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1 Hydraulics Laboratory, Institute Biomedical Technology, Ghent University, 9000 Gent; 2 Hemodynamic Research Center, University of Liege, 4000 Liege; and 3 Centre for Experimental Surgery and Anaesthesiology, Katholieke Universiteit Leuven, 3000 Leuven, Belgium
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Maximal left ventricular (LV)
hydraulic power output (PWRmax), corrected for preload as
PWRmax/(Ved)
(where
Ved is the end-diastolic volume and 
is a constant
coefficient), is an index of LV contractility. Whereas
preload-adjusted maximal power (PAMP) is usually calculated with
= 2, there is uncertainty about the optimal value of ( = 1 for the normal LV and 2 for the dilated LV). The aim of
this work is to study the determining factors of . The data set
consisted of 245 recordings (steady state and vena cava occlusion) in
10 animals in an ischemic heart pig model. The occlusion data
yielded the slope (Ees; 2.01 ± 0.77 mmHg/ml, range 0.71-4.16 mmHg/ml) and intercept (V0;
11.9 ± 22.6 ml; range 76 to 39 ml) of the end-systolic
pressure-volume relation, and the optimal -factor (assessed by
fitting an exponential curve through the
Ved-PWRmax relation) was 1.94 ± 0.88 (range 0.29-4.73). The relation of with Ved was
weak [ = 0.60 + 0.02(Ved);
r2 = 0.20]. In contrast, we found an
excellent exponential relation between V0 and [ = 2.16
V0)2, incorporating V0, yielded
0.47 ± 0.26 mW/ml2 (range 0.09-1.42
mW/ml2) and was highly correlated with
Ees (r = 0.89, P < 0.001). In conclusion, correct preload adjustment of maximal LV
power requires incorporation of V0 and thus of data
measured under altered loading conditions.
hemodynamics; ventricular function; blood flow; blood pressure; contractile function
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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THE SLOPE of the end-systolic pressure-volume (P-V) relation (Ees), measured during progressively altered cardiac loading conditions, is still considered as the golden standard method for the assessment of left ventricular (LV) contractility, independent of preload and afterload (19, 20). Its clinical application, however, is limited by technical difficulties associated with instantaneous volume measurements, by the necessity of complicated off-line analysis, and by medical and ethical limitations related to the required episodes of load alteration. Therefore, clinically applicable indexes for LV contractility are still the subject of research.
One such potentially useful index is "preload-adjusted maximal
power" (PAMP) (4, 10, 14), generally defined as
PWRmax/(Ved). In this formula,
PWRmax is the maximal value of the hydraulic power
generated by the LV [with power calculated as the instantaneous product of aortic pressure (PAo) and flow
(QAo)] (4, 8, 9), Ved is the LV
end-diastolic volume, and is a constant coefficient. PAMP can be
derived from the measurement of arterial pressure and flow during
steady-state conditions and an estimate of Ved and thus
does not require measurement of P-V loops. Originally, this index was
described using = 2 (4, 14), but in later work
Kass and co-workers (10) reported that depends on
Ved. They proposed to use = 1 for normal
LVs, whereas = 2 was reported to be more appropriate for
dilated LVs (10). We have recently shown that, for the
right ventricle, the optimal -factor for preload correction may vary
over a wide range (from ~1 to 4) (12).
From a clinical perspective, there are no strict guidelines concerning
which -value to use in which conditions, and there is no clear
cutoff value for Ved classifying the LV as normal or
enlarged. Therefore, the aim of this study was to study, for the LV,
the relationship of with Ved and, more generally, to assess the determinants of and hence of PAMP.
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MATERIALS AND METHODS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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For this study, we used data obtained from experiments investigating the hemodynamic effects of a thromboxane antagonist (2, 11) [BM-573; a compound obtained from the Laboratory of Medicinal Chemistry of the University of Liège consisting of (2-(4'-methylphenylamino)-5-nitrobenzene N-terbutyl-N'-sulfonylurea)] in an open-chest ischemic heart pig model. In this methodological work, however, we focused on PAMP as an index of LV contractility. As such, the effect of the thromboxane antagonist on LV systolic or diastolic function is beyond the scope of this work and will not be discussed.
Animal preparation.
The investigation conformed with the National Institutes of Health
Guide for the Care and Use of Laboratory Animals (NIH Pub. No. 85-23, Revised 1996) and was approved by the ethical committee of
the Medical Faculty of the University of Liege. Experiments were
performed on 10 healthy Pietran pigs of either sex weighing from 20 to
26 kg. The animals were premedicated with intramuscular ketamine (20 mg/kg) and diazepam (1 mg/kg). Anesthesia was then induced and
maintained by a continuous infusion of sufentanil (0.5 µg · kg
1 · h1)
and pentobarbital sodium (3 mg · kg1 · h1).
Spontaneous movements were prevented with pancuronium bromide (0.1 mg/kg). After endotracheal intubation through a cervical tracheostomy,
the lungs were artificially ventilated with a volume-cycled ventilator
(Evita 2, Dräger; Lübeck, Germany). Any metabolic acidosis
was corrected by slow intravenous administration of sodium bicarbonate.
Normothermia was maintained by means of a heating blanket.
Experimental protocol.
To provide similar states of vascular filling, the animals were
continuously infused with lactated Ringer solution (5 ml · kg1 · h1)
and, when necessary, with hydroxyethylstarch (6%) to increase central
venous pressure to 6-7 mmHg, whereafter baseline hemodynamic recording was obtained during steady-state conditions. Subsequently, venous return was reduced by inflation of the caval balloon to generate
stepwise decreases in preload for the assessment of LV function
parameters [Ees and intercept of the
end-systolic P-V relation (V0)]. The occlusion was limited
to a few seconds in duration to avoid reflex responses. All
measurements were taken immediately with the ventilation suspended in
end expiration. After deflation of the inferior vena cava balloon, the
animals were allowed to stabilize for an additional 30 min.
1 · h1
with either a solution with the thromboxane antagonist BM-573 (6 animals) or a placebo solution (4 animals). Either infusion was
maintained throughout the experiment. A snare embedded with a 50%
FeCl3 solution was then placed around the left anterior descending coronary artery (without occluding it) distal to the first
diagonal for a period of 45 min and then removed. The FeCl3 solution diffuses through the vascular wall and damages the
endothelium, hereby initiating thrombus formation. Data (steady state
and caval vein occlusion) were recorded during the infusion of the
antagonist or placebo (A/P), 30 min after the snare was placed
(T30), and subsequently every 30 min until
minimally 300 min
(T60-T300) and maximally 390 min (T390) of reperfusion.
Volume measurements.
LV volumes were assessed using the dual-field conductance catheter
technique (1, 17). Measured segmental conductances [G(i)] were converted to absolute segmental
volumes [V(i)] using V(i) = (1/
)(L2/
b)[G(i) Gp(i)], where L is the
interelectrode distance of the catheter and b is the
specific conductivity of the blood, which was measured frequently
during the experiments. Gp(i) is the
parallel conductance of the ith segment and is introduced to
correct the spreading of the electric field in the structures surrounding the ventricular cavity.
Gp(i) was determined at the end of
each acquisition by the saline method (16), where 1-2 ml of 10% NaCl solution were injected into the pulmonary artery. The
slope factor was computed by identifying cardiac output (CO) with
mean QAo, as measured by the flow probe.
Data collection. All measurements were performed at end expiration. The conductance catheter was connected to a Sigma-5 signal conditioner processor (CD Leycom). The electromagnetic flow probe was connected to a flowmeter (HT 207, Transonic Systems), and each micromanometer-tipped catheter was connected to the appropriate monitor (Sentron pressure monitoring, Cordis).
All analog signals and the ventricular P-V loops were displayed on a screen for continuous monitoring. The analog signals were continuously converted to digital form with appropriate software (Codas, DataQ Instruments; Akron, OH) at a sampling frequency of 200 Hz. Data were stored on hard disk for subsequent analysis using customized software written in Matlab (Mathworks; Natick, MA). Individual cardiac cycles were identified using the onset of LV isovolumic contraction, which was taken as the beginning of the positive time derivative of LV pressure (dP/dt) deflection.Experimental data analysis. Steady-state data were averaged over at least five cycles and yielded one cycle of LV pressure and volume, PAo, and QAo. Heart rate (HR) was obtained from the duration of the average cardiac cycle. Systolic, diastolic, and mean aortic pressure (MAP) were calculated from PAo. Stroke volume (SV) was calculated as the area under the aortic flow curve, and CO was obtained from HR and SV. Total vascular resistance (TVR) was calculated as the ratio of MAP and CO, and total arterial compliance (CPPM) was estimated using the pulse pressure method (18). Effective arterial elastance (Ea) was calculated as the ratio of SV and end-systolic pressure (6). LV Ved was defined as the maximum value of the calibrated conductance catheter signal. PWRmax was calculated as the maximum of the instantaneous product of PAo and QAo. PAMP was calculated as PWRmax/(Ved)2.
To assess Ees and V0 of the end-systolic P-V relation, 5-10 successive beats were selected from the P-V loops measured during vena cava occlusion. An iterative method was used to identify the end-systolic points. Elastance [E(t)] was first calculated as PLV/(VLV V0) with an
initial value for V0 = 0. The points in the P-V plane
corresponding to maximal E(t) for each cycle were
identified as the end-systolic points. Linear regression analysis on
these points yielded a first estimate of Ees and
a new estimate of V0. This procedure was repeated with the
resulting V0 until successive values for V0 did
not differ by more than 0.1%. For all data, convergence was reached
within three to four iterations.
Optimal preload correction for maximal power.
To study the optimal preload correction for maximal power, we assessed
the -factor that should optimally be used to correct maximal power
for preload. For this purpose, PWRmax was calculated for
each beat within the caval vein occlusion sequence as the maximum of
the instantaneous product of PAo and QAo. For
each cycle, the PWRmax value was plotted against
Ved, and a power law of the form PWRmax = (Ved) was fitted through these points,
being the optimal correction factor and , in general
terms, being the preload-corrected maximal power [ = PWRmax/(Ved)]. In addition, the
determinants of were assessed using correlation analysis,
best-subset multiple linear regression analysis, and nonlinear
regression tools. It was then studied in how far the "standard"
definition of PAMP can be modified to account for the variability of
.
Statistical analysis. For this methodological study, data from the control and antagonist group are pooled. Hemodynamic data are given as mean values ± SD and presented as a function of time (BL, A/P, and T30-T300). One-way repeated-measures ANOVA was used to assess variations of hemodynamic parameters with time (SPSS 10, SPSS Science; Chicago, IL). If ANOVA tests reached statistical significance (P < 0.01), each condition was compared with BL in a post hoc test (no confidence interval adjustment) with P < 0.05 considered statistically different. Correlation between parameters was assessed in SigmaStat 2.0 (SPSS Science), whereas nonlinear regression analysis was done in SigmaPlot 3.0 (SPSS Science).
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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Hemodynamic data.
Systolic and diastolic arterial blood pressure at baseline were 93 ± 16 and 58 ± 22 mmHg, respectively, and did not change throughout the experiment (Fig. 1). In
contrast, CO decreased from 3.9 ± 1.0 l/min at baseline to
3.2 ± 0.9 l/min after the 5-h experiment (P < 0.001) despite an increase in HR (P < 0.001, from
110 ± 13 beats/min at baseline to 136 ± 28 beats/min after 5 h), indicating an important reduction in SV (from 36 ± 9 ml at baseline to 24 ± 3 ml, P < 0.001; Fig. 1).
Because LV Ved did not change, end-systolic volume
(Ves) increased significantly (P < 0.001;
Fig. 1). There was a trend toward an increased TVR (P = 0.13, from 1.24 ± 0.58 mmHg · s · ml1
at baseline to 1.62 ± 0.75 mmHg · s · ml1
after 5 h) and decreased CPPM (from 0.68 ± 0.27 to 0.56 ± 0.12 ml/mmHg, P = 0.45; Fig.
2). Because of these arterial effects and
the increase in HR, Ea increased from 2.56 ± 1.12 mmHg/ml at baseline to 4.18 ± 1.07 mmHg/ml
(P < 0.001; Fig. 2). LV Ees increased throughout the experiment (P = 0.009; Fig.
3), from 1.79 ± 0.71 at baseline to
2.09 ± 0.72 after 300 min. Post hoc analysis, however, revealed
that none of the Ees values was different from
that at baseline. It is only when compared with
Ees at T30 and
T60 (where contractility is somewhat depressed)
that values become different from T120 and
T150 on, respectively. This increase in
Ees was paralleled by a rightward shift in
V0 from 31 ± 19 ml at baseline to 1 ± 18 ml
after 5 h (P < 0.001). On the other hand,
PWRmax/(Ved)2 decreased throughout
the experiment (P = 0.004). Interestingly, the optimal
preload correction factor varied over the experiment (P < 0.001) and increased from a value of 1.13 ± 0.30 at baseline to 2.26 ± 0.84 after 300 min (Fig. 3).
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Determinants of .
The lowest and highest observed values of were 0.29 and 4.73, respectively, with an overall mean of 1.94 ± 0.88. Calculating Pearson correlation coefficients showed that correlated with HR
(r = 0.558, P < 0.001), LV
Ved (r = 0.443, P < 0.001;
Fig. 4), and LV Ves
(r = 0.555, P < 0.001), but best with
V0 (r = 0.799, P < 0.001).
The use of HR, Ved, Ves, and V0 as
independent variables in a best-subset multiple linear regression
analysis yielded the following model: = 0.974 + 0.00732(HR) + 0.00811(Ves) + 0.0234(V0), with r2 = 0.68. Although the model statistics indicated HR, Ves, and V0 as highly significant (P < 0.001) model
parameters, there was, however, a significant colinearity between HR
and V0 (r = 0.527, P < 0.001) and between Ves and V0
(r = 0.508, P < 0.001). Subsequent data analysis indicated that the relation between and
V0 was better described using a nonlinear exponential
relation. In this way, a monoparametric model was obtained that
provided a better estimate of than the model obtained from the
multiple linear regression analysis: = 
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Optimal preload correction of PAMP.
Given the involvement of V0 in the value of , we tested
an alternative preload correction for maximal power:
PWRmax/(Ved V0)2, which has been previously shown to
correctly reflect contractility for the right ventricle
(12). The correlation of Ees with
PWRmax/(Ved)2 and for the proposed
alternative formulation is shown in Fig. 5. It can be observed that, whereas
PWRmax/(Ved)2 lacks correlation
with Ees, the newly proposed index
[PWRmax/(Ved V0)2] correlates well with
Ees (r = 0.87, P < 0.001).
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
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The concept of PAMP is based on the observation that the power-law
relation PWRmax = (Ved)
can be fitted through PWRmax-Ved data points
obtained under altered loading conditions. Optimal preload correction
is then obtained by dividing PWRmax by
(Ved), whereas is a measure of
contractility. In our experimental data, the overall mean value of is 1.94, which is close to the value of 2 that is commonly used when
calculating PAMP. However, varies over a very wide range, and we
have demonstrated a nonlinear exponential function of with
V0. It turns out that approximates 2 only when
V0 is negligible. For V0 = 0, is 2.16. The presented data confirm earlier findings for the right ventricle,
where it was also found that varies over a wide range
(12).
Kass and co-workers (10) reported the optimal -value
for preload correction to vary with LV size, with = 1 for the
normal LV, whereas = 2 should be more appropriate for dilated
ventricles. In our acute animal model study, there was indeed a
correlation of with LV Ved, but the relation with
V0 was much stronger. It can be assumed that in the normal
LV, V0 is small or even negative (3). For
these V0, is <2 (V0 = 40 ml
corresponds to = 1). With LV enlargement, absolute volumes and
V0 shift to the right, and the optimal value for becomes >2. Our study thus indirectly supports the observations of
Kass et al., but whereas they attribute the variation of to changes
in LV cavity size, we relate it to changes in V0, the
volume intercept of the end-systolic P-V relation. One could also
deduce from the work of Kass et al. that is restricted to only two
discrete integer values. As our data demonstrate, however, is a
value from a continuous spectrum (Fig. 4), and it is likely that, as
the heart function shifts from normal to progressively worsening
failure, increases from values close 1 to values of 2 and possibly higher.
It is important that, for a generally applicable index of contractility
based on a preload correction of maximal power, the index and the
coefficients used in the index are constant, independent of
physiological variables such as Ved or V0. It
also makes an enormous difference whether PWRmax is
corrected for preload using = 1 or 2. For instance, assuming
PWRmax = 4,000 mW and Ved = 100 ml,
PWRmax/Ved yields 40 mW/ml, whereas
PWRmax/(Ved)2 gives 0.4 mW/ml2. These indexes differ not only by two orders of
magnitude, but also have different dimensions and cannot be directly
compared. As such, it is our feeling that a modified index with a
variable is not clinically useful.
In our study, there was only a poor correlation of
PWRmax/(Ved)2 with
Ees, a validated index of LV contractility. As
such, it is hard to consider
PWRmax/(Ved)2 as a reliable index
of LV systolic function. Taking into account the involvement of
V0 in the variability of and in analogy with an earlier
study for the right ventricle (12), we tested an alternative correction of maximal power for preload, i.e.,
PWRmax/(Ved V0)2. This index showed an excellent
correlation with Ees. V0 is the theoretical volume, derived from linear extrapolation, for which the
ventricle does not generate any pressure. It is only when filled to
volumes higher than V0 that the ventricle generates pressure. Within the linear time-varying elastance concept,
Ved V0 is perhaps a more appropriate
marker of ventricular preload than Ved by itself.
The conductance catheter is increasingly often used to measure LV and
right ventricular volumes. It is, however, an indirect technique, and
the measured signals require calibration to be converted into absolute
volumes (1). As such, shifts in volumes or in
V0 may be due to (patho)physiological phenomena but also due to errors in calibrating the conductance catheter signal (parallel conductance). This aspect is most important when PWRmax is
corrected for preload as
PWRmax/(Ved)2, but less important
for our newly proposed index. Errors in parallel conductance have the
same effect on Ved as on V0, and thus not on
Ved V0. Therefore, the exact position
of the P-V loop on the volume axis is less important for the modified
preload correction of maximal power. In our study, parallel conductance
was measured twice at the end of each set of data acquisition, with
consistent results throughout the experiment. It is therefore unlikely
that our observations are based on an erroneous calibration of the conductance catheter.
The rationale for using PAMP as an index of ventricular contractility
is that it obviates the need for multiple P-V loops recorded under
altered loading conditions, as is required to calculate "traditional" indexes such as the slope of the end-systolic P-V relation or preload-recruitable stroke work. In addition, it has the
potential of noninvasive assessment through noninvasive measured arterial pressure (applanation tonometry at the carotid artery) and
flow (Doppler echocardiography) (5). Our data, however, indicate that PWRmax should be corrected for preload using
(Ved V0)2. Because
V0 can only be determined from multiple P-V loops measured under altered loading conditions, the index that we propose requires the same measurements as Ees, and it has no
practical advantage over Ees. We can only
conclude that there is no simple index for LV contractility based on
measuring LV hydraulic power output during steady-state conditions.
Others have developed "single beat" methods to estimate LV
contractility based on the recording of P-V loops during steady state
only (13, 15, 21). In recent work, however, Kjorstad et
al. (7) concluded in a comparative study of these methods
that it is doubtful whether any of the single beat methods allow the
assessment of contractility.
In this work, we used data from an experimental protocol on the
hemodynamic effect of a thromboxane antagonist in an ischemic pig model, where the pig was infused with either a placebo solution or
the thromboxane antagonist. We pooled all data because 1)
there was no group difference in the time evolution for any of the
parameters that we considered, and 2) our work is merely of
a methodological nature. Nevertheless, differences in hemodynamics (and
possible physiological effects of the thromboxane antagonist) could
theoretically be relevant if they caused selective inaccuracies in
PWRmax/(Ved)2 or
PWRmax/(Ved V0)2. This, however, seems unlikely. The
derived relation between and V0 and the improved
correlation of PWRmax/(Ved V0)2 with Ees is similar
to our earlier observations in computer simulations and measurements in
the canine right ventricle in a different experimental protocol
(12). Also, in Figs. 4 and 5, data from both groups are
displayed using group-specific (open and closed) symbols. All derived
relations are general in nature and are essentially similar for both
groups. Nevertheless, fully excluding the possible impact of the
thromboxane antagonist on the results would require either a different
statistical approach or, preferably, a different experimental design,
which is beyond the scope of the current paper.
The data allowed us to demonstrate that PAMP, as it is currently being used, requires correction for V0 of the end-systolic P-V relation. This work, however, is not to be considered as a validation study of the modified PAMP, which would require data thoroughly showing its insensitivity to induced changes in HR, preload, and afterload and its sensitivity to modulation of cardiac inotropic properties. Considering the fact that the proposed index has no practical advantages over Ees, the relevance of performing such a validation study is debatable. Our study also has some limitations related to the experimental settings (open-chest, open-pericardium model), which may have caused larger volume changes than in a closed-chest, closed-pericardium setting. It is unlikely, however, that this would influence our observation that incorporation of V0 is required for an adequate correction of PAMP.
In conclusion, we demonstrated that in our animal model, PAMP poorly
correlates with Ees. Moreover, the -factor,
optimally used for preload correction, is not constant, but varies with V0. An alternative formulation, incorporating this
V0 dependency, resolves these shortcomings.
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ACKNOWLEDGEMENTS |
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The study was supported by Fonds voor Wetenschappelijk Onderzoek-Vlaanderen Grant 1.5.208.99 (to P. F. Wouters) and by grants from the Fonds National de la Recherche Scientifique, Communauté Francaise de Belgique, and the Fondation Léon Frederiq, Université de Liège. P. Segers was the recipient of a postdoctoral grant from the Fonds voor Wetenschappelijk Onderzoek-Vlaanderen. P. Kolh and V. Tchana-Sato were recipients of a postdoctoral grant and Doctoral Grant 3.4505.01, respectively, from the Fonds National de la Recherche Scientifique, Communauté Francaise de Belgique.
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FOOTNOTES |
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Address for reprint requests and other correspondence: P. Segers, Hydraulics Laboratory, Institute Biomedical Technology, Ghent Univ., Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium (E-mail: patrick.segers{at}rug.ac.be).
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.
First published March 13, 2003;10.1152/ajpheart.01110.2002
Received 18 December 2002; accepted in final form 12 February 2003.
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
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