INTRODUCTION

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WE DISCOVERED EXPERIMENTALLY that cardiac cooling from 36°C to 29°C changed neither the contractile efficiency of cross-bridge (CB) cycling nor the excitation-contraction (E-C) coupling energy despite a considerably enhanced contractility in the left ventricle (LV) of excised cross-circulated (blood-perfused) canine hearts (24, 26). Thus myocardial energetics under the cooling inotropy (11, 15, 28) contrasts with that under the positive inotropism of catecholamines, Ca²⁺, and many other cardiotonic agents (24-28). The mechanoenergetics under cooling inotropy suggests that cooling does not augment the Ca²⁺ handling in the E-C coupling (24, 25, 26). This seems reasonably accounted for by the increased maximum Ca²⁺-activated contractility of a cooled heart (10). However, the mechanism of the constant contractile efficiency of CB cycling to generate total mechanical energy remains entirely unknown (24, 26).

We first anticipated an increased contractile efficiency of CB cycling and a decreased E-C coupling energy in the cardiac cooling study (26). This anticipation derived from a higher efficiency of a decelerated CB cycling and a decreased Ca²⁺ handling as the result of the cooling-suppressed adenosinetriphosphatases (ATPases) of the myosin and sarcoplasmic reticulum (SR) Ca²⁺ pump (2, 4, 6, 11, 13, 30). The experimentally observed increased Ca²⁺ transient (6) does not necessarily mean an increased Ca²⁺ handling in the E-C coupling, because free Ca²⁺ is a small fraction of the total Ca²⁺ that the SR releases and then sequesters by utilizing ATP in the E-C coupling (19, 16, 21, 24). Besides, temperature dependence of Ca²⁺ sensitivity (or responsiveness) of the contractile proteins and the maximal Ca²⁺-activated force is controversial between intact and skinned myocardium (8, 10). Moreover, our previous simulation (29) suggests that the contractile efficiency of CB cycling is a complex function of Ca²⁺ transient, Ca²⁺ kinetics, and CB kinetics. Therefore, there is no agreement on the mechanisms of cooling inotropy, including the unchanged contractile efficiency in the heart.

We hypothesized that the experimentally observed constant contractile efficiency of CB cycling and E-C coupling energy under cooling inotropy could reasonably be accounted for by appropriate combinations of myocardial CB and Ca²⁺ kinetics. We tested this hypothesis in a computer simulation that integrates basic mechanisms of myocardial contraction. The present simulation involved the Ca²⁺ release and uptake by the SR, the Ca²⁺ binding to and dissociation from troponin C, and the CB cycling to generate both contractile force and mechanical energy by using ATP. We assumed the ATPase-dependent Ca²⁺ pump and CB detachment to decelerate by cooling at Q₁₀ = 2 (2, 17). This simulation suggested that the experimentally observed constant contractile efficiency of CB cycling under cardiac cooling inotropy could occur only when cooling decelerated the ATPase-dependent CB and Ca²⁺ kinetics in an appropriate manner.

	METHODS

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The present myocardium model consisted of 1) the SR to release Ca²⁺ and sequester it, 2) Ca²⁺ transient or sarcoplasmic free Ca²⁺ concentration, 3) troponin C to bind Ca²⁺ (TnCa) and dissociate it as a function of Ca²⁺ transient with Ca²⁺ association and dissociation rate constants, and 4) TnCa-triggered CB cycling with on and off rate constants. Note that the sarcoplasmic free Ca²⁺ concentration (~0.1-10 µmol/kg) is only a small fraction (a few percent) of the total amount of Ca²⁺ (10-200 µmol/kg) handled in the E-C coupling and that most of the released Ca²⁺ is bound with troponin C, whose concentration is ~70 µmol/kg and whose dissociation constant (K_d; see below) of free Ca²⁺ is ~1 µmol/kg (6, 12, 18, 19, 23). The amount of Ca²⁺ that is directly related to energetics is the total Ca²⁺ handled in the E-C coupling but not the free Ca²⁺ detected as a Ca²⁺ transient (16, 24, 25, 28, 29). This model is similar to our previous ones (16, 21, 29), which have facilitated better understanding of cardiac mechanoenergetics in an integrative manner.

We used the following basic equations and simplifying assumptions so that we could explicitly attribute any computational results to specific parameters incorporated into the model. Despite the simplicity of the present model, it retained the essential elements needed to affect the contractile efficiency of the CB cycling of our main interest.

First, we assumed the rate of Ca²⁺ release from the SR into the sarcoplasm to be given as a triangular curve of total released Ca²⁺ as follows

(1)

where t = time from the onset of contraction when the Ca²⁺ release starts. The area under this Ca²⁺ release rate curve is equal to the total released Ca²⁺. This curve approximated actual Ca²⁺ release rate curves (but not Ca²⁺ transient) (23). We have shown (21) that the shape of the triangular curve of total released Ca²⁺ does not substantially affect simulation curves of myocardial contraction.

Next, the Ca²⁺ transient [Ca²⁺(t)], is given as a function of the total amount of released Ca²⁺ in the E-C coupling in the following differential equation

(2)

where d[Ca²⁺(t)]/dt is the rate of change in the Ca²⁺ transient, k₃ is the rate constant of Ca²⁺ uptake by the SR Ca²⁺ pump, and d[TnCa(t)]/dt is the rate of change of Ca²⁺ from Ca²⁺-bound troponin C.

For Ca²⁺ binding to troponin C, we assumed

(3)

where TnCa(t) is the instantaneous amount of Ca²⁺-bound troponin C as a function of time, total Tn is the total amount of troponin C, k₁ is the Ca²⁺ association (binding) rate constant of Ca²⁺-free troponin C, and k₂ is the Ca²⁺ dissociation rate constant of Ca²⁺-bound troponin C. Equation 3 is similar to that used previously by Robertson et al. (18) and our group (16, 21, 29). The ratio of k₁ to k₂ indicates the affinity (K_a) of Ca²⁺ to troponin C, and its reciprocal is K_d, which is the free Ca²⁺ concentration at which one-half of the Ca²⁺ binding sites of troponin C are bound with Ca²⁺.

For the CB on and off kinetics, we modified Huxley's 1957 model (9) [dn/dt = f (1  n)  g · n, where n = no. of attached CBs] as follows

(4)

where CB_on(t) is the instantaneous number of attached CBs as a function of time, d[CB_on(t)]/dt is the rate of change in CB_on(t), total CB is the total number of CBs, f is the attachment (on) rate constant of detached CB, and g is the detachment (off) rate constant of attached CB. The first term on the right side of Eq. 4 indicates the rate of CB attachment as a second-order reaction in which TnCa(t) is a time-varying parametric forcing function; the second term indicates the rate of CB detachment as a first-order reaction. We considered f and g only in the forward position of CB in sarcomere-isometric contractions, where we do not need to define g in the backward position. We assumed the forward f and g to be constant in sarcomere-isometric contractions as in our previous simulation (29). Equations 1-4 are the basic differential equations to be solved for the time courses of Ca²⁺(t), TnCa(t), and CB_on(t) in control and under myocardial cooling.

In the present analyses, we assumed that SR releases a constant amount of Ca²⁺ in every twitch contraction in the control as well as under cooling and that the released Ca²⁺ is entirely sequestered by the SR Ca²⁺ pump consuming ATP at a Ca²⁺:ATP stoichiometry of 1:2 (12, 19). We neglected Ca²⁺ handling by the non-SR routes (such as the sarcolemmal Ca²⁺ channel and Na⁺/Ca²⁺ exchange) as in our previous simulation (16). Because we have found no change in the E-C coupling energy under cooling inotropy (26), we reasonably assumed the total amount of released and then sequestered Ca²⁺ to be constant.

We also assumed myocardial cooling to primarily decelerate the SR Ca²⁺ pump ATPase and the myosin ATPase for CB detachment and, hence, assumed their respective rate constants, k₃ and g, on the basis of their Q₁₀ = 2-3 (5, 22). On the other hand, we simply assumed cooling to not decelerate the ATPase-independent processes of the SR Ca²⁺ release, k₁, k₂, and f to approximate their Q₁₀ = 1-1.3 (13, 30).

In the first part of the simulation (part I), we fixed total released Ca²⁺ at 35 µmol/kg, total Tn at 70 µmol/kg, and total CB at 150 µmol/kg as values for controls and under cooling. We used k₁ = 5 × 10⁶ µmol¹ · kg · s¹, k₂ = 10 s¹, k₃ = 1,000 s¹, f = 0.4 × 10⁶ µmol · kg¹ · s¹, and g = 10 s¹ as control values. Under these conditions, one-half (35 µmol/kg) of the total Ca²⁺-binding sites of total Tn (70 µmol/kg) is to be bound with 35 µmol/kg of Ca²⁺ at a steady-state free Ca²⁺ concentration of 2 µmol/kg (K_d, which equals k₂/k₁) or pCa of 5.7. This is acceptable as a physiological condition (12). We simulated 10°C cooling by decreasing k₃ and g in three different steps while keeping k₁, k₂ (and hence K_d), and f constant. In the first cooling step, we halved k₃ to 500 s¹ without changing the other values. In the second cooling step, we restored k₃ to 1,000 s¹ and instead halved g to 5 s¹. The final cooling step is a combination of the first and second steps, with k₃ = 500 s¹ and g = 5 s¹.

In each of these control and three cooling steps, we obtained the time curves of Ca²⁺ transient, released Ca²⁺, sequestered Ca²⁺, TnCa, attached CBs (CB_on), cumulative CB_on (Cum CB_on), and cumulative CB_off (Cum CB_off). We defined these variables as follows

(5)

(6)

(7)

(8)

The difference between Eqs. 5 and 6 theoretically is the amount of Ca²⁺ remaining in the sarcoplasm, consisting of the Ca²⁺ bound with troponin C and the free Ca²⁺. At t = end of contraction, released Ca²⁺(t) = sequestered Ca²⁺(t) and their difference vanishes. The difference between Eqs. 7 and 8 theoretically is the amount of attached CBs. At t = end of contraction, Cum CB_on(t) = Cum CB_off(t) and their difference also vanishes.

We assumed each CB on-off cycle to hydrolyze one ATP as in the Huxley 1957 model (9). The amount of ATP hydrolyzed in each twitch contraction (total ATP) is then given as follows (29)

(9)

We assumed the developed force [F(t)] to be proportional to the amount of attached CBs (16, 21, 29). The peak F is then given as

(10)

We then assumed the total mechanical energy generated by each twitch contraction to be proportional to the peak F at a fixed myocardial length. This assumption is based on the established concept of the total mechanical energy of contraction (namely, ventricular systolic pressure-volume area or myocardial systolic force-length area) (24-29). Therefore, the ratio of peak F to total ATP is considered to be proportional to the efficiency of energy conversion from ATP to total mechanical energy generated by CB cycling (so-called "contractile efficiency") as follows (29)

(11)

From Eqs. 1-4, we obtained the standard Michaelis-Menten steady-state CB_on-pCa relationships in control and under cooling as

(12)

and

(13)

where [Ca²⁺] represents steady-state sarcoplasmic free Ca²⁺ concentration. From Eqs. 12 and 13, we further obtained

(14)

To draw the TnCa-pCa and CB_on-pCa curves, we converted [Ca²⁺] in Eqs. 12 and 14 to pCa = log [Ca²⁺].

In the second part of the simulation (part II), we increased and decreased k₁, k₂, and f, one at a time, by four- to fivefold; we kept these values constant in part I. We studied whether these ATPase-independent rate constants would affect the results obtained in part I.

In the third and final part of the simulation (part III), we not only decreased but also increased the ATP-dependent k₃ and g in smaller steps and over wider ranges than in part I. We studied whether the same contractile efficiency as obtained in the control would be obtained for different combinations of k₃ and g in general. This was the most important part directly related to the validation of our present hypothesis.

We carried out the entire simulation on a Power Macintosh 8100/80 using simulation software EX.TD version 3.0 (Imagine That).

	RESULTS

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Figures 1 and 2 compare the simulation results in the control (Figs. 1A and 2A) and the three cooling steps (Figs. 1, B-D, and 2, B-D) in part I. The vertical axes indicate the absolute magnitudes of Ca²⁺ transient (magnification ×100, see below), released Ca²⁺, sequestered Ca²⁺, TnCa, CB_on, Cum CB_on, and Cum CB_off as functions of time. Although the raw Ca²⁺ transient curves were drawn in Fig. 1, their peaks were <1 µmol/kg and can barely be seen on the abscissas.

View larger version (26K): [in this window] [in a new window]   Fig. 1.   Time curves of released Ca2+, sequestered Ca2+, Ca2+ transient (magnification ×100; raw Ca2+ transient curves are barely seen on abscissas), and Ca2+-bound troponin C (TnCa) in control (A) and under cooling with 0.5× Ca2+ uptake rate alone (B), 0.5× CB off rate alone (C), and both combined (D).

View larger version (29K): [in this window] [in a new window]   Fig. 2.   Time curves of TnCa, attached cross bridges (CBon), cumulative CBon (Cum CBon), and cumulative detached CB (Cum CBoff) in control (A) and under cooling with 0.5× Ca2+ uptake rate (B), 0.5× CB off rate (C), and both combined (D).

In Fig. 1, the Ca²⁺ transient curve rose immediately after the onset of contraction and sharply fell toward zero in every case. The TnCa curve rose and fell gradually. The released Ca²⁺ curve, which integrates the Ca²⁺ release rate (Eq. 1), sharply rose during the Ca²⁺ release period (t = 0-0.1, see Eq. 1) and leveled off thereafter. The sequestered Ca²⁺ curve rose more slowly than the released Ca²⁺ curve. The difference between these two curves corresponds to the sum of the TnCa curve and the (raw) Ca²⁺ transient curve. Because the latter was negligibly small compared with the former, the TnCa curve virtually corresponded to the difference.

In Fig. 2, in which all TnCa curves were transcribed from Fig. 1, the CB_on curve gradually rose and fell, with its peak after the peak of the TnCa curve in every case. The CB_on curve corresponds to the difference between the Cum CB_on and Cum CB_off curves.

In Fig. 1, the peak Ca²⁺ transient and the peak TnCa were greater in B and D than in A and C, as compared more explicitly in Fig. 3, A and B. This indicates that the cooling-decreased Ca²⁺ uptake rate (k₃) increased both peak Ca²⁺ transient and peak TnCa. In Fig. 2, the peak CB_on increased from that in A to that in C, B, and D, as shown more explicitly in Fig. 3C. The plateau level of the Cum CB_on curve changed in a different order, increasing in Fig. 2 from that in A to the level in B, decreasing to that in C, and finally increasing to the level in D. These changes occurred despite the constant total amount of released and then sequestered Ca²⁺, as explicitly shown by the same plateau levels (35 µmol/kg) of released and sequestered Ca²⁺ curves in Fig. 1, A-D.

View larger version (28K): [in this window] [in a new window]   Fig. 3.   Comparisons of Ca2+ transient (A), TnCa (B), and CBon time curves (C) between control and cooling with 0.5× Ca2+ uptake rate alone, 0.5× CB off rate alone, and both combined.

The value for (peak CB_on)/[Cum CB_on(t = end of contraction)], which is proportional to contractile efficiency (Eq. 11), was 0.31 (dimensionless, or 31%) in control, 0.27 at the 0.5× Ca²⁺ uptake rate, 0.44 at the 0.5× CB off rate, and 0.39 after both combined. Therefore, as a whole, cooling increased contractile efficiency by 1.26-fold in part I.

Figure 4 shows the Michaelis-Menten TnCa-pCa (A) and CB_on-pCa curves (B) in control and the last cooling step with both 0.5× Ca²⁺ uptake rate and the 0.5× CB off rate combined in part I. In Fig. 4A, in which the two TnCa-pCa curves are identical, cooling did not change the sigmoidal TnCa-pCa curve. The K_d (k₂/k₁) of troponin C remains unchanged because we fixed the k₁ and k₂ values.

View larger version (19K): [in this window] [in a new window]   Fig. 4.   Michaelis-Menten TnCa-pCa (A) and CBon-pCa (B) relationships in control and under cooling with both 0.5× Ca2+ uptake rate and 0.5× CB off rate combined. Dissociation constant (Kd) is pCa at midpoint of each sigmoidal curve where one-half of Tn is bound with Ca2+ (A) or one-half of CBs are attached (B).

However, in Fig. 4B, cooling shifted the sigmoidal CB_on-pCa curve and its K_d (free Ca²⁺ or pCa for half-saturation of the curve) to the left and simultaneously increased the saturation level corresponding to the maximum Ca²⁺-activated number of CB_on and hence force. As a whole, the CB_on-pCa curve looks to be shifted left and upward. This means an augmented Ca²⁺ responsiveness of CB force development. Therefore, a greater force is generated at the same pCa, or the same force is generated at a higher pCa or a lower free Ca²⁺ concentration.

In part II, we used widely varied values for k₁, k₂, and f that differed from their control values in part I. However, we obtained changes in the curves (data not shown) similar to those shown in Figs. 1-4 for part I. The different combinations of the parameter values yielded widely varied peak raw values of the Ca²⁺ transient, TnCa, and CB_on in any of the control and the three cooling steps in a similar manner to those of part I. However, after their peak values were normalized relative to their control values, the normalized values responded to the three cooling steps in a similar manner among all the cases. These changes with cooling steps resemble those of part 1 (Figs. 1-3). The resulting contractile efficiency, or more appropriately, (peak CB_on)/[Cum CB_on(t = end of contraction)] (Eq. 11), calculated in part II resembled the results of part I. Namely, contractile efficiency slightly decreased from the control in the first step with the 0.5× Ca²⁺ uptake rate but increased 1.44-fold on average from both the control and the first step in the second step with the 0.5× CB off rate. Contractile efficiency increased 1.33-fold on average from the control in the final step of cooling with the combination of both 0.5× Ca²⁺ uptake rate and 0.5× CB off rate. The variance of contractile efficiency was markedly smaller than those of the peak values of Ca²⁺ transient, TnCa, and CB_on.

Figure 5 shows the results of part III. We widely varied g from 2 to 20 s¹ in steps of 2 s¹ and k₃ from 200 to 2,000 s¹ in steps of 200 s¹, with the other parameters fixed at the control values used in part I. Figure 5, A-D, shows how the peak values of Ca²⁺ transient, TnCa, CB_on, and contractile efficiency changed, respectively. Again, contractile efficiency replaced the more appropriate (peak CB_on)/[Cum CB_on(t = end of contraction)], both of which are proportional to each other (Eq. 11). In Fig. 5, A and B, neither the peak value of Ca²⁺ transient nor that of TnCa changes with g, but both increase with decreases in k₃. In Fig. 5C, peak CB_on increases with decreases in either k₃ or g, or both. The iso-y-value contours in Fig. 5, A-C, indicate that different combinations of k₃ and g can produce the same peak values of Ca²⁺ transient, TnCa, and CB_on, respectively, but the k₃-g combinations for their iso-y-values vary among A-C. Figure 5, A-C, indicates that peak values of all Ca²⁺ transient, TnCa, and CB_on always increase with any combinations of decreasing g and k₃, generalizing the results of parts I and II.

View larger version (86K): [in this window] [in a new window]   Fig. 5.   Three-dimensional graphs of peak Ca2+ transient (A), peak TnCa (B), peak CBon (C), and contractile efficiency (D; see Eq. 11) as functions of k3 and g. k3 was changed from 200 to 2,000 s1 in steps of 200 s1, and g was changed from 2 to 20 s1 in steps of 2 s1. The direction of k3 coordinate in D is opposite those in A-C. Border lines between adjacent planes with different shading densities are iso-y-value contours, which are isoefficiency contours in D. Isoefficiency contours indicate 0.2-0.6 (dimensionless) in steps of 0.1 of (peak CBon)/[Cum CBon(t = end of contraction)], which is proportional to both contractile efficiency and (peak F)/(total ATP) as shown in Eq. 11.

Figure 5D is the most important output of the present simulation. It indicates that contractile efficiency (Eq. 11) increases with decreases in g but slightly decreases with decreases in k₃. The iso-efficiency contours in Fig. 5D indicate that different combinations of k₃ and g can produce the same contractile efficiency. Unlike the peak values in Fig. 5, A-C, contractile efficiency increases or decreases depending on how g and k₃ decrease. This result indicates that the 1.20- to 1.40-fold increases in contractile efficiency with cooling inotropy in parts I and II are not general responses. The isoefficiency curves in Fig. 5D indicate that an isoefficiency condition is maintained only when g and k₃ decrease in an appropriate manner by cooling.

	DISCUSSION

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The present mechanoenergetics simulation of cooled myocardial contraction has yielded results (particularly Fig. 5D) to support our present hypothesis. Namely, contractile efficiency can be constant, but only when myocardial cooling decelerates both CB cycling and SR Ca²⁺ handling appropriately. This simulation result supports the unchanged contractile efficiency that we had intriguingly observed in canine hearts (26).

The simulation has also supported the following mechanisms as the basis for the constant contractile efficiency. First, cooling inotropy occurs despite no increase in the total amount of released Ca²⁺ from the SR (Figs. 1-3), as speculated from our previous mechanoenergetics data in excised, cross-circulated canine hearts (26). Second, cooling augments both peak Ca²⁺ transient and peak force (Figs. 1-3), as observed in isolated superfused myocardium (6). Third, cooling augments the Ca²⁺ responsiveness of CB force development by increasing the maximum Ca²⁺-activated force and shifting the force-Ca²⁺ curve to a lower Ca²⁺ concentration (Fig. 4B), as observed in ferret hearts (10). As a whole, the present simulation suggests that cooling inotropy occurs without an increased energy for Ca²⁺ handling and an increased contractile efficiency of CB cycling despite an increased Ca²⁺ transient, as observed experimentally (6, 10, 26). These individual responses would be predictable intuitively from myocardial Ca²⁺ and CB kinetics. However, the existence of the iso-efficiency conditions (Fig. 5D) could not be obtained without such a theoretical simulation as the present one.

The similarity of the simulated cooling inotropy to the experimental observations (6, 10, 26) suggests that common mechanisms underlie both the simulated and the real cooling inotropy. We would speculate a reduced SR Ca²⁺ uptake rate constant (k₃) and a reduced CB off rate constant (g) to be the most probable key mechanisms of the cooling inotropy and the resultant energetics observed in canine hearts (26). Although a reduced SR Ca²⁺ uptake rate constant alone has reasonably simulated experimental observation in myocardium (6), we would consider it more reasonable to assume that a reduced CB off rate constant coexists. This coexistence is supported by the increased maximum level of the CB_on-pCa relationship (Fig. 4B), which is consistent with the increased maximum Ca²⁺-activated pressure of ferret hearts (10).

The constant contractile efficiency under cooling does not mean that the conventional mechanical (or work) efficiency of the heart is not affected by cooling. Cardiac efficiency is theoretically a fraction of contractile efficiency, and this fraction varies with cardiac preload and afterload (24, 25), as is well known. Therefore, the experimentally observed dependence of cardiac efficiency on temperature (4) does not contradict the constant contractile efficiency. Moreover, the constancy of contractile efficiency may not always be guaranteed because it requires appropriate changes in g and k₃ (Fig. 5).

Although we did not change the ATPase-independent k₁, k₂, and f with cooling, they were markedly different among the different cases in part II. In each case with a different combination of k₁, k₂, and f, essentially the same relative changes in peak values of Ca²⁺ transient, TnCa, and CB_on, as well as contractile efficiency, are observed as in the control case. Therefore, we consider that slight temperature-dependent changes in k₁, k₂, and f would not significantly affect the present simulation results.

The present simulation results may also account for the negative inotropism of myocardial warming; cardiac warming from 36°C to 41°C depressed LV contractility but did not change contractile efficiency and Ca²⁺ handling energy of the LV in dogs (20). Figure 5D indicates that appropriately increased k₃ and g could simulate such an observation.

Some limitations exist in the present simulation. We did not include complex cooperativities in both Ca and CB kinetics (1, 7), because much is unknown about their mechanisms and temperature dependence (1, 12). We assumed sarcomere-isometric twitch contractions at a given length in this study. Fiber-isometric contractions at a varied length will overcomplicate the simulation, because the mechanisms of the length- and load-dependent Ca and CB kinetics are not well known (1, 12). We did not include transsarcolemmal Ca²⁺ handling because of its small fraction in normal hearts (12, 19).

Although these limitations may deviate the present simulation from the reality, a constant contractile efficiency only under appropriate combinations of CB and Ca²⁺ kinetic parameters will facilitate better understanding of cardiac mechanoenergetics. Because we incorporated the essential temperature-sensitive CB and Ca²⁺ kinetics, the present results would also be helpful to account for the temperature dependence of pharmacological effects on cardiac contraction (14) as well as the advantages of cardiac cooling in a clinical setting (3), both of which have not yet been explained explicitly. As long as a simple simulation can predict the reality of our interest, the simplicity of the model is effective. When the simple model cannot predict the reality of interest, the model becomes ineffective and should be improved.

After all, the present simulation has shown that system performance such as the ventricular mechanoenergetics is determined as a complex integration of parameter changes of such elements as CB and Ca²⁺ kinetics. In other words, the system performance is not always straightforwardly predictable from the performances of the elements, or the former does not directly reflect the individual of the latter. Therefore, modeling or simulation is a powerful and reasonable method to bridge a system and its elements in physiology.

In summary, the present basic simulation of myocardial contraction suggests that the known mechanoenergetics of cooled heart and myocardium is integratively accounted for mainly by appropriate changes in the cooling-decelerated ATPase-dependent Ca²⁺ sequestration and CB detachment.