not be
extended to compute peripheral resistances. Nevertheless, it is
possible with the existing mathematical model to set the total
peripheral resistance
(Rp) as a
constant function of age, where
Rp= 9.7409 × age + 853.97 dyn · s · cm
5
(17) and then compute the entire arterial input impedance spectrum.
Synthesis of left ventricular outflow patterns.
For each synthesized arterial impedance, we defined a unique left
ventricular outflow pattern. For this purpose, the diastolic behavior
of the left ventricle was defined by a constant end-diastolic pressure-volume (EDPV) relationship, according to the equation
|
(1)
|
where
P is pressure, V is volume, and a
(intercept) and K (volume constant)
are given as 0.72 and 0.02, respectively (1). The work
output of the left ventricle was also constrained by the
preload-recruitable stroke work (PRSW) relationship, described by the
equation
|
(2)
|
where
SW and Ved are the stroke work and
end-diastolic volume of the left ventricle, respectively, and
Mw and
Vw represent the slope and
volume-axis intercept of the relationship, respectively (6). In this
study, we have set Vw as constant
and altered Mw
within a realistic range (Ref. 5; Table 1). The end-systolic point
reached by the left ventricle was defined by the end-systolic pressure
volume (ESPV) relationship, described by the equation
|
(3)
|
where
Pes and
Ves are the end-systolic pressure
and volume, respectively, and
Ees and
V0 are the slope and volume-axis
intercept of the relationship, respectively (21). We kept
V0 constant but altered
Ees within a
realistic range (Ref. 22; Table 1).
These three descriptors of the systolic and diastolic function of the
heart do not provide a complete definition of a unique outflow pattern
of the left ventricle. There is also a need to describe the pattern of
outflow in a closed form. Unfortunately, the point (ESPV relationship)
and integral (PRSW relationship) descriptions of left ventricular
systolic function are necessary but not sufficient to describe the path
of shortening under different loads. Although, at first sight, the
time-varying ventricular elastance concept
[E(t)]
could be seen to be useful for this purpose, the lack of a closed-form
description of a unique
E(t)
makes it impossible to define particular
E(t)
curves during ejection. Also, there is little empirical evidence
describing the precise contour of the
E(t)
curve during ejection in vivo. In fact, the available evidence
indicates that the
E(t)
curve is most highly variable and unpredictable during the ejection
period (22), rendering the choice of an
E(t)
trajectory during ejection arbitrary.
The alternative we chose was to select specific patterns of the aortic
flow waveform within the constraints provided by the three descriptors
of left ventricular systolic and diastolic function described above.
This method constrains the choice of left ventricular outflow patterns
as a function of independently quantifiable physiological parameters.
For this purpose, in a template aortic flow waveform representing a
heart rate of 72 beats/min and an ejection duration of 310 ms, we
defined several feature points in relation to the foot of the wave
(Fig. 1A). These were the time to
peak flow velocity (T1), time to a
shoulder defined on the flow deceleration phase (T2), and the
amplitude of this shoulder normalized to the peak flow velocity
[flow shoulder index (FSI)]. With the exception of FSI (see
Data analysis and statistics), we
altered these parameters over the entire range that was reported
previously (Refs. 11, 17; Table 1).
Once all these model constraints (i.e., the arterial impedance, the
EDPV, ESPV, and PRSW relationships, and a specific pattern of the
aortic flow waveform) were established, we used the following computational procedure. 1) For a
given end-diastolic volume, stroke volume, and flow pattern, a
calibrated aortic flow waveform was calculated.
2) The calibrated aortic flow
waveform was given as input to the arterial impedance, and aortic
pressure waveforms were synthesized.
3) The end-systolic elastance (slope
of ESPV relationship) was calculated using Eq. 3. 4) If this
end-systolic elastance was found to be different from the preset
elastance, the end-diastolic volume was allowed to change.
5) If the stroke work calculated for
this new end-diastolic volume was different from stroke work derived
from Eq. 2, the stroke volume was
allowed to change. 6) Finally,
processes
1-5 were repeated until all the external constraints were met. We used a generic Newton-Ralphson method
(see Ref. 20) to find this point in the parameter space, with
convergence to this point usually achieved within 10 iterations (Fig. 2).
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Fig. 2.
Calculation of left ventricular outflow patterns for a given set of
boundary conditions. Patterns of arterial impedance and template
outflow patterns are given, and left ventricle is modeled with a given
set of parameters describing end-diastolic pressure-volume relationship
(EDPVR), end-systolic pressure-volume relationship (ESPVR), and
preload-recruitable stroke work relationship (PRSWR). Under these
boundary conditions, several ejection trajectories are calculated by
varying stroke volume and end-diastolic volume
(Ved). Note that pattern of
pressure-volume trajectory during ejection is identical for each
computational step. Computational process stops whenever stroke work
(SW) for a synthesized pressure-volume loop matches one predicted from
given PRSW relationship. Note that there is only 1 unique point in
entire parameter space that satisfies all boundary conditions. LVP,
left ventricular pressure.
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Data analysis and statistics.
Initially, we subdivided the parameter space of the left ventricular
outflow patterns linearly. We encountered difficulties, however, with
this approach. First, the linear steps had to be coarse for realistic
allocation of computational time. This precluded detailed examination
of the parameter space. Second, this method implied that these
parameters are uniformly distributed across the range. This assumption,
in contrast to observed situations in vivo, puts undue weight on the
extremes of each parameter range. We defined each parameter, therefore,
as a Gaussian function with mean and standard deviation (Table 1), with
the exception of FSI. Because we could not find any published data for
the FSI range, we employed a uniform distribution. To enable
comparisons with the measurements done in vivo, the features of the
derived left ventricular outflow patterns, peak flow acceleration, peak aortic flow
(PFT1) and
aortic flow at shoulder point (PFT2)
were analyzed.
To quantify the pressure wave augmentation, we extracted the features
of the synthesized ascending aortic pressure waveform corresponding to
the timing of the peak flow
(PT1) and to the timing of reflected waves
(PT2)
(Fig. 1C) using techniques described
previously (24). These feature points and the pressures measured at the
wave foot
(PTf) then
were related to define the shoulder index (SI) as a measure of the late
systolic pressure augmentation: SI = PPT2/PPT1, where PPT2 = PT2 
PTf and
PPT1 = PT1 PTf. This index is
similar to the widely accepted augmentation index, defined as AP/PP,
where AP is the augmented pressure
(PT2 PT1) and
PP is the pulse pressure (11). By definition, the augmentation index
can be negative whenever the peak pressure occurs early in systole. In
contrast, the SI is always positive. Thus SI values of 0, 1, and 2 correspond with augmentation indexes of 100, 0, and 100%, respectively.
Analyses were performed using a commercially available statistical
package (SPSS for Windows version 7.5, SPSS). For each dependent
parameter, univariate regression was first performed and the predictors
that had significant correlations were included in the final
multiple-regression model. The variables with a high degree of
multicollinearity, quantified as a variance inflation factor > 2.0, were excluded (23). For example,
Ved was found to be collinear with
the flow waveform features
(PFT1, PFT2, and
T2) and
therefore was not utilized in the final model. The stepwise
multiple-regression analysis was then performed, and the standardized
regression coefficient (
) for each parameter was calculated. The
importance of each independent model parameter was assessed by the
ratio of part r2
(defined as the square of the correlation coefficient after controlling the effects of additional variables) to model-adjusted
r2 (RPM). Data
are expressed as means ± SD, and the
P < 0.05 level was accepted as significant.
| |
RESULTS |
The simulations carried out in the parameter space represented 330 different arterial impedance patterns coupled to 10,000 different left
ventricular outflow patterns. The hemodynamic parameters calculated
from these simulations yielded results that were comparable to those
observed in vivo (Table 2). Figure
3A
illustrates changes in the pressure contour accompanying changes with
aging, simulated by increasing Young's modulus
E of the arterial tree nonuniformly. The arterial pulse pressure and the amplitude of the first and second
pressure peaks were increased, but the arterial pressure contour was
little affected, with no change in the ratio of the peaks, the SI (Fig.
3A,
left,
top). This suggests that early return of reflected
waves caused by increased wave velocity does not affect the SI.
Increased distal vascular compliance, which decreases the arterial
impedance moduli at middle frequencies (1-3 Hz), reduced the
second pressure peak and AP but had no effect on the SI (Table
3).
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Fig. 3.
Simulation results showing effect of increased
E to simulate aging
(A), resistive mismatches
(B), and FSI
(C) on pressure waveforms. Numbers
above flow waveforms indicate values of respective parameters. Unless
otherwise noted, all other parameters were fixed at
E = 5.30 × 106 dyn/cm2,
0 = 0.6, = 300 ms,
T1 = 70 ms,
T2 = 260 ms, FSI = 35%, slope of PRSWR
(Mw) = 1.0 × 105 erg/ml, and slope of
ESPVR (Ees) = 2 mmHg/ml.
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|
This contrasts with the effects of increasing the resistive component
of the terminal mismatches
(0), which increases the arterial impedance moduli at lower frequencies (<1 Hz) (Fig.
3B, left,
top) and the FSI (Fig.
3C,
left,
top), where the entire pressure
contour was altered. The second pressure peak, AP, and SI were all
increased. In each of these simulations,
Ved,
Pes, and stroke work increased
(Fig. 3, right).
Table 3 summarizes the main predictors of various multiple-regression
models. The model-adjusted regression coefficients were high, ranging
between 0.77 and 0.93. As in the case of increased arterial wall
elastance, increased early shortening of the left ventricle
[indexed as aortic flow at
T1
(PFT1)]
also increased the first aortic pressure peak. Because there was no corresponding increase in the second pressure peak, this decreased the
SI. This contrasts with the effect of increased late-systolic shortening, which did not influence the first pressure peak and had a
minor effect on the second pressure peak but otherwise dominated the
other left ventricular contraction trajectory parameters. It increased
the AP and SI to an extent similar to that caused by the increased wave
reflection coefficient.
Analysis of the multiple-regression coefficients indicated that the
combination of the impedance-related parameters
(E,
0, and ) explained the
variability of pulse pressure at the flow shoulder point
(T2) better
(RPM = 0.90) than did the combination of all parameters of the left
ventricular outflow patterns (RPM = 0.09). In contrast, parameters of
the left ventricular outflow patterns were stronger than
impedance-related parameters as determinants of the amplitude of the
first pressure peak (RPM = 0.56 vs. 0.40), SI (RPM = 0.53 vs. 0.33),
and AP (RPM = 0.48 vs. 0.38).
Among the descriptors of left ventricular systolic function (i.e., PRSW
and ESPV relationships), only the slope of the PRSW relationship
(Mw) had an
impact on the aortic pressure waveform: there was a small but positive
association between
Mw and the amplitude of the second pressure peak.
| |
DISCUSSION |
In this study, with the exception of FSI, we used previously published
data as input to our model simulations (Table 1) to synthesize arterial
impedances and left ventricular outflow patterns. These simulations
yielded hemodynamic parameters that were similar to those observed in
vivo (Table 2; Refs. 5, 22).
Using arterial impulse response functions derived from arterial
impedances, Latson and colleagues (12) found that the contour of the
input aortic flow waveform influenced the calculated aortic pressure
waveform. Unfortunately, that study did not systematically explore the
extent of this influence. It has been suggested that the observed
increase in the augmentation index with aging could be caused by two
factors, the early return of reflected waves, a result of increased
arterial stiffness with aging, and the increased intensity of reflected
waves caused by an increase in the reflection coefficient (11, 17). The
former explanation is inconsistent with our results, which show that
increased wave velocity influences not only the late systolic peak but
also the pulse pressure and the first peak, so that the SI is little
altered (Table 3).
Our results indicate that the wave reflection coefficient has a
definitive impact on the pressure waveform. It is equally possible,
however, that the left ventricular outflow patterns, independent of the
arterial impedance patterns, can also affect the wave reflection
indexes derived from the pressure waveform. This finding suggests that
the increased intensity of reflected waves may not be the sole factor
in the formation of the late systolic pressure augmentation.
Limitations.
In this study, ascending aortic impedances were derived from a
mathematical model of the human arterial system. Although this mathematical model reproduces most of the features of the human arterial system, there might still be differences caused by some of the
physiological parameters used as constants in the model. Although the
model uses realistic parameters such as physical dimensions, wall
viscosities, and anatomic organization of the arteries, together with
blood viscosity and density, the specific values of these parameters
might be different in individuals. Also important to note is that the
model employed is linear, and, although small, there are certain
nonlinearities in the arterial system. The nonlinear pressure-diameter
relationship of the arterial wall and the convective terms in the
governing equations might have influenced our results.
Also not considered in the determination of the left ventricular
outflow patterns were possible nonlinearities of the ESPV relationship
(13), the positive and/or negative inotropic effects of the ejection
(4, 7), and the possible curvilinearities of the early and late
systolic portions of the outflow pattern. In this study, we did not
attempt to model these effects. Nevertheless, the current simulations
yielded hemodynamic parameters that were in close agreement with their
counterparts in vivo (Table 2).
In conclusion, our results indicate that left ventricular outflow
patterns can be a major determinant of late systolic pressure augmentation. The relevance of this finding to the observed late systolic pressure augmentation in vivo in human subjects would depend,
however, on the relative range of variation in the left ventricular
outflow patterns and aortic input impedance in human subjects, which
has yet to be determined. This study indicates a need to examine
alterations in the left ventricular outflow patterns due to age, sex,
coronary artery disease, left ventricular contractility changes, and
administration of vasoactive substances in vivo.
Finally, because pressure wave augmentation observed in the central
aortic pressure waveform is a function of both the arterial impedance
and the left ventricular outflow pattern, "wave reflection" indexes derived from the aortic pressure waveform alone may not be
accurate measures of the true extent of wave reflection.
| |
ACKNOWLEDGEMENTS |
This study was supported by a grant from the National Health and
Medical Research Council of Australia (NH&MRC 0980225).
| |
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: M. Karamanoglu,
Cardiology Dept., St. Vincent's Hospital, Victoria St., Sydney,
Australia 2010 [E-mail: m.karamanoglu{at}unsw.edu.au].
Received 9 December 1998; accepted in final form 31 March 1999.
| |
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0002-9513/99 $5.00
Copyright © 1999 the American Physiological Society
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