## Abstract

Postischemic myocardial stunning halved left ventricular contractility [end-systolic maximum elastance (*E*
_{max})] and doubled the O_{2} cost of *E*
_{max} in excised cross-circulated canine heart. We hypothesized that this increased O_{2} cost derived from energy-wasteful myocardial Ca^{2+} handling consisting of a decreased internal Ca^{2+} recirculation, some futile Ca^{2+} cycling, and a depressed Ca^{2+} reactivity of *E*
_{max}. We first calculated the internal Ca^{2+} recirculation fraction (RF) from the exponential decay component of postextrasystolic potentiation. Stunning significantly accelerated the decay and decreased RF from 0.63 to 0.43 on average. We then combined the decreased RF with the halved *E*
_{max}and its doubled O_{2} cost and analyzed total Ca^{2+}handling using our recently developed integrative method. We found a decreased total Ca^{2+} transport and a considerable shift of the relation between futile Ca^{2+} cycling and Ca^{2+} reactivity in an energy-wasteful direction in the stunned heart. These changes in total Ca^{2+} handling reasonably account for the doubled O_{2} cost of*E*
_{max} in stunning, supporting the hypothesis.

- stunning
- end-systolic maximum elastance
- mechanoenergetics
- postextrasystolic potentiation

abnormalities of myocardial total Ca^{2+}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 O_{2} consumption (Vo
_{2}) for excitation-contraction (E-C) coupling, doubling the O_{2} 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 O_{2} cost of *E*
_{max} would be a manifestation of energy-wasteful Ca^{2+} 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 Ca^{2+} handling in postischemic stunning: first, a decreased internal Ca^{2+} recirculation fraction; second, some futile Ca^{2+} cycling via the sarcoplasmic reticulum (SR); and third, a decreased Ca^{2+} reactivity of*E*
_{max} (11, 12, 14, 27, 35). As the internal Ca^{2+} recirculation fraction (RF) decreases, a greater fraction of total Ca^{2+} must be handled by the transsarcolemmal route, whose Ca^{2+} handling primarily via the Na/Ca^{2+} exchange is one-half as economical as internal Ca^{2+} handling via the SR Ca^{2+} pump (5-7,22, 29, 36). As the futile Ca^{2+} cycling via the SR occurs, part of the Ca^{2+} 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 Ca^{2+}reactivity to *E*
_{max} decreases, total Ca^{2+} transport (or flux) must be increased for the same*E*
_{max}, or the same total Ca^{2+} transport can develop a smaller *E*
_{max} (27). Therefore, any of these changes in total Ca^{2+} handling could account for an increased ATP and Vo
_{2} 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 Vo
_{2}) data (19), we found a considerable shift of the relation between futile Ca^{2+} cycling and Ca^{2+} 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

#### 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 O_{2} content difference was measured with a custom-made analyzer (PWA-200S, Shoei-Technica, Tokyo, Japan). Cardiac Vo
_{2} per minute was calculated as the product of coronary flow and coronary arteriovenous O_{2}content.

#### Mechanoenergetics.

We utilized LV mechanoenergetics data [*E*
_{max}, pressure-volume area (PVA), and Vo
_{2}] 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 (V_{0}) 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 V_{0} and the P-V point at the left upper shoulder of each P-V trajectory on the computer (Fig. 1
*A*) (19).

LV PVA is the systolic P-V area as a measure of the total mechanical energy generated by each LV contraction (19, 30, 31). PVA is equal to the area bounded by the *E*
_{max} line, the end-diastolic P-V curve, and each systolic P-V trajectory (Fig.1
*A*) (19, 30, 31). It consists of external work and elastic potential energy. PVA linearly correlates with Vo
_{2}, and the Vo
_{2}-PVA relation shifts with maneuvers that are known to influence*E*
_{max} by altering E-C coupling (Fig. 1, *B*and *C*) (19, 30, 31). PVA was calculated using the computer.

LV Vo
_{2} per minute was obtained by subtracting right ventricular unloaded Vo
_{2} from the cardiac Vo
_{2}. LV Vo
_{2} per beat was obtained as LV Vo
_{2} per minute divided by the heart rate. For more details, please refer to our original paper (19).

LV *E*
_{max}, PVA, and Vo
_{2} data were first obtained under different LV loads to determine the Vo
_{2}-PVA relation and its slope (α) in control contractility (Fig. 1
*B*, solid line). Slope α represents the O_{2} cost of PVA (30, 31). Its reciprocal (1/α) reflects the contractile efficiency as the product of the Vo
_{2}-to-ATP efficiency in the oxidative phosphorylation and the ATP-to-PVA efficiency in the chemicomechanical energy transduction of cross-bridge cycling (30, 31). The Vo
_{2} intercept (β) of the Vo
_{2}-PVA relation divides Vo
_{2} into the PVA-dependent and PVA-independent components (Fig. 1
*B*, dashed line) (30, 31). The latter component consists of the Vo
_{2} component primarily for basal metabolism and total Ca^{2+} handling (30,31). We had confirmed that virtually the same Vo
_{2}-PVA relation was obtainable in both isovolumic and ejecting modes of contraction (30).

Next, coronary perfusion was stopped for 15 min at 36°C and then gradually restored over 1 min (19). *E*
_{max} recovered over a 20- to 60-min period after the onset of reperfusion (19). The heart was successfully stunned with a depressed*E*
_{max} but with a slightly decreased Vo
_{2}, relative to that of both control and sham hearts, and these mechanoenergetics were stable over the next hour (19). During this period, *E*
_{max}, PVA, and Vo
_{2} data were obtained under different LV loads to determine the Vo
_{2}-PVA relation and slope α in stunning (19). For more details, refer to our previous paper (19).

After each of the volume runs in the stunned and sham hearts, intracoronary Ca^{2+} infusion rate was increased in several steps from 0 to 0.05 mmol/min and increasing *E*
_{max}, PVA, and Vo
_{2} were measured at a fixed intermediate end-diastolic volume (Fig. 1
*C*) (19). These data were used to determine the composite Vo
_{2}-PVA relation (Fig. 1
*C*, heavy arrow). The*E*
_{max}, PVA, and Vo
_{2} data obtained during the increased Ca^{2+} infusion were used to obtain the PVA-independent Vo
_{2}-*E*
_{max} relation in control (Fig. 1
*D*, thick line) and stunned hearts (Fig.1
*D*, thin line). Its slope (γ) represents the O_{2} cost of *E*
_{max}. Slope γ was nearly doubled in stunning (19). The PVA-independent Vo
_{2} intercepts (δ) represent basal metabolism (19, 30), although the latter was obtained directly as follows.

After Ca^{2+} infusion was stopped, we continuously infused KCl intracoronally at a rate gradually increased toward 3 mmol/min until cardiac arrest occurred. Basal metabolic Vo
_{2} was then determined (19). The E-C coupling Vo
_{2} was then obtained by subtracting basal metabolic Vo
_{2} from the PVA-independent Vo
_{2} in control and stunned hearts (19, 30). The Vo
_{2} for total Ca^{2+} handling, or total Ca^{2+} handling Vo
_{2} (Fig. 1,*B* and *D*), represents nearly the entire E-C coupling Vo
_{2} because Na^{+} handling Vo
_{2} for membrane excitation is a negligibly small fraction (13). We had confirmed that the KCl-arrest Vo
_{2} was comparable between the stunning and sham groups (19).

On the basis of the *E*
_{max}, PVA, and Vo
_{2} data, stunning was concluded not to have suppressed the basal metabolism. This finding was consistent with the results of a direct basal metabolic study (24). Furthermore, the slightly decreased slope α in stunning suggested that it was unlikely that stunning decreased the efficiency of oxidative phosphorylation, as discussed previously (19). This finding was also consistent with a direct mitochondrial study (23). Therefore, we considered that the total Ca^{2+} handling Vo
_{2} obtained in the original study was reasonably reliable and useful in the following analysis.

#### 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 V_{0} 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).

#### 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 (τ_{e}) and second (τ_{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 (*r*
^{2}) served as an indicator of goodness of fit.

#### Recirculation fraction.

We calculated internal Ca^{2+} RF from τ_{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 Ca^{2+} 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/τ_{e} is a dimensionless fraction of one beat interval relative to τ_{e}. Therefore, exp (−1/τ_{e}) indicates the exponential decay rate of PESP within one beat.

This rate also represents the fraction of total Ca^{2+} that recirculates intracellularly via the SR in our integrative Ca^{2+} handling model (Fig. 1
*E*) (11, 12, 14, 27, 28,35). This model retains Morad and Goldman's internal Ca^{2+}recirculation model (16), to which we ascribed the exponential decay component of the alternans PESP decay (11, 12, 14, 27, 28, 35). The exponential nature of the decay means that the beat-by-beat decay rate, and hence the RF, is maintained constant over the beats not only during the PESP decay but also during the regular beats before and after the PESP (16, 27).

RF had never been combined with cardiac Vo
_{2}before our previous studies (11, 12, 14, 27, 28, 35). However, RF is essential in cardiac energetics because total Ca^{2+} handling Vo
_{2} is a significant fraction of LV Vo
_{2}, and the internal and external Ca^{2+} handling routes have Ca^{2+}:ATP stoichiometries with a twofold difference (5-7, 11, 12, 14, 27,28, 35). The SR Ca^{2+}-ATPase pump has a 2Ca^{2+}:1ATP stoichiometry (36). The Na^{+}-K^{+}-ATPase pump coupled with the Na^{+}/Ca^{2+} exchange has a net 1Ca^{2+}:1ATP stoichiometry under Ca^{2+} and Na^{+} homeostasis (5-7, 22). This difference in the Ca^{2+}:ATP stoichiometry means that the transsarcolemmal Ca^{2+} handling route is twice as energy-wasteful as the internal Ca^{2+} handling route. Therefore, the smaller RF makes total Ca^{2+} handling more energy wasteful in relation to contractility (or *E*
_{max}) (11, 12, 14, 27, 28,35).

The sarcolemmal Ca^{2+}-ATPase pump contributes to some Ca^{2+} extrusion, but its stoichiometry is 1Ca^{2+}:1ATP (7). Therefore, we neither needed to nor could differentiate transsarcolemmal Ca^{2+} handling between the sarcolemmal Ca^{2+} pump and the Na^{+}/Ca^{2+} exchange (27). We neglected Ca^{2+} influx in the reverse mode of the Na^{+}/Ca^{2+} exchange (6). We neglected Na^{+} handling via the Na^{+}-K^{+} pump for membrane repolarization because its energy is negligibly small in cardiac energetics (13). We also neglected Ca^{2+} as a second messenger (6, 21) and ATP consumption for protein phosphorylation and synthesis (21, 30).

#### Futile Ca^{2+} cycling.

The Ca^{2+}-leaky SR in stunning may release part of the once sequestered Ca^{2+} (20, 26, 36, 40). Reuptake of this extra released Ca^{2+} requires additional ATP, although it does not directly contribute to contractility. We designated this extra Ca^{2+} release and removal as futile Ca^{2+} cycling (27). The SR will consume more ATP as the futile Ca^{2+}cycling increases, even if the internally recirculating Ca^{2+} remains the same. We quantified the number (*N*) of futile Ca^{2+} cycles relative to and in excess of the presumably single cycle of Ca^{2+} release and uptake via the normal SR (i.e., *N* = 0) (27). The shaded loop (*N* ⋅ RF) in Fig. 1
*E* represents the futile Ca^{2+} cycling.

#### Total Ca^{2+} handling and transport.

*Equation 3 *(Table 1) yields ATP for total Ca^{2+}handling (in μmol/kg wet myocardium) as a function of total Ca^{2+} transport, RF, and *N* (27). It sums the amounts of Ca^{2+} handled or transported internally and transsarcolemmally, as conceptually modeled in Fig. 1
*E*. Because we defined the futilely cycling Ca^{2+} to be part of the recirculating Ca^{2+}, it is part of total Ca^{2+}transport. Therefore, *Eq. 3* is the most basic equation for combining total Ca^{2+} transport and its energetic demand with both RF and *N* as parameters in the total Ca^{2+}handling model (27).

*Equations 4–7* (Table 1) were derived from *Eq. 3. Equation 4 *converts total Ca^{2+} handling ATP to Vo
_{2} (in μmol/kg). *Equation 5 *yields total Ca^{2+} transport (in μmol/kg) from *Eq. 4. Equation 6 *obtains total Ca^{2+} transport (in μmol/kg) from total Ca^{2+} handling Vo
_{2} (in ml/100 g myocardium; 0°C, 1 atm, and dry). Solving *Eq. 6* for *N* yields *Eq. 7*. Here, the constant 6 in *Eqs. 4–6* (derived from the constant 12 in *Eqs. 7, 9*, and *10*) came from the nominal P-to-O ratio (P:O, where P is the high-energy phosphate of ATP) of 3 (see Table 1, *Constants*) in control and stunning (19). We assumed P:O to be hardly changed in stunning, as discussed in detail previously (19), although mitochondrial oxidative phosphorylation speed may have been slowed in stunning (41). Our assumption of an unchanged P:O is consistent with a mitochondrial ATP synthesis study using^{31}P NMR (23).

#### Ca^{2+} reactivity of E_{max}.

To obtain total Ca^{2+} 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 Ca^{2+} handled in the E-C coupling, abbreviated to Ca^{2+} reactivity of*E*
_{max} or simply Ca^{2+} reactivity (27). R differs from the conventional Ca^{2+} sensitivity of troponin C and Ca^{2+} responsiveness of contraction because that Ca^{2+} refers to free Ca^{2+} concentration rather than the total Ca^{2+} transport, our present interest (5, 7,29). R incorporates not only the Ca^{2+} sensitivity and Ca^{2+} 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 Ca^{2+}handling Vo
_{2} as a variable.

#### N-R relation.

*Equation 9* describes *N* as a linearly increasing function of R with Ca^{2+} handling Vo
_{2}, *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 Ca^{2+} 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 Ca^{2+} transport from total Ca^{2+} handling Vo
_{2}, 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; Table2). 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

Figure 2 shows transient alternans PESPs in isovolumic (Fig.2
*A*) and ejecting (Fig. 2
*B*) 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. 3
*A*) and stunning (Fig. 3
*B*). The solid curve was best fitted to data points of the alternating PES1-PES6 in each case. *r*
^{2} 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 τ_{e} from control but hardly changed τ_{s}. The RF value calculated from τ_{e} using *Eq. 2* was smaller in stunning.

We obtained τ_{e} values from 85 PESPs resembling these representative cases. RF values were then obtained from these 85 τ_{e} values using *Eq. 2*. The goodness of fit was always excellent with *r*
^{2} = 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}, Ca^{2+}handling Vo
_{2}, the best-fit parameters*a*, τ_{e}, *b*, τ_{s}, and*r*
^{2}, and the resultant RF, *N*, R, and total Ca^{2+} transport as well as its internal and external components in isovolumic and ejecting beats in control and stunning. Of these, *E*
_{max} and Ca^{2+} handling Vo
_{2} were transcribed from the previous paper (19). On average, τ_{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 τ_{e} and RF values were comparable to those in our previous studies (11, 12, 14, 27, 28, 35). Stunning slightly decreased τ_{s}, though not significantly. The present Ca^{2+} handling analysis did not need τ_{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 Ca^{2+} handling Vo
_{2},*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 Ca^{2+} handling in stunning as explained below.

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 Ca^{2+} 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 O_{2} cost of*E*
_{max} as a function of R, *N*, and RF. This equation explicitly shows that the O_{2} 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 O_{2} cost of *E*
_{max} and, hence, an energy-wasteful total Ca^{2+} handling. Table 2 also lists the corresponding ranges of the calculated total, recirculating, and extruded Ca^{2+}.

## DISCUSSION

We succeeded in characterizing the increased O_{2} cost of*E*
_{max} in the stunned hearts in terms of the energy-wasteful total Ca^{2+} handling by using our recently developed integrative method (27). The main results that we obtained are *1*) a decreased decay beat constant (τ_{e}) of the exponential decay component of the PESP, *2*) a decreased internal Ca^{2+} recirculating fraction (RF), and *3*) a shifted relation between the Ca^{2+} reactivity of*E*
_{max} (R) and the futile Ca^{2+} cycling (*N*) in the direction of energy-wasteful total Ca^{2+}handling. These results evidently support our present hypothesis on the abnormal Ca^{2+} 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 Ca^{2+} analysis methods (6, 27).

Previously, we were only able to speculate that either Ca^{2+}-leaky SR or decreased Ca^{2+} sensitivity and responsiveness (4, 8) (not yet a decreased R), or both, caused the doubled O_{2} 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 O_{2} cost of *E*
_{max} in stunning (19). This account is based on the difference of the Ca^{2+}: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 O_{2} cost of*E*
_{max} when either futile Ca^{2+} cycling or a decreased Ca^{2+} 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 Ca^{2+}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 Ca^{2+} 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 Ca^{2+} transport values listed in Table 2are reasonable according to data for protein (troponin C, calmodulin, and others)-bound Ca^{2+} (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 Ca^{2+} values are incomparably greater than the Ca^{2+} 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 Ca^{2+} transport values we obtained are, however, smaller by one to two orders of magnitude than intramyocardial total Ca^{2+} content (2–10 mmol/kg) (1). Most of this total Ca^{2+} content is stably bound to intramyocardial proteins, including the two high-affinity Ca^{2+} binding sites of troponin C (6). Intramyocardial total Ca^{2+} content is of an order of magnitude comparable to the extracellular and blood Ca^{2+} concentrations (3, 6). Therefore, the cardiac total Ca^{2+} transport of our interest must be clearly differentiated from both the total Ca^{2+}content and the blood Ca^{2+} concentration (5-7). These different orders of magnitude and the complexity of Ca^{2+}binding proteins in the myocardium have hindered direct determination of total Ca^{2+} 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 Ca^{2+} 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 Ca^{2+} transport values. However, R would become greater by 17% in *Eq. 8*. These changes would occur even though the O_{2} cost of*E*
_{max} remains unchanged, because its denominator and numerator are measured values. Nevertheless, these 17% changes in the total Ca^{2+} 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 Ca^{2+} transport may depend on the Ca^{2+} handling model. Our model (Fig. 1
*E*) (27) incorporates futile Ca^{2+} cycling into Morad and Goldman's model (16), which consisted of the internal and transsarcolemmal Ca^{2+} handling routes. Although any deviation of the model from reality would yield unrealistic results, the present Ca^{2+} 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 Ca^{2+} transient methods for better understanding of total Ca^{2+} handling abnormalities in failing, beating hearts.

In conclusion, this study has clearly characterized the abnormality of total Ca^{2+} handling in the postischemically stunned left ventricle of the excised cross-circulated canine heart. The abnormality consisted of a decreased internal Ca^{2+}recirculation, some futile Ca^{2+} cycling, and a decreased Ca^{2+} reactivity of contractility. These changes reasonably account for the energy-wasteful total Ca^{2+} handling underlying the doubled O_{2} 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 Ca^{2+} 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.

## Acknowledgments

This work was partly supported by Grants-in-Aid for Scientific Research (07508003, 09470009, 10470010, 10558136, 10770307, 10877006, 11898028) from the Ministry of Education, Science, Sports and Culture, a Research Grant for Cardiovascular Diseases (11C-1) from the Ministry of Health and Welfare, a 1998 Frontier Research Grant for Cardiovascular System Dynamics from the Science and Technology Agency, and a Suzuken Memorial Foundation Research Grant, all of Japan.

## Footnotes

Address for reprint requests and other correspondence: H. Suga, Dept of Physiol II, Okayama Univ. Medical School, 2-5-1 Shikatacho, Okayama 700-8558, Japan (E-mail: hirosuga{at}cc.okayama-u.ac.jp).

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