Myocardial oxygen consumption of fibrillating ventricle in hypothermia

Myocardial oxygen consumption of fibrillating ventricle in hypothermia Successful account by new mechanical indexes-equivalent pressure-volume area and equivalent heart rate We studied the effects of cardiac hypothermia on myocardial oxygen consumption of a fibrillating

ventricle and evaluated whether myocardial oxygen consumption of a fibrillating ventricle in hypothermia can be accounted for by new mechanical indexes: equivalent pressure-volume area and equivalent heart rate in the isolated cross-circulated canine heart preparation. Equivalent pressure-volume area is the area that is surrounded by a horizontal pressure-volume line at the pressure of a fibrillating

ventricle and the end-systolic and end-diastolic pressure-volume relations in the beating state in the pressure-volume diagram. Equivalent pressure-volume area is an analog of the pressure-volume area of a beating heart and has been proposed to be a measure of the total mechanical energy of a fibrillating

ventricle. Equivalent heart rate was calculated from myocardial oxygen consumption per minute in both beating and fibrillating states under unloaded conditions as an estimate of the frequency of contractions of individual. myocytes on the assumption that individual myocytes during ventricular fibrillation have the same contractility as that in the beating state. We estimated myocardial oxygen consumption per minute of the fibrillating ventricle at various ventricular volumes as a function of both equivalent pressure-volume area and equivalent heart rate. The myocardial oxygen consumptionequivalent pressure-volume area relation during ventricular fibrillation in hypothermia was highly linear, with a correlation coefficient of 0.90 (mean). The relation between estimated and directly measured myocardial oxygen consumption values of a fibrillating ventricle in hypothermia was highly linear (r = 0.98), and the regression line (y = O.SOx + 0.48) was close to the identity line in the working range. Therefore we conclude that equivalent pressure-volume area is the primary determinant of myocardial oxygen consumption during ventricular fibrillation in hypothermia, and myocardial oxygen consumption of a fibrillating ventricle in hypothermia can be accounted for by the combination of equivalent pressure-volume area and equivalent heart rate as in normothermia. (J THORAC CARDIOVASC SURG

1992;104:364--73)

Hitoshi Yaku, MD,a Yoichi Goto, MD,a Shiho Futaki, MD, Yuichi Ohgoshi, MD,a Osamu Kawaguchi, MD,a and Hiroyuki Suga, MD,b Osaka and Okayama, Japan

From the Department of CardiovascularDynamics, National Cardiovascular Center (NeVe) Research Institute," Suita, Osaka, Japan, and The Second Department of Physiology, Okayama University Medical School,b Okayama City, Okayama, Japan. Partly supported by Grants-in-Aid (63570045,01770069) for Scientific Research from the Ministry of Education, Science, and Culture, by Research Grants (63A-2, lA-i) for Cardiovascular Diseases from the Ministry of Health and Welfare of Japan, and by a grant from the Nissan Science Foundation. Received for publication Jan. 23, 1991. Accepted for publication June 24, 1991.

Addressfor reprints: HiroyukiSuga, MD, The Second Department of Physiology, Okayama University Medical School, 2-5-1 Shikatacho, Okayama 700, Japan.

12/1/32011

364

We often encounter ventricular fibrillation while coolingor rewarming the heart during cardiopulmonary bypass in cardiac operations. Sometimes a heart is operated on during ventricular fibrillation under hypothermia. Therefore it is important to know how much oxygen a fibrillating ventricle consumes under hypothermia.Some studies have been performed on myocardial oxygen con-

sumption (Vo 2) during ventricular fibrillation under hypothermia.l' However, no study has been done to discern the primary determinants of V02 during ventricular fibrillation under hypothermia and how to account for V0 2 during ventricular fibrillation under hypothermia by mechanical parameters.

Volume 104

Number2 August 1992

Recently we have proposed two mechanical parameters to account for V02 of a fibrillating ventricle': 5 on the basis of a mechanical model for ventricular fibrillation, called a multicompartment model. 5 These parameters are equivalent pressure-volumearea (ePVA) and equivalent heart rate (eHR). ePVA is the area surrounded by an imaginary pressure-volume line drawn horizontally at the pressureof ventricular fibrillation and the end-systolic and end-diastolic pressure-volume relations in the beating state in the pressure-volume diagram (Fig. 1, C). ePVA is an analog of the pressure-volumearea (PVA) of a beating heart (Fig. I, A and 8),6-8whichhas been shown to represent the total mechanical energy generated by a ventricular contraction and to be the primary determinant of V02 of a beating ventricle. We applied this PYA conceptof a beating heart to a fibrillating heart and found that ePVA represented the total mechanical energy of a fibrillatingventricle.' eHR was calculated from V02 per minute (Voz/min) in both beating and fibrillating states under mechanicallyunloaded conditionsas an estimate of the frequency of contractions of myocytes during ventricular fibrillation on the assumption that, in each myocyte, V02 for each excitation-contraction coupling (calcium cycling) during ventricular fibrillation was the same as that in the beating state. In our recent study we successfully accounted for V02 of a fibrillatingventricle in normothermia by ePVA and eHR. 4 In the present study in the isolated cross-circulated. canine heart preparation, we attempted to account for V02 of a fibrillating heart in hypothermia by ePVA and eHR. We estimated V02/min of a fibrillating ventriclein hypothermia at variousventricular volumesand correlated it with directly measured V02. The combination of ePVA and eHR enabled us to account for V02 of a fibrillating ventricle in hypothermia in the same manner as in normothermia. Methods and materials Heart preparation. The surgical procedure of the isolated cross-circulated canine heart preparation was the same as described elsewhere," Briefly, in each experiment, we used a pair of mongrel dogs anesthetized with pentobarbital sodium (25 mg/kg intravenously) after premedication with ketamine hydrochloride (5 mg/kg intramuscularly). A smaller dog (heart donor, 13 ± 1 kg [standard deviation]) was subjected to thora-

cotomy whilesupportedby artificialventilation.After both dogs were heparinized, the left subclavian artery and the right ventricle, via the right atrium of the smaller dog, were cannulated. They were connected via cross-circulation tubes to both common carotidarteries and the right externaljugular vein, respectively,of the other dog (metabolic supporter, 14 ± 1 kg). After cross-circulation was started, we isolated the donor dog's heart from both systemic and pulmonary circulations and excised it from the chest cavity. Thus the coronary circulation of the excised heart was not interrupted throughout the procedure. To

Fibrillating ventricle in hypothermia

365

prevent hypotension of the support dog, we administered indomethacin solution (0.3 mg/kg intravenously). The support dog's lungs were ventilated with room air appropriately mixed with oxygen. The dog's arterial pH, oxygen tension,and carbon dioxide tension were measured with a blood gas analyzer (IL system 1303, Instrumentation Laboratories, Inc., Boston, Mass.) and were maintained within their physiologic ranges by adding bicarbonate solution or by adjusting oxygen gas flow and ventilation rate as needed. The left atrium of the excised heart was opened, and all chordae tendineae of the mitral valve were cut. A thin latex balloon(unstressedvolume50 ml) mounted on a rigid connector was placed in the left ventricle and connected to a volume servo pump/' A ventricular pressure gauge (modelP-7, Konigs .. berg Instruments, Inc., Pasadena, Calif.) had been placed inside the apical endof the balloon, and its cable was pulled out of the apex through a stab incision. Coronary flow was continuously measured with an electromagnetic flowmeter (MVF-2100, Nihon Koden, Corp., Tokyo, Japan) in the venous drainage tube from the right ventricle. This tube drained total coronary venous blood except for negligible thebesian flow.'' Coronary arteriovenous oxygen content difference was measured continuously with a PWA...200S oximeter (Erma Optical Works Ltd., Tokyo, Japanj.? which functioned on the same principle as an A..VOX oximeter (A-VOX Systems Inc., San Antonio, Tex.)!? by bypassing parts of both arterial and venous blood from the cross-circulation tubes through the cuvettes of the oximeter. The oximeter was calibrated against an IL-282 CO-Oximeter (Instrumentation Laboratories) at the beginning of each experiment. To minimize the contribution of V 02 of the right ventricleto the measured total V02, we kept the right ventricle collapsed by continuous hydrostatic drainage of the coronary venous return. The mean coronary perfusion pressure was constant at 97 ± 11 mm Hg throughout the experiment. The epicardial electrocardiogram was monitored by a pair of screw-in electrodes on the surface of the left ventricle. At the end of each experiment, the left ventricle (with the interventricular septum) and the right ventricle (free wall only) were weighed. They weighed 59.4 ± 10.3 and 20.6 ± 4.8 gm, respectively. All dogs received humane care in compliance with the "Guiding Principles in the Care and Use of Animals" approved by the Council of the American Physiological Society (revised 1980) and the "Guide for the Care and Use of Laboratory Animals" prepared by the National Academy of Sciences and published by the National Institutes of Health (NIH Publication No. 85-23, revised 1985). Experimental protocol Normothermia run. In five hearts we measured left ventricular pressure, volume, and V0 2 of steady state isovolumic contractions at five to seven different left ventricular volumes, including Vo, maintaining the temperature of the heart at 35° to 37 0 C with heaters around the arterial cross-circulation tube and under the box in which the excised heart was placed. V o is the volume at which peak isovolumic pressure was zero. Hearts were not paced. We waited 1 to 2 minutes until steady state was reached in both left ventricular contraction and V02 under each loaded condition. The steady state was defined as the state in which end-systolic (peak systolic) pressure and V02/min no longer changed at each ventricular volume. Then ventricular fibrillation was induced by temporarily stimulating the left ventricle electrically with 60 Hz sine waves of 3 to 5 volts. The cross-circulation maintained the coronary

366

The Journal of Thoracic and Cardiovascular

Yakuetal.

A

Surgery

EJECTING CONTRACTION

B

. ISOVOLUMIC CONTRACTION

EDPVR

c

VENTRICULAR FIBRILLATION

UJ

a::: en en w

::)

= CL

Fig. 1. Pressure-volume area. (PVA) of an ejecting contraction (A)and an isovolumic contraction (B). PVA is area surrounded by end-systolic pressure-volume relation (ESPVR) and end-diastolic pressure-volume relation (EDPVR) and systolic pressure-volume trajectory, and it represents the total mechanical energy generated by each contraction. In ejecting contractions, PYA consists of potential energy (PE) and external work (EW). In isovolumic contractions, all of the energy generated is potential. C, Equivalent pressure-volume area (ePVA) during ventricular fibrillation. ePV A is area surrounded by horizontal line at pressure of ventricular fibrillation and ESPVR and EDPVR in beating state. ePVA has been proposed to represent total mechanical energy during ventricular fibrillation. Vois volume at which peak isovolumic pressure is zero. perfusion pressure at the normal level even during ventricular fibrillation. During ventricular fibrillation, V02 and pressurevolume data at five to six different volumes, including Yo, were obtained. We waited I to 2 minutes until steady state was reached in both ventricular fibrillation pressure and V02 under each loaded condition. Hypothermia run. All five hearts subjected to the normothermia run were subjected to hypothermia run. After the normothermia run, the fibrillating heart was defibrillated with a direct-current shock of 5 joules. When ventricular contractility recovered to the prefibrillatory level, usually within 30 minutes after defibrillation,'! the heart began to be cooled. We gradually cooled the heart to around 30 0 C (29.8 0 ± 1.6 0 C) for 30 minutes by immersing the arterial cross-circulation tube in an ice water bath. When a stable contractile state was attained in hypothermia, V0 2 and pressure..v olume data of isovolumic contractions were obtained in the same manner as in the normothermia fun. Then ventricular fibrillation was induced again electrically, and V0 2 and pressure-volume data during ventricular fibrillation were obtained in the same manner as in the normothermia run.

Hypothermia arrest run, At the same temperature as in the hypothermia run, cardiac arrest was induced by a 3 to 5 ml intracoronary injection of potassium chloride solution 0.8 Eq/L followed by its continuous infusion (10 to 15 ml/hr). A pressure-volume relation during arrest was determined up to a high arrested pressure (around 40 mm Hg). Normothermia arrestrun. Then the heart was rewarmed to normothermia (35 0 to 37° C) with the heaters around the arterial cross-circulation tube and under the box in which the heart was placed. A pressure-volume relation during arrest was also determined in the same manner as in the hypothermia arrest run. We used these pressure-volume data of the hypothermia and normothermia arrest runs, together with the end-diastolic pressure-volume data in beating state, to determine the end-diastolic pressure-volume relation of hypothermia and normothermia, respectively, for calculation of ePV A as described in the Data analyses section. Data analyses. All data were sampled at 2 msec intervals, on-line processed with a signal processor (NEe San-ei, Instruments, Ltd., Tokyo, Japan, 7TI8), and stored in a floppy disk. VOl. V02 was determined as the product of coronary flow and coronary arteriovenous oxygen content difference. Left ventricular V02 was determined by subtracting the unloaded right ventricular V02 from the measured total V02 in the beating and fibrillating states. The unloaded right ventricular V0 2 was determined as (total VOz at Vol X (right ventricular weight)/ (right ventricular weight + left ventricular weight). Ventricular contractility (Emax). The contractile state of the isovolumically beating left ventricle was quantified by Emax, which is the maximum value for the instantaneous pressurevolume ratio: pet) I(V - Vo),12 where pet) and V are left ventricular instantaneous pressure and isovolumic volume. PVA. PYA is the area bounded by the end-systolic and enddiastolic pressure-volume relations and the systolic pressurevolume trajectory in the pressure-volume diagram" 7 (Fig. 1, A and B). PVA represents the total mechanical energy generated during systole by a beating ventricle, based on the time-varying elastance model ofa ventricle.'We calculated PVA on-linewith the computer as in Appendix A. ePVA. We have proposed ePV A as a measure of the total mechanical energy of single contractions of all individual myocytes in a fibrillating ventricle. ePYA is the specific area surrounded by the horizontal line at the pressure of a fibrillating ventricle and the end-systolic and end-diastolic pressurevolume relations in the beating state (Fig. 1, C). We calculated ePVA off-line as in Appendix B. eHR. We obtained eHR as the average frequency of contractions of each myocyte in a fibrillating ventricle from V02/ min in both beating and fibrillating states under mechanically unloaded conditions. Mechanically unloaded VOz in the beating and fibrillating states consists of V0 2 for excitation-contraction coupling and that for basal metabolism.f In this calculation we assumed that, in each myocyte, V02 for each excitationcontraction coupling is the same between beating and fibrillating states. The actual calculation is shown in Appendix C. Estimation of Vol/min during ventricular fibrillation at various ventricular volumes. We estimated Vo 2/ min during ventricular fibrillation as a function of ePV A and eHR. Because ePV A is considered to represent the total mechanical energy generated by single contractions of all myocytes in a fibrillating ventricle, we estimated V02/min used exclusively for mechan-

Volume 104

Number2

Fibrillating ventricle in hypothermia

August 1992

A <:>

mV02 (ml 02/mln/100g)

10r---------~----------r

o

C'\J

ESPVR

8

Sl

re

~

b ••tl na (Normo)

~ YF (Norma)

b••tlr'llil (H,po)

-e- VF (H,po)

4

2

VFPVR

Sl A EDPYR

20 LV VOLUME (ml)

-

.......

6

a NORNOTt£RMIA x COOLING

O'"'---...l----.....L--_-L-_ _----I...-_ _---L._ _----J o 10 15 20 25 30 LV VOLUME (ml)

30

Fig. 2. End-systolic pressure-volume relations (ESPVR) and end-diastolic pressure-volume relations (EDPVRj in beating state and pressure-volume relations during ventricular fibrilla-

tion (VFPVR) in normothermia(open circles) and hypothermia (crosses) in a representative heart.

ical purposes as the product of ePVA and eHR. Then total V02

was estimatedas the sum of V02 for mechanicalpurposesand mechanically unloaded Vo2 • The details of the calculation are described in Appendix D. Estimated V0 2 during ventricular fibrillation at various left ventricular volumes was correlated with directly measured Vo2• Statistics. Valuesare expressed as mean ± standard deviation. V0 2 duringventricularfibrillation wascomparedby paired t test withthat in the beatingstate in comparablevolumeranges in both normothermiaand hypothermia.eHR during ventricular fibrillation was compared by paired t test with HR in the beating state in both normothermia and hypothermia. Regression analysis was performedbetween V 02 and PV A or ePVA and between estimated and directly measured V02 duringventricularfibrillation in both normothermia and hypothermia. We judged p < 0.05 as statisticallysignificant. Results

Fig. 2 shows the end-systolic and end-diastolic pressure-volume relations in beating state and pressurevolume relations during ventricular fibrillation in both normothermia (open circles) and hypothermia(crosses) in onerepresentative case. HRs in the beating state were 120 beats/min in normothermia and 67 beats/min in hypothermia. The end-systolic pressure-volume relation in hypothermia slightly shifted to the left and upward from the end-systolic pressure-volume relation in normothermia. Emax values were 3.3 and 5.5 mm Hg · ml"! · 100 gm LV* in normothermia and in hypothermia, respectively. However, mean Emax values of five hearts were not different between normothermia and hypothermia (6.1 ± 2.4 versus 6.5 ± 3.7 mm Hg · ml" · 100 gm LV, respectively). The end-diastolic pressure-volume *LV = Left ventricle.

367

B mV02 (ml 02/mln/100g)

11

10

o

1.1······

_

b••tlng (Normo)

~ YF (Normo)

D

b••tlng (Hypo)

~ YF (Hypo)

·..·············· ..,,···· ··

YO

n.··..·······..···

•

1-18

10-20

* p < 0.05 ·..··· ·

·····..

20 ...

LV VOLUME (ml)

Fig. 3. A, Myocardial oxygen consumption per minute (mVo2) in beating state and during ventricular fibrillation at

comparable left ventricular volumes in normothermia and hypothermia in one experiment. B, m V02 in beating state and during ventricular fibrillation in comparable left ventricular volume ranges in normothermia and hypothermia in all experiments. Data are expressed as mean ± standard deviation. Normo, Normothermia; Hypo, hypothermia; ns, not significant.

relation in hypothermiadid not alter from that in normothermia. The mean valuefor a (see Appendix B) in hypothermia ([3.68 ± 4.13] X 10-3) was not different from that in normothermia ([3.04 ± 2.12] X 10-3) . The pressure-volume relation during ventricular fibrillation in hypothermia was slightly lowered from that in normothermia. The pressure-volume relationduring ventricular fibrillation always revealed downward convexity in both normothermia and hypothermia. Fig.3, A, shows V02/min in the beating state and duringventricular fibrillation as a function of left ventricular volume in normothermia and .hypcthermia in one representativeheart. In normothermia, V0 2 during ventricular fibrillation was obviously higher than that in the beating

The Journal of Thoracic and Cardiovascular Surgery

Yaku et al.

368

beat8/mln

mVo2 (ml 02/min/100g)

15,...---------------------,

300

•

beating (Normo)

+-

VF (Normo)

x

beati ng (Hypo)

o

VF (Mypo)

p < 0.05

...l

Db••llng

[SSIJ VF

~

..

260 200 160 .' 100 .:

60 0'---------'------'----------'-------'---------' 500 1000 1500 2000 2500 o

PVA or ePVA (mmHg ml/beat/100g)

Fig. 4. Relation between myocardial oxygen consumption per minute (m V02) and pressure-volume area (PVA) in beating sta te (beating) and relation between m V02 and equivalent pressurevolume area (ePVA) during ventricular fibrillation (VF) in normothermia (Norma) and hypothermia (Hypo). Thick solid lines are regression lines of data during ventricular fibrillation, and thin solid lines are regression lines of data in beating state.

state at any comparable volume. In hypothermia, however, there was no remarkable difference between V0 2 during ventricular fibrillation and that in the beating state. V0 2 tended to increase with the increase in left ventricular volume in both the beating and fibrillating states and in both normothermia and hypothermia. Fig. 3, B, compares V02/min during ventricular fibrillation with that in the beating state in comparable ventricular volume ranges in both normothermia and hypothermia in all the hearts. In normothermia, V02 during ventricular fibrillation was almost always higher than that in the beating state. In contrast, in hypothermia,

V0 2 duringventricular fibrillation wasnotdifferent from that in the beating state in any comparable volume range. Fig. 4 shows Vo 2-PVA relations in the beating state and Vo2-ePVA relations during ventricular fibrillation in normothermia and hypothermia in one representative heart. The V02- PV A relation in the beating sta te in normothermia (dots and thin solid line) was highly linear (correlation coefficient [r] = 0.965) at a heart rate of 117 beats/min. In all experiments, mean r of the V02-PVA relations in the beating state in normothermia was 0.99 after z transformation 13 (Table I). The Vo 2-ePV A relation during ventricular fibrillation in normothermia (pluses and thick solid line) was also highly linear (r = 0.994). In all experiments, mean r of the Vo 2-ePVA relations during ventricular fibrillation was 0.98 after z transformation (see Fig. 4 and Table I). The Vo 2-PVA relation in the beating state in hypothermia (crosses and thin solid line) was also highly linear (r = 0.997) at an HR of 72 beats/min. In all exper-

NORMOTHERMIA

HYPOTHERMIA

Fig. 5. Heart rate (HR) in beating state and equivalent heart rate (eHR) during ventricular fibrillation (VF) in normothermia and hypothermia. Data are expressed as mean ± standard deviation. ns, Not significant.

iments, mean r of V02-PVA relations in the beating state in hypothermia was 0.94 after z transformation (see Fig. 4 and Table I). The V02-ePVA relation during ventricular fibrillation in hypothermia (open squares and thick solid line) was also linear (r = 0.965), and mean r of all experiments was 0.90 after z transformation (see Fig. 4 and Table I). Fig. 5 shows mean values for HR in the beating state (space bars) and eHR during ventricular fibrillation (hatched bars) in both normothermia and hypothermia. In normothermia, eHR during ventricular fibrillation was significantly higher than HR in the beating state (129 versus 198 beats/min in the beating state and during ventricular fibrillation, respectively). In contrast, in hypothermia, HR in the beating state was not significantly different from eHR during ventricular fibrillation (75 versus 82 beats/min, respectively). Fig. 6 shows the correlation of estimated V02/min of a fibrillating ventricle with directly measured Vo 2/ min in pooled data (Table II). In normothermia (Fig. 61 A) the relation was highly linear (r = 0.969), and the regression line was close to the identity line (regression coefficient 1.24; constant -0.97). In hypothermia (Fig. 6, B) the relation was also highly linear (r = 0.983), and the regression line was close to the identity line (regression coefficient 0.80; constant 0.48). Discussion In the present study we assessed Vo 2' and pressure-volume relation of the left ventricle during ventricular fibrillation in hypothermia and related V0 2 during ventricular fibrillation in hypothermia to the mechanical indexes that we had recently proposed: ePVA and eHR.4 ePVA is considered to represent the total mechanical energy gen-

Volume 104 Number 2

Fibrillating ventricle in hypothermia

August 1992

Table I. Regression data Mode

Nonno Beating

VF

Hypo Beating

VF

369

of the relation between Vo-fmin and PVA or ePVA Slope (X la- 3ml 02' min"! . mm Hg- 1 • ml-Jj

Intercept (ml02' min:' . 100 gm LV-I)

0.98*

2.29 ± 0.57 2.48 ± 0.91

3.94 ± 1.22 5.17 ± 1.73

0.95* 0.90*

1.29 ± 0.11 1.64 ± 0.65

2.44 ± 0.51 2.68 ± 0.66

n

HR (eHR) (beats/min)

r

5 5

129 ± 15 198 ± 50

5

75 ± 9

5

82 ± 16

0.99*

Data are expressed as mean ± standard deviation. VOl, Myocardial oxygen consumption; PVA. pressure-volume area; ePVA. equivalent pressure-volume area; Mode. contraction mode; n, number of experiments; HR. heart rate in beating state; eHR, equivalent heart rate during ventricular fibrillation (VF); r, correlation coefficient of regression of Vo 2/min on PYA or ePVA; Slope, regression coefficient or slope of regression line; Intercept, constant or Voj-axis intercept of regression line; Normo, normothermia run; Hypo, hypothermia run. *Mean value for rafter z transformation.

Table II. Regression data of relation between estimated Vofmin and directly measured Vo2/ m in during ventricular fibrillation Slope

Intercept

n

r

(dimensionless)

(ml Or- min"! . 100 gm LV-I;

5

0.98* 0.90*

1.37 ± 0.40 0.77 ± 0.18

-2.12 ± 2.69 0.61 ± 0.48

0.969 0.983

1.24

-0.97

0.80

0.48

Nanna Hypo

5

Pooled Norrno

53

Hypo,

36

Data are expressed as mean ± standard deviation. V02, Myocardial oxygen consumption; n, number of experiments (number of data in pooled data); r, correlation coefficient of relation between estimated values and measured values; Slope, regression coefficient or slope of regression line; Intercept, constant or VOr axis intercept of regression line; Norma, normothermia run; Hypo, hypothermia run; Pooled, pooled data of all experiments. *Mean value for rafter z transformation.

erated by singlecontractionsof all individual myocytes in a fibrillating ventricle and has a unit of energy (mm Hg · ml, or joule). eHR is supposed to be an estimate of the frequency of contractions per minute of individual myocytes. Therefore, ePVA multiplied by eHR should represent the total mechanical energy per minute and should be equivalent to Vo-/min used for mechanical purposes in a fibrillating ventricle. This hypothesis was validated in hypothermiaas well as in normothermia by comparing estimated V0 2 during ventricular fibrillation inhypothermia withdirectlymeasured V02 in the present study. Several aspects of the present study will be discussed later herein. V02 during ventricular fibrillation in hypothermia. Oneof the important findings in the presentstudy is that V02 during ventricular fibrillation in hypothermia was not different from that in the beating state at the subject's own HR at any ventricularvolume, although in normothermia V0 2 during ventricular fibrillation was higher than that in the beating state at comparable ventricular volumes. A few studiescompared V02 during ventricular fibrillation with that in the beating state in hypothermia. Buckberg and coworkers' showed that V02 during ven.. tricular fibrillation 'vas lower than V0 2 in the beating

state at the subject's own HR at both 32° C and 28° C. Brazier and coworkers- showed that V02 at 28° C was comparable in fibrillating and.beating hearts. Our finding wasconsistentwith the resultsof Brazier and cowork.. ers.' However, they compared V0 2 only under an unload.. ed ventricular condition. We compared V02 during ventricular fibrillation with that in the beating state at various comparable ventricular volumes and found that the V02 duringventricularfibrillation in hypothermiawas comparablewith that in the beating state at any ventricular volume. Consequences of hypothermia on left ventricular contractility (Emax), Enhancement of ventricular contractility by cooling is a widely accepted phenome.. noo.I 4- 16 Suga and coworkers!" have shown that the cooling by 7° C increased Emax by 46%. In three of the five hearts in the presentstudy, however, the coolingby 7° C lowered Emax, and mean Emax of all five hearts in hypothermiawasnot significantly differentfrom Emax in normothermia (6.1 mm Hg · mr' · 100 gm LV in nor.. mothermia versus 6.5 mm Hg · ml- 1 • 100 gm LV in hypothermia). We could attribute this unchanged Emax by the cooling in our present study to the staircase phenomenon of ventricular contractility with heart rate.'? In

370

A

The Jourrial of Thoracic and Cardiovascular Surgery

Yaku et al.

e.tlm.ted mV02 (ml 02/rnln/100g)

16r-----------------rT'"---~

c

NORMOTHERMIA 10

Y=AX+B A = 1.24 B :: -0.97 r = 0.869 P < 0.01

......

o""'------~-""'----------'-------

o

6

10

16

measured mV02 (ml 02/min/100g)

B

e.tlmated mV02 (ml 02/mln/100g)

6r----------~--------.....,.

HYPOTHERMIA

3

Y=AX+B A = 0.80 B = 0.48 r = 0.983 P < 0.01

2

Ow:::.....---........-l.-------I..------L-----....L..------J

o

1

:2

3

4

measured mV02 (ml 02/min/100g)

Fig. 6. Correlation of estimated myocardialoxygenconsurnption per minute (m V02) during ventricular fibrillation with directly measured mV02 in normothermia (A) and hypothermia (B). Thick solid lines are regression lines, and thin solid linesare identity lines.

the study ofSuga and coworkers, 14 HR was fixedconstant by atrial pacing at around 125 beats/min. In contrast, in our present study hearts were not paced and HR was allowed to decrease with sinus bradycardia by cooling; mean HR in hypothermia was 75 beats/min. Because such a staircase of ventricular contractility is remarkable at lower HRs (60 to 120 beats/rninl.!" it would cancel enhancement of contractility by the cooling.

Consequences of hypothermia on the end-diastolic pressure-volume relation. It has been reported that diastolic compliance decreases as myocardial temperature is lowered in beating hearts. 1, 19 Grossman and Mel.aurin!" attributed it to both an increase in viscous stiffness and a decrease in the rate of relaxation. In contrast, Monroe and coworkers!" reported that no significant difference was seen in the end-diastolic pressure-volume relations obtained in both normothermia and hypothermia when HR was sufficiently low to allow

complete relaxation at the lower temperature. The results of our experiment, in which the heart was not paced, were consistent with the results of Monroe and coworkers. We can consider from the results that the cooling affected only the rate of relaxation, not the extent of relaxation. We speculate that the cooling effects on the end-diastolic pressure-volume relation depend on the cooling speedand the extent of the cooling. Because the elucidation of the mechanism of cooling effects on the end-diastolic pressure-volume relation is not the goal of the present study, we did not discuss the cooling effects further. In the present study we used pressure-volume data from potassium chloride-arrested hearts, together with the end-diastolic pressure-volume data in the beating state, and approximated the end-diastolic pressure-volume relation by a third power function (see Appendix B). Our method of obtaining the end-diastolic pressurevolume relation seems reasonable because it has been reported that the pressure-volume relation of the potassium chloride-arrested heart is comparable with the enddiastolic pressure-volume relation in the beating state,20 and the end-diastolic pressure-volume relation has been shown to be fitted well by a third power function"; another study, however,22 has shown that the potassium chloride-arrested heart is less compliant than the beating diastolic properties.

Estimation of Vo 2 / min of a fibrillating ventricle.

There are some problems in estimation of V0 2 of a fibrillating ventricle. One is that the concept of e~V A is based on the major assumption that contractility and diastolic properties in each myocyte during ventricular fibrillation are the same as in the beating state. Changes in the contraction mode23 and the frequency of contractions of myocytes'" 18 from the beating to the fibrillating state may affect the systolic or diastolic (or both) performance and may be modified by cooling. The overestimation of V02 during ventricular fibrillation in normothermia (see Fig. 6, A) in our present study can be attributed to the decreased left ventricular contractility because of subendocardial underperfusion of coronary flow with increases in the volume.i" The underestimation of V0 2 in hypothermia (see Fig. 6, B) can be partially attributed to the change in Emax with changes in the frequency of contractions from 75 beats/min in the beating state to 82 beats/min during ventricular fibrillation. Maughan and coworkers'f showed more than 50% of the increase in Emax with the increase in HR from 60 to 120 beats/min. Thus even the trivial change in HR from the beating to the fibrillating state in hypothermia in the present study might increase Emax during ventricular fibrillation and induce the underestimation of V0 2 during ventricular fibrillation in hypothermia.

Volume 104 Number 2

Fibrillating ventricle in hypothermia

August 1992

Another problem is that when eHR was calculated, we considered that, in each myocyte, VOz for each excitationcontraction coupling during ventricular fibrillation was the same as that in the beating state regardless of the change in HR. In normothermia, because HR and eHR were relatively high (above 120 beats/min), the change in HR might not affect ventricular contractility'f and, hence, might not affect V02 for each excitation-contraction coupling.. In contrast, in hypothermia in which HR and eHR were low (below 120beats/min), the change in HR may have affected ventricular contractility and hence V0 2 for each excitation-contraction coupling in the estimation of eHR. It was reported, however, that enhancement of Emax by 46% with 7° C cooling did not change unloaded V02 per beat.!" Therefore we considered that the change in Emax with the change in HR did not affect V02 for each excitation-contraction coupling in hypothermia. Why was not V02 during ventricular fibrillation in hypothermia higher than that in the beating state? We consider that eHR represents the frequency of contractions of myocytes in a fibrillating heart. 4 We suspect that the frequency of contractions of myocytes would be higher during ventricular fibrillation than that in the beating state in normothermia. In hypothermia, however, HR in the beating state and eHR during ventricular fibrillation were not significantly different. We can suspect that the frequency of contractions of myocytes is not higher during ventricular fibrillation than that in the beating state, although its mechanism is unknown. We would speculate that the comparable frequencies of contractions of myocytes are the basis for the comparable V0 2 between beating and fibrillating states in hypothermia. Applicability of the ePVA concept to profound hypothermia. Energetics of the ventricle under profound hypothermia is another matter of concern for cardiac surgeons. The ePV A concept we have proposed as a measure of the total mechanical energy during ventricular fibrillation has been constructed on the basis of the PVA concept of a beating heart, and ePVA is determined from the pressure-volume relation in the beating state. In addition, eHR, an estimate of the average frequency of contractions of individual myocytes during ventricular fibrillation, is calculated from actual V02 in both the beating and fibrillating states. It has not been elucidated whether the PVA concept ofa beating heart can hold even in profound hypothermia, although the PV A concept has been reported to hold in moderate hypothermia (around 30° C).14 Moreover, it is questionable that a heart can keep beating even under profound hypothermia. Therefore the application of the ePVA concept during ventricular fibrillation to the heart under profound hypothermia

37 1

seems difficult for the time being. However, because usual cardiac operations are performed under moderate hypothermia, this study seems to give useful information to cardiac surgeons.

Conclusion ePV A is the primary determinant of V02 during ventricular fibrillation in hypothermia. Vo 2/ min during ventricular fibrillation in hypothermia can be accounted for by the new mechanical indexes: ePVA and eRR.. The comparable V0 2 during ventricular fibrillation with that in the beating state in hypothermia is supposed to be attributable to the comparable frequency of contractions of myocytes during ventricular fibrillation with that in the beating state. H. Y. acknowledges throughout this study the continuous encouragement by Prof. Takahiro Oka, of the Second Department of Surgery of Kyoto Prefectural University of Medicine, from which H. Y. was on leave (1988 to 1990).

REFERENCES 1. Buckberg GD, Brazier JR, Nelson RL, Goldstein SM, McConnell DH, Cooper N. Studies of the effects of hypothennia on regional myocardial blood flow and metabolism during cardiopulmonary bypass. I. The adequately perfused beating, fibrillating, and arrested heart. J THORAe CARDIOVASC SURG 1977;73:87-94. 2. Brazier JR, Cooper N, McConnell DH, Buckberg GD. Studies of the effects of hypothermia on regional myocardial blood flow and metabolism during cardiopulmonary bypass. III. Effects of temperature, time, and perfusion pressure in fibrillating hearts. J THORAC CARDIOVASC SURG 1977;73:102-9. 3. Vians JF, Fewel JG, Arom KV, Trinkle JK, Grover FL. Effects of systemic hypothermia on myocardial metabolism and coronary blood flow in the fibrillating heart. J THORAC CARDIOVASC SURG 1979;77:900-7. 4. Yaku H, Goto Y, Futaki S, Ohgoshi Y, Kawaguchi 0, Suga H. Equivalent pressure-volume area accounts for oxygen consumption of fibrillating heart. Am J Physiol

1991;261:H 1534-44. 5. Yaku H, Goto Y, Futaki S, Ohgoshi Y, Kawaguchi 0, Suga H. Multicompartment model for mechanics and energetics of ventricular fibrillation. Am J Physiol 1991; 260:H292-9.

6. Suga H, Hayashi T, Shirahata M. Ventricular systolic pressure-volume area as predictor of cardiac oxygen consumption. Am J PhysioI1981;240:H39-44.

7. Suga H. Total mechanical energy of a ventricle model and cardiac oxygen consumption. Am J Physiol 1979;236: H498-505. 8. Suga H, HisanoR, Goto Y, Yamada 0, Igarashi Y. Effect of positive inotropic agents on the relation between oxygen

372

9.

10.

11.

12.

13.

14.

15.

16.

17. 18.

The Journal of Thoracic and Cardiovascular Surgery

Yaku et al.

consumption and systolic pressure volume area in canine left ventricle. Circ Res 1983;53:306-18. Suga H, Futaki S, Ohgoshi Y, Yaku H, Goto Y. Arteriovenous oximeter for O 2 content difference, 02 saturations, and hemoglobincontent. Am J PhysioI1989;257:H1712-6. Shepherd AP, Burger eG. A solid-statearteriovenous oxygen difference analyzer for flowing whole blood. Am J Physiol I 977;232:H437-40. Yaku H, Goto Y, Futaki S, Ohgoshi Y, Kawaguchi 0, Suga H. Ventricular fibrillationdoes not depress postfibrillatory contractility in blood-perfuseddog hearts. J THORAC CARDIOVASC SURG 1992;103:514-20. Suga H, Sagawa K. Instantaneous pressure-volume relationshipsand their ratio in the excised,supported canine left ventricle. Circ Res 1974;35:117-26. Snedecor GW, Cochran WG. Correlation. In: Snedecor GW, Cochran WG, ed. Statistical methods. 8th ed. Iowa: Iowa State University Press, 1989:177-95. Suga H, Goto Y, Igarashi Y, et a1. Cardiac cooling increases Emax without affecting relation between 02 consumptionand systolic pressure-volume area in dog leftventricle. Circ Res 1988;63:61-71. Goldberg LI. Effects of hypothermia on contractility of the intact dog heart. Am J Physiol 1958;194:92-8. Monroe RG, Strang RH, LaFarge CG, Levy J. Ventricular performance, pressure-volume relationships, and O 2 consumption during hypothermia. Am J Physiol 1964; 206:67-73. Bowditch HP. Ueber die Eigenthumlichkeiten der Reizbarkeit, welche die Muskelfasern des Herzens zeigen. Arb Physio1 Anstalt zu Leipzig 1871;6:139-76. Maughan WL, Sunagawa K, Burkhoff D, Graves WL Jr, Hunter we, Sagawa K. Effect of heart rate on the canine end-systolic pressure-volume relationship. Circulation 1985;72:654-9.

19. Grossman W, McLaurin LP. Diastolicpropertiesof the left ventricle. Ann Intern Moo 1976;84:316-26. 20. Monroe RG, French G. Ventricular pressure-volume relationships and oxygenconsumption in fibrillationand arrest. Circ Res 1960;8:260-6. 21. Suga H, Hisano R, Ninomiya 1. Digital on-line computation of a predictor of cardiac oxygen consumption:left ventricular systolic pressure volume area. Jpn Heart J 1982; 23:749-58. 22. Maruyama Y, Nunokawa T, Koiwa Y, et al. A comparison of left ventricular volume-pressure relations of excised perfused canine hearts in isovolumic contraction, arrest and fibrillation. Tohoku J Exp Med 1982;136:141-55. 23. Brady AJ. Length-tension relations in cardiac muscle. Am Zoologist 1967;7:603-10.

24. Hottenrott C, Buckberg G. Studies of the effects of . ventricular fibrillation on the adequacy of regional myocardial flow. I. Effects of ventricular distention. J THORAC CARDIOVASC SURG 1974;68:626-33. 25. Gibbs CL, Papadoyannis DE, Drake AJ, Noble MIM. Oxygen consumption of the nonworking and potassium chloride-arrested dog heart. Circ Res 1980;47:408-17.

26. Nozawa T, Yasumura Y, FutakiS, Tanaka N,SugaH. No significantincrease in O 2 consumption of KCI-arrested dog heart with filling and dobutamine. Am J Physiol 1988; 255:H807-12.

Appendixes Appendix A. We obtained PVA of a beating left ventricleas the sum of small triangular areas swept by the lines connecting Vo(the left ventricular volume at which isovolumic left ventricular pressure was zero) and instantaneous pressure-volume data points obtained at 2 msec intervals from end-diastole to endsystole as described elsewhere." The apexes of the small triangular areas were Vo, and their bases were the segments between two adjacent pressure-volume data points (2 msec apart) of the systolicpressure-volumetrajectory. An additional part of PYA to be computed is the crescent area between the straight line connecting Vo and the enddiastolic pressure-volume point and the actual end-diastolic pressure-volume relation. We can reasonably approximate the end-diastolicpressure-volumerelation by a third powerfunction to compute the additional crescent area.?' This area was added to the sum of small triangular areas to complete PVA. Appendix B. When we calculated ePVA during ventricular fibrillation, we approximated the end-diastolicpressure-volume relation in the beating state by a third power function21: P = a(V - Vo),3 to extrapolate it from a low pressure range to the maximum ventricular fibrillation pressure level(around 40 mm Hg). We used end-diastolic pressure-volume data of isovolumic contractions combined with pressure-volume data of the potassium chloride-arrested left ventricle to determine constant a in the preceding equation. Practically, we obtained log,« from every end-diastolic and arrested pressure-volumedata as

logea =

lo~P

- 3loge(V - Yo) .

and determined a representative value for a from the mean value for log,«, We then obtained ePYA mathematically on the pressure-volume diagram as the area surrounded by the endsystolicpressure-volumeline (P = Emax[V - Vo]), the end-diastolic pressure-volume curve (P = a[V - Vo]3), and the horizontal pressure-volume line at the pressure of ventricular fibrillation. We neglected any pressure-volumearea below the volume axis in the same way as before.8 Appendix C. When we calculated eHR, we tacitly assumed that each myocyte in a fibrillating ventricle had the same contractility and hence the same V02 for each excitation-contraction coupling'' as their levels in the beating state. We also assumed that individual myocytes had the same contraction frequency. Then we calculated eHR as an estimate of the frequency of contractions of the individual myocytes by comparing the measuredVo-/rnin (Cr) of the fibrillatingventriclewith that in the beating state (Cb) under unloaded conditions at Vo. An unloaded V02 has been reported to consist of V02 for basal metabolism (BM) and that for excitation-contractioncoupling. 8 When one-beat V02 for excitation-contraction coupling was unchanged even under ventricular fibrillation, eHR was calculated as follows": eHR = HR(Cr- BM)/(Cb- BM)

(1)

where HR is heart rate in the beating state, Cf is directly measured V02 of a fibrillating ventricle under an unloaded condition at Vo, Cb is the intercept of a regression line of Vo2/ min

Volume 104 Number 2

Fibrillating ventricle in hypothermia

August 1992

on PVA in the beating state, and BM is V0 2 for basal metab-

olism. In this calculation, BM in normothermia is assumed to be 1.4 ml 02' min-I. 100 gm LV- 1 according to previous studies. 20, 25,26 In hypothermia, we calculated BM assuming that it decreases with temperature at a QlO of 1.4,14 whichindicates that the temperature change of 100 C causes a change in metabolism of a heart by 400/0. Appendix D. We estimated V0 2 during ventricular fibrillation at various ventricular volumes using both ePVA and eHR. In the previous studies in an ordinarycontractingventricle, 6, 8. 14 PVA is highly linearly correlated with one-beat VOz in a stable contractile state. Therefore, when heart rate -is constant, V02/ min in beating state can be described as follows: V0 2b=Kb·PVA+Cb

(2)

where K, and Cb are regression coefficient and constant,or the

slope and the Vo--axis intercept, respectively, of the Vo 2-PYA

373

regression linein the beatingstate. Ki,is equal to HR . K where

HR is heart rate in the beating state and K is the slope of the one-beat V02-PVA relation.i Assuming that the myocardial contractility and hence one-beat VOz for excitation-contraction couplingis unchanged, and K is the same even during ventric-

ular fibrillation, estimated V02 during ventricular fibrillation

(V0 2f) can be described as follows:

V02f = K, · ePV A

(3)

+ Cr

where Kr is equal toeHR . K and Cr is a directly measured V02 during ventricular fibrillation at Vo. From equations 1 and 3, V0 2f = K . eHR. ePVA+C r = K . HR . ePVA(Cf- BM)/(Cb- BM) =

Kb • ePVA(Cr- BM)/(Cb - BM) + Cr

+ Cr

(4) (5)

(6)