## Abstract

Maximal left ventricular (LV) hydraulic power output (PWR_{max}), corrected for preload as PWR_{max}/(V_{ed})^{β} (where V_{ed} is the end-diastolic volume and β is a constant coefficient), is an index of LV contractility. Whereas preload-adjusted maximal power (PAMP) is usually calculated with β = 2, there is uncertainty about the optimal value of β (β = 1 for the normal LV and 2 for the dilated LV). The aim of this work is to study the determining factors of β. 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 (*E*
_{es}; 2.01 ± 0.77 mmHg/ml, range 0.71–4.16 mmHg/ml) and intercept (V_{0}; −11.9 ± 22.6 ml; range −76 to 39 ml) of the end-systolic pressure-volume relation, and the optimal β-factor (assessed by fitting an exponential curve through the V_{ed}-PWR_{max} relation) was 1.94 ± 0.88 (range 0.29–4.73). The relation of β with V_{ed} was weak [β = 0.60 + 0.02(V_{ed});*r*
^{2} = 0.20]. In contrast, we found an excellent exponential relation between V_{0} and β [β = 2.16
*r*
^{2} = 0.70]. PAMP, calculated from the steady-state data, was 0.64 ± 0.40 mW/ml^{2} (range 0.14–2.83 mW/ml^{2}) with a poor correlation with*E*
_{es} (*r* = 0.30, *P*< 0.001). An alternative formulation of PAMP as PWR_{max}/(V_{ed} − V_{0})^{2}, incorporating V_{0}, yielded 0.47 ± 0.26 mW/ml^{2} (range 0.09–1.42 mW/ml^{2}) and was highly correlated with*E*
_{es} (*r* = 0.89, *P*< 0.001). In conclusion, correct preload adjustment of maximal LV power requires incorporation of V_{0} and thus of data measured under altered loading conditions.

- hemodynamics
- ventricular function
- blood flow
- blood pressure
- contractile function

the slope of the end-systolic pressure-volume (P-V) relation (*E*
_{es}), 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 PWR_{max}/(V_{ed})^{β}. In this formula, PWR_{max} is the maximal value of the hydraulic power generated by the LV [with power calculated as the instantaneous product of aortic pressure (P_{Ao}) and flow (Q_{Ao})] (4, 8, 9), V_{ed} is the LV end-diastolic volume, and β is a constant coefficient. PAMP can be derived from the measurement of arterial pressure and flow during steady-state conditions and an estimate of V_{ed} and thus does not require measurement of P-V loops. Originally, this index was described using β = 2 (4, 14), but in later work Kass and co-workers (10) reported that β depends on V_{ed}. They proposed to use β = 1 for normal LVs, whereas β = 2 was reported to be more appropriate for dilated LVs (10). We have recently shown that, for the right ventricle, the optimal β-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 β-value to use in which conditions, and there is no clear cutoff value for V_{ed} classifying the LV as normal or enlarged. Therefore, the aim of this study was to study, for the LV, the relationship of β with V_{ed} and, more generally, to assess the determinants of β and hence of PAMP.

## MATERIALS AND METHODS

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} · h^{−1}) and pentobarbital sodium (3 mg · kg^{−1} · h^{−1}). 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.

The chest was opened with a midsternotomy, the pericardium was incised and sutured to the chest wall to form a cradle for the heart, and the root of the aorta was dissected clear of adherent fat and connective tissue. A conductance micromanometer-tipped catheter (CD Leycom; Zoetermeer, The Netherlands) was inserted through the right carotid artery and advanced into the LV. A micromanometer-tipped catheter (Sentron, Cordis; Miami, FL) was inserted through the right femoral artery and advanced into the ascending aorta. A 14-mm-diameter perivascular flow probe (Transonic Systems; Ithaca, NY) was fitted around the aorta 2 cm distal to the aortic valve. The micromanometer-tipped catheter was manipulated so that the pressure sensor was positioned just distal to the flow probe. Right atrial pressure was measured with a micromanometer-tipped catheter inserted through the superior vena cava. A 6-Fr Fogarty balloon catheter (Baxter Healthcare; Oakland, CA) was advanced into the inferior vena cava through a right femoral venotomy. Inflation of this balloon produced a titrable leftward shift in P-V loops by reducing venous return.

#### Experimental protocol.

To provide similar states of vascular filling, the animals were continuously infused with lactated Ringer solution (5 ml · kg^{−1} · h^{−1}) 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 [*E*
_{es} and intercept of the end-systolic P-V relation (V_{0})]. 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.

After the basal measurements [baseline (BL)], the animals were infused at 10 mg · kg^{−1} · h^{−1}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% FeCl_{3} 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 FeCl_{3}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 (*T*
_{30}), and subsequently every 30 min until minimally 300 min (*T*
_{60}–*T*
_{300}) and maximally 390 min (*T*
_{390}) 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/α)(*L*
^{2}/ς_{b})[*G*(*i*) − *G*
_{p}(*i*)], where *L* is the interelectrode distance of the catheter and ς_{b} is the specific conductivity of the blood, which was measured frequently during the experiments. *G*
_{p}(*i*) is the parallel conductance of the *i*th segment and is introduced to correct the spreading of the electric field in the structures surrounding the ventricular cavity.*G*
_{p}(*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 α was computed by identifying cardiac output (CO) with mean Q_{Ao}, 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/d*t*) deflection.

#### Experimental data analysis.

Steady-state data were averaged over at least five cycles and yielded one cycle of LV pressure and volume, P_{Ao}, and Q_{Ao}. Heart rate (HR) was obtained from the duration of the average cardiac cycle. Systolic, diastolic, and mean aortic pressure (MAP) were calculated from P_{Ao}. 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 (C_{PPM}) was estimated using the pulse pressure method (18). Effective arterial elastance (*E*
_{a}) was calculated as the ratio of SV and end-systolic pressure (6). LV V_{ed} was defined as the maximum value of the calibrated conductance catheter signal. PWR_{max} was calculated as the maximum of the instantaneous product of P_{Ao} and Q_{Ao}. PAMP was calculated as PWR_{max}/(V_{ed})^{2}.

To assess *E*
_{es} and V_{0} 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 P_{LV}/(V_{LV} − V_{0}) with an initial value for V_{0} = 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 *E*
_{es} and a new estimate of V_{0}. This procedure was repeated with the resulting V_{0} until successive values for V_{0} 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 β-factor that should optimally be used to correct maximal power for preload. For this purpose, PWR_{max} was calculated for each beat within the caval vein occlusion sequence as the maximum of the instantaneous product of P_{Ao} and Q_{Ao}. For each cycle, the PWR_{max} value was plotted against V_{ed}, and a power law of the form PWR_{max} = α(V_{ed})^{β} was fitted through these points, β being the optimal correction factor and α, in general terms, being the preload-corrected maximal power [α = PWR_{max}/(V_{ed})^{β}]. In addition, the determinants of β 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 β.

#### 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*T*
_{30}–*T*
_{300}). 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).

## RESULTS

#### 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 V_{ed} did not change, end-systolic volume (V_{es}) 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 · ml^{−1}at baseline to 1.62 ± 0.75 mmHg · s · ml^{−1}after 5 h) and decreased C_{PPM} (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, *E*
_{a} increased from 2.56 ± 1.12 mmHg/ml at baseline to 4.18 ± 1.07 mmHg/ml (*P* < 0.001; Fig. 2). LV *E*
_{es}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 *E*
_{es} values was different from that at baseline. It is only when compared with*E*
_{es} at *T*
_{30} and*T*
_{60} (where contractility is somewhat depressed) that values become different from *T*
_{120} and*T*
_{150} on, respectively. This increase in*E*
_{es} was paralleled by a rightward shift in V_{0} from −31 ± 19 ml at baseline to −1 ± 18 ml after 5 h (*P* < 0.001). On the other hand, PWR_{max}/(V_{ed})^{2} decreased throughout the experiment (*P* = 0.004). Interestingly, the optimal β 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).

#### Determinants of β.

The lowest and highest observed values of β were 0.29 and 4.73, respectively, with an overall mean of 1.94 ± 0.88. Calculating Pearson correlation coefficients showed that β correlated with HR (*r* = 0.558, *P* < 0.001), LV V_{ed} (*r* = 0.443, *P* < 0.001; Fig. 4), and LV V_{es}(*r* = 0.555, *P* < 0.001), but best with V_{0} (*r* = 0.799, *P* < 0.001). The use of HR, V_{ed}, V_{es}, and V_{0} as independent variables in a best-subset multiple linear regression analysis yielded the following model: β = 0.974 + 0.00732(HR) + 0.00811(V_{es}) + 0.0234(V_{0}), with *r*
^{2} = 0.68. Although the model statistics indicated HR, V_{es}, and V_{0} as highly significant (*P* < 0.001) model parameters, there was, however, a significant colinearity between HR and V_{0} (*r* = 0.527, *P* < 0.001) and between V_{es} and V_{0}(*r* = 0.508, *P* < 0.001). Subsequent data analysis indicated that the relation between β and V_{0} was better described using a nonlinear exponential relation. In this way, a monoparametric model was obtained that provided a better estimate of β than the model obtained from the multiple linear regression analysis: β =
with *r*
^{2} = 0.70 (Fig. 4).

#### Optimal preload correction of PAMP.

Given the involvement of V_{0} in the value of β, we tested an alternative preload correction for maximal power: PWR_{max}/(V_{ed} − V_{0})^{2}, which has been previously shown to correctly reflect contractility for the right ventricle (12). The correlation of *E*
_{es} with PWR_{max}/(V_{ed})^{2} and for the proposed alternative formulation is shown in Fig.5. It can be observed that, whereas PWR_{max}/(V_{ed})^{2} lacks correlation with *E*
_{es}, the newly proposed index [PWR_{max}/(V_{ed} − V_{0})^{2}] correlates well with*E*
_{es} (*r* = 0.87, *P*< 0.001).

## DISCUSSION

The concept of PAMP is based on the observation that the power-law relation PWR_{max} = α(V_{ed})^{β}can be fitted through PWR_{max}-V_{ed} data points obtained under altered loading conditions. Optimal preload correction is then obtained by dividing PWR_{max} by (V_{ed})^{β}, whereas α is a measure of contractility. In our experimental data, the overall mean value of β is 1.94, which is close to the value of 2 that is commonly used when calculating PAMP. However, β varies over a very wide range, and we have demonstrated a nonlinear exponential function of β with V_{0}. It turns out that β approximates 2 only when V_{0} is negligible. For V_{0} = 0, β is 2.16. The presented data confirm earlier findings for the right ventricle, where it was also found that β varies over a wide range (12).

Kass and co-workers (10) reported the optimal β-value for preload correction to vary with LV size, with β = 1 for the normal LV, whereas β = 2 should be more appropriate for dilated ventricles. In our acute animal model study, there was indeed a correlation of β with LV V_{ed}, but the relation with V_{0} was much stronger. It can be assumed that in the normal LV, V_{0} is small or even negative (3). For these V_{0}, β is <2 (V_{0} = −40 ml corresponds to β = 1). With LV enlargement, absolute volumes and V_{0} shift to the right, and the optimal value for β becomes >2. Our study thus indirectly supports the observations of Kass et al., but whereas they attribute the variation of β to changes in LV cavity size, we relate it to changes in V_{0}, the volume intercept of the end-systolic P-V relation. One could also deduce from the work of Kass et al. that β is restricted to only two discrete integer values. As our data demonstrate, however, β 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, β 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 V_{ed} or V_{0}. It also makes an enormous difference whether PWR_{max} is corrected for preload using β = 1 or 2. For instance, assuming PWR_{max} = 4,000 mW and V_{ed} = 100 ml, PWR_{max}/V_{ed} yields 40 mW/ml, whereas PWR_{max}/(V_{ed})^{2} gives 0.4 mW/ml^{2}. 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 β is not clinically useful.

In our study, there was only a poor correlation of PWR_{max}/(V_{ed})^{2} with*E*
_{es}, a validated index of LV contractility. As such, it is hard to consider PWR_{max}/(V_{ed})^{2} as a reliable index of LV systolic function. Taking into account the involvement of V_{0} in the variability of β and in analogy with an earlier study for the right ventricle (12), we tested an alternative correction of maximal power for preload, i.e., PWR_{max}/(V_{ed} − V_{0})^{2}. This index showed an excellent correlation with *E*
_{es}. V_{0} 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 V_{0} that the ventricle generates pressure. Within the linear time-varying elastance concept, V_{ed} − V_{0} is perhaps a more appropriate marker of ventricular preload than V_{ed} 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 V_{0} 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 PWR_{max} is corrected for preload as PWR_{max}/(V_{ed})^{2}, but less important for our newly proposed index. Errors in parallel conductance have the same effect on V_{ed} as on V_{0}, and thus not on V_{ed} − V_{0}. 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 PWR_{max} should be corrected for preload using (V_{ed} − V_{0})^{2}. Because V_{0} can only be determined from multiple P-V loops measured under altered loading conditions, the index that we propose requires the same measurements as *E*
_{es}, and it has no practical advantage over *E*
_{es}. 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 PWR_{max}/(V_{ed})^{2} or PWR_{max}/(V_{ed} − V_{0})^{2}. This, however, seems unlikely. The derived relation between β and V_{0} and the improved correlation of PWR_{max}/(V_{ed} − V_{0})^{2} with *E*
_{es} 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 V_{0} 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 *E*
_{es}, 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 V_{0} is required for an adequate correction of PAMP.

In conclusion, we demonstrated that in our animal model, PAMP poorly correlates with *E*
_{es}. Moreover, the β-factor, optimally used for preload correction, is not constant, but varies with V_{0}. An alternative formulation, incorporating this V_{0} dependency, resolves these shortcomings.

## Acknowledgments

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, CommunautéFrancaise de Belgique.

## Footnotes

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

- Copyright © 2003 the American Physiological Society