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Cardiovascular Biophysics Laboratory, Cardiovascular Division, Department of Internal Medicine and Department of Physics, College of Arts and Sciences, Washington University, St. Louis, Missouri
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ABSTRACT |
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diastasis; chamber stiffness
P)/change in volume (V)] or its inverse, compliance (V/P), obtained from the slope of the end-diastolic pressure-volume (P-V) relation (EDPVR) (18). Among these invasively obtained diastolic function parameters, chamber stiffness remains an area of active investigation (6, 34). A pathophysiological increase in chamber stiffness, usually manifesting as an elevation of LVEDP, may lead to diastolic heart failure (3, 4, 12, 17, 19, 41).
Chamber stiffness can be determined through single-beat or multiple-beat methods. In the single-beat approach, stiffness is P/V, the ratio of P over V during a specified portion of diastole (18). This ratio is equivalent to the slope of the corresponding segment of the P-V loop if the segment is approximated by a straight line (24). In the multiple-beat approach to stiffness determination, the response to volumetric load variation during consecutive heart beats is recorded. The end-diastolic P-V loop points inscribe a slightly (concave up) curved set of points, which, when fit mathematically, determine the EDPVR (see Fig. 1) (18). These points are conventionally fit by an assumed exponential P-V relation of the following form:
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To determine whether an elastic model with parallel viscous element is the best way to characterize diastolic chamber stiffness, in 1977, Rankin et al. (32) used the multiple-beat approach to determine the D-PVR. An EDPVR to D-PVR comparison was not a component of their analysis.
Although both the EDPVR and D-PVR contain information about chamber stiffness, whether these two relationships are the same P-V relationship at different volumes or are two inherently distinguishable relationships is unknown.
We hypothesized that because the physiology of diastasis (static equilibrium) and end diastole (a state when the ventricle has been stretched and the atrium is contracted) are distinguishable, the D-PVR and EDPVR are similarly experimentally distinguishable.
We test this hypothesis by analyzing LV pressure and volume changes associated with load variation due to respiration, Valsalva maneuver, or premature ventricular contractions (PVCs). The chamber stiffness defined by the D-PVR and EDPVR was also determined and compared.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Thirty-one data sets were selected from the Cardiovascular Biophysics Laboratory Database of simultaneous micromanometric catheter-recorded LV pressure, LV volume, and echocardiographic data. Subjects were scheduled for elective diagnostic cardiac catheterization at the request of their referring cardiologists to rule out the presence of coronary artery disease and provided informed consent prior to the procedure in accordance with a protocol approved by the Barnes-Jewish Hospital/Washington University Human Research Protection Office. The criteria for data selection from the database included normal LV function and ejection fraction (LV ejection fraction 
55%), normal sinus rhythm, normal end-diastolic volume (EDV), and normal valvular function. None of the 31 subjects had previous myocardial infarction, peripheral vascular disease, cardiomyopathy, congestive heart failure, or active ischemia.
Data Acquisition
The method of simultaneous high-fidelity, in vivo P-V and echocardiographic data recording has been previously described (5, 21). Briefly, LV pressure and volume were acquired using a micromanometric conductance catheter (SPC-560, SPC-562, or SSD-1034, Millar Instruments, Houston, TX) at the commencement of elective cardiac catheterization. Pressure signals from the transducers were fed into a clinical amplifier system (Quinton Diagnostics, Bothell, WA, and General Electric). Conductance catheterization signals were fed into a custom personal computer via a standard interface (Sigma-5, CD Leycom). Conductance volume data were recorded in five channels. Only data from low-noise channels providing physiological readings were used. The selected channels were averaged and calibrated to provide EDVs consistent with the calibrated ventriculographic volumes obtained during the same procedure.
Load Variation
In 18 subjects, LVEDP varied physiologically in response to respiration or during the recovery phase of the Valsalva maneuver. P-V measurements recorded during the recovery phase of the Valsalva maneuver were analyzed. In 13 subjects, either catheter-generated or isolated spontaneous PVCs caused the expected compensatory pause and associated load variation. P-V data recorded during both pre- and post-PVC beats were analyzed.
Data Analysis
After ventriculography-based calibration of conductance volume, LV pressures and volumes at both diastasis and end diastole were measured beat by beat using a custom LabView program (National Instruments, Austin, TX). Diastatic points were taken at ECG P wave peaks, and end-diastolic points were taken at ECG R wave peaks. We analyzed an average of 7 beats from 31 subjects (225 beats in total). Both diastatic and end-diastolic P-V data points were fit by the conventional exponential P-V relation (Eq. 1). Within the range of beat-to-beat volume changes, the exponential P-V curve was well approximated as a line (Eq. 2).
Two approaches have been used to construct a P-V relationship: the single-beat approach and the multiple-beat approach (18). We chose to use the multiple-beat approach for the analysis of diastasis. For each heart beat, as a result of the slight change in load, the ventricle reaches diastasis (becomes fully relaxed and passive) at a slightly different pressure and volume. This variation of equilibrium volume (38) and the associated beat-to-beat variation of pressure provides an unambiguous measure of passive stiffness.
Difference Between D-PVR and EDPVR
To elucidate and characterize the relationship between the D-PVR and EDPVR, we employed two approaches in each subject, as shown in Fig. 2. In the first "forward-extrapolation approach," we extrapolated the exponential fit of diastatic P-V points for each subject to the corresponding EDVs of the same heart beats and thereby estimated LVEDP. The estimated LVEDP from this extrapolation was compared with the measured LVEDP for the same heart beats in each individual subject. The errors of the estimation (measured LVEDP – estimated LVEDP) in each individual subject were averaged. All heart beats (225 beats) were also pooled together to compare the estimated LVEDP and measured LVEDP for the entire group. The estimated LVEDP combined with the measured LVEDV were used to generate the estimated EDPVR. The slope of the estimated EDPVR, which is a measurement of passive stiffness, was calculated in all 31 subjects and compared with the measured slope of EDPVR.
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To determine if the end-diastolic P-V points fit on the same exponential regression relation as the diastatic P-V points, we also fit the entire data set (average of 7 beats in each subject) of the diastatic P-V points and end-diastolic P-V points (average of 14 data points total in each subject) using one single exponential in each subject with a goodness-of-fit measurement [mean square error (MSE) of combined fit (MSEComb)]. We compared MSEComb with the MSE of the two separate exponential fits for diastatic P-V points (MSEexp_D-PVR) and end-diastolic P-V points (MSEexp_EDPVR) in all subjects as a group. The MSE is defined as follows:
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is the average of the measured pressure, and n is the number of beats measured. Linearity of D-PVR and EDPVR
Since the slope of the curved P-V relationship at a specific volume characterizes ventricular stiffness, we evaluated whether linear fits to the D-PVR and EDPVR are adequate within the range of volume variation we encountered. The goodness of fit for both exponential (Eq. 1) and linear (Eq. 2) approximations for D-PVR and EDPVR were determined for each subject and compared. The goodness of fit of the exponential and linear approximations was determined using two methods. The first utilized the linear correlation coefficient R2 of the linear, least-squared error best fit between pressure and volume for both diastatic and end-diastolic P-V points in all individual subjects (n = 31). The second method utilized the MSE of linear (MSElin_D-PVR and MSElin_EDPVR) and exponential fits (MSEexp_D-PVR and MSEexp_EDPVR) to both D-PVR and EDPVR for all individual subjects. MSEs for all subjects were combined as a group so D-PVR and EDPVR could be compared.
Statistical Analysis
The estimated LVEDP using the exponential extrapolation of D-PVR and the measured LVEDP for the same heart beats were compared in each subject. The estimated diastatic pressure using the exponential extrapolation of EDPVR and the measured diastatic pressure for the same heart beats were compared in each subject. The slopes of the estimated D-PVR and EDPVR were compared with the corresponding slopes of the measured D-PVR and EDPVR.
MSEComb was compared with MSEexp_D-PVR and MSEexp_EDPVR in all subjects as a group.
MSEexp_D-PVR and MSEexp_EDPVR were compared with the corresponding MSElin_D-PVR and MSElin_EDPVR.
The slopes of the two linear regressions of D-PVR and EDPVR in all 31 subjects were compared.
All measurements obtained via the different load variation methods were also compared. All comparisons were made using an unpaired two-tailed Student's t-test. All analyses were performed using MS Excel (Microsoft, Redmond, WA).
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RESULTS |
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In 29 of 31 subjects, extrapolation of the exponential fit of diastatic P-V points to the corresponding EDVs underestimated LVEDP. An example of extrapolation is shown in Fig. 2. In 21 of 31 subjects, the differences between estimated LVEDP and measured LVEDP were statistically significant, as shown in Table 2. In all 225 analyzed heart beats, the averaged measured LVEDP was higher than the averaged estimated LVEDP (18.1 ± 6.2 vs. 15.1 ± 5.0 mmHg, P < 0.001). The averaged error of the estimation was 3.0 ± 4.0 mmHg (measured LVEDP – estimated LVEDP), as shown in Fig. 3A. In 184 of 225 (82%) heart beats analyzed, the estimated LVEDP was lower than the measured LVEDP, as shown in Fig. 3B. As LVEDP increased, the estimation error increased (linear regression R2 = 0.35). When the estimated LVEDP was combined with measured corresponding EDVs to construct the estimated EDPVR, the slope of the estimated EDPVR was consistently smaller than the measured slope of the EDPVR (0.20 ± 0.14 vs. 0.24 ± 0.15 mmHg/ml, P < 0.01), as shown in Fig. 3C.
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In 28 of 31 subjects, when the exponential EDPVR was extrapolated back to the corresponding diastatic volumes, the estimated diastatic pressure was higher than the measured diastatic pressure. In 23 of 31 subjects, the differences between estimated diastatic pressure and measured diastatic pressure were statistically significant, as shown in Table 3. In all 225 analyzed heart beats, the averaged measured diastatic pressure was lower than the averaged estimated diastatic pressure (11.8 ± 4.9 vs. 14.6 ± 5.8 mmHg, P < 0.001). The averaged error of the estimation was –2.8 ± 3.4 mmHg (measured diastatic pressure – estimated diastatic pressure), as shown in Fig. 4A. In 188 of 225 (84%) heart beats analyzed, the estimated diastatic pressure was higher than the measured diastatic pressure, as shown in Fig. 4B. When the estimated diastatic pressure was combined with the measured corresponding diastic volume to construct the estimated D-PVR, the slope of the estimated D-PVR was similar to the measured slope of the D-PVR (0.16 ± 0.11 vs. 0.16 ± 0.11 mmHg/ml, P = not significant), as shown in Fig. 4C.
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As shown in Table 4, compared with the individual exponential fits of diastatic P-V points and end-diastolic P-V points, the fit to the combined diastatic P-V and end-diastolic P-V points using one single exponential curve was significantly worse, as measured by the corresponding MSEs (MSEexp_D-PVR and MSEexp_EDPVR). An example is shown in Fig. 5.
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The results of the goodness-of-fit comparisons for both linear and exponential fits in the entire group are shown in Table 5. MSElin_D-PVR and MSEexp_D-PVR were statistically indistinguishable for all subjects as a group. MSElin_EDPVR and MSEexp_EDPVR were also statistically indistinguishable for the group. The R2 value of the linear fits for both D-PVR and EDPVR indicated that they could be well approximated by straight lines within the physiological range of variation encountered.
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Stiffness Difference From D-PVR Versus EDPVR
As a group, the stiffness, i.e., slope of the D-PVR (dP/dVD-PVR), was significantly less than the slope of the EDPVR (dP/dVEDPVR) (0.16 ± 0.11 vs. 0.24 ± 0.15 mmHg/ml, P < 0.001) for the 31 subjects. As shown in Fig. 6, the slopes of D-PVR and EDPVR were linearly correlated with a regression relation of dP/dVEDPVR = 1.24 x dP/dVD-PVR + 0.04 (R2 = 0.86). Figure 6 also shows that the values of the slope of D-PVR are consistently smaller than those of EDPVR slopes. There was no significant correlation between LVEDP and the slopes of D-PVR or EDPVR (R2 = 0.06 and 0.09, respectively). Slopes for all individual subjects are shown in Table 6.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Determination of the EDPVR and D-PVR
Volume variation. P-V relationships have been previously determined using the multiple-beat approach by varying volume using transient vena cava occlusion. Pak et al. (30) achieved a range of 31–67% EDV variation using vena cava occlusion in different patient groups. Other investigators determined EDPVRs with EDV variation ranging from 25% to 50%. The numbers of cardiac cycles used were typically <10 in some studies (11, 13, 23, 25). In the present study, the average EDV variation was 31 ± 16% (relative to the maximum EDV) and the average diastatic volume variation was 40 ± 21% (relative to the maximum diastatic volume). Although the volume change and beat number in this study were not as great as those in Pak et al.'s work, the 30–40% variation of diastatic volumes and EDVs used in this study are consistent with what has been used in the literature. After acute load variation (after PVC and Valsalva), the ventricle returns to steady state and manifests respiratory variation of P-V points. Additional steady-state beats can be added to the data set to increase the overall number of beats from which the P-V relationship is determined. However, since respiratory variation is already part of the data set for each subject, inclusion of additional beats will not affect the statistics of the fit.
Correcting for relaxation.
The extent of relaxation has been considered previously in the determination of diastolic P-V relationships by correcting for the effect of relaxation (15, 31, 39) during all of diastole. To correct for relaxation, the measured LV pressure data are modified by subtracting the decaying LV pressure, which is the continuum of the exponential decay during isovolumic relaxation, from the actual ventricular pressure during diastole (31). The EDPVR and D-PVR we used were obtained using the multiple-beat approach (1 data point from each beat) without explicit correction for relaxation. Indeed, as described by Jaber et al. (15), incorporating the effect of relaxation as a correction generates a P-V relationship from one single diastolic portion, which can substitute the P-V relationship obtained from multiple heart beats with varying EDVs. However, correcting for the effect of relaxation has minimum effect on D-PVR if the multiple-beat approach is used, since relaxation is complete after 3–4 
(where is the time for the pressure to drop by a factor of 1/e = 0.37 from its value near peak negative dP/dt) (35). For most patients, is typically 50–60 ms and the early filling E wave duration is 
200–300 ms; hence, by the time diastasis is achieved, the ventricle is fully relaxed. Further evidence that full relaxation has been achieved is provided by the fact that during diastasis dP/dt = 0 and there is no transmitral flow. If the ventricle was continuing to relax, then we would expect the pressure to be decreasing (38). If the diastatic points were to be corrected for relaxation, the corrected diastatic pressure for each heart beat will be (very slightly) lower than the measured diastatic pressure value. In contrast, the end-diastolic points (100 ms later) will not require correction because relaxation is even more complete by then. In this work, we observed that diastatic points always have lower pressure than end-diastolic points and that D-PVR is always below EDPVR. So the effect of correcting the diastatic points for relaxation would be to further lower the diastatic points and displace the D-PVR on the P-V plane. This further reinforces our conclusion that D-PVR and EDPVR are two different relationships by separating the two data sets even further.
Previous Work on the Diastatic P-V Relationship
We are not the first to use D-PVR in physiological studies. Rankin (32) also used the physiology of diastasis and the D-PVR to investigate the stiffness of the ventricle. In his work, the multiple-beat method was utilized to construct the D-PVR, which was fit by an exponential similar to Eq. 1. The single-beat method used the entire diastolic portion of a P-V loop generated from one beat. The goal of Rankin's study was to compare different mathematical elastic models in their ability to fit the P-V relationship during all of diastole in a single beat using the D-PVR as a reference P-V relationship. He did not compare D-PVR and EDPVR using the multiple-beat approach, as in this study. We note that, although the (multiple beat) D-PVR appears very similar to the single-beat P-V relationship obtained using the model with a parallel viscous element from a single beat, whether these two P-V relationships are statistically distinguishable was not part of Rankin's investigation.
Difference Between D-PVR and EDPVR
The results of estimating EDP and stiffness by extrapolating the D-PVR underscore the difference between EDPVR and D-PVR (see Fig. 2). Also, if the diastatic P-V points and end-diastolic P-V points were combined and fit as a single exponential curve, the goodness of fit was always worse than if the two data sets were fit separately. Importantly, the EDPVR was not merely the extension of D-PVR to a higher volume. Otherwise, the estimation of LVEDP using the extrapolation of D-PVR should agree with the measured LVEDP. Similarly, the extrapolation via the EDPVR back to the diastatic volume regime did not agree with the measured diastatic pressure. The systematic differences between LVEDP and diastatic pressure estimations by extrapolation and the worse fit to the combined data indicate that atrial contraction generates a different P-V relationship than the one inscribed by diastasis. As a result, although diastatic volume is always smaller than EDV, the difference between the two linear fit slopes cannot be explained by Eq. 1.
Both D-PVR and EDPVR are exponential relationships; the slope of the exponential curve changes as the volume increases, and the amount that the slope changes depends on the parameters of the curve. It is quite possible that the slopes of two different curves are similar at one volume regime but different at another volume regime. We noticed that the estimated D-PVR slope was similar to the measured D-PVR slope, whereas the estimated EDPVR slope and measured EDPVR slope were significantly different. This highlighted the fact that the slope increase between diastatic volume regime to EDV regime on the D-PVR and EDPVR are different, which also indicated that the two relationships are different.
Diastasis is the equilibrium state of the ventricle, and the atrium is passive during early filling before diastasis. The P-V relationship measured by diastasis should reflect the stiffness property primarily of the ventricle alone. Since the D-PVR and EDPVR are different and the EDPVR slope is always higher than the D-PVR slope, using D-PVR to characterize passive LV stiffness is physiologically more justified than using the EDPVR.
Potential Mechanisms for the Difference Between D-PVR and EDPVR
Our results suggest that although at end diastole the pressure and volume measured in the LV and their variation (ventricular dP/dV at end diastole) are usually ascribed to the LV, they must, in part, be confounded by atrial properties. Because it is impossible to isolate and determine in vivo atrial pressure and volume and differentiate it from ventricular properties, one can explore the effect of the atrium indirectly, by comparing D-PVR and EDPVR for the LV. D-PVR reflects mainly ventricular properties because during early filling the atrium is passive and functions as a conduit. If the EDPVR conveyed only LV passive properties, it should be the extension of the D-PVR to greater volumes. This is not what we observe. Importantly, the left atrium contracts to move the LV from diastasis to end diastole; hence, the left atrial inotropic state should be a factor. Atrial systolic function attributes, pericardial constraint, and interventricular and interatrial factors may be part of the ultimate explanation for the difference between the two observed relationships.
Correlation Between LVEDP and D-PVR and EDPVR Slopes
Although all subjects had normal EDV, 11 of 31 subjects had somewhat elevated LVEDP (LVEDP > 19 mmHg) and 22 of 31 subjects had somewhat increased values for the time constant of isovolumic relaxation (>50 ms). It is accepted that elevated LVEDP is associated with increased stiffness of the chamber (39), whereas delayed relaxation is related to calcium handling (19, 40), elastic recoil (20, 27), and both chamber and myocardial viscoelasticity (5, 19, 40). The mechanical and elastic roles of the visceral pericardium in diastolic function are being actively elucidated (16). We found a very weak correlation between LVEDP and the slopes of the D-PVR and EDPVR. One reason may be due to the modest sample size. Alternatively, each chamber follows its own EDPVR. The fact that some of the subjects had elevated LVEDP or somewhat prolonged time constants of isovolumic relaxation does not affect our conclusions because each subject serves as his/her own control when the volumes are varied and the individual D-PVR and EDPVR are inscribed.
Effect of Load Variation Methods
This study made use of three methods of physiological load variation: post-Valsalva recovery, respiratory variation, and post-PVC pressure recovery. We opted for these because none of these physiological load-varying methods require additional pharmacological intervention (inotropes or β-blockers). The P-V value measurements observed using these load-varying methods do not differ from each other significantly. This implies that the physiological response generated during the recovery phase of the Valsalva maneuver, as a result of respiration, or the compensatory pause after PVC are comparable.
Intrathoracic pressure affects the volumetric load of the heart. When intrathoracic pressure changes in response to Valsalva, the change of load generates different P-V points, allowing construction of the P-V relationship. The diastatic and end-diastolic points for the same heart beats experience the same effects from intrathoracic pressure change and move in tandem due to the brief (100 ms) interval between end diastasis and end diastole. So it is not likely that the differences between D-PVR and EDPVR are due to differential effects of intrathoracic pressure change generated by the Valsalva.
Active and Passive Stiffness
To avoid confusion, our use of "stiffness" is intended to mean passive stiffness rather than active stiffness, when the LV is changing volume and viscoelastic attributes are likely to affect the P-V relationship. If the chamber had no viscoelastic attributes during diastole, the D-PVR and EDPVR would still be different as a result of atrial effects. Although it is conceivable that viscoelasticity converts part of the energy of atrial contraction into heat and changes the EDPVR, it is unlikely that the observed difference between D-PVR and EDPVR can be fully explained just by viscoelastic effects.
Absolute Versus Relative Measurements
Because diastasis is an equilibrium state, where forces are balanced and a static condition is attained, it is a relative rather than absolute measure; hence, knowledge of the absolute pressure is not needed. Diastatic and end-diastolic pressure and volume change in response to respiration. More significant variation is observed during the Valsalva maneuver or after PVC beats. In response to the change of load by PVC, Valsalva maneuver, and breathing P-V points are displaced in the P-V plane. The load-dependent displacements of the respective P-V points define the D-PVR and EDPVR. Determining the absolute pressure during breathing is not required because measurement of the variation of the pressure (P) and the corresponding variation in LV volume (V) suffice to define the stiffness (P/V).
Limitations
The conductance catheter method of volume determination has known limitations related to noise, saturation and calibration (2, 5, 9, 22, 36). In this study, the channels that provided physiologically consistent P-V loops were selected and averaged. As a result, systematic calibration-related errors could be introduced. However, since there was no significant drift of the volume signal during recording, any systematic offset related to calibration of the volume channels did not affect the result when the conductance volume was calibrated via ventriculography. If the two absolute measures (end-systolic volume and EDV) have slight systematic differences, resulting in a systematic volume calibration offset, the absolute values of the slopes could generate errors. However, even in this case, the relative relation of the two slopes of D-PVR and EDPVR and the error of estimation of LVEDP from D-PVR are unaffected because the error affects all the measurements in the same way.
In P-V relationship-determining physiology experiments, not only volumes are conventionally varied to generate P-V loop variation, but the inotropic state may be varied by pharmacological means via positive and negative inotropic stimulation. Although the inotropic state during the recovery phase of the Valsalva maneuver varies from the resting state, it is in response to physiological rather than pharmacological stimulation and remains within the normal physiological range. Our data obtained during the course of cardiac catheterization and the associated informed consent procedure did not allow for interventions involving external (nonphysiological) inotropic agents. This limitation is obviated somewhat by the fact that the load variation was entirely physiological and did not include the complexities of reflex mechanisms associated with pharmacological interventions. However, this limitation underscores the importance of carrying out similar experiments in intact, closed-chest mammals, where pharmacological interventions are the norm and the physiology of the diastatic P-V relationship can be further elucidated.
The results generated by different load variation methods (PVC, Valsalva maneuver, and respiration) did not differentiate between themselves (P > 0.05, results not shown) among the groups. This permits the merging of subject data for the determination of the difference between D-PVR and EDPVR.
As in previous work (36), the P-V measurements were guided by ECG R and P waves, which are unambiguous. Using this method, the interobserver dependence of the pressure and volume measurements has been determined to be <5%.
Conclusions
Although both the D-PVR and EDPVR contain information about ventricular stiffness, whether they are distinguishable is unknown. Because they are conceptually different in physiological terms, we tested the hypothesis that they are experimentally distinguishable. We found that the D-PVR and EDPVR are distinguishable. Based on the physiology of diastasis (no wall motion, no transmitral flow), D-PVR-determined stiffness better conveys passive LV stiffness, whereas EDPVR-derived stiffness is confounded by the contracted atrium. Hence, interpreting the slope of the EDPVR as passive stiffness of the LV has limitations.
The physiology of the D-PVR and its attributes in health and disease is under investigation.
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FOOTNOTES |
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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.
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