## Journal of the American College of Cardiology

# Comparison of ventricular pressure relaxation assessments in human heart failureQuantitative influence on load and drug sensitivity analysis

## Author + information

- Received May 21, 1998.
- Revision received May 27, 1999.
- Accepted June 28, 1999.
- Published online November 1, 1999.

## Author Information

- Hideaki Senzaki, MD
^{a}, - Barry Fetics, MA
^{a}, - Chen-Huan Chen, MD
^{a}and - David A Kass, MD
^{a},* (dkass{at}eureka.wbme.jhu.edu)

- ↵*Reprint requests and correspondence: Dr. David A. Kass, Halsted 500, Department of Cardiology, The Johns Hopkins Hopital, 600 North Wolfe Street, Baltimore, Maryland 21287

## Abstract

OBJECTIVES

We contrasted various methods for assessing ventricular pressure decay time constants to test whether sensitivity to slight data instability or disparities between model-assumed and real decay are systematically altered by cardiac failure. We hypothesized that such discrepancies could result in apparent increased relaxation sensitivity to load and drug stimulation.

BACKGROUND

Deviation of relaxation behavior from model-assumed waveforms may be worsened by failure, enhancing instability and apparent load and drug sensitivity of commonly used indexes.

METHODS

Pressure-volume relations were measured in patients with normal (n = 14), hypertrophic (hypertrophic cardiomyopathy [HCM], n = 15) and dilated-myopathic (dilated cardiomyopathy [DCM], n = 37) hearts before and during preload reduction or inotropic stimulation. Relaxation parameters (monoexponential [ME] model assuming zero-*T*_{ln}or non-zero-*T*_{D}*, T*_{F}asymptote:, hybrid logistic-*T*_{L}, linear-*T*_{LR}, and pressure halftime-*T*_{1/2}) were contrasted regarding sensitivity to slight data range manipulation and loading or drug changes.

RESULTS

In DCM, *T*_{D}and *T*_{F}prolonged 15% to 25% (p < 0.0001) by deletion of only 1–2 data points, whereas this had minimal effect on controls or HCM. This stemmed from systematic deviation of relaxation from an ME decay in DCM. *T*_{1/2}and *T*_{ln}were highly sensitive to pure pressure offsets, whereas *T*_{L}was most stable to both manipulations in all hearts. As a result, *T*_{D}and *T*_{F}appeared to be much more sensitive to systolic load in DCM than *T*_{1/2}or *T*_{L}and disproportionately sensitive to increased cyclic adenosine monophosphate (cAMP).

CONCLUSIONS

Relaxation consistently deviates from an ME decay in DCM resulting in instability and amplified relaxation systolic load or drug dependence of ME-based indexes in failing versus control (or HCM) hearts. The hybrid-logistic method improves quantitative analyses by providing more consistent data fits with all three heart types.

Delay of ventricular pressure decline plays an important role in the pathophysiology of hypertrophic cardiomyopathy (HCM) and dilated cardiomyopathy (DCM) (1–4). In addition to baseline delay, relaxation is further slowed by increased systolic loading (5,6), an effect reportedly enhanced by heart failure (7). Quantitation of pressure decline in normal and failing hearts is generally based on model fits to the decay waveform, with monoexponentials (MEs) being most common (8,9). Alternative models have been proposed, including biexponentials (10), linear fits (11)and a hybrid-logistic (HL) fit (12,13). However, pressure decay does not necessarily follow any of these waveforms (14), and systematic discrepancies between real and assumed pressure decay for healthy versus diseased hearts could potentially affect quantitative disparities in relaxation load dependence or drug sensitivity. This means that a seemingly arbitrary choice of relaxation model might yield very different results from such interventions.

Ideally, an index of pressure decline should be sensitive to underlying relaxation behavior, yet be fairly insensitive to slight noise in the portion of data from which it is derived or to pure pressure offsets. Such minor data fluctuations are almost inevitable when relaxation is assessed in vivo. Parameters derived from curve fits that closely follow both pressure decay and its first derivative are more likely to satisfy these criteria. Accordingly, the goal of this study was two-fold. First, we sought to contrast widely used relaxation indexes with respect to these criteria, testing for systematic discrepancies when comparing normal to failing hearts. Second, we tested the hypothesis that apparent systolic-load and pharmacologic influences on pressure relaxation critically depend on the index used—particularly in heart failure, due largely to such systematic discrepancies. Our study finds that the HL model (12,13)provides the most consistent fit to pressure decay in healthy and diseased hearts, thereby conferring practical advantages for quantitative relaxation analyses.

## Methods

Sixty-six adult patients referred for diagnostic cardiac catheterization were studied. Fourteen had normal ventricular function, without coronary artery, valvular or other identified cardiac disease. Fifteen had nonobstructive HCM with an average wall thickness of 1.6 ± 0.25 cm. Nonobstructive HCM was chosen because other forms of the disease pose recognized difficulties for relaxation-decay analysis due to the abrupt release of obstruction during pressure decline (15). The remaining patients had DCM from ischemic (n = 5) or nonischemic (n = 32) etiologies. Age ranged from 38 to 80 years (mean 56). All patients provided informed consent, and the protocol was approved by The Johns Hopkins Joint Committee on Clinical Investigation.

### Procedures

Patients were premedicated with benzodiazepam (5 to 10 mg) and diphenhydramine (25 to 50 mg). After routine coronary angiography, left ventriculography and right heart catheterization, left ventricular (LV) pressure and volume were measured by the volume catheter method (SPC-562/7, 562/4, Millar) (15). Data were obtained at rest and during transient preload reduction induced by transient obstruction of inferior vena caval inflow. The latter maneuver also yielded data testing the influence of varying end-systolic pressures on relaxation time constants. In 26 DCM patients, data were also obtained after intravenous (IV) dobutamine (5 μg/kg/min, n = 19) or toborinone (5 to 10 μg/kg/min, n = 7). The latter is a quinolinone derivative that increases contractility and hastens relaxation (16).

### Data analysis

Data were digitally recorded at 200 Hz using custom acquisition-display software. Left ventricular pressure decay analysis was based on data spanning the point at minimal first derivative of pressure (dP/dt_{min}) to 2 mm Hg above end-diastolic pressure (EDP). dP/dt was determined by digital filter, while EDP was defined as the pressure when dP/dt reached a threshold of 10% of maximum.

Six pressure relaxation assessments were calculated. Pressure half time (*T*_{1/2}) was the time required for pressure at dP/dt_{min}to decline 50%. Monoexponential-based tau was calculated assuming pressure decayed to a zero (*T*_{ln}) or non-zero (*T*_{D}and *T*_{F}) asymptote. *T*_{ln}was the negative reciprocal of the linear slope relating the natural logarithm of pressure to time (8). *T*_{D}was calculated from regression of pressure versus dP/dt (9), whereas *T*_{F}was determined by non-linear regression (Marquardt), using: P(t) = (P_{o}−P_{∞})e^{−t/TF}+ P_{∞}, where P_{∞}is the pressure decay asymptote, and P_{o}is near the pressure at dP/dt_{min}. A (HL)-based tau (*T*_{L}) was determined from the equation P(t) = 2(P_{o}′−P′_{∞})/(1+e^{t/T}) + P_{∞}′ (12). Finally, pressure-time data were fit by linear regression, and the inverse negative slope (*T*_{LR}) was used to index decay rate.

The sensitivity of each index to slight alterations in the input data was tested two ways. First, the lower pressure cutoff value was varied from EDP + 2 to EDP + 10 mm Hg. This cutoff is somewhat arbitrary in practice, being designed to restrict analysis to isovolumic data. Second, LV pressures were shifted −5 or −10 mm Hg (as might accompany inspiration) without altering the waveform. The sensitivity of each index to disease condition was determined from rest data in each group.

The implication of differences in index behavior determined in the first part of the study were then tested with respect to the quantitative analysis of load and drug effects. To test the extent to which altered load sensitivity of relaxation in DCM depended on the decay analysis used, relations between tau and end-systolic pressure were generated from data recorded during vena caval occlusion. Relation slopes were plotted versus contractile state indexed by end-systolic elastance (E_{es}) (15)or dP/dt_{max}for each heart. Tau responses to dobutamine/toborinone (16)were also contrasted.

Results are presented as mean ± SEM, with resting differences between groups tested by analysis of variance (ANOVA). Sensitivity of tau parameters to data range or pressure offset manipulation were tested by a two-way repeated measures ANOVA, with the patient serving as the second categorical variable.

## Results

### Baseline hemodynamics

Table 1summarizes hemodynamics data in each group. Data for ischemic and nonischemic DCM are combined since they were statistically indistinguishable. All pressure relaxation indexes yielded qualitatively similar results, with decay prolongation in HCM patients and even longer time courses in DCM. However, there were substantial quantitative differences, with DCM being between +42% to +137% longer than controls depending upon the index used. *T*_{D}and *T*_{F}yielded the largest differences and *T*_{LR}and *T*_{ln}the smallest. Both ME and HL models yielded two additional fit parameters, P_{o}and P_{∞}, and there were substantial differences in the latter between models. P_{∞}, or the estimated pressure decay asymptote, was negative in all patient groups with the ME model and was considerably so (−37 ± 5.4 mm Hg) in DCM. In contrast, P_{∞}was small, positive and did not significantly change between disease states with the HL model. P_{o}—or the pressure at the onset of relaxation—was similar from both models in each respective group.

### Responses to small data range manipulation and pressure offsets

Figure 1displays results of input data range and offset sensitivity testing. Data are shown as percent change for each index as a function of a given manipulation, normalized to the basal condition. Top panels show the effects of varying the lower pressure cutoff point (i.e., EDP + 2, EDP + 6) typically altering the analysis by one or two data points. In normal and HCM hearts, varying this cutoff pressure had little quantitative effect. *T*_{LR}, however, shortened >10% with this maneuver in controls. In contrast, *T*_{D}and *T*_{F}were quite sensitive to this change in DCM, prolonging nearly 25 msec (20%, p < 0.0001). Smaller but consistent rises were also observed in *T*_{ln}(p < 0.0001). In contrast, *T*_{L}shortened relatively little (∼1 ms, or 5%) in each heart type. *T*_{1/2}was unaltered by this change by its definition.

The lower panels display the effects of shifting the pressure data by an absolute offset. As predicted from their definitions, *T*_{D}*, T*_{F}*, T*_{L}and *T*_{LR}were unaltered by this manipulation. However, *T*_{ln}and *T*_{1/2}significantly and substantially shortened as much as 25%∼30% in all heart types (p < 0.0001) by varying the offset. Thus, the index that consistently displayed the least change to slight alterations in the input data range or pressure offset was *T*_{L}.

### Comparison of model fits

One explanation for the disparity in behavior of ME versus HL models related to their goodness-of-fit. The more accurate the fit, the better it described not only the time course of pressure decline but also the instantaneous rate of decline. Pressure-time plots were equally well fit by ME or HL models in all groups (Fig. 2, top); however, there were substantial discrepancies in the capacity of each model to predict the local slope (dP/dt) of pressure fall (Fig. 2, middle). In DCM patients, the ME fit (dashed line) failed to describe the dP/dt course, whereas the HL fit predicted the derivative well. Similar results were observed in control and HCM patients.

When dP/dt is plotted versus P (Fig. 2, lower panels), a pure ME decay process appears as a line. While each heart type deviated from a linear relation, the greatest discrepancy occurred systematically with DCM. P-dP/dt nonlinearity was significant (p < 0.05 for quadratic term) in 57% of control subjects, 73% of HCM and 91% of DMC (p < 0.05 by Chi-square analysis). The corresponding sum-of-squares errors for ME models were 17%, 70% and 469% higher than with HL fits (p < 0.001). Furthermore, because the ME-decay model fit a line to P-dP/dt relations, the linear slope (negative inverse is *T*_{D}) was very sensitive to deletion of even a single data point if the real P-dP/dt data were nonlinear (e.g., DCM). The more linear the dP/dt-P plot (e.g., control subjects), the less ME tau varied from this maneuver. The HL model fit nonlinear P(t) and dP/dt data more consistently in all heart types.

### Contractility and relaxation-load dependence: influence of index selection

Prior studies using ME-based pressure relaxation analysis have shown that prolongation of decay time with increasing end-systolic pressure is exacerbated as contractility falls (5–7). However, our observation that pressure decline deviated more from an ME waveform in DCM than it did in control hearts suggested that a substantial component of this behavior might be methodologically based. To test this, we regressed relations between the percent change in relaxation index for a given percent change in end-systolic pressure (Pes) from multiple cycles (Table 2). Again, there was qualitative agreement in that all of the indexes indicated some systolic load dependence of relaxation. However, quantitative differences were striking. For all ME-based indexes (*T*_{ln}*T*_{F}and *T*_{D}), the results suggested a >4-fold increase in load sensitivity in DCM hearts versus controls. In contrast, *T*_{1/2}and *T*_{L}slopes were smaller, and differences between DCM and controls were not statistically significant. *T*_{LR}relation slopes yielded the complete opposite effect, i.e., *T*_{LR}increased with reduced load.

Figures 3A and Bdisplay plots of tau -Pes relation slopes versus cardiac contractility for each patient, using *T*_{D}and *T*_{F}, respectively. These data demonstrate a hyperbolic dependence, similar to that previously reported (5,7). Figure 3Cshows the same plot using dP/dt_{max}as the contractile index, demonstrating that the choice of E_{es}was not critical to this result. However, when either *T*_{L}or *T*_{1/2}were used, the results suggested minimal change in load sensitivity with varying contractility (Fig. 3D and E). Thus, the observation of greater load dependence of tau at reduced contractility was itself critically dependent on the precise method chosen to assess pressure decay. To further test if the hyperbolic relation shown in panels A–C of Figure 3primarily reflected the extent to which pressure decay waveform deviated from an ME model at reduced contractility, we calculated differences in sum-of-squares error for linear versus nonlinear fits to dP/dt-P plots. The greater the difference, the more the deviation from the ME decay. Substitution of this difference as the ordinate, instead of tau load-dependence, yielded results (Fig. 3F)similar to the hyperbolic relations in Figure 3A–C.

### Pharmacologic stimulation

Another consequence of systematically greater deviation from a ME-decay in DCM is that pharmacologic agents altering this disparity can disproportionately influence tau indexes based on ME models. Both dobutamine and toborinone elevate cyclic adenosine monophosphate (cAMP), enhancing ejection and improving relaxation. The net effect was a transition to a more ME decay, demonstrated by increasing linearity of P-dP/dt relations (the SS-error was 410% higher for ME vs. HL model fits before drug, and 170% higher after drug [p < 0.05]). As a result, ME-based indexes exhibited significantly greater absolute and percent tau reduction (20% to 24%) with drug (Table 3). In contrast, the HL equation fit pre- and post-drug data similarly, and *T*_{L}was shortened by 10%. A similar discrepancy was observed with *T*_{LR}(linear fit) which also shortened half as much as ME indexes, whereas *T*_{1/2}declined similarly as ME indexes.

## Discussion

This study reports two major findings. First, systematic deviation of relaxation in DCM from an ME waveform increases the sensitivity of ME-based time constants to small changes in input data. Furthermore, this deviation greatly enhances apparent load sensitivity of ME indexes with worsening failure and amplifies responses to pharmacologic change. Simply substituting alternative indexes such as *T*_{1/2}or *T*_{L}, a seemingly arbitrary choice, yields very different magnitudes of response, particularly with respect to changes in relaxation-load sensitivity. Second, *T*_{L}derived from an HL model consistently provides the least variability with small changes in the input or pure pressure offsets and better fits the time course of pressure decay and its first derivative (particularly in DCM). These are attractive features for clinical applications, because they reduce methodologic bias when comparing data between normal and depressed hearts and reduce data noise from uncertainties in absolute LV pressure (i.e., influence of external constraints or EDPS).

### Relaxation analysis assumptions and comparative performance

Whereas previous studies have examined pitfalls of relaxation indexes, this is the first to systematically compare tau sensitivity with small variance in the input data in diseased and normal human hearts. By using the natural logarithm of pressure, *T*_{ln}diminishes noise, but it is sensitive to pure offset pressures (17)by forcing pressure to decline to zero. *T*_{F}and *T*_{D}circumvent this limitation but display greater sensitivity to small alterations in the data range used for analysis in DCM hearts. The lower cutoff pressure is often arbitrarily set to EDP + 5 mm Hg, with the goal being to assure that the data fall within the isovolumetric period. The finding that only a few mm Hg difference in this cutoff in DCM can have marked effects on ME-tau quantitation is a nontrivial limitation, because there is frequently ambiguity as to the exact value of EDP from pressure data (particularly in DCM hearts), and small beat-to-beat fluctuations can change this value. Finally, differences in this effect among normal and HCM hearts can amplify apparent differences in response to interventions when comparisons are made to DCM.

Three non-ME based indexes were also tested. Of these, *T*_{L}provided the least sensitivity to small changes in data range and pressure offsets. The primary reason for this was that the HL model yielded the most consistent fit to P and dP/dt data. Pressure decay results from an interaction of crossbridge relaxation, elastic recoil and geometric configurational change, so it is difficult if not impossible to explain the improved fit of the HL model on crossbridge mechanics. Nonetheless, our data clearly demonstrated improved fits particularly in DCM ventricles, which should assist analysis of pressure decay in this disease.

The key difference between ME and HL goodness-of-fit was not evident by their ability to fit P(t) data but in their predictive accuracy to the pressure derivative and thus P-dP/dt plots. In normal human hearts such data appear near-linear. However, in isolated, denervated canine hearts (12)and failing human hearts, such plots reveal consistent (>90% of subjects) convex nonlinearity. Under these conditions, elimination of even one data point yields very different ME tau. An alternative approach is to employ a biexponential model, fitting upper and lower portions of the nonlinear P-dP/dt plot to two separate lines (10). This enhances fit stability, but does not resolve other issues—such as the markedly increased load-sensitivity. The HL model better fits both pressure-time and dP/dt data, and this assists consistency of characterization in both control and DCM hearts.

### Implications for loading and drug effects

Recent studies have reported reduced inotropic response to adrenergic stimulation in DCM despite apparent preservation of relaxation-shortening (18,19). To date, a precise cellular or molecular explanation for this disparity has remained unclear. However, these observations were based on ME and *T*_{1/2}analyses, and the current study shows such indexes can yield larger proportional changes in tau due to changes in offset pressures or decay waveform shape. This suggests caution when a more quantitative analysis is applied using ME-derived parameters in DCM.

Eichhorn et al. (7)reported that slopes of relations between *T*_{D}and P_{es}increased as systolic function (E_{es}) declined. Ishizaka et al. (20)reported similar findings using *T*_{D}in conscious dogs with tachycardia-induced DCM. Had either investigator used *T*_{L}or *T*_{1/2}, a seemingly arbitrary choice from the standpoint of relaxation analysis, this behavior would not have been observed. Our results do not refute studies showing greater tau load-dependence at high afterload in hearts with depressed contractility (5,6). However as found by Gillebert et al. (6), this load dependence is very nonlinear, with minimal effects at normal or reduced loads, consistent with our results using *T*_{L}or T_{1/2}.

It should be noted that there is no real in vivo standard with which to compare any of these indexes of pressure relaxation. As a result, one might argue that indexes such as *T*_{L}or *T*_{1/2}are simply underestimating real load or drug effects. However, these differences were principally related to an improved goodness-of-fit with the HL model, which implies greater robustness rather than artifactual error to the measurements.

### Conclusions

Assessment of diastolic function by rate of pressure decline based on commonly used ME tau or *T*_{1/2}can be influenced by varying discrepancies between real and model-assumed decay behavior. This can result in systematic bias when quantifying and comparing systolic load and drug-induced effects between normal or HCM to DCM. An alternative fit based on an HL equation appears to minimize these factors, providing a sensitive but more robust assessment of pressure decay in DCM.

## Footnotes

☆ Dr. Kass was supported by NIA Grant AG:12249; Dr. Fetics was a recipient of the Colin Research Fellowship Award; and Dr. Senzaki was a recipient of the American Heart Association-Md. Affiliate GIA.

- Abbreviations
- ANOVA
- analysis of variance
- cAMP
- cyclic adenosine monophosphate
- DCM
- dilated cardiomyopathy
- EDP
- end-diastolic pressure
- Ees
- end-systolic elastance
- HCM
- hypertrophic cardiomyopathy
- HL
- hybrid-logistic
- LV
- left ventricle or ventricular
- ME
- monoexponential
- Pes
- end-systolic pressure

- Received May 21, 1998.
- Revision received May 27, 1999.
- Accepted June 28, 1999.

- American College of Cardiology

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