INTRODUCTION

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ABNORMALITIES OF MYOCARDIAL total Ca²⁺ handling in postischemic stunning (4, 8, 19-21, 23, 24, 26, 34, 40, 41) remain to be elucidated at the beating whole heart level. We have found that postischemic myocardial stunning halved left ventricular (LV) contractility [end-systolic maximum elastance (E_max) (33)] in the excised cross-circulated canine heart (19). The stunning, however, slightly decreased LV O₂ consumption (VO₂) for excitation-contraction (E-C) coupling, doubling the O₂ cost of E_max (19, 30, 31). In this respect, postischemic stunning resembles acidosis, postacidotic stunning, and ryanodine treatment of the heart (9-11, 37), contrasting with ordinary negative inotropism (3, 17, 30, 32, 38). We previously speculated (19) that the doubled O₂ cost of E_max would be a manifestation of energy-wasteful Ca²⁺ handling in stunning. Although subcellular evidence (4, 8, 20, 26, 34, 40) supports our speculation indirectly, it should be verified or quantified at the whole heart level.

We hypothesized that the following three mechanisms could account for the energy-wasteful Ca²⁺ handling in postischemic stunning: first, a decreased internal Ca²⁺ recirculation fraction; second, some futile Ca²⁺ cycling via the sarcoplasmic reticulum (SR); and third, a decreased Ca²⁺ reactivity of E_max (11, 12, 14, 27, 35). As the internal Ca²⁺ recirculation fraction (RF) decreases, a greater fraction of total Ca²⁺ must be handled by the transsarcolemmal route, whose Ca²⁺ handling primarily via the Na/Ca²⁺ exchange is one-half as economical as internal Ca²⁺ handling via the SR Ca²⁺ pump (5-7, 22, 29, 36). As the futile Ca²⁺ cycling via the SR occurs, part of the Ca²⁺ that was once released and then sequestered via the SR would be released and sequestered again within the same cardiac cycle, leading to extra ATP consumption without contributing to contractility (6, 36). As the Ca²⁺ reactivity to E_max decreases, total Ca²⁺ transport (or flux) must be increased for the same E_max, or the same total Ca²⁺ transport can develop a smaller E_max (27). Therefore, any of these changes in total Ca²⁺ handling could account for an increased ATP and VO₂ to achieve a given contractility. The present hypothesis became testable in a beating LV by taking advantage of our recently proposed integrative method (27).

To this end, we analyzed the postextrasystolic potentiation (PESP) cases recorded in the original pressure tracing (19) to calculate RF in the same way as in our previous studies (2, 11, 12, 14, 15, 27, 28, 35). We neglected all these tracing parts contaminated by the PESP in our previous study (19), in which the mechanoenergetics analyses required stable LV contractility and the utility of the PESP in cardiac mechanoenergetics had not been recognized. After the present analysis, we found a significantly decreased RF in the canine stunned heart. By combining this newly obtained RF with the original mechanoenergetics (E_max and VO₂) data (19), we found a considerable shift of the relation between futile Ca²⁺ cycling and Ca²⁺ reactivity of E_max in an energy-wasteful direction in stunning. These findings for the first time account for the characteristic cardiac mechanoenergetics in stunning, supporting our hypothesis.

	METHODS

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Heart preparation. Adult mongrel dogs (12-19 kg) were anesthetized with pentobarbital sodium (30 mg/kg iv). Ten excised cross-circulated hearts were prepared (19) as usual (3, 9, 10, 17, 30-32, 37, 38) in accordance with institutional animal care and experiment guidelines. Briefly, the heart was excised from an open-chest dog under cross-circulation with a support dog without stopping coronary circulation during surgery. The heart was kept at 36°C and paced left atrially at 150 beats/min. A flabby balloon (unstretched volume 50 ml) was fitted into the LV, filled with water, and connected to our custom-made volume-servo-pump (AR Brown, Osaka, Japan) to precisely control and accurately measure LV volume. The mode of LV contraction was either isovolumic or ejecting with a stroke volume of 3-10 ml. LV pressure was measured with a Konigsberg P-6 miniature pressure gauge inside the balloon. Pressure and volume signals were processed using a computer. Coronary flow was measured with an electromagnetic flowmeter in venous cross-circulation. Coronary arteriovenous O₂ content difference was measured with a custom-made analyzer (PWA-200S, Shoei-Technica, Tokyo, Japan). Cardiac VO₂ per minute was calculated as the product of coronary flow and coronary arteriovenous O₂ content.

Mechanoenergetics. We utilized LV mechanoenergetics data [E_max, pressure-volume area (PVA), and VO₂] in the control state before stunning and in the stunned state in the same heart group, as documented in details in the original paper (19). We also provided a sham group to compare the mechanoenergetics between the stunned and nonstunned hearts in the same time period (19). E_max is the end-systolic pressure-volume (P-V) ratio that Suga et al. (33) developed as a relatively load-independent index of LV contractility in the canine heart. E_max has been used for over a quarter of a century in many whole heart studies (3, 9, 10, 17, 19, 24, 30, 31, 32, 37, 38). The end-systolic P-V points lined up linearly over the fully tested range of LV volume in stunned hearts as well as in controls (19). To obtain LV E_max, LV end-systolic unstressed volume (V₀) was first determined as the volume at which peak isovolumic pressure was zero (19). E_max was then determined as the slope of the line connecting V₀ and the P-V point at the left upper shoulder of each P-V trajectory on the computer (Fig. 1A) (19).

View larger version (35K): [in this window] [in a new window]   Fig. 1.   Schematic illustration of mechanoenergetics framework and total Ca2+ handling. A: left ventricular (LV) pressure-volume (P-V) diagram. Emax, end-systolic maximum elastance equal to slope of end-systolic P-V relation (ESPVR) connecting left upper shoulder of P-V loop and V0 (unstretched volume at which end-systolic pressure is 0); PVA, P-V area equal to total mechanical energy consisting of external work (EW; area within P-V loop) and potential energy (PE; triangular area under ESPVR). B: cardiac O2 consumption (VO2)-PVA relation (solid line) with slope  (O2 cost of PVA) at constant Emax. VO2 consists of PVA-dependent fraction for cross-bridge (CB) cycling (area above dashed line at VO2 intercept ) and PVA-independent fraction for total Ca2+ handling (area between dashed and dotted lines) and basal metabolism (area under dotted line). Namely, total Ca2+ handling VO2 =   basal metabolism. C: VO2-PVA relation elevating with increasing Emax and , keeping O2 cost of PVA () constant. Heavy arrow indicates inotropism run. D: increased O2 cost of Emax () as slope of PVA-independent VO2 () vs. Emax relation in direction of leftward arrow. Therefore, total Ca2+ handling VO2 =   , where  is basal metabolism. E: large arrows represent internally recirculating, transsarcolemmally extruded, and futilely cycling Ca2+ in myocardium. SR, sarcoplasmic reticulum; SL, sarcolemma; R, Ca2+ reactivity of Emax; RF, internal Ca2+ recirculation fraction; 1  RF, Ca2+ extrusion fraction; N, number of futile Ca2+ cycles relative to and in excess of normally 1 cycle via SR.

Postextrasystolic potentiation. The new data obtained in the present study from the original tracing (19) are explained below. Spontaneous supraventricular and ventricular extrasystoles occurred sporadically in both control and stunning in all experiments (19), as shown in Fig. 2. The extrasystole was always followed by a compensatory pause under constant atrial pacing, and the PESP decayed in alternans (19) as usual (2, 11, 12, 14, 15, 27, 28, 35). The servo-pump kept constant either LV volume in isovolumic beats or both end-diastolic and end-systolic volumes, and hence stroke volume, in ejecting beats during each PESP. All PESPs of the transient alternans type were retrieved. From each PESP, we obtained E_max values of the regular beat and the first through sixth postextrasystolic beats (PES1-PES6). Here, we assumed that V₀ remained unchanged during the PESP, as in our previous studies (2, 11, 12, 14, 15, 27, 28, 35). The alternating E_max values of PES1-PES6 were normalized relative to the E_max of the regular beat, as was done previously (2, 11, 12, 14, 15, 27, 28, 35).

View larger version (37K): [in this window] [in a new window]   Fig. 2.   Representative examples of transient alternans type of postextrasystolic potentiation in an isovolumically contracting stunned LV (A) and an ejecting stunned LV (B). LVP, LV pressure; LVV, LV volume; ECG, LV epicardial electrocardiogram; Rg, regular beat; ES, extrasystole; PES1-PES6, 1st-6th postextrasystolic beats.

Curve fitting. Table 1 lists all the necessary equations that we recently developed (27) and used in the present study. Their details were described in our previous paper (27). We have already shown that Eq. 1 (Table 1) fits all PESP decay patterns, whether alternans or monotonic, in canine hearts under normal as well as various enhanced and depressed contractile states (11, 12, 14, 15, 27, 28, 35). The first term of Eq. 1 represents either an exponential decay component of the alternans PESP decay or the entire monotonic PESP decay. The second term represents an exponentially decaying sinusoidal component, which does not exist in the monotonic PESP decay (28). To normalize E_max values in each transient alternans PESP, we fitted Eq. 1 to obtain best-fit decay beat constants (in number of beats) of the first (_e) and second (_s) exponential terms, respectively, as explained in detail previously (11, 12, 14, 27, 28, 35). We used DeltaGraph 4.0 (Delta Point, Monterey, CA) for least-squares fitting. The coefficient of determination (r²) served as an indicator of goodness of fit.

Recirculation fraction. We calculated internal Ca²⁺ RF from _e using Eq. 2 (Table 1) (11, 12, 14, 27, 28, 35). Equation 2 is essentially the same as the equation that Morad and Goldman (16) originally developed for monotonic PESP decay on the basis of their total Ca²⁺ handling model. Other investigators (18, 25, 39) used it before we did (11, 12, 14, 27, 28, 35). In Eq. 2, the numerator 1 means one beat, and hence 1/_e is a dimensionless fraction of one beat interval relative to _e. Therefore, exp (1/_e) indicates the exponential decay rate of PESP within one beat.

Futile Ca²⁺ cycling. The Ca²⁺-leaky SR in stunning may release part of the once sequestered Ca²⁺ (20, 26, 36, 40). Reuptake of this extra released Ca²⁺ requires additional ATP, although it does not directly contribute to contractility. We designated this extra Ca²⁺ release and removal as futile Ca²⁺ cycling (27). The SR will consume more ATP as the futile Ca²⁺ cycling increases, even if the internally recirculating Ca²⁺ remains the same. We quantified the number (N) of futile Ca²⁺ cycles relative to and in excess of the presumably single cycle of Ca²⁺ release and uptake via the normal SR (i.e., N = 0) (27). The shaded loop (N · RF) in Fig. 1E represents the futile Ca²⁺ cycling.

Total Ca²⁺ handling and transport. Equation 3 (Table 1) yields ATP for total Ca²⁺ handling (in µmol/kg wet myocardium) as a function of total Ca²⁺ transport, RF, and N (27). It sums the amounts of Ca²⁺ handled or transported internally and transsarcolemmally, as conceptually modeled in Fig. 1E. Because we defined the futilely cycling Ca²⁺ to be part of the recirculating Ca²⁺, it is part of total Ca²⁺ transport. Therefore, Eq. 3 is the most basic equation for combining total Ca²⁺ transport and its energetic demand with both RF and N as parameters in the total Ca²⁺ handling model (27).

Ca²⁺ reactivity of E_max. To obtain total Ca²⁺ transport and N, both unknown until Eq. 7, we adopted our previously introduced index (R), defined by Eq. 8 (27). R is the reactivity of E_max to total Ca²⁺ handled in the E-C coupling, abbreviated to Ca²⁺ reactivity of E_max or simply Ca²⁺ reactivity (27). R differs from the conventional Ca²⁺ sensitivity of troponin C and Ca²⁺ responsiveness of contraction because that Ca²⁺ refers to free Ca²⁺ concentration rather than the total Ca²⁺ transport, our present interest (5, 7, 29). R incorporates not only the Ca²⁺ sensitivity and Ca²⁺ responsiveness but also the force-transmission system from cross-bridge cycling to E_max through various cytoskeletons and extracellular matrices (21, 34). Substituting R into Eq. 7 yields Eq. 9, which has total Ca²⁺ handling VO₂ as a variable.

N-R relation. Equation 9 describes N as a linearly increasing function of R with Ca²⁺ handling VO₂, E_max, and RF as known parameters. We obtained the N-R relations for control and stunning. Any difference in the two N-R relations quantifies the difference of the total Ca²⁺ handling dynamics as a whole, but not in terms of N and R individually. However, once either N or R was determined or assumed, we could obtain the other from the given N-R relation and finally calculate total Ca²⁺ transport from total Ca²⁺ handling VO₂, RF, and N using Eq. 5.

Statistics. We used one-way ANOVA for significant differences in the best-fit parameters and RF among the four groups (isovolumic and ejecting contraction in each control and stunned heart; Table 2). These data were not obtained in a paired manner. When ANOVA was significant (P < 0.05), we performed multiple comparison with the Student-Newman-Keuls test, using StatView 5.0 (Abacus Concepts).

	RESULTS

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Figure 2 shows transient alternans PESPs in isovolumic (Fig. 2A) and ejecting (Fig. 2B) contractions in stunned hearts. All PESPs during control and stunning decayed in transient alternans, resembling our previous findings (2, 11, 12, 14, 15, 27, 28, 35). The alternating peak isovolumic LV pressures at a fixed volume in the isovolumic contractions indicate the changes in E_max values of the PES1-PES6. The alternating end-systolic pressures at a fixed end-systolic volume in the ejecting contractions also indicate the changes in E_max values of the PES1-PES6. In all the PESP cases analyzed, we confirmed that the compensatory pause between the extrasystole and the first postextrasystolic beat (PES1) was a prerequisite to the emergence of the transient alternans PESP.

Figure 3 compares best-fit curves to transient alternans PESPs in control (Fig. 3A) and stunning (Fig. 3B). The solid curve was best fitted to data points of the alternating PES1-PES6 in each case. r² was very close to unity in both control and stunning. In Fig. 3, the solid curve represents the sum of an exponential component, shown by the dotted curve, and a sinusoidal component, whose exponential term is shown by the dashed curve (Eq. 1). Stunning markedly shortened _e from control but hardly changed _s. The RF value calculated from _e using Eq. 2 was smaller in stunning.

View larger version (19K): [in this window] [in a new window]   Fig. 3.   Representative curves best fitted to data points of transient alternans type of postextrasystolic potentiation (PES1-PES6) in control (A) and stunning (B). Ordinate indicates normalized contractility relative to regular-beat contractility. Solid curve indicates best-fit Eq. 1 in Table 1. Dotted curve indicates exponential decay component (e) of best-fit Eq. 1. Dashed curve indicates exponential term of sinusoidal decay component (s) of best-fit Eq. 1. Both dotted and dashed curves were drawn on unity lines.

We obtained _e values from 85 PESPs resembling these representative cases. RF values were then obtained from these 85 _e values using Eq. 2. The goodness of fit was always excellent with r² = 0.996 ± 0.007 (mean ± SD). This means that Eq. 1 could account for as much as 99.6% on average of the transient alternans contractility of the PESP.

Table 2 lists values of E_max, Ca²⁺ handling VO₂, the best-fit parameters a, _e, b, _s, and r², and the resultant RF, N, R, and total Ca²⁺ transport as well as its internal and external components in isovolumic and ejecting beats in control and stunning. Of these, E_max and Ca²⁺ handling VO₂ were transcribed from the previous paper (19). On average, _e decreased significantly by 46%, and hence RF decreased significantly by 32% with stunning regardless of contraction modes. Although the number of PESP cases from which RF values were obtained was small in control, the obtained _e and RF values were comparable to those in our previous studies (11, 12, 14, 27, 28, 35). Stunning slightly decreased _s, though not significantly. The present Ca²⁺ handling analysis did not need _s or the dimensionless best-fit parameters a or b, although they are listed.

Figure 4 shows the N-R relations in control and stunning that were obtained by substituting the mean values for total Ca²⁺ handling VO₂, E_max, and RF as listed in Table 2 into Eq. 9. The N-R relations for isovolumic and ejecting contractions were virtually superimposable on each other; they are mathematically linear. The stunning N-R relation was markedly elevated from the control N-R relation. In addition to the decreased RF, this elevation characterized an energy-wasteful total Ca²⁺ handling in stunning as explained below.

View larger version (25K): [in this window] [in a new window]   Fig. 4.   Comparison of futile Ca2+ cycling vs. Ca2+ reactivity of Emax (N-R) relations between control and stunning. Solid lines indicate isovolumic contractions; dashed lines indicate ejecting contractions. Encircled numbers indicate working points, and arrows indicate different N-R combinations. Working point 1 is the most likely control working point. Working point 2 is one extreme case of stunning working point with same R as working point 1 but with an increased N (>0). Working point 4 is the other extreme case of stunning working point with the same N = 0 as working point 1 but with a decreased R. Working point 3 is an example working point in stunning with a decreased R and a simultaneously increased N.

Each N-R relation allowed infinite possibilities of N-R combinations. Once we knew or assumed either N or R, we could obtain the other variable (R or N, respectively) graphically from the N-R diagram or numerically from Eq. 9. The highest possibility in control would be N = 0 (Fig. 4, working point 1). N = 0 on the control N-R relation yielded R = 0.126, as shown by working point 1 in Fig. 4 and Table 2. Substituting this N-R combination into Eq. 6 yielded total and then recirculating and extruded Ca²⁺ in control (Table 2, working point 1).

We could also obtain various N-R combinations on the single stunning N-R relation in Fig. 4. Assuming the same value R = 0.126 (working point 1) as that used for the control yielded N = 1.22 (working point 2) on this stunning N-R line. However, assuming the same N = 0 (working point 1) as used for the control yielded R = 0.095 (working point 4) on the same N-R line (Fig. 4 and Table 2). These two N-R combinations (working points 2 and 4) on the same N-R line suggest the two extreme cases of the possible N-R combinations in stunning because it is unlikely that stunning increased R from the control value (1, 4, 8-10, 19, 26, 34). The R and N values in the range from working point 2 to working point 4 were characterized by the same R = 0.126 (working point 1) as the control or an R with a lesser value (<0.126) and by the same N = 0 (working point 1) as the control or an N with a greater value (>0). Therefore, except for these two extremes of the range from working point 2 to working point 4, the possible N-R combinations including working point 3 were characterized by a decreased R (<0.126) and an increased N (>0) in relation to the control. R decreased as working point 3 approached working point 4; and N increased as working point 3 approached working point 2.

Equation 10 expresses the O₂ cost of E_max as a function of R, N, and RF. This equation explicitly shows that the O₂ cost increases with a decrease in R, an increase in N, and a decrease in RF. Therefore, any combination of a subnormal R and a supernormal N on the stunning N-R relation (such as working point 3 between working points 2 and 4) would lead to an increased O₂ cost of E_max and, hence, an energy-wasteful total Ca²⁺ handling. Table 2 also lists the corresponding ranges of the calculated total, recirculating, and extruded Ca²⁺.

	DISCUSSION

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We succeeded in characterizing the increased O₂ cost of E_max in the stunned hearts in terms of the energy-wasteful total Ca²⁺ handling by using our recently developed integrative method (27). The main results that we obtained are 1) a decreased decay beat constant (_e) of the exponential decay component of the PESP, 2) a decreased internal Ca²⁺ recirculating fraction (RF), and 3) a shifted relation between the Ca²⁺ reactivity of E_max (R) and the futile Ca²⁺ cycling (N) in the direction of energy-wasteful total Ca²⁺ handling. These results evidently support our present hypothesis on the abnormal Ca²⁺ handling in the stunned heart (see Introduction). The physiological or integrative results of these systems have never been obtained in the beating whole heart level by any conventional myocardial Ca²⁺ analysis methods (6, 27).

Previously, we were only able to speculate that either Ca²⁺-leaky SR or decreased Ca²⁺ sensitivity and responsiveness (4, 8) (not yet a decreased R), or both, caused the doubled O₂ cost of E_max in stunning (19). However, the present results confirm our previous contention (19) more explicitly because of the advantage of our recently developed integrative method (27). Thus the present study seems to provide indispensable information about the pathophysiology of myocardial stunning at a beating whole heart level.

The newly found decrease in RF alone could partly account for the increased O₂ cost of E_max in stunning (19). This account is based on the difference of the Ca²⁺:ATP stoichiometry between economical internal recirculation and wasteful or one-half economical transsarcolemmal extrusion (11, 12, 14, 15, 27, 28, 34). However, the decreased RF alone cannot fully account for the increased O₂ cost of E_max when either futile Ca²⁺ cycling or a decreased Ca²⁺ reactivity, or both, are suspected (11, 27).

A shift of the N-R relation itself may provide information leading to a better understanding of abnormal total Ca²⁺ handling even when a specific N-R working point on the N-R relation is unknown, as shown in Fig. 4. Once either N or R is known or assumed, the other value is solved for and then a unique solution of total Ca²⁺ handling abnormality is obtained on the N-R relation graphically (Fig. 4) or numerically from Eq. 6. The present study has confirmed this advantage in the stunned heart.

The estimated total Ca²⁺ transport values listed in Table 2 are reasonable according to data for protein (troponin C, calmodulin, and others)-bound Ca²⁺ (20-100 µmol/kg wet myocardium) biochemically obtained from excised or homogenized myocardial preparations obtained from the literature (6). The biochemical approach is not applicable to the whole beating heart model that we used. These total Ca²⁺ values are incomparably greater than the Ca²⁺ transient (0.1-2 µmol/l) by about two orders of magnitude, with the latter being unbound leftover of the former (4, 6, 8). The total Ca²⁺ transport values we obtained are, however, smaller by one to two orders of magnitude than intramyocardial total Ca²⁺ content (2-10 mmol/kg) (1). Most of this total Ca²⁺ content is stably bound to intramyocardial proteins, including the two high-affinity Ca²⁺ binding sites of troponin C (6). Intramyocardial total Ca²⁺ content is of an order of magnitude comparable to the extracellular and blood Ca²⁺ concentrations (3, 6). Therefore, the cardiac total Ca²⁺ transport of our interest must be clearly differentiated from both the total Ca²⁺ content and the blood Ca²⁺ concentration (5-7). These different orders of magnitude and the complexity of Ca²⁺ binding proteins in the myocardium have hindered direct determination of total Ca²⁺ transport in a functioning heart (5-7). Therefore, our present study corroborated the integrative analysis methodology that we recently proposed (19).

In contrast to the nominal P:O of 3 that we used (Table 1), there are reports that the actual measured P:O was ~2.5 in both control and stunning, 17% smaller than the nominal value (23, 30). If this holds true in the canine heart, the constants 6 and 12 in Eqs. 4-6 must be replaced by 5 and 10, respectively. This modification would yield 17% smaller total Ca²⁺ transport values than those we calculated using the nominal P:O of 3 (Table 2). However, N would not differ from the values listed in Table 2, because the use of 10 instead of 12 in Eq. 7 would be compensated by the 17% smaller total Ca²⁺ transport values. However, R would become greater by 17% in Eq. 8. These changes would occur even though the O₂ cost of E_max remains unchanged, because its denominator and numerator are measured values. Nevertheless, these 17% changes in the total Ca²⁺ transport, N, and R do not qualitatively affect the present findings in both control and stunning.

Major limitations of our integrative method were discussed previously (27). Briefly, estimated total Ca²⁺ transport may depend on the Ca²⁺ handling model. Our model (Fig. 1E) (27) incorporates futile Ca²⁺ cycling into Morad and Goldman's model (16), which consisted of the internal and transsarcolemmal Ca²⁺ handling routes. Although any deviation of the model from reality would yield unrealistic results, the present Ca²⁺ transport values seem reasonable as discussed above. We cannot attribute the decreased R to any particular cause because decreases in any one or more of the variables Ca⁺ sensitivity, responsiveness (6), or force transmission via cytoskeletons and extracellular matrix (34) can decrease R. Despite these limitations, the present approach will complement the Ca²⁺ transient methods for better understanding of total Ca²⁺ handling abnormalities in failing, beating hearts.

In conclusion, this study has clearly characterized the abnormality of total Ca²⁺ handling in the postischemically stunned left ventricle of the excised cross-circulated canine heart. The abnormality consisted of a decreased internal Ca²⁺ recirculation, some futile Ca²⁺ cycling, and a decreased Ca²⁺ reactivity of contractility. These changes reasonably account for the energy-wasteful total Ca²⁺ handling underlying the doubled O₂ cost of E_max in the stunned heart (19). Thus our present hypothesis was supported. These results have also reinforced the utility of the present integrative analysis to characterize pathophysiology of total Ca²⁺ handling in failing, beating hearts. A prospective study to reconfirm the present conclusion is also warranted in which a greater number of data would be collected systematically.