INTRODUCTION

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IF CONTRACTING CARDIAC MUSCLE is allowed to shorten, the shortening process itself affects the contractile properties and performance of the muscle. For example, ejection has been shown to have variable effects on the inotropic state: augmentation or depression, depending on the amount of ejection (7, 22, 37). Recent experimental work has shown that these shortening-mediated phenomena exist at the cardiac muscle level (11). Moreover, theoretical modeling supports the notion that these shortening-mediated phenomena may originate from the cross-bridge properties (28). Given that contraction and relaxation are governed by many of the same physical processes (e.g., activation, cross-bridge kinetics, activation-cross bridge interaction), it is likely that the ejection-mediated effects on relaxation are also variable.

Although many experiments have been performed to elucidate the determinants of relaxation speed, a quantitative description that unifies data from various ejection conditions is still lacking. The amount of ejection as well as the timings of the onset and end of ejection all seem to affect the speed of isovolumic relaxation (19, 20, 42). This dependence of relaxation speed on ejection has also been treated in terms of arterial system load (3, 27). A common observation has been that increasing ejection hastens relaxation (6, 14, 20). Recently, Tobias et al. (39) clarified the picture considerably for nonejecting conditions, finding that relaxation in isovolumically beating hearts is uniquely determined by the developed (active) stress such that relaxation is prolonged with increasing stress. Janssen and Hunter (25) have reported similar observations using an isolated cardiac muscle preparation. Thus it seems reasonable that any attempt to understand relaxation in normally ejecting hearts should start from and extend Tobias' observation.

Figure 1 contains an example of data from previous experiments (4) and shows left ventricular pressure (P_v) for steady-state ejection followed by isovolumic P_v. Data corresponding to three levels of peripheral resistance, resulting in a wide range of stroke volumes (SV), are shown. Clearly shown in Fig. 1A is that postejection peak isovolumic pressure increases with increasing SV (ejection-mediated positive inotropy). Figure 1B shows normalized active isovolumic P_v from the same data. With the data in this form, it is clear that increased SV, either directly or indirectly through its effects on increasing peak isovolumic pressure, or both, also leads to longer relaxation times in the subsequent isovolumic beats. It is this observation that led us to the hypothesis that ejection can also slow relaxation (i.e., ejection has a positive effect on relaxation). Thus we designed a new set of experiments, using isolated rabbit hearts, to test the hypothesis that ejection can have both negative and positive effects on relaxation. An attempt to quantify these phenomena in terms of the amount of ejection and load on the heart is presented. Finally, we discuss the possible mechanisms underlying the experimental observations, including the positive effect of ejection on relaxation, the new finding of the present study.

View larger version (16K): [in this window] [in a new window]   Fig. 1.   A: steady-state left ventricular (LV) pressure (Pv) for 3 levels of stroke volume (SV) followed by postejection isovolumic Pv at same end-diastolic volume. SV was altered by changing peripheral resistance (see text). Begin- and end-ejection times are denoted by  and , respectively. B: normalized isovolumic active Pv from data in A. Note that Pv appears to fall slower when previous steady-state SV is higher.

	METHODS

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All protocols were reviewed and approved by The University of Chicago Institutional Animal Care and Use Committee and conform with the Guide for the Care and Use of Laboratory Animals published by the National Institutes of Health [DHHS Publication No. (NIH) 85-23, Revised 1985, Office of Science and Health Reports, Bethesda, MD 20892].

Experimental Preparation and Isolated Heart Setup

A thin latex balloon, secured at the end of a piston-cylinder device, was positioned in the left ventricle via the mitral orifice. A thread tied to the end of the balloon was passed through the apex of the left ventricle to secure the balloon in the chamber. A purse string tied around the mitral orifice secured the heart to the piston-cylinder device attached to a linear motor. The piston position was sensed by a linear voltage displacement transformer. All hearts were paced using unipolar electrodes attached to the apex of the left ventricle. More comprehensive details of the isolated heart setup can be found elsewhere (4, 36).

Experimental Protocols

SBFS. In the SBFS protocol (Fig. 2A), the heart was allowed to beat isovolumically at a constant reference volume (V_ref) until it reached steady state, at which time the volume (V_v) was changed over a short period of time in late diastole. After several cardiac cycles occurred at this perturbed volume, V_v was changed back to V_ref. The P_v and V_v from two cardiac cycles were sampled: one steady-state cycle at V_ref and the other as the first beat after the volume change (the beat that will be analyzed). A full SBFS protocol consisted of 10-12 equispaced volume changes centered around V_ref. If an arrhythmia occurred during the data collection, for example, a mechanically induced premature contraction, the P_v-V_v pair was omitted from the analysis.

View larger version (29K): [in this window] [in a new window]   Fig. 2.   Examples of Pv and LV volume (Vv) from all 3 protocols. A: single-beat Frank-Starling (SBFS) protocol wherein Vv was changed incrementally during diastole to produce a range of passive (end-diastolic) and active Pv. Vref, end-diastolic reference volume. B: steady-state ejection (SSEJ) protocol wherein the heart was allowed to eject until steady state, at which time ejection was stopped. Steady-state ejection and postejection isovolumic beats were analyzed. 1, heart beat isovolumically at Vref until steady state; 2, heart was allowed to eject; 3, Pv and Vv were sampled at steady-state ejection; 4, ejection was halted and next 10 beats sampled; 5, every 3rd isovolumic beat sampled for a total of 10 more beats. C: transient ejection (TREJ) protocol wherein steady-state Vv time course (from SSEJ) was imposed for 1 beat. A model developed from SBFS and SSEJ protocols was used to predict relaxation in transient ejection. 1, heart beat isovolumically at Vref until steady state; 2, 1 transient ejection was then achieved by imposing Vej(t) obtained from SSEJ protocol. Pv and Vv from this beat were sampled.

SSEJ. In the SSEJ protocol, the real-time artificial arterial loading system controlled the instantaneous V_v (4). With reference to Fig. 2B, the following order of events was executed: 1) the heart beat isovolumically at V_ref until steady state; 2) the heart was allowed to eject into the artificial load that mimics the arterial system (4); 3) on reaching steady-state ejection (~45 s), P_v and V_v were sampled, and the steady-state ejection-volume time course [V_ej(t)] also was stored for use in the next protocol; 4) ejection was halted and the next 10 isovolumic beats were sampled; and 5) thereafter, every third isovolumic beat was sampled for a total of 10 more beats. Thus, over a period of 20 s, a total of 20 postejection isovolumic beats were sampled. These data were acquired for a range of SV as described in Data Collection.

TREJ. The TREJ protocol was similar to the SSEJ protocol, except that ejection was imposed using direct volume control. This protocol consisted of the following two steps (Fig. 2C): 1) the heart beat isovolumically at V_ref until steady state, and 2) one transient ejection was then achieved by imposing V_ej(t) obtained from the SSEJ protocol. P_v and V_v from this beat were sampled.

Data Collection

View larger version (9K): [in this window] [in a new window]   Fig. 3.   Schematic showing order of protocol execution for each heart. For a given Vref, an SSEJ-TREJ protocol pair was performed at 5 levels of peripheral resistance (Rs). These ejection protocols were flanked by SBFS protocols. This entire sequence of data acquisition was repeated for 3 values of Vref.

The range of R_s used in the ejection protocols was large and, together with different V_ref, resulted in a range of ejection fractions at similar SV. An entire series of ejection protocols (5 SSEJ-TREJ pairs) for a given V_ref took ~20 min to execute. The second SBFS protocol was performed so we could be sure that the condition of the heart did not degrade during this time. Thus the total experimental duration (3 V_ref values) was ~1 h. A total of five hearts were used.

Data Analysis

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View larger version (10K): [in this window] [in a new window]   Fig. 4.   LV active () and end-diastolic () pressure-volume relationships derived from an SBFS protocol. End-diastolic pressure-volume (Ped-Ved) relationship was fit to Eq. 1 as displayed (where , , and Vo are constants) and used later to calculate LV active pressure (Pact) from measured Pv (Eq. 2).

Left ventricular active wall stress () was estimated using a thick-walled spherical model

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where M_v and  are left ventricular muscle mass and density, respectively (13).

Isovolumic relaxation time (T_r) was characterized by T_r = T₂₅  T₇₅. For isovolumic beats, T₇₅ and T₂₅ are the times at which stress falls to 75 and 25% of its peak active stress (_max), respectively (Fig. 5) (39). For ejection beats, T_r was determined in a manner similar to that for the isovolumic beats, except that T₇₅ and T₂₅ refer to end-ejection stress (_ee) rather than _max (see Fig. 5B). The rationale for using _ee as a reference will be discussed later.

View larger version (15K): [in this window] [in a new window]   Fig. 5.   LV Pv (top) and Vv (bottom) for a steady-state ejection beat followed by a postejection isovolumic beat (A). Data were analyzed as follows. First, Pact was calculated using Eq. 2. Next, with assumption of a thick-walled spherical model, Pact and Vv were used to calculate active wall stress (B). From active stress, isovolumic relaxation time (Tr) was calculated for isovolumic beats as difference between times for active stress to fall to 75 (T75) and 25% (T25) of its maximum value. For ejection beats, Tr was similarly defined, except that reference stress was end-ejection stress. Tmax and Tee, Times for active stress to reach its maximum and end-ejection values, respectively.

As described by Tobias et al. (39), the left ventricular relaxation process for the isovolumic beats was characterized by relating T_r to _max. By extension, the relaxation process for the ejection beats was characterized by relating T_r to _ee. To determine the effects of ejection on relaxation, several indexes of ejection were quantified: SV, ejection fraction (EF = SV/V_ed), linear midwall (half-mass point) circumferential shortening (stroke) length (SL), and linear midwall shortening fraction (SF). Again, assuming a thick-walled sphere where L is the linear midwall (half-mass point) circumferential length and L_ed and L_ee are its end-diastolic and end-ejection values, respectively.

Multiple regression analysis was used to evaluate the determinants of T_r. The regression model was developed in a stepwise manner, incorporating additional independent variables as data from the different protocols were combined. All regression analyses were performed with SigmaStat, version 1.0 (Jandel, San Rafael, CA). In some ejection beats from the SSEJ and TREJ protocols, T₂₅ was difficult or impossible to determine. This occurred only for ejections with very large ejection fractions (very low R_s) and was attributed to noisy pressure signals due either to abnormal early rapid filling or transducer contact with the endocardium, or both. Data from such beats were not used in the analysis.

	RESULTS

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Data from the three protocols were used in a stepwise manner to develop a unified analytical framework that describes isovolumic relaxation. We will show this development in detail for one heart, the results of which are representative. For the remaining four hearts, results are presented for the final model only.

Relaxation in Isovolumic Beats

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View larger version (11K): [in this window] [in a new window]   Fig. 6.   A: relationship between Tr and peak active stress (max). Data are from 6 SBFS protocols from a single heart, 2 at each of 3 Vref values. Solid symbols are reference Tr-max points (i.e., at Vref), 2 for each Vref. B: data from A were converted to Tr and by subtracting appropriate reference Tr and max values from each point (see text). Tr- relationship was fit well by a 2nd-degree polynomial (Eq. 4) and used as a nomogram.

Relaxation in Steady-State Ejection Beats

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View larger version (14K): [in this window] [in a new window]   Fig. 7.   Steady-state ejection beat Tr- data from SSEJ protocols. Tr- nomogram (SBFS protocol) from Fig. 6B is superimposed to facilitate comparison. Note that all ejection beat Tr- points fall below nomogram, and, as SV is reduced, ejection beat Tr- point approaches reference Tr- point (i.e., origin) indicated by dotted lines. Regression model in Eq. 5 described this data set well.

We analyzed alternative independent variables to quantify ejection (e.g., SV, EF, SL) in place of SF. Although the model fits were all good (r² > 0.94), SF appeared to be slightly superior: residual sum of squares was lowest with SF in four of five hearts. Moreover, using more than one independent variable for ejection did not improve the model-based fits.

Relaxation in Postejection Isovolumic Beats

View larger version (16K): [in this window] [in a new window]   Fig. 8.   Tr- data from 1st postejection isovolumic beats. Data from Fig. 7 are superimposed to facilitate comparison. All Tr- points from 1st postejection isovolumic beats fell above nomogram (SBFS protocol). Similar to steady-state ejection beats, postejection isovolumic Tr- points approach reference Tr- as SV becomes smaller. Full regression model in Eq. 10 fit this entire data set well.

Dynamics of Positive Effect of Ejection on Relaxation

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View larger version (16K): [in this window] [in a new window]   Fig. 9.   Time course of recovery of max and Tr in isovolumic beats following steady-state ejection. Data are from 4 combinations of Ved and SV.

View larger version (21K): [in this window] [in a new window]   Fig. 10.   Time course of recovery of normalized excess Tr (see text) in a single heart for several combinations of Ved and SV. Data were fit to a monoexponential; beat constant (b) for this example was 4.14 (or ~2 s).

To describe quantitatively the dynamics of the positive effect of ejection, we assumed the following. 1) Because the positive effect dissipates slowly, its onset is also slow. In other words, both the onset and dissipation of the positive effect depend on the history of ejection. 2) Like dissipation, the onset time course follows a first-order process. 3) The steady-state value of the positive effect () is proportional to the amount of ejection, i.e., SF. Thus the positive effect for beat n (_n) can be written as

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where _bd and _bo are the dissipation and onset beat constants, respectively, and _n  1 is the value of the positive effect of the previous beat. The first term in Eq. 7 is the dissipation of the existing positive effect, and the second term is the additional positive effect due to current beat ejection. In the following analyses, we assumed that _bd = _bo and that this common value is given by _b (Eq. 6; Table 2). Thus the steady-state value of  is given by

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where the subscript ss denotes steady state. For the special case of steady-state isovolumic contractions (SF_n = SF_n  1 = SF_ss = 0), Eq. 7 reduces to _n = _n  1  0.

Relaxation in Steady-State Ejection and Isovolumic Beats: A Unified Description

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Data from SBFS and SSEJ protocols consist of three special cases of Eq. 9: 1) for steady-state isovolumic beats (SBFS protocol), SF_n = 0 and _n  1 = 0; 2) for steady-state ejection beats (SSEJ protocol), SF_n = SF_ss and _n  1 = _ss = b₄SF_ss; and 3) for the first isovolumic beat after steady-state ejection, SF_n = 0 and _n  1 = _ss = b₄SF_ss. When considering these three cases only, the general description in Eq. 9 reduces to

(10)

where D₃ and D₄ are dummy variables given by Comparing Eq. 10 to Eq. 5, we see that a₃ emerges as the sum of b₃ and b₄ for steady-state ejection. This final regression model described well the entire data set from protocols SSFS and SSEJ (r² = 0.99). Again, coefficients a₁ and a₂ retained their values (Table 1). Coefficient b₃ had a negative value, indicating a negative effect on relaxation due to the current beat ejection. In contrast, coefficient b₄ had a positive value, indicating a positive effect on relaxation due to the steady-state (history of) ejection. Coefficient b₃ had a larger negative value compared with a₃ (0.300 vs. 0.176), whereas the sum of b₃ and b₄ was equal to a₃; thus regression Eqs. 5 and 10 yielded quantitatively consistent results for steady-state ejection beats, and the net effect of steady-state ejection on relaxation was negative. Lastly, the magnitude of the b₄-to-b₃ ratio was 0.473, meaning that in this heart, the positive effect of ejection on relaxation was 47% as strong as the negative effect.

Once again, the use of any other independent variable to quantify ejection in place of SF yielded the same quantitative results. That is, whereas values of the coefficients that relate ejection to T_r (b₃ and b₄) varied in absolute magnitude, the following was always true: b₃ < 0 and b₄ > 0, and the positive-to-negative ratios (i.e., b₄/b₃) were similar.

Table 2 contains coefficient values for the final regression model (Eq. 10) along with their errors and coefficients of determination for all hearts. In every case, the regression model fit the data well (r²  0.98) and all coefficients were statistically significant. Furthermore, b₃ was always negative and b₄ was always positive. The positive-to-negative coefficient ratio was also consistent between hearts, ranging from 44 to 54% (Table 2).

Prediction of Relaxation Times for Transient Ejection Beats

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View larger version (17K): [in this window] [in a new window]   Fig. 11.   Tr- data for transient ejection beats (TREJ protocol). Data from Fig. 8 are superimposed to facilitate comparison.

View larger version (12K): [in this window] [in a new window]   Fig. 12.   Predicted vs. measured Tr for transient ejection beats (TREJ protocol). Parameters of regression model (Eq. 10) were first estimated using data from SBSF and SSEJ protocols and then used to predict Tr of transient ejection beats (Eq. 11).

	DISCUSSION

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The major finding of this study is that ejection has both a negative and a positive effect on the rate of fall of left ventricular pressure during the isovolumic relaxation phase and that the negative effect dominates. In this section we will discuss first the rationale for this conclusion, which is qualitative and does not depend on any of the models developed above. Next, we will discuss our attempt to quantify the phenomena on the basis of muscle load and shortening. Last, we will discuss our results in the light of previous studies and consider the possible underlying mechanisms.

Interpretation of T_r-_max and T_r-_ee Relationships

This argument applies only to isovolumic beats. When relaxation is compared between isovolumic and ejection beats, _max is not a good index for muscle load at end systole in the ejection beats. We chose instead end ejection as a landmark in the ejection beats for several reasons. First, we wanted to refer to some load on the cardiac muscle in the early phase of relaxation. In isovolumic beats, _max occurs at end systole and is the appropriate choice. In ejection beats, _max occurs long before end systole and this time is highly dependent on arterial system load. Furthermore, it is possible that if _max occurs early enough, the T₇₅-T₂₅ interval could begin before end ejection; such T_r measurements would not be a proper index of isovolumic relaxation. Thus _ee, which occurs very near end systole, is the appropriate and practical choice. Second, if we consider the isovolumic contraction to be a special case of ejection (i.e., SV = 0), then the transition from ejection to isovolumic beats (i.e., SV  0) will force end systole, _max, and _ee to occur at the same time (see Fig. 5B). Thus the analyses of isovolumic and ejection beats are consistent with each other. With these criteria in mind we may now interpret and compare the results from the different protocols.

Qualitative Analysis of Data from SBFS and SSEJ Protocols

Because of positive inotropic effect, the first postejection isovolumic beat would have increased _max. If ejection only hastens relaxation (i.e., negative effect), we would expect that the T_r- point from the first postejection beat would lie to the right of the reference T_r- either 1) on the nomogram or 2) below the nomogram. The first case would mean that any negative effect on relaxation is short-lived and is only present in the ejection beat. The second case would indicate that the negative effect on relaxation persists and will disappear gradually. We see from Fig. 8 that neither of these expectations are met; the first postejection isovolumic T_r- points all lie above the nomogram, which indicates a positive effect on relaxation. The amount of this positive effect is directly related to SF (Figs. 1 and 8) and dissipates relatively slowly as evidenced by the values of _b (Table 2). At this time we can conclude that in addition to the negative effect on relaxation observed in steady-state ejection, a positive effect of ejection exists. It is logical to assume that these two competing effects are present simultaneously in the ejection beats (with the negative effect dominating). The positive effect is unmasked in the postejection isovolumic beats because the negative effect is fleeting. This positive effect of ejection on relaxation has not been observed until now, and we have attempted to incorporate this phenomena into a more complete quantitative understanding of relaxation in the ejecting heart.

Quantitative Analysis

One would also predict that if both positive and negative effects of ejection on relaxation exist, they should be present simultaneously in the steady-state ejection beats. In other words, regression coefficient a₃ from Eq. 5, the coefficient relating T_r to SF, should contain information on both the positive and negative effects. This is revealed to be true in the full regression model (Eq. 10), where the sum of coefficients b₃ and b₄ is equal to a₃. If only steady-state ejection beat data were presented, the positive effect could not be identified. That the magnitude of b₃ is greater than that of b₄ is also consistent with the net negative effect found in the steady-state ejection beats; the negative effect dominates. Because both b₃ and b₄ linearly relate the amount of shortening to the speed of relaxation, their ratio represents their relative influences on T_r. The b₄-to-b₃ ratio for the five hearts was 0.45 ± 0.04 (mean ± SD), which demonstrates that, although the negative effect always dominates during ejection, the positive effect is not insignificant. Given these quantitative results, we feel that we were able to identify definitively both the negative and positive effects of ejection on isovolumic relaxation.

The final model (Eq. 9), developed to some extent on an ad hoc basis, yielded excellent descriptive fits to experimental data. However, the prediction of T_r in transient ejection beats, which were not used in the regression analysis, was quite good (r² = 0.80 for all hearts combined). This prediction of an independent data set further establishes the validity of the model.

Possible Sources of Error

View larger version (12K): [in this window] [in a new window]   Fig. 13.   A: LV (passive) Ped-Ved relationship obtained using SBFS protocol (see Fig. 2A) at 3 levels of coronary perfusion pressure (Pcor). As Pcor was raised, LV passive pressure increased, especially at higher volumes. B: relationship between LV isovolumic Tr and max was not affected by changes in Pcor.

A second potential source of error is our assumption that left ventricular shape is spherical for all volumes. Given that different geometries yield different stresses for any pressure-volume pair, this assumption can affect stress calculations in two ways. First, when volume changes, as during ejection or in SBFS protocol, the shape could change (17, 30). Second, even during isovolumic conditions, the shape of the ventricle is known to change. Shape changes during isovolumic relaxation will alter the time course of stress, affecting T_r calculations. Thus we would like to be certain that our assumption of spherical chamber does not impact on the results so as to render the observed phenomena artifactual.

The positive effect of ejection on relaxation was deduced by comparing the _max-T_r data for steady-state isovolumic and postejection isovolumic beats. Olsen et al. (30) have shown unique volume-shape relationships for diastole and systole, independent of loading conditions (i.e., different preloads and ejection patterns). Thus, because left ventricular volume was the same for the two isovolumic conditions, it is reasonable to conclude that they have the same chamber shape and shape change during relaxation. Consequently, more realistic assumptions regarding left ventricular geometry will not eliminate the positive effect.

For the net negative effect during ejection beats to be artifactual, stress would have to be overestimated by ~50% (moving the T_r-_ee point too far right) or T_r would have to be underestimated by ~15% (moving the T_r-_ee point too far down), or some combination of both. Regarding the first possibility, due to ejection-mediated effects on inotropic state, an ejection beat with _ee equal to _max of an isovolumic beat can have a different V_v throughout the isovolumic relaxation period (7, 37). However, the differences in V_v in our data at common levels of stress are very small (< 5%). Therefore, errors in stress estimation due to volume-induced shape differences between isovolumic and ejection beats are expected to be insignificant. For the second possibility to have an impact, one would have to postulate that the left ventricular shape change during relaxation is significantly slower in the ejection beat compared with that in the isovolumic beat. Existing data (17, 30, 31), although not from experimental conditions precisely the same as ours (especially controlled V_ed and heart rate), do not support this postulate. From these considerations we are confident that more realistic assumptions regarding the geometry of the left ventricle will not eliminate the net negative effect during ejection beats.

It is acknowledged that other sources of error may exist. For example, differences in behavior exist between blood-perfused and crystalloid-perfused hearts. However, these differences are mostly quantitative, and therefore the existence of the positive effect of ejection on relaxation, the new finding of this study, is not likely to be an artifact of the crystalloid perfusion.

Comparison With Previous Studies

Sys and Brutsaert (38), using cat papillary muscle, and de Tombe and Little (11), using rat trabeculae, related relaxation to muscle length and reported that relaxation time constant was directly proportional to end-systolic length in both isometric and shortening contractions. Given that the peak active stress in an isometric contraction is directly related to the end-systolic length over the physiological range, this observation is consistent with our data. However, de Tombe and Little (11) found that the relationship between relaxation time constant and end-systolic sarcomere length was the same for isometric and shortening contractions. This is inconsistent with our observations that the relaxation process is quite different between ejection and isovolumic beats at common end-systolic stress (which is very nearly the same as common end-systolic volume). Although we cannot definitively identify the reasons for this discrepancy, possibilities include species difference (rat vs. rabbit), specifics of the loading protocol (e.g., sarcomere length vs. ventricular volume control), and analysis of data (grouped vs. individual experiment).

Investigators also have focused on ejection pattern as determining relaxation rate. For example, Hori et al. (19, 20) found, in isolated dog hearts, that for constant SV and EF, delays in end-ejection time increased the speed of relaxation. In contrast, they found that changes in the begin-ejection time did not affect relaxation. Although we did not include these timing aspects of ejection in the analysis, they are unlikely to affect our conclusions for the following two reasons. First, reducing R_s to increase SV (SSEJ protocol) resulted in a marked earlier begin-ejection time, with almost no effect on end-ejection time (Fig. 1). This is so because reducing R_s yields much lower end-diastolic aortic pressures (2). Second, although a given transient ejection beat had an identical ejection pattern to a steady-state ejection beat, the transient beat relaxed faster. However, it is possible that, had the protocols further uncoupled SV from begin- and end-ejection times, the end-ejection time would emerge as an independent determinant of isovolumic relaxation in ejection beats; such protocols are under development.

That ejection exerts a positive inotropic effect has been demonstrated by others, both at the muscle (1, 26, 32, 33) and the ventricular (7, 22, 37) level. These studies indicate that ejection-mediated changes in inotropic state are better described by the relative amount of ejection (e.g., EF) (7, 37). In contrast, different measures of ejection described the positive effect of ejection on relaxation equally well in the present study. Because T_r is so strongly dependent on _max (or _ee), it is possible that the ranges of V_ref and R_s used did not sufficiently uncouple absolute amounts of ejection (SV or SL) from relative amounts (EF or SF).

Potential Mechanisms for Effects of Ejection on Relaxation

With regard to the positive effect of ejection on relaxation, increased inotropic state combined with slower relaxation observed in the postejection isovolumic beats is curious, because positive inotropic agents that mobilize intracellular Ca²⁺ (e.g., -agonists, sympathetic stimulation, phosphodiasterase inhibitors, digitalis-like compounds) hasten relaxation (8, 14, 16, 29). Conversely, conditions that typically prolong relaxation are also negative inotropes (e.g., -antagonists, hypocalcemia) (14, 43).

It was shown long ago (26, 32) that peak tension in isometrically contracting muscle strips immediately following shortening is larger than that of a steady-state isometric contraction at the same length. This phenomena demonstrates a dependence of contraction on the history of shortening. Series-coupled viscoelasticity was suggested as a possible mechanism (32). Although series-coupled viscoelasticity can, in principle, yield higher postejection peak isovolumic pressures (any mechanism that increases the end-diastolic contractile element length will do this), the decay of postejection _max, T_r, and excess T_r appears too slow to be explained by series- or parallel-coupled viscoelastic behavior (monoexponential time constants on the order of seconds, Figs. 9 and 10). For example, using isolated rat trabeculae at 25°C, de Tombe and ter Keurs (12) determined that the time constants for series and parallel viscoelasticity were ~6 ms and 100 ms, respectively. Similar findings for cat papillary muscle were reported by Chiu et al. (10).

Recent experimental studies have shown that the positive inotropic effect of ejection is a property of cardiac muscle, perhaps related to the effects of ejection on myofilament interaction with cytosolic free Ca²⁺ (11). These experiment-based inferences are supported by the model-based study of Landesberg (28). It is tempting to postulate that the positive effect of ejection on relaxation also has its basis at the muscle level and is related to the positive inotropic effect. One possible mechanism could be ejection-induced increased Ca²⁺ sensitivity. Tobias et al. (40) recently showed that the Ca²⁺ sensitizer EMD-57033 acted to increase T_r greater than would be expected due to increased _max alone (similar to excess T_r in our postejection isovolumic beats). Furthermore, _max and excess T_r were augmented by similar amounts. We too find that both excess T_r and _max were augmented by 8-10% (depending on the amount of ejection) in the immediate postejection isovolumic beats. Therefore, our results are consistent with the hypothesis that the positive effects of ejection on ventricular relaxation are mediated via increased myofilament Ca²⁺ sensitivity. That postejection excess T_r and _max decay at different rates (Figs. 9 and 10) could indicate that some intermediate mechanism links the two and that this intermediary has different dynamic relationships between inotropic state and relaxation. Given the mechanisms for the negative effect described here, ejection might have a dual effect on myofilament Ca²⁺ sensitivity and the physical transducers for the positive and negative effects must be distinct. The specific molecular mechanisms linking the mechanical event of shortening to changes in Ca²⁺ sensitivity remain unknown.