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Departments of 1 Cardiovascular Physiology, 2 Anesthesiology and Resuscitology, and 3 Cardiovascular Medicine, Okayama University Graduate School of Medicine and Dentistry, Okayama, 700-8558; and 4 National Cardiovascular Center Research Institute, Suita, Osaka, 565-8565, Japan
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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We have found that cardiac temperature proportionally changes O2 cost of contractility, defined as O2 consumption for myocardial total Ca2+ handling normalized to contractility in terms of the end-systolic pressure-volume ratio (maximal elastance, Emax), in the canine left ventricle (temperature sensitivity, Q10 = 2). We have separately found that a decrease in the recirculation fraction (RF) of Ca2+ within myocardial cells underlies an increased O2 cost of Emax in stunned hearts. We therefore hypothesized that a similar change in RF would underlie the Q10 of O2 cost of Emax. We tested this hypothesis by analyzing RF calculated from an exponential decay component of the transiently alternating postextrasystolic potentiation in the canine left ventricle. RF decreased from 0.7 to 0.5 as cardiac temperature increased from 33 to 38°C with Q10 of 0.5, reciprocal to that of O2 cost of Emax. We conclude that Q10 of ATP-consuming reactions involved in Ca2+ handling and Emax response to it could reasonably account for the reciprocal Q10 of RF and O2 cost of Emax.
excitation-contraction coupling; calcium handling; ventricular contractility; sarcoplasmic reticulum
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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MYOCARDIAL Ca2+ handling in excitation-contraction (E-C) coupling determines not only cardiac contractility but also O2 consumption for the Ca2+ handling (30). To quantify the O2 consumption for Ca2+ handling relative to left ventricular contractility in terms of end-systolic pressure-volume ratio (maximum elastance, Emax), we had proposed the O2 cost of Emax (30). We defined it as the ratio of O2 consumption for total Ca2+ handling, namely, other than contraction and basal metabolism, to Emax (30).
We have attributed an increased O2 cost of Emax to a decrease in the recirculation fraction (RF) of Ca2+ within myocardial cells as well as a decrease in the response of Emax to total released Ca2+ (Emax reactivity, R) in canine failing (e.g., stunned and ryanodine-treated) hearts (3, 10, 13, 27). We have separately found that cardiac cooling from 40 to 30°C considerably decreased the O2 cost of Emax with a temperature sensitivity (Q10) of ~2 in canine hearts (18). However, the underlying mechanisms in the temperature-dependent O2 cost of Emax remain to be elucidated (18, 24, 31).
Therefore, in the present study, we hypothesized that cardiac temperature would also change either RF or Emax reactivity or both, and thereby change the O2 cost of Emax. We tested this hypothesis in the canine heart. We used our recently developed method to obtain RF by extracting an exponential decay component from the transient alternans decay of postextrasystolic potentiation (PESP) (3, 10, 13, 16, 19, 26-28). We obtained interesting results to support that the temperature-dependent ATP-consuming activities in Ca2+-handling processes could largely account for the temperature-dependent changes in both RF and Emax reactivity, and hence Q10 = 2 of O2 cost of Emax.
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MATERIALS AND METHODS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Surgical preparation. We used a standard-type excised, cross-circulated canine heart preparation that we have been consistently using in cardiac mechanoenergetics studies (18, 31). All procedures were conducted in conformity with the "Guiding Principles for Research Involving Animals and Human Beings" endorsed by the American Physiological Society as well as the Physiological Society of Japan. The details of the surgical preparations were described elsewhere (18, 31).
Briefly, in each of seven experiments, a metabolic support dog (20.2 ± 5.6 kg) and a heart donor dog (13.1 ± 1.5 kg), both adult mongrels, were anesthetized with pentobarbital sodium (25 mg/kg iv) and fentanyl (0.1-0.2 mg/h iv) after premedication with ketamine hydrochloride (25 mg/kg im). They were intubated, air-ventilated, and heparinized (15,000 units per support dog and 10,000 units per donor dog iv). Bilateral common carotid arteries and unilateral external jugular vein of the support dog were cannulated and connected to the arterial and venous cross-circulation tubes, respectively. The chest of the donor dog was opened midsternally. The arterial and venous cross-circulation tubes from the support dog were cannulated into the left subclavian artery and the right ventricle (RV) via the right atrial appendage of the donor dog, respectively. All systemic and pulmonary vascular connections to the heart were ligated. The metabolically supported beating heart was excised from the chest of the donor dog under continuous cross circulation from the support dog. The coronary perfusion of the excised donor heart was never interrupted during the surgical preparation. The left atrium of the donor heart was opened, and all the left ventricular (LV) chordae tendineae were cut. Complete atrioventricular block was made by chemical (0.2-0.5 ml injection of 36% formaldehyde solution) or electrical (direct current of 20-30 J) ablation of the His bundle. A bipolar pacing electrode was placed on the upper portion of the ventricular septal endocardium via the left atrium for para-Hisian pacing. A thin flabby latex balloon with an unstretched volume of ~50 ml mounted on a rigid connector was fit into the LV. The connector was secured at the mitral annulus. The balloon was connected to our custom-made volume servo pump (AR-Brown; Tokyo, Japan). Both the balloon and the water housing of the servo pump were primed with water. The servo pump allowed us to measure LV volume (LVV) accurately and control it precisely. LV pressure (LVP) was measured with a miniature pressure gauge (model P-7, Konigsberg Instruments; Pasadena, CA) placed inside the apical end of the balloon. The pressure gauge was calibrated against the fluid-filled pressure transducer. LV temperature of the excised donor heart was maintained at 33, 36, and 38°C by cooling and warming the arterial cross-circulation tube through a thermostatic bath. LV temperature was measured with a thermistor placed between the endocardium and the balloon. We used this temperature range because sustained alternans tended to occur after a premature beat below 33°C, whereas spontaneous premature beats tended to occur frequently above 38°C in the present heart preparation. An LV epicardial electrocardiogram was recorded with a pair of screw-in electrodes to trigger data acquisition. All LVP, LVV, and electrocardiogram signals were digitized at 2-ms intervals with an analog-digital converter (Lab-NB, National Instruments), displayed on a computer, and stored on a hard disk. The systemic arterial blood pressure of the support dog served as coronary perfusion pressure of the excised donor heart. We prevented the tendency to hypotension and maintained systemic arterial pressure of the support dog around 90 mmHg by electrically stimulating Neiguan (PC-6) acupoints in bilateral forearms (32). Briefly, we inserted two stainless steel needles vertically into the acupoints. They were 3 cm above the transverse crease of the wrist and between the tendons of the long palmar muscle and the radial flexor muscle of the wrist. The stimulation was 5 V, 40 Hz, and 5-ms biphasic pulses. Arterial pH, PO2, and PCO2 of the support dog were repeatedly measured with a blood gas analyzer and maintained within their physiological ranges with supplemental O2 and intravenous NaHCO3 or by adjusting the ventilator setting. The weights of the LV, including the septum (84.0 ± 17.6 g), and RV (33.7 ± 6.3 g) were measured after each experiment.Pacing. We used a fixed pacing stimulus pattern. It consisted of a single extrasystole (ES) inserted at an extrasystolic interval (ESI) of 320 ms after 10 or more regular beat intervals (RIs) of 500 ms (120 beats/min). The first postextrasystolic beat (PES1) interval (PESI1) was 500 ms with no compensatory pause. The 10 or more subsequent PESIs were also 500 ms. We allowed no compensatory pause because we wanted to know how the ESI alone would affect the PESP beats at different LV temperatures. We have already found that even the PESP decay after no compensatory pause in PESI1 contained an alternans decay component, although smaller than after a compensatory pause (26). These pacing stimuli were produced with a stimulator controlled by a computer installed with LabView 3.1 (National Instruments).
Normalized contractility. To evaluate the beat-to-beat changes in LV contractility during each PESP decay, we used Emax (maximum elastance, or end-systolic pressure-volume ratio) as an index of ventricular contractility (30). In isovolumic contractions as we used, end systole corresponds to peak systole. Emax values of PES1-6 were calculated as the ratio of peak isovolumic LVP to LVV minus V0, identified as the LVV at which peak LVP was zero (30). These Emax values were normalized (nEmax) relative to the Emax of the preceding regular beats. The changes in nEmax values during the PESP decay were therefore proportional to those in the peak LVP values at a fixed LVV.
Curve fitting.
We examined whether the obtained nEmax values of
PES1-6 during each PESP decay at any LV temperature could be fit
by the same equation that we had proposed and used in the previous
studies (3, 10, 13, 16, 19, 26-28)
![n<IT>E</IT><SUB>max</SUB><IT>=a· </IT>exp[−(<IT>i−</IT>1)<IT>/&tgr;</IT><SUB>e</SUB>]](/content/vol282/issue2/fulltext/H403/img001.gif)
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(1) |
![<IT>+b </IT>exp[−(<IT>i−</IT>1)<IT>/&tgr;</IT><SUB>s</SUB>] cos [<IT>&pgr;</IT>(<IT>i−</IT>1)]<IT>+</IT>1](/content/vol282/issue2/fulltext/H403/img002.gif)
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e and s are
the beat constants of the first and second exponential terms,
respectively. Their unit is the number of beats but not time (such as
milliseconds). Subscripts e and s refer to exponential and sinusoidal.
Although we used the cosine function in Eq. 1, the term
could be any oscillatory or alternating function as long as it fits the
discrete PESi data points (11).
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Ca2+ handling model. The conventional, monotonic, or exponential decay of the PESP has been accounted for by the beat-by-beat decreasing Ca2+ recruitability in E-C coupling from its transiently augmented level in PES1 toward the steady-state level of regular beats (21, 34, 35). The most potentiated PES1 is due to both an increased transsarcolemmal Ca2+ influx and an increased availability of sarcoplasmic reticulum (SR) Ca2+ associated with the preceding extrasystole and PESI1 (37). The gradual monotonic decay over the following PES2-6 is due to the transsarcolemmal Ca2+ extrusion exceeding the influx and hence the gradually decreasing Ca2+ releasability over these beats. Stable regular beats are restored due to the Ca2+ homeostasis (3-5, 21).
Figure 1 illustrates the myocardial Ca2+ handling model that we modified to include the transient alternans decay (10, 13, 16, 19, 26-28). Intramyocardial Ca2+ recirculation and gradual Ca2+ extrusion could account for the monoexponential decay component to the homeostatic Ca2+ level (11, 21). The Ca2+ release from the SR would alternate transiently and could account for the sinusoidal decay component (1, 11, 25). This model indicates that the monoexponential decay term of our proposed Eq. 1 is related to the RF and the exponentially decaying sinusoidal term to the Ca2+ uptake-release characteristics of SR (see APPENDIX). We have proposed that this Ca2+ handling model enables us to assess the mass dynamics of total Ca2+ handling from cardiac mechanoenergetics at the organ level (3, 27).Recirculation fraction.
We calculated RF from the beat constant e in the first
term of Eq. 1 best fit to the alternans decay over
PES1-6 (10, 13, 16, 19, 26-28). We considered
this RF to be equivalent to the RF obtained from the beat constant of the conventional monotonic PESP (21, 34) (see
APPENDIX). Both quantify the fraction of the total amount
of Ca2+ handled in E-C coupling that recirculates
intracellularly via the SR without being extruded transsarcolemmally.
Reciprocally, 1 
RF quantifies the fraction of the total amount
of Ca2+ handled in E-C coupling that is extruded and enters
transsarcolemmally, i.e., Ca2+ extrusion fraction.
Data analyses.
We performed curve fitting of Eq. 1 by the least-squares
method using LabView 3.1 (National Instruments) on a computer. We obtained a, b, e,
s, and RF from the best-fit Eq. 1. We
compared them among 33, 36, and 38°C. Goodness of the curve fitting
was evaluated by correlation coefficient (r).
e, s, RF, and
Emax. By definition, Q10 is equal to
the ratio of a variable value M10 at temperature (t + 10)°C over its value M0 at t°C, i.e.,
Q10 = M10/M0. When M5 is obtained at temperature (t + 5)°C instead of
M10, Q10 = (M5/M0)2. Therefore, we obtained
Q10 as the square of its change per 5°C rise from 33 to
38°C.
Statistics.
Best-fit a, b, e,
s, and RF values were presented as their means ± SD. They were compared among 33, 36, and 38°C by one-way repeated-measures ANOVA. When ANOVA was significant (P < 0.05), we performed multiple comparisons between LV temperature by
Bonferroni's test. We considered a P value <0.05 to
indicate statistical significance. Correlation coefficient
(r) of the curve fitting was obtained in each PESP decay. We
used StatView 4.5 (Abacus Concepts; Berkeley, CA) to perform these statistics.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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PESP decay patterns.
Figure 2 depicts a representative set of
the PESP decays at 33°C (Fig. 2A), 36°C (B),
and 38°C (C) in one heart. Isovolumic LVV during regular
beats and each PESP decay was maintained at a relatively small constant
volume regardless of LV temperature. The small volume had to be chosen
to avoid LVP of PES1 above 200 mmHg at 33°C. This in turn caused a
relatively low LVP (50-60 mmHg) in regular beats at 38°C. LVP
over 200 mmHg tended to cause spontaneous extrasystoles, and in the
worst case, damage the aortic valve resulting in herniation of the
intraventricular balloon.
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Curve fitting.
Figure 3 depicts a representative set of
the alternating curves (solid curves) best fit with Eq. 1 to
nEmax (normalized Emax) of PES1-6 (closed circles) at 33°C (Fig. 3A), 36°C
(B), and 38°C (C) in one heart. Figure 3 also
shows their monoexponential decay terms (first term of Eq. 1, dashed curves) and exponentially decaying sinusoidal terms
(second term of Eq. 1, dotted curves). The sinusoidal curves
are meaningful only at integer i values corresponding to PES1-6 and meaningless at other noninteger i values
(11).
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e and s
also decreased with increasing temperature. All the other hearts showed
essentially the same results. The r values obtained by fitting Eq. 1 to the alternans decays at 33, 36, and 38°C
in seven hearts were 0.9997 ± 0.0005, 1.0000 ± 0.0001, and
0.9999 ± 0.0001, respectively. All these r values were
virtually 1. This result indicated that Eq. 1 excellently
fit all alternans decays at 33, 36, and 38°C.
We have confirmed that the extremely high correlation was not due to
the closeness between the numbers of unknown variables (= 4) and data
(= 6) (10). Moreover, a polynomial equation even with four
unknown variables (y = ai3 + bi2 + ci + d)
did not fit the same PESi data with an almost unity r
comparable to those with Eq. 1. Furthermore, our recent
theoretical study supported the reliability of Eq. 1
(11). We therefore considered that Eq. 1 could
reasonably well characterize the alternans PESP for the purpose of RF
calculation in a beating heart (3, 26).
Amplitude constants a and b.
Figure 4, A and B,
plots means ± SD values (dimensionless) of amplitude constants
a and b of Eq. 1 best fit to the
alternans PESPs at 33, 36, and 38°C in the seven hearts. Both
a and b decreased significantly with increasing
temperature. Figure 4, C and D, plots means ± SD values (dimensionless) of amplitude constant ratios
a/(a + b) and
b/(a + b). Because
a + b is equal to the normalized magnitude
of PES1, these ratios mean the fractional magnitudes of a
and b in PES1. a/(a + b) increased but b/(a + b) decreased significantly as the temperature increased.
These changes were consistent with the visual impression that the
alternans as well as its oscillatory component gradually disappeared,
and the monoexponential component became dominant as the temperature increased in Figs. 2 and 3.
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Beat constants e and s.
Figure 5, A and B,
plots means ± SD values (beats) of beat constants
e and s of the Eq. 1 best fit
to the alternans PESPs at 33, 36, and 38°C in the seven hearts. Both
e and s decreased significantly with
increasing temperature. Multiplication of e and
s by RI in milliseconds converted these beat constants
to time constants in time unit (in ms). Figure 5, C and
D, plots means ± SD values (beats) of time constants
e times regular beat interval (RI) and s
times RI. Both time constants decreased significantly with
increasing temperature. Because RI was fixed constant at 500 ms in the
present study, these changes in time constants happened to be
proportional to those in beat constants e and
s per se.
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Recirculation fraction.
Figure 6A plots RF values
(dimensionless) given by exp(1/e) using
e of Eq. 1 best fit to the alternans decays
at 33, 36, and 38°C in the seven individual hearts. This RF = exp(1/e) is after the method by Morad and Goldman
(21). We have confirmed the reliability of this RF
calculation by a new discrete fitting method (11). Figure
6B plots their means ± SD values. RF decreased significantly with increasing temperature in every heart as well as on
the average after pooling all the hearts. RF decreased by 18% on
average from 33°C to 36°C, by 13% on average from 36°C to
38°C, and by 28% on average from 33°C to 38°C.
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Temperature sensitivity.
Table 1 lists Q10 of
a, b, e, s, RF, and
Emax. All the obtained Q10 values
were smaller than unity. Therefore, their 1/Q10 values were
greater than unity. For example, RF had Q10 = 0.5 and
1/Q10 = 2 on average. Similarly,
Emax of regular beats had Q10 = 0.6 and 1/Q10 = 1.7.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Postextrasystolic alternans decay. The present result on Emax confirmed the temperature dependence of Emax of regular beats preceding PESP that we have reported previously (18, 24, 31). Q10 of Emax in the present study (Table 1) was similar to 0.44 ± 0.13 for 30-40°C in our previous study (18).
The present results (Fig. 2) show that the transient alternans decay of PESP is the most representative decay pattern at heart rates of 100-150 beats/min under normothermia in the excised, cross-circulated heart. This confirmed our previous studies (3, 10, 13, 16, 19, 26-28). Moreover, it supports for the first time the generality of the alternans PESP decay even under hypothermia (33°C) and hyperthermia (38°C) in the same canine heart at the pacing rate of 120 beats/min. Moreover, the alternans PESP at 33-38°C always fit precisely the same equation (Eq. 1) that we used in the previous studies (3, 10 13, 16, 19, 26-28), namely, the sum of an exponentially decaying monotonic component and an exponentially decaying oscillatory component (Fig. 3). The spontaneous heart rate range we naturally encounter in this type of canine heart preparation is 100-120 beats/min before atrioventricular block under normothermia (3, 10, 13, 16, 19, 26-28). Our recent unpublished observations show that the PESP decay appeared less alternating and more monotonic when heart rate decreased below 100 beats/min after atrioventricular block even under normothermia. The heart rate range above 100 beats/min seems to be the reason that the alternans PESP has been the representative type in our canine heart preparation under normothermia (3, 10, 13, 16, 19, 26-28). Nevertheless, PESP always contained an exponentially decaying monotonic component from which we were able to calculate RF over 33-38°C in this study. Our present study has revealed that amplitude constants a and b and beat constantse and
s of the two decay components of the alternans PESP
decreased sensitively with increasing temperature (Figs. 4 and 5).
Because Q10 < 1 of a, b,
e, and s are comparable to each other
(Table 1), we suspect them to be inversely related to the
temperature-dependent rates of chemical reactions in the Ca2+ handling. In other words, 1/a,
1/b, 1/e, and 1/s
(1/Q10 > 1) may be more directly related to these
chemical reactions.
e, s, and RF.
In our Ca2+ handling model (Fig. 1) (3, 10, 13, 16,
19, 26-28), e of the monotonic decay
component of the transient alternans PESP reflects essentially the same
RF as of the monotonic PESP decay does (11, 21, 34,
35) (see APPENDIX). The present study revealed that
e and RF decreased with increasing temperature. Note,
however, that we kept RIs and PESIs constant regardless of the
temperature changes. Therefore, e times RI, which has time units, also decreased in proportion to e with
increasing temperature. Therefore, e times RI and
e alone have the same Q10, although their
dimensions are different. Their Q10 (<1)
and 1/Q10 (>1) suggest temperature accelerated chemical
reactions behind the smaller RF.
s also decreased with increasing
temperature. In our previous studies, positive and negative inotropic interventions (catecholamines, Ca2+, ryanodine, and
postischemic stunning) did not significantly affect
s (3, 10, 13, 27). Exceptionally,
2,3-butanedione monoxime decreased both s and
e (16). These results seem to support our
contention that s reflects different Ca2+
kinetics from e. We would therefore consider
e and s to be related to different
temperature-dependent chemical reactions in the Ca2+
handling. In our model (Fig. 1), e seems to be related
to the SR Ca2+ pump and sarcolemmal
Na+/Ca2+ exchange, whereas s
related to SR Ca2+ handling between the Ca2+
pump and ryanodine-sensitive release channel (Fig. 1). Although Q10 = 0.3 of e and s
suggests temperature-dependent reactions, their association to any
specific pumps, channels, and exchanges is beyond the present scope.
Cooling inotropism. The present Q10 = 0.6 for Emax is consistent with our previous results (18, 24, 31). However, O2 consumption for total Ca2+ handling is temperature independent (18, 24, 31). This leads to the temperature-dependent O2 cost of Emax with Q10 = 2 (18, 24, 31).
Multiple mechanisms (4) seem to underlie the temperature-dependent Emax and O2 cost of Emax with Q10 < 1 and > 1, respectively, reciprocal to each other. Myocardial cooling inhibits SR Ca2+ uptake via the SR Ca2+ pump and the Ca2+ efflux via the Na+/Ca2+ exchange coupled with the Na+-K+ pump as well as via the sarcolemmal Ca2+ pump (4-6, 14, 22). Not only these ATPase-dependent processes but also ATPase-independent processes such as L-type Ca2+ channel and ryanodine-sensitive Ca2+ release channel have Q10 of 2-4 (2). The cooling-suppressed Na+/Ca2+ exchange also suppresses the reverse mode of the Na+/Ca2+ exchange and increases Ca2+ transient (8). The Na+ pump is also inhibited by cooling (Q10 around 3) (9) and intracellular Na+ rises (7), leading to increases in sarcoplasmic Ca2+ concentration, SR Ca2+ content, and Ca2+ availability for E-C coupling (4). The slowed Ca2+ handling not only decelerates but also prolongs contraction (Q10 around 3) (4, 22). Cooling enhances the Ca2+ responsiveness so that contractile force increases for a given sarcoplasmic Ca2+ concentration (12). Cooling suppresses myosin ATPase and hence cross-bridge cycling, leading to a slower contraction and relaxation (4-6, 14). Cooling thus accounts for not only the positive inotropism and negative lusitropism seen in Fig. 2 but also for the decreased O2 cost of Emax (18). Our previous computer simulation of myocardial Ca2+ handling and cross-bridge cycling has simulated these temperature-dependent changes in myocardial mechanoenergetics to reasonable extent (17). In this simulation, we changed all ATP-consuming processes in the E-C coupling and force development. Therefore, we would speculate that the temperature-dependent changes in the parameters of the transient alternans PESP could largely be related to the ATP-consuming reactions in myocardial excitation, E-C coupling, and contraction.Ca2+ and ATP consumption. A change in RF affects ATP consumption for myocardial total Ca2+ handling according to the different energy cost between the major internal and external Ca2+ handling routes (25, 31). The internal Ca2+ handling route via the SR is nominally twice more economical than the transsarcolemmal route (4, 27, 33).
In mass Ca2+ dynamics, the RF is exclusively related to the SR Ca2+ pump, and the 1 RF is related predominantly
to the sarcolemmal Na+/Ca2+ exchange coupled
with the Na+-K+ pump (4, 27, 33).
We had observed the economical O2 cost of
Emax in the hypothermic canine hearts
(31). As the cause of this economical state, we previously
speculated that the Ca2+ responsiveness of contractility
increased primarily by cooling (18). However, the present
study has revealed increases in e and RF at hypothermia.
Therefore, the decreased O2 cost of
Emax at hypothermia (18, 31) seems
to have resulted from increases in Ca2+ responsiveness of
contractility and RF. Similarly, the increased O2 cost of
Emax at hyperthermia (18, 24) seems
to have resulted from decreases in Ca2+ responsiveness of
contractility and RF.
RF versus O2 cost of Emax.
Although the present Q10 = 0.5 of RF is inversely
proportional to the previous Q10 = 2 of O2
cost of Emax (18), this does not
immediately mean that the latter is fully accountable by the former.
Table 2 lists the equations relating
total Ca2+ handling, its O2 consumption (its
O2, or total Ca2+ handling
O2), RF, and Emax
(3, 27). Equation A in Table 2 is the
stoichiometric equation relating total Ca2+ handling, its
O2, and RF. Equation B
defines the reactivity (R) of Emax to total
Ca2+ handling. The substitution of Eq. B into
Eq. A yields Eq. C after conversion of the
dimensions of O2 (from µmol/kg into ml
O2/100 g). Equation D defines the O2
cost of Emax. The substitution Eq. D
into Eq. C yields Eq. E. It relates
O2 cost of Emax with RF and R.
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RF and 1/R, but not 1/RF. This means theoretically that
Q10 of O2 cost of Emax
is neither proportional to nor accountable by Q10 of 1/RF,
although they appear reciprocal to each other. Therefore,
Q10 = 2 of O2 cost of
Emax in our previous study (18)
should not be directly accounted for by the present Q10 = 0.5 of RF.
Figure 7 shows a set of theoretical
relations given by Eq. E in Table 2 with R as a parameter.
Theoretically, the decrease in RF from 0.7 at 33°C to 0.5 at 38°C
with Q10 of 0.5 in the present study (Fig. 6 and Table 1)
causes an inversely proportional increase in O2 cost of
Emax with Q10 of ~1.3 at any
constant R, as shown by four slant lines. This Q10 is only
~65% of the Q10 = 2 of O2 cost of
Emax (18). A theoretically possible
mechanism to account for this discrepancy would be a simultaneous
change in reactivity R in the same direction as O2 cost of
Emax, as indicated by the heavy steep line
connecting the two working points (open circles) at 33 and 38°C in
Fig. 7. For a change in R to account for the Q10 = 2 of O2 cost of Emax, R has to
decrease by ~40% from 0.022 to 0.018 with 5°C change from 33 to
38°C. This suggests the Q10 of R to be ~0.5 comparable
to that of RF. This Q10 of R is comparable to Q10 = 0.5-0.6 of Emax in our previous studies
(18, 24, 31).
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Limitations. The present model of total Ca2+ handling has a limitation. Our Ca2+ handling model combines the oscillatory component of the SR Ca2+ handling with the Morad and Goldman model (21). Their model assumes that SR has little delay in the availability of sequestered Ca2+ for the next release (21). This holds as long as the mechanical restitution is fully recovered, namely, after a relatively long beat interval (37). However, beat intervals even without pacing in the present heart preparation are too short for the full recovery of mechanical restitution (20). This seems to generate the oscillatory component on top of the exponential decay (20) (see APPENDIX).
We calculated RF from the exponential component of the alternans PESP after removing its oscillatory component using Eq. 1. Therefore, any possible interactions between the exponential and oscillatory components are excluded in the RF calculation. We have separately shown that RF is independent of the magnitude of the oscillatory component in the alternans PESP (26). We have also observed no significant electrical alternans during the alternans PESP (26). This supported little if any alternation of transsarcolemmal Ca2+ influx (26). However, more direct evidence remains to be obtained to support our RF calculation. Although RF seems to help our understanding of cardiac mechanoenergetics (3), one may suspect that the alternans PESP as we have reported in series (3, 10, 13, 16, 19, 26-28) may not occur in the intact in situ heart. At least we have confirmed its existence in intact in situ left ventricles of anesthetized open-chest dogs using a conductance volumetric catheter with a pressure gauge (unpublished observation). Generality of the alternans PESP remains to be confirmed in normal human hearts. However, when the alternans PESP does not occur, RF will simply be obtained by the conventional method (21, 34, 35). One must be careful to interpret Q10 < 1 of RF obtained in this study. We fixed the heart rate against the temperature-dependent chronotropism in the present study. However, when we changed the heart rate at a constant temperature of 37°C, RF increased with heart rate (26). Therefore, RF would remain unchanged (Q10 = 0) or even increase (Q10 > 0) under the temperature-dependent chronotropism. This situation seems to account for the previously reported decreased RF at a lower temperature accompanied by a lower pacing rate in guinea pig papillary muscles (29). Q10 has its own limitation. In general, Q10
1.5 of a variable suggests it related directly or indirectly to
chemical processes, whereas 1.4 > Q10 1 related to
physical processes. 1/Q10 > 1.5 and 1.4 > 1/Q10 1 suggests them to be inversely related to
chemical and physical reactions, respectively. However, when a variable of interest is of a complex biological (physicochemical) system, its
Q10 or 1/Q10 could fall between 1.4 and
1/1.4 = 0.7 even when its subsystem(s) is or are related to
chemical processes (23). Nevertheless, the strength of
Q10 in this study is the elucidation that all
1/Q10 values of RF and the other related variables
characterizing the PESP are >1.4. This suggests that they are closely
related to chemical reactions most likely including ATPase activities and hence ATP consumption in myocardial Ca2+ handling, but
not merely to physical processes such as diffusion. Attribution of RF
and the other related variables in Eq. 1 to the individual
processes of Ca2+ handling is beyond the present scope.
We therefore conclude that the present findings validated our tested
hypothesis. The temperature dependence of the Ca2+ handling
chemical processes could largely account for the temperature-dependent change in O2 cost of Emax. The
involved chemical processes are related to the recirculation fraction
of Ca2+ within myocardial cells (RF) and contractile
reactivity (R) to released Ca2+. This finding would provide
insights into better pathophysiological understanding and effective
treatment of failing hearts.
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APPENDIX |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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In relation to recirculation fraction (RF of Ca2+ within myocardial cells) briefly explained in MATERIALS AND METHODS, the entire sarcoplasmic Ca2+ that are recruited (i.e., released and then removed) for each E-C coupling could be lumped into two fractions. The major fraction is the Ca2+ that is released into the sarcoplasma via the ryanodine-sensitive Ca2+ channel from SR and sequestered by its Ca2+ pump back into the SR in each contraction (4, 5, 21, 33-35). The other fraction is the Ca2+ that enters transsarcolemmally into the sarcoplasma predominantly via L-type Ca2+ channel and auxiliarily via the reverse mode of Na+/Ca2+ exchange (4, 5, 21). This fraction is extruded predominantly via the forward mode of Na+/Ca2+ exchange and auxiliarily via the sarcolemmal Ca2+ pump (4, 5, 21). Note that the total Ca2+ flux or transport of our interest is of the order of 10-100 µmol/kg, which is 50-100 times greater than the much more popular, free Ca2+ or Ca2+ transient of the order of 0.1-2 µmol/l (3, 4).
In steady-state, regular beats, these internal and external fractions are balanced under Ca2+ homeostasis (4, 5, 21). The former fraction is RF of our present interest. However, no method has been developed to determine the RF directly in steady-state contractions of a beating whole heart.
The standard method to estimate the RF is to perturb the
Ca2+ homeostasis by inserting an extrasystole or a test
stimulation and analyze the decay rate of the following potentiated
beats on the basis of the Morad and Goldman model (21, 34,
35). Figure 8A
graphically shows RF in regular beats and potentiated beats
(PESi, i = 1-6) decaying exponentially,
as reported to be the most representative (21, 34, 35).
Here, we defined the constant height of the lower dashed zone relative
to unity (RFo) as the RF of regular beats and the
exponentially decaying height of the upper dashed zone relative to the
potentiated component of PESi (RFp) as the RF of
PESi above unity.
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The model assumes that RFo maintains the same released Ca2+ as the regular beat level for the unity contractility component below the horizontal line at 1 even during PESi, whereas RFp suddenly appearing in PES1 and then decreasing at a constant rate over PES2-6 causes the extra-released Ca2+ component (+a) for the potentiated contractility component above the horizontal line at 1.
We could reasonably assume ventricular contractility or
Emax is to be proportional to the total released
Ca2+ on the basis of the constancy of O2 cost
of Emax despite the 70% increase in
Emax in our previous studies (30).
Then PESi has the potentiated contractility or
released Ca2+ of 1 + a · RF
1)] = RF
[1 + a · RF(i1)]
/[1 + a · RF(i1)] = RF
regardless of PESi and regular beats around PESP. This condition is nothing but what Morad and Goldman assumed
(21).
There are two methods to obtain this RF. One is the slope method.
Contractilities of PESi (i = 1-6) are
plotted on the abscissa against those of next potentiated beats
(PESi + 1) on the ordinate (21, 34, 35).
They line up linearly toward regular beat contractility point, although
not shown here (21, 34, 35). This relationship means that
contractility and hence released Ca2+ decay at a constant
rate over PESi toward the regular beat level. This constant
decay rate obtained as the slope of the linear regression line
indicates the RF (21, 35). Therefore, although RF is obtained from PESi, the same RF is assumed to hold during
the regular beats before and after PESi (21, 34,
35). The other method is to fit an monoexponential curve,
a · exp[(i 1)/], to PESi
above the regular beat level (21, 34, 35). Mathematically, RF = exp(1/) (21, 35).
However, neither of these conventional methods is applicable to the
alternans PESi that we observed consistently in canine hearts in the present and previous studies (Fig. 8B)
(3, 11, 27). We have developed Eq. 1 to extract
the same monoexponentially decaying component as in Fig. 8A
by peeling off the oscillatory decay component from the alternans
PESi (3, 11, 26, 27). We have already confirmed
that beat constant e, and hence RF obtained by this
method, remain unchanged despite wide changes in the extrasystolic
coupling interval and the first postextrasystolic interval
(26). This constancy of e and RF also held,
although a and b of Eq. 1
simultaneously changed considerably (26). We have also
found that e and RF change sensitivity with pathological conditions of canine hearts (3, 10, 13, 16, 27). We have
therefore concluded Eq. 1 to facilitate a better
understanding of physiology and pathophysiology of myocardial
Ca2+ handling in a beating heart, although yet limited to
canine excised, cross-circulated (blood-perfused) hearts
(3).
Moreover, we have successfully confirmed that the mechanical restitution mechanism (37) could account for the oscillatory component of the alternans PESP at a relatively high heart rate (Iribe G, Kajiya F, Araki J, and Suga H, "A new myocardial calcium dynamics model in E-C coupling." Presented as a poster A-462 at Experimental Biology 2001, March 31-April 4, 2001, Orlando, FL; unpublished observations). We (i.e., Iribe et al.) have concluded in this unpublished study that our RF calculation based on the model (Fig. 1) and Eq. 1 is theoretically reasonable.
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ACKNOWLEDGEMENTS |
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We greatly thank Kimikazu Hosokawa for animal supply and care.
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FOOTNOTES |
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This study was partly supported by Scientific Research Grants 10044330, 10470010, 10558136, 10770307, 10877006, 11898028, 12480269, 12680832, 13558113, 13770350, 13878185, and 13878192 from the Ministry of Education, Science, Technology, Sports, and Culture; Research Grant 11C-1 for Cardiovascular Diseases; a 2000 Health Sciences Research grant for Human Genome and Regenerative Medicine from the Ministry of Health, Labor, and Welfare; 1999-2001 Cardiac Physiome grants from Okayama New Industry Promotion Foundation; and research grants from the Suzuken Memorial Foundation and the Vehicle Racing Commemorative Foundation, all of Japan.
Address for reprint requests and other correspondence: H. Suga, National Cardiovascular Center Research Institute, 5-7-1 Fujishirodai, Suita, Osaka 565-8565, Japan (E-mail: hsuga{at}ri.ncvc.go.jp).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
10.1152/ajpheart.00427.2000
Received 21 May 2001; accepted in final form 10 October 2001.
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REFERENCES |
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TOP
ABSTRACT
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DISCUSSION
APPENDIX
REFERENCES
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