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1 Department of Physiology II, and 2 Department of Cardiovascular Medicine, Okayama University Medical School, Okayama 700-8558; and 3 Department of Physiology II, Nara Medical University, Nara 634-8521, Japan
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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In isolated, blood-perfused canine hearts, postextrasystolic potentiation (PESP) decays monotonically after a noncompensatory pause following a spontaneous extrasystole (ES). The monotonic PESP decay yields myocardial internal Ca2+ recirculation fraction (RF). We have found that after a compensatory pause (CP), PESP decays in alternans, consisting of an exponential and a sinusoidal decay component. We have proposed that this exponential component also yields RF. In the present study, we examined the reliability of this alternative method by widely changing the ES coupling interval (ESI), CP, and heart rate in the canine excised, cross-circulated left ventricle. We found that all PESP decays consisted of the sum of an exponential and a sinusoidal decay component of variable magnitudes whether a CP existed or not. Their decay constants as well as the calculated RF were independent of the ESI and CP. This confirmed the utility of our alternative RF determination method regardless of the ESI, CP, and heart rate. Direct experimental evidence of Ca2+ dynamics supportive of this alternative method, however, remains to be obtained.
cardiac contractility; extrasystole; mechanical potentiation; mechanical alternans; transient alternans
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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WE HAVE REPORTED THAT the postextrasystolic (PES) potentiation (PESP), after an extrasystole (ES) and a compensatory pause (CP), decays in transient alternans over several beats in canine hearts (3, 8, 10, 14, 15, 20, 21, 25). We confirmed that the PESP after a non-CP decayed exponentially, as other investigators reported (6, 11, 16, 17, 28, 30, 32, 33). The alternans PESP decay, including transient mechanical alternans after other types of arrhythmia, has generally been recognized as a sign of abnormal cardiac conditions such as ischemia, hypothermia, and so forth (7, 19, 29, 31). By contrast, we have found that existence and absence of a CP consistently determine the decay patterns of the PESP even in canine normoxic blood-perfused, normothermic hearts (3, 8, 10, 14, 15, 20, 21, 25).
We then found that the alternans PESP decay pattern could reasonably be
described by the sum of an exponential decay component and a sinusoidal
decay component (8, 10, 14,
15, 20, 21, 25).
The formula we have proposed is y = a
· exp[
(x 1)/
e] + b · exp[(x 1)/s]cos[
(x 1)] + 1, where the
first term corresponds to the exponential decay component and the
second term corresponds to the sinusoidal decay component
(8, 10, 14, 15,
20, 21, 25). We have proposed
that the beat constant, e, in the first term of the
above equation can also be used to calculate myocardial internal
Ca2+ recirculation fraction (RF) (16), an
integrative measure of myocardial Ca2+ handling
(8, 10, 14, 15,
20, 21, 25). The RF has conventionally been calculated from the beat constant of the
exponential PESP decay after a non-CP (16,
17, 28).
We proposed that RF, combined with cardiac mechanoenergetics in
the Emax-PVA-
O2
framework (23) (see METHODS), enables indirect
assessment of total Ca2+ handling in a beating heart
(8, 10, 14, 15,
20, 21, 25). Here,
Emax is an index of ventricular contractility (maximum elastance), PVA is a measure of ventricular total mechanical energy, and O2 is ventricular O2
consumption (23). In those studies, all the ESs were
spontaneous, and their extrasystolic coupling intervals (ESIs) were
uncontrolled under constant atrial pacing (8,
10, 14, 15, 20,
21, 25). Therefore, the generality of the
equation and the reliability of the alternative RF calculation method,
over wide ranges of ESI, CP, and regular beat interval (RI), remain to
be investigated in a prospective study.
To this end, we performed this study by widely changing ESI with and
without a CP at three different RIs in a precisely controlled manner.
We used the canine excised, cross-circulated, blood-perfused, complete
atrioventricular block heart preparation and performed para-Hisian
pacing by precisely programmed stimuli. We first confirmed that the
PESP consistently decayed in transient alternans with a CP, regardless
of RI or ESI. We also found that the PESP, even without a CP, had a
small but obvious transient alternans component, which is contrary to
the general belief (16, 17, 28).
Thus all the transient alternans PESP proved to consist of an
exponential and a sinusoidal decay component, although their magnitudes
considerably varied depending on the RI, ESI, and CP. Beat constants
e and s and RF values calculated from
both PESPs with and without a CP were respectively comparable
regardless of ESI but decreased as RI increased. However, their
products, e · RI and s · RI, were independent of RI. These results provided firm evidence
supportive of the generality of the equation and the reliability of the
alternative RF calculation method that we have recently developed
(8, 10, 14, 15,
20, 21, 25).
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Surgical preparation. All the experiments were conducted in conformity with the "Guiding Principles for Research Involving Animals and Human Beings" endorsed by the American Physiological Society. The heart preparation we used has been described in detail elsewhere (4, 12, 13, 18, 20-27).
Briefly, two mongrel dogs were anesthetized with ketamine hydrochloride (50 mg im) and pentobarbital sodium (25 mg/kg iv) for each experiment. Arterial and venous cross-circulation tubes were cannulated into the common carotid arteries and the external jugular vein of the support dog. The metabolically supported heart was excised from the chest under cross circulation from the support dog. The coronary circulation was never interrupted during the surgery. A complete atrioventricular block was made by either formaldehyde injection or electrical ablation. Para-Hisian pacing was performed with a bipolar electrode. A thin latex balloon (unstretched volume of 50 ml) fitted in the left ventricle (LV) was filled with water and connected to our custom-made volume servo pump (4, 12, 13, 18, 20-27). The servo pump enabled us to accurately measure and precisely control LV volume (LVV). LV pressure (LVP) was measured with a miniature pressure gauge (P-7, Konigsberg) placed within the apical end of the balloon. Temperature of the blood and the heart was kept constant at 37°C with heaters. LV epicardial electrocardiogram (ECG) was recorded with a pair of screw-in electrodes. Monophasic action potential (MAP) was also recorded with an epicardial electrode pressed on the LV anterolateral surface in four of the seven hearts. LVP, LVV, ECG, and MAP signals were digitized at 2-ms intervals with an A/D converter (Lab-NB, National Instruments), displayed on a computer, and stored on a hard disk (Power Macintosh 7100/80; Apple Computers, Cupertino, CA).Pacing protocol.
Figure 1, A and B,
shows the two different pacing patterns. The pacing pattern consisted
of 10 or more stimuli at RIs of 400, 500, or 600 ms in a priming
period. One extrasystolic stimulus at a variable coupling interval
(ESI > 300 ms) was then inserted. The first PES stimulus at a PES
beat interval (PESI 1) was given either with a CP (Fig.
1A) or without the CP (Fig. 1B); both were followed by the same RI for 10 or more PES beats. The three RIs correspond to heart rates of 150, 120, and 100 beats/min, respectively. Thus the pacing pattern in Fig. 1B differed from that in
Fig. 1A only in the PESI 1, which was equal to
the RI with no CP.
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Data analyses.
To evaluate the beat-to-beat changes in LV contractility during each
PESP decay, we used the maximum LV elastance
(Emax) as an index of ventricular contractility
(22-24). Emax was calculated for the first through sixth PES beats (PES 1-6) as the
ratio of peak LVP to the corrected LVV (22-24). We
obtained the corrected LVV by subtracting from LVV the unstressed
V0, which we identified as the LVV at which peak isovolumic
LVP was zero (22-24). We normalized the
Emax values relative to the
Emax of the preceding regular beat (mean
Emax of the 3 stable beats). Because LVV was a fixed constant (9.5-20.5 ml) in each experiment, the changes in
Emax were proportional to those in isovolumic LVP at a
fixed LVV. Mean ± SD of Emax of regular
beats was 8.54 ± 3.04 mmHg/ml, or 3.75 ± 0.77 mmHg · ml
1 · 100 g LV wt1, at RI of 600 ms,
indicating usual LV contractility.
![n<IT>E</IT><SUB>max</SUB><IT>=a·</IT>exp[−(<IT>i−1</IT>)<IT>/&tgr;</IT><SUB>e</SUB>]<IT>+b·</IT>exp[−(<IT>i−1</IT>)<IT>/&tgr;</IT><SUB>s</SUB>]](/content/vol279/issue1/fulltext/H225/img001.gif)
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![cos[<IT>&pgr;</IT>(<IT>i−1</IT>)]<IT>+1</IT>](/content/vol279/issue1/fulltext/H225/img002.gif)
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(1) |
e and
s are the beat constants of the first and second
exponential terms, respectively, expressed in beat number but not in
time unit (16). We calculated RF as
exp(1/e) (8, 10,
14, 20, 21, 25).
This equation was developed by Morad and Goldman (16) and
has been proven useful by other investigators (17,
28). Neither a, b, nor s is related to the RF determination.
The first term is a monoexponential function that has conventionally
been used for the monotonic PESP decay (16,
17, 28). This term has been related to the
Ca2+ efflux exceeding the Ca2+ influx during
the PESP to recover Ca2+ homeostasis in regular beats
(16, 17). The second term could be related to
the delay of the Ca2+ releasability via the sarcoplasmic
reticulum (SR) (1, 2). We suspect that this
sinusoidal term is partly related to the potentiation and restitution
mechanisms (15, 30, 33).
We used LabVIEW 3.1 for the curve fitting by the Levenberg-Marquart
method on a Power Macintosh computer. The goodness of the curve fitting
was evaluated by the correlation coefficient (r).
The duration of the MAP (action potential duration; APD) was obtained
by determining the duration at 90% repolarization of the full
amplitude of the MAP in all the regular beats, ES beats, and PES
1-6.
Statistics.
The data were presented as means ± SD. Differences in
a, b, e, and s were
analyzed by two-way repeated measures ANOVA. Significance of their
multiple comparisons was tested by the Student-Newman-Keuls method on
StatView 5.0. We considered P < 0.05 to indicate
statistical significance.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Decay patterns.
Figure 1A shows a representative transient alternans PESP
decay following an ESI of 324 ms and a CP (476 ms; PESI
1 = 2RI ESI) at an RI of 400 ms. Peak LVP of the
PES 1 was greater than that of the regular beat. However,
the PES 2 was considerably weaker than not only the
PES 1 but also the regular beat. The PES 3 was
moderately stronger than not only the PES 2 but also the
regular beat. PES 4-6 gradually returned to the regular
beat level in small alternans. All other PESP cases following different RIs and ESIs with CPs in this heart as well as in all the other hearts
decayed in transient alternans similar to those in Fig. 1A.
This transient alternans PESP resembled the PESP decay pattern that we
consistently observed in our retrospective studies (3, 8, 10, 14, 20,
21, 25).
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Curve fitting.
Figure 3 shows a representative set of
the best-fit Eq. 1 curves (solid line) together
with their exponential decay component (dashed line) and exponential
term (dotted line) of the sinusoidal decay component in one heart. RI
was varied from 600 to 500 and 400 ms from left to
right with CP (Fig. 3, A-C) and without CP (Fig. 3, D-F) at an ESI of 300 ms. The solid
alternating curves best fit the data points with r > 0.999.
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e, and s as a function of
ESI at RIs of 600, 500, and 400 ms, both with (Fig. 4,
A-C) and without CP (Fig. 4,
D-F) in one heart. In Fig. 4, A-C,
amplitude constant a was much smaller than b at
any RIs and ESIs. In Fig. 4, D-F, amplitude constant
a was comparable with b at any RIs and ESIs. Both
a and b decreased as the ESI increased in all the
panels. Mean a-to-b ratio over the entire range
of ESI without CP was significantly greater (P < 0.01)
than that with CP at any RI, as summarized in Table
1. In other words, the amplitude of the exponential decay component was significantly greater in the PESP decays without CP than with CP.
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e and s were
largely independent of ESI at any RI, regardless of CP. Percent
coefficients of variation (CVs; CV = SD/mean) of e
and s were 4.5 and 7.2 in Fig. 4A, 3.7 and
2.8 in Fig. 4B, 7.9 and 3.1 in Fig. 4C, 4.6 and
6.9 in Fig. 4D, 3.7 and 7.3 in Fig. 4E, and 3.7 and 1.4 in Fig. 4F. These CV values were practically small,
indicating the reasonable independence of e and
s from ESI. Plots of e are lacking above
an intermediate ESI at which the convergence of the curve fitting
became poor. The poor fitting occurred when parameter a
decreased below a certain level (<0.094 ± 0.055 with CP and
0.113 ± 0.058 without CP) at longer ESIs. This poor fitting
seemed likely attributable to the decreasing signal-to-noise ratio of
the decreasing nEmax values of PES
1-6 with increasing ESI, as discussed elsewhere
(8). At the longer ESIs, where e was not
obtainable, the first exponential term with a and
e was neglected, and the second term with b
and s was fit to the data (8,
10, 14, 15, 20,
21, 25). For this reason, a reliable
s value continued to be obtained for increasing ESI,
even after a reliable e was no longer obtained, as shown
in Fig. 4. Within the ESI ranges with reliable e and s, e was always two to three times
greater than s. Similar results were obtained in all the
other hearts.
Table 2 lists mean ± SD values of
e and s in the number of beats (i.e.,
beat constants) as well as their products with RI in seconds (i.e.,
time constants) at all ESIs in all the hearts. Both e
and s significantly decreased with increasing RI,
regardless of CP. However, no difference existed in either
e or s between those with and without CP.
Mean ± SD values of CVs of e and s are also listed. Their mean values were only 10 ± 6% for
e and 8 ± 6% for s with CP and
10 ± 3% for e and 7 ± 3% for
s without CP, indicating the reasonable independence of
e and s from ESI regardless of CP.
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e · RI and
s · RI. In contrast to e and
s, e · RI and
s · RI were not significantly changed with RI
regardless of CP. Neither e nor s (and
neither e · RI nor s · RI)
was significantly different between those with and without CP.
Table 2 lists RF [=exp(1/e)]. There was no
significant difference in RF, with or without CP, at any RI. RF had a
greater SD with CP than without CP at any RI. RF significantly
decreased with increasing RI without CP, but similar decreases in RF
with increasing RI were not significant with CP.
MAP duration.
No MAP tracing showed electrical alternans during the PESP at any RIs
and ESIs, regardless of CP in any of the hearts. Figure 5 shows two
representative examples (mean ± SD) of ADP at 90% duration
(APD90) of the MAPs over the PESPs with (Fig.
5A) and without (Fig. 5B) CP in one heart. Figure
5A averaged eight cases, with an RI of 600 ms and a varied
ESI between 300 and 500 ms with CP. Figure 5B averaged 21 cases, with an RI of 600 ms and a varied ESI between 300 and 500 ms
without CP.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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The present study revealed for the first time that the PESP, regardless of whether the PESI 1 has a CP, always decayed in transient alternans consisting of an exponential decay component and an exponentially decaying sinusoidal component. This observation was made in canine blood-perfused normally functioning hearts under physiological perfusion conditions. This heart preparation is the same type that we have been using consistently over many years with expertise (4, 12, 13, 17, 20, 22, 23, 25, 26). The present finding evidently supports the utility of our recently developed method of RF (internal Ca2+ RF) determination (3, 8, 10, 14, 15, 20, 21, 25), as discussed below.
Both exponential and sinusoidal components decayed over PES 1-6 at heart rates of 100, 120, and 150 beats/min. This consistent observation of the alternans PESP decay seems to refute the conventional belief that the PESP normally decays exponentially but in alternans only under abnormal contractile conditions (e.g., ischemia, hypothermia) (7, 11, 16, 18, 27, 28, 30, 31).
Against both the conventional, generally held belief (11, 16, 27, 31) and our expectation from our previous studies (3, 8, 10, 14, 15, 20, 21, 25), we did not observe a representative case of exponential or monotonic PESP decay in the present study at all. This intriguing result could be related to the obvious difference in the PESP without CP between the present controlled cases (Figs. 1-3) and the previous spontaneous cases. In other words, the ES always originated from the same para-Hisian pacing site as the constant pacing in the controlled PESPs in the present study. In contrast, the ES not followed by a CP was exclusively of supraventricular origin in the spontaneous PESPs under no constant atrial pacing in our previous studies (3, 8, 10, 14, 15, 20, 21, 25). However, we cannot yet conclude that this pacing difference has caused the difference of the PESP decay pattern between the present controlled PESP experiment and our previous spontaneous PESP experiments.
The exponential PESP decay has been accounted for by myocardial Ca2+-handling models consisting of the internal Ca2+ uptake store, the Ca2+ release store, and the Ca2+ moving path within the SR plus the transsarcolemmal Ca2+ influx and efflux paths (16, 17, 28, 32). In addition, there is proportionality, although not linear, between sarcoplasmic-bound Ca2+ and peak force (5, 9). On these bases, the exponential nature of the conventional monotonic PESP decay has been accounted for by a gradual beat-by-beat recovery of the Ca2+ influx-efflux balance (or Ca2+ homeostasis) from the once augmented sarcoplasmic Ca2+ before the PES 1 (16, 17, 32).
This recovery of the transient Ca2+ influx-efflux imbalance
has been modeled by Morad and Goldman (16). This model is
the basis of the concept of myocardial internal Ca2+ RF, to
be obtained by exp(1/beat constant) (16). We have shown the utility of this Ca2+-handling model in combination with
our mechanoenergetic
(Emax-PVA-O2) framework. The present findings of the dependence of e,
s, and RF on RI and the independence of
e · R and s · R from RI
indicate that the restoration of the Ca2+ homeostasis is a
function of time during PESP rather than the beat number of PES
1-6.
The absence of electrical alternans seems to negate the possibility that the alternans decay component of the PESP is primarily derived from alternating Ca2+ influx (31). It rather supports the notion that the alternans component is derived from the Ca2+-handling mechanism that is inherent in the SR. In fact, Adler et al. (1, 2) proposed Ca2+-handling models that could simulate transient mechanical alternans without assuming alternating Ca2+ influx. Our recent simulation has shown that the transient alternans component of the PESP could be partly derived from the postextrasystolic potentiated restitution (15). Because the restitution and potentiation primarily manifest the beat interval-dependent Ca2+-handling properties of the SR (33), we would consider that the exponentially decaying cosine term in Eq. 1 also primarily manifests the SR characteristics.
In our retrospective studies (3, 8,
10, 14, 15, 20,
21, 25), we have found that e
and hence RF changed sensitively with cardiac contractile conditions.
Therefore, the present study reinforces our integrative approach to the
study of myocardial Ca2+ handling at the beating whole
heart level. Although s seems to characterize the
alternans decay and hence the SR Ca2+-handling properties,
we have found that s was insensitive to the cardiac
contractile conditions (3, 8,
10, 14, 15, 20,
21, 25). However, our unpublished studies
show that s sensitively changes with myocardial
temperature and 2,3-butanedione monoxime treatment. Therefore, we
believe that simultaneous determination of both e and
s would help elucidate myocardial total Ca2+
handling in a beating heart.
There are some limitations in this study. Eq. 1 is a practically reasonable, phenomenologically integrative equation to describe the PESP but not a physiologically ideal, constitutive one. Direct experimental evidence of Ca2+ dynamics supportive of Eq. 1 remains to be obtained. Nevertheless, both the exponential term and the product of the exponential and cosine terms in Eq. 1 are popular in analogy to describe any decay at a constant rate and any sinusoidal oscillation decaying at another constant rate, respectively. This analogy is theoretically allowable, although the PESP data are discrete but not continuous. We do not intend to imply in Eq. 1 that myocardial Ca2+ handling contains any continuously exponential and sinusoidal mechanisms. These terms only characterize myocardial Ca2+-handling mechanisms related to the peak isovolumic pressure development at a given ventricular volume, i.e., contractility or Emax. Taking advantage of this, we have succeeded in characterizing total Ca2+ handling in our canine heart model (8, 10, 14, 15, 20, 21, 25).
In conclusion, we have discovered that in our model, the PESP always
decays in transient alternans consisting of an exponential decay
component and an exponentially decaying sinusoidal component, regardless of a CP. We systematically obtained the amplitudes and beat
constants of the respective decay components of the PESP as a function
of both regular beat and ESIs with and without a CP for the first time.
The results show that the beat constant (e) of the
exponential decay component reliably yields internal Ca2+
RF, regardless of the extrasystolic and postESIs and heart rate. These
novel findings validate the reliability of our method of RF
determination recently developed (20). This validation
reinforces the utility of our combination of RF with cardiac
mechanoenergetics in the
Emax-PVA-O2 framework
for better understanding of myocardial total Ca2+ handling
in a beating whole heart (3, 8,
10, 14, 15, 21,
25).
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ACKNOWLEDGEMENTS |
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We thank Dr. Daniel Burkhoff, Div. of Circulatory Physiology, Dept. of Medicine, Columbia Presbyterian Medical Center, 177 Fort Washington Ave., New York, NY 10032 (where J. Shimizu is now a postdoctoral fellow) for the critical comments to an early draft of this manuscript.
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FOOTNOTES |
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This work was supported in part by Grants-in-Aid for Scientific Research 09470009, 10470010, 10558136, 10770307, and 10877006 from the Ministry of Education, Science, Sports and Culture; Cardiovascular Research Grant 11C-1 from the Ministry of Health and Welfare; a 1999 Cardiovascular Physiome Grant from the Science and Technology Agency; and a research grant from Suzuken Memorial Foundation, all of Japan.
Address for reprint requests and other correspondence: J. Shimizu, Dept. of Physiology II, Okayama Univ. Medical School, 2-5-1 Shikatacho, Okayama 700-8558, Japan.
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. §1734 solely to indicate this fact.
Received 21 September 1999; accepted in final form 7 January 2000.
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REFERENCES |
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TOP
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METHODS
RESULTS
DISCUSSION
REFERENCES
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) and
b (
) (on left ordinates) and time constants
) and 
) (on
right ordinates) of first and second exponential terms in
Eq. 