Basic Research in
Cardiology
Basic Res Cardio188:167-178 (1993)
Effect of coronary occlusion and reperfusion on local electrical resistivity of myocardium in dogs P. Steendijk, A. D. van Dijk, G. Mur, E. T. van der Velde, and J. Baan Leiden University Hospital, D e p a r t m e n t of Cardiology, Leiden, The Netherlands
Summary: The effect of coronary occlusion and reperfusion on myocardial electrical resistivity was studied in nine anesthetized open-chest dogs. Anisotropic resistivity was measured on the anterior free wall of the left ventricle (LV) before (control) and during transient occlusion of the left anterior descending (LAD) coronary artery, and during reperfusion. To measure local resistivity longitudinal (RE) and transverse (Rr) to epicardial muscle fiber direction, a sensor was developed based on the four electrode (FE) technique with an electrode distance of 1 ram. Previous calculations showed that measurements with this system were confined to a 2-mm-thick epicardial layer. Control values for RL and Rr were 243 _+32 92- cm and 358 + 45 92- cm (mean â&#x20AC;˘ SD, n - 9) respectively. During a 2-rain LAD occlusion, RL increased gradually by 12.4% (p < 0.05) and R x by 7.8% (p < 0.05) above the preceding control values. During a 5 min reperfusion period resistivities returned towards control values, but tended to remain elevated. R L showed a slight initial further increase during the first rain of reperfusion and remained significantly above control values during 3 min of reperfusion, e T returned to values not significantly different from control after about 1 min of reperfusion. Key words: Myocardial electrical resistivity - electrical anisotropy - LAD occlusion - reperfusion four electrode technique
Introduction
Passive electrical properties govern the electrotonic spread of current through the myocardium and directly influence the activation wave (4, 28, 29, 32). The anatomical inhomogeneities of the myocardium are reflected in its passive electrical properties. At the microscopic level (10 100 gm), intra- and extracellular media, cell membranes and bloodcontaining capillaries all have distinct electrical properties. A t an intermediate scale (100--1000 ~m) the elongated structure and parallel alignment of the muscle cells and vasculature result in an electrical anisotropy. A t the macroscopic level (1-10 mm) a gradual transmuraI change in fiber direction (34) further complicates the description of the myocardium as an electrical volume conductor. Given this heterogeneity, measured electrical parameters reflect "effective" properties characterizing a part of the tissue, with dimensions determined by the m e a s u r e m e n t technique employed. Ten to 15 % of the wall is occupied by blood (14, 23), which is less resistive than muscle tissue, and capillaries run largely parallel to the muscle fibers (3). Thus, myocardial blood volume and perfusion may have a sizeable influence on the passive electrical properties of the heart wall. Based on this hypothesis, perfusion-related changes in the myocardium would have a measurable effect on, and consequently might be monitored by local myocardial resistivity. 776
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Our objective was to study anisotropic myocardial resistivity before, during and after temporary interruption of local myocardial perfusion in open-chest dogs. We aimed to measure effective electrical resistivities on a scale large enough to overcome microscopic inhomogeneities and small enough to obtain the resistivity longitudinal and transverse to the local fiber direction. For this purpose, we developed a small epicardial sensor and used a four electrode (FE) technique. To relate the macroscopic measurements to microscopic geometric and electrical properties we used a mathematical tissue model. Methods
The four electrode resistivity tecl~nique
The FE technique generally employs a linear array of four electrodes: the outer two are used to apply a current to the medium while the inner pair is used to sense the resulting potential difference. By using non-current-carrying sensing electrodes problems with electrode polarization are minimized (38). To calculate resistivity an electrical volume conductor model must be chosen which approximates the real geometry and allows an exact evaluation of the current distribution. For our measurements the myocardium was modeled as a uniform anisotropic volume conductor with resistivity RE in the fiber direction and RT in the two transverse directions (25, 31, 38). Although RT and RL are related to the resistivities of, e.g., intra- and extracellular compartments, this model ignores microscopic structures. Therefore, during occlusion and reperfusion the changes in the resistivities of the different compartments are not measured directly, but their effects (combined with the effects of changes in their relative volumes) on macroscopic anisotropic resistivity are obtained. This volume conductor model is meaningful only if the assumption of parallel fibers is valid in the sample volume of the array, while on the other hand the electrode distances should be large enough to overcome the cellular inhomogeneities. To meet these requirements, we used electrode distances of 1 mm; in a previous theoretical study we derived that in that case the penetration depth is approximately 2 mm (33). When applied to the surface of a semi-infinite anisotropic medium, the potential difference between the inner electrodes (~) of a FE array depends on its orientation with respect to the fiber direction (31, 33). When a is taken as the angle between the array and the transverse direction we have (see Fig. 1): ~ ( c t , RE, RT) = (I/2~a) 9[COSaa/(RL 9RT) + sina0~/RT2]-t/2,
(1)
where I is the applied current and a the electrode spacing. If the FE array is aligned along the fiber direction (a = a,/2), we define ~ as ~L and Eq. (1) reduces to: c) L = (I/2=a) 9RT.
(2)
With ct = 0 (i.e., perpendicular to fiber direction) q b is defined as ~T: ~ v = (I/2=a). (RL" RT) 1/2. When r
(3)
and ~T are measured, the two resistivities are obtained as: RT = (2=a/I)" d0L
(4)
RL = (2ga/I) 9(~T)2/(qbL).
(5)
The sensor
To obtain local measurements in two perpendicular directions, we developed an epicardial sensor (Fig. 1). Two perpendicular arrays of four equidistant platinum electrodes (diameter 0.4 ram, spacing 1 ram) were inserted in a perspex disk. The electrode system is
Steendijk et al., Myocardial electrical resistivity
169
A
WIRING
FLEXIBLE FLEXIBLE SUCTION CUP
) 8 Pt ELECTRODES (Do 0.4 ram)
B 4x~ 3 ~.
~
.
fiber direction
Fig. I. A) Tile sensor, art eight-electrode transducer consisting of two perpendicular arrays of four platinum electrodes (inter-electrode distance 1 mm) inserted in a perspex holder, incorporated in a small flexible suction cup. B) Linear array of four electrodes, separated by a distance a, applied on an anisotropic medium with rcsistivities Rr and RL. The outer two electrodes (1 and 4) carry an applied current, I, the inner pair (electrodes 2 and 3) senses the resulting potential difference, ~. The angle between the array and the direction transverse to the fibers is a.
incorporated in a flexible silicone suction cup with a 16-mm outer diameter. Using a slight vacuum, maintained with a pump via a suction tube, the sensor is affixed to the beating heart (40). The non-penetrating electrode system avoids cell damage, which would affect measurements at such a small scale. Resistivities were measured using a signal conditioner-processor (Leycom Sigma-5, CardioDynamics, Rijnsburg, The Netherlands) developed for intraventricular volumeconductance measurements (1). Basically, a 30 b~A (RMS), 20 kHz sinusoidal current is applied to the outer two electrodes of one of the FE arrays and the voltages on the inner two electrodes of that array are fed into a high input impedance (>1 Mr2) differential amplifier. The system uses synchronous detection to select the component in phase with the excitation current and delivers the reaI component of the sample impedance. Calibration and Iinearity tests were performed by submerging the sensor in diluted saline solutions with resistivities measured with a calibrated instrument (Leycom rho-cuvette, CardioDynamics, Rijnsburg, The Netherlands).
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Instrumentation and protocol Studies were performed in nine dogs (20-25 kg). The dogs were anesthetized with i.v. infusion of m e t h a d o n e (Symoron, 2.5 mg/hr) and droperidol (Dehydrobenzperidol, 12.5 mg/hr) and ventilated with a volume respirator (Dr~iger-Pulmomat, Lt~beck, Germany) using a 3:1 mixture of N 2 0 and 02. Pancuronium (Pavulon, 2 mg/hr i.v.) was used as a muscle relaxant. After thoracotomy, the pericardium was opened, the L A D exposed and a snare occluder placed around it. A dual m i c r o m a n o m e t e r catheter (Dr~iger Medical Systems, Best, The Netherlands) was inserted into the L V via the right carotid artery with the proximal pressure transducer above the aortic valve and the distal transducer in the LV. The sensor was placed in the perfusion region of the L A D distal to the occluder with one of the electrode arrays along the epicardial fiber direction as estimated by visual inspection. A f t e r reading the measured resistance values from the two arrays the sensor was rotated slightly as needed to maximize the difference between the two signals. In this position the higher value was taken to represent RT and the lower value (RT" RL) 1/2 (Eqs. (2) and (3)). Visual inspection showed no migration of the sensor on the beating heart. Resistivities were monitored semicontinuously by switching between the arrays every 5 s. Recordings were obtained during periods of about 10 min: Preceded by a control period of 1-2 rain, we aimed to occlude the L A D for 3 rain, but in several experiments we released the occlusion prematurely upon initiation of arrhythmias. The occlusion was followed by a reperfusion period of 5 rain.
Results
Four electrode system The linearity tests of the F E system showed highly linear correlations (p < 0.001) over the range of interest (100-600 f2- cm). We tested the penetration depth by placing the sensor in a container with a saline solution with known resistivity and measuring the apparent resistivity while advancing the sensor towards the surface of a block of non-conductive material. The results were in accordance with previous theoretical findings (33): the overestimation of saline resistivity was smaller than 10 % as long as the distance between the sensor and the non-conducting boundary was more than 1.9 -+ 0.2 ram. This indicates that the sample volume is largely confined to a 2-ram-thick layer. Table 1. Control values (mean + SD) for longitudinal (RL) and t r a n s v e r s e (RT) resistivity (fa 9cm), n = number of measurements per dog. Dog
RL
RT
n
1 2 3 4 5 6 7 8 9
310 +_40 266 + 12 274 _+42 225_+12 213 + 21 212 -- 40 232 -- 18 224 + 46 225 _+90
408 + 38 383 + 19 413 + 27 299-+ 9 290 _+20 348 +_21 345 _+44 398 + 56 341 _+58
10 8 4 3 7 2 5 9 7
Mean
243 _+32
358 _+45
Steendijk et M., Myocardial electrical resistivity
MYOCARDIAL RESISTIVITY (ohm era)
171
300 4 '
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~ ! - ~ % ~ , 4 ~ - : ~ ~ ~ - ~
LEFT V E N T R I C ~ PRESSURE (kPa)
~ .......
15 0, ~
~
i
;
.
Fig. 2. Effects of a transient occlusion of the LAD. The upper tracing shows the measurement of myocardial resistivities with the sensor, alternatively 5 s parallel (upper level) and 5 s perpendicular (lower level) to fiber direction.
AnhnaI experiments Control values during normal perfusion were obtained in each dog from, typically, six measurements at slightly different sites on the anterior free wall of the LV (Table 1). A v e r a g e RL and RT were 243 _+ 32 ~ - c m and 358 _+ 45 ~2. cm respectively (mean _+ SD, n = 9); this difference was highly significant (p < 0.0001). The effects following occlusion and subsequent reperfusion in a typical experiment are shown in Fig. 2. The first tracing shows the alternating m e a s u r e m e n t of myocardial resistivities: The upper level represents RT, the lower level (RT- RL) u2. F r o m these two levels RT and RL were obtained, which both increased during the occlusion and decreased during the reperfusion albeit to a different extent. The results were analYzed statistically using a repeated-measures analysis of variance. Measurements of RT and RL, made every 15 s during occlusion and reperfusion, were compared with the control value at t = 0 s using Scheffe's F-test for multiple comparisons (44). The m e a n occlusion time of all experiments (n = 16, in a total of nine dogs) was
A
B Occlusion
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Fig. 3. A) Mean R L (Q) and R T ( 0 ) (-4- SD) during the first 2 min of transient occlusion of the LAD coronary artery (n = 12) and B) during a subsequent 5-rain reperfusion period (n = 8). *: p < 0.05 vs control (t = 0 at start occlusion).
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Basic Research in Cardiology, Vol. 88, No. 2 (1993)
139 -+ 55 s. Four occlusions, which had to be released because of severe arrhythmias at less than 90 s, were not considered representative for the series as a whole and excluded from the analysis. The mean occlusion period for the remaining 12 measurement series (seven dogs) was 160 _-2-46 s and the results of these are shown over their common time base (the shortest occlusion period was t20 s) in Fig. 3A. During this 2-min occlusion period, RE increased gradually by 12.4% from 258 + 56 to 290 + 48 f2 .cm and RT increased by 7.8%, from 375 + 62 to 403 +_73 g2.cm. Statistical analysis indicated that RL rose significantly above control after 45 s and RT after 75 s. To analyze the effects of subsequent reperfusion, we aligned the time scales of the experiments shown in Fig. 3A at the start of reperfusion (Fig. 3B). From four of the 12 measurements series no data could be obtained during the reperfusion: In one case the dog developed ventricular fibrillation and in three other cases the sensor dislodged prematurely. During reperfusion, RE initially tended to increase slightly more and started to return towards control values about 60 s after release of the occlusion, but remained significantly above control for more than 180 s. RT decreased more rapidly and remained significantly above control values for only 75 s. However, both RT and RL tended to remain elevated compared to their pre-occlusion control values during the full observed reperfusion period (5 min).
Discussion Volume conductor model and myocardial resistivity In this study the myocardium was modeled as a semi-infinite uniform anisotropic volume conductor with resistivity RE in the fiber direction and RT in the transverse directions. In reality, the myocardium is a bounded heterogeneous structure which can be viewed as consisting of three conducting regions: the intracellular, the interstitial, and the intravascular region. In most studies concerning myocardial resistivities, the vascular region is not explicitly modeled but incorporated in the extracellular region. To relate macroscopic resistivity to microscopic geometric and electrical properties, we adapted a tissue model originally described by Cole and Curtis (5). In this model muscle fibers are represented by closely packed parallel cylinders. The "intracellular" medium is separated from the "extracellular" medium by a membrane. The membrane impedance Zm is made up by a membrane resistance Rm in parallel with a capacitance Cm: Zm
=
Rm/(1 + i" 2~f- Rm-Cm),
where f is the frequency of the excitation current and i = ( - 1 ) 1/2. I n this model macroscopic R L and RT are: RL = Ri" Re/[Ri "(1-Fi) + Re" Fi]
Rr = Re
(I-F~)- R~ + (1 + F~)- (Rc + Zm/Ac) (1 + Fi)" Re + (l-F0" (R~ + Zm/A~)
The parameters, with typical values obtained from the literature, are defined and listed in Table 2. With these parameter estimates, the model yields RL = 188 f2.cm and RT = 490 f~-cm, whereas we measured 243 + 32 O-cm and 358 _+45 O.cm, respectively. Obviously, the real geometry is over-simplified by using parallel cylinders to represent muscle fibers and the vascular system was not modeled explicitly. In addition, intra- and extracellular media are assumed to be homogeneous and isotropic, the membrane impedance is represented by a simple electrical analog in the transverse direction and assumed to be negligible in the longitudinal direction: assumptions which all can be challenged. Further-
SteelMijk et al., Myocardial electrical resistivity
173
Table 2. Parameter estimates for the parallel cyIinder model obtained from the literature (2, 4, t9, 24, 30, 41, 43). Intracellular resistivity Cytoplasmic resistivity Effective gap junctions resistivity Extracellular resistivity Intracellular volume fraction Cell radius Membrane resistance Membrane capacitance
Ri- Rc+Rj R c - 200 f~ - cm O) Rj= 100 f 2 - c m Re = 100 f2 9 cm (2) Fi = 0.7 A~ = 5 gm Rm = 1 kff2 - cm 2(3) Cm = 10 ,aF/cmz
(i) Includes any effects due to myofibrils or mitochondria in the cells. (2)Was taken higher than generally reported (41, 43) since those values were obtained in Tyrode pcrfused preparations and, as demonstrated by Kleber et al. (19), R~ is significantly higher in blood perfused myocardium. (3) Reported membrane parameter values are typically R m = 10 kf~ - cm 2 and Cl~ 2 1 btF/cm2 (4, 41). However, those values are based on the actual membrane surface area which has been shown to be about 10 times greater than that calculated from the assumption of a smooth cylinder (11, 21). Therefore, we modified the values as indicated.
more, the resistivities in the model are obtained by applying h o m o g e n e o u s transverse or longitudinal electric fields on an infinite medium, whereas in the experimental situation a field is generated via two closely spaced electrodes which may affect the measured resistivity values (26, 27). Besides the uncertainties in the parameters estimates, other factors that may explain the difference between model and experimental results are misalignment of the sensor with the fiber direction or non-uniformity of fiber direction within the sample volume, both of which cause an overestimation of RL and an underestimation of RT. Given the above limitations a detailed quantitative correspondence may not be expected, but the model may be used to assess the effects of changes in tissue parameters on the effective macroscopic resistivities in a qualitative sense. For this purpose, RT and R> were plotted as a function of each individual parameter (R~, Re, R i, Pi, Ac, Rm, Gin, and f) in Fig. 4 A - H . All parameters, except the frequency f, were varied from 5 0 % below to 5 0 % above its estimated value. Although f is not a tissue parameter and resistivities were measured at a fixed frequency, Fig. 4H was included to show that, at 20 kHz, RT is still close to its D C limit. The calculations show that RT is influenced most strongly by changes in Ro and Fi, while RL is affected most by changes in Re, Rc and R i. The relative independence of RT on Rc and its frequency dependence (RT vs f) reveal that, at 20 kHz, the transmembrane current is limited and, thus, most transverse current pathways are in the extracellular medium. Some investigators described macroscopic electrical properties of cardiac tissue by recognizing its bidomain structure (20, 27, 30). tn this concept cardiac muscle consists of two domains, which represent the intra- and extracellular spaces averaged over many cells. Current passes from one domain to the other through a cell membrane. Both domains are assumed uniform and extend effectively throughout the region of the tissue. Plonsey and Barr (26) analyzed the F E method for uniform, anisotropic bidomain media. They achieved analytical solutions for intra- and extracellular potential fields assuming equal anisotropy ratios of intra- and extracellular resistivities in the three principal directions. With this assumption, in principle, all pertinent resistivity values can be deduced from a combination of F E measurements with small and large electrode distances. H o w e v e r , the practical application of this concept for epicardial measurements is limited: The small electrode
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Fig. 4. influence of individual myocardial tissue parameters on RL (dashed curves) and RT (solid curves) in a stacked cylinder model (see text). Paramcters were plotted over a range of 50 % below to 50 % above values estimated from the literature (except f, see Table 2). A) Extracellular ~esistivity, Re; B) Cytoplasmic resistivity, R~; C) Effective gap-junctional resistivity, Ri; D) Intraceiiuiar volume fraction, F~; E) Ceil radius, A~; F) Membrane resistance, Rm; G) Membrane capacitance, Cm; H) Frequency of excitation current, f.
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Steendijk et al., Myocardial electrical resistivity
175
distance, required to obtain extracellular resistivities, approaches cardiac celt length, in which case the assumption of uniform properties is no longer valid. The large electrode distance on the other hand, through which a combination of intra- and extracellular resistivities is obtained, results in a sample volume in which the fiber direction cannot be considered uniform. In addition, as realized by Plonsey and Barr (26) and also by Roth (30), the assumption of equal anisotropy ratios for intra- and extracellular resistivities is unlikely to be valid in cardiac muscle. Therefore, although it can be argued that the parameters R T and RL, as obtained in our measurements, are more sensitive to changes in some tissue parameters than to others, their interpretation in terms of microscopic properties remains speculative.
Effects of flow reduction and reperfusion Previously, Van Oosterom et al. (38) and Tranum-Jensen et al. (37) have shown that myocardial resistivity changes dramatically when local ischemia is induced over a period of 30 rain to several hours. Wojtczak (43) demonstrated changes in the passive electrical properties of cow ventricular nmscle with hypoxia. The present study indicates that flow reduction by L A D occlusion is reflected by gradual but significant increases in RE and RT occurring within 2 min. With subsequent reperfusion resistivities return towards control values but tend to remain slightly elevated. The time-course of changes differed: RL changed faster and to a relatively larger extent after occlusion, and after reperfusion it remained significantly elevated for a longer period than RT. Our hypothesis is that, using the FE technique as described, changes in RT mainly reflect changes in extracellular resistivity and changes in the volume fractions of the tissue compartments. RL may reflect both intra- and extracellular resistivity and be less sensitive to shifts in volume fractions. Since the vasculature occupies up to 50 % of the extracellular space (8), it is expected to have a substantial effect on myocardial resistivities. Blood at a normal hematocrit has a resistivity about twice that of the cell-free plasma. Therefore, the current through the blood, especially in the capillaries, is influenced strongly by the presence of erythrocytes: Accumulation of blood cells in case of impeded flow is most likely to affect RE, since this may block preferential current pathways in the longitudinal direction, whereas R~r would be more sensitive to changes in vascular volume per se. Occlusion of the L A D typically resulted in a 10 % increase in resistivity during the first 2 rain. In part, this may be due to a decrease in intravascular blood volume. However, such changes probably occur within the first few seconds (39) and consequently can explain only an initial increase. Tillmanns et al. (35, 36) reported an accumulation of platelets in ischemic areas after 10 min of coronary artery ligation. The leukocytes were found to be trapped in the terminal arterioles and capillaries and provoked an aggregation of red cells. This process might contribute to a more gradual increase in resistivities, and especially in RE. Several additional effects may have contributed. Tranum-Jensen et al. (37) showed a significant increase in tissue osmolality after 5 rain of L A D occlusion which was accounted for by production of osmotically active particles through anaerobic metabolism. They argued that in the first minutes of ischemia the majority of these breakdown products remain intracellular, thus, creating an osmotic gradient across the cell membrane, by which extracellular water is drawn into the cell. According to the parallel cylinder model an increase in cell radius does not increase resistivities; on the contrary, Rx will decrease (Fig. 4E). However, as a consequence of cell swelling, the intracellular volume fraction may be increased which, according to the model, causes a much larger increase in macroscopic resistivities, especially in RT (Fig. 4D).
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Hypoxia, as a constituent of ischemia, produces electrical uncoupling of myocardial cells causing an increase in intracellular resistance of 50-100 % within 30 min (13, 43). However, in isolated perfused papillary muscle, the onset of uncoupling does not occur until about 10-12 rain after interruption of flow (19). Therefore, the contribution of this effect is probably very limited in our experiments. Coronary artery occlusion also causes an accumulation of K + in the extracellular space, which has been associated with a variety of electrophysiological changes (6, 7, 9, 15, 18, 22, 42). The change in potassium starts with an initial rapid rise during the first 5-8 min to a typical K + concentration ([K+]) of 10 mM (12, 17, 42). After release of the occlusion during this phase, [K +] rapidly falls to levels near control (12). The change in extracellular [K +] depolarizes the membrane by changing the potassium equilibrium potential. Several groups have shown that such changes may be accompanied by changes in the passive electrical membrane properties (7, 10, 16). On the basis of these reports, we estimate that during the short-term occlusions in the present study membrane resistance may decrease by 50 %, whereas membrane capacitance is largely unaffected. However, according to our model RT and RL are very insensitive to changes in Rm (Fig. 5F) and even a substantial change would not affect our macroscopic measurements. The decreases in both resistivities during reperfusion may be explained by a reversal of the processes during L A D occlusion. A difference in the time-course of changes in RT and RL is most prominent during this phase. Whereas RT drops relatively fast, RL remains high and does, only until after about 1 rain, start to decrease very slowly. We speculate that the drop in RT may reflect fast changes in vascular volume possibly accompanied by a reversal of cell swelling. The delay in the return of RL towards normal values could be due to the occurrence of local plugging of the capillaries by blood cells, which may only gradually disappear (35). However, resistivities tended to remain elevated up to 5 min after the start of reperfusion, suggesting that morphological or microvascular hemodynamic conditions did not fully return to control conditions during this reperfusion period. While further investigations are indicated to gain insight in the physiological and anatomical factors causing the observed behavior, it appears that the simple, on-line technique developed by us is promising to study perfusion-related changes in the electrical properties of the myocardium. The significant changes following occlusion of the L A D coronary artery and subsequent reperfusion imply that the present technique may be applied experimentally to monitor local ischemia in the open-chest preparation, or clinically, e.g., during coronary artery bypass grafting surgery, to investigate effectiveness of reperfusion of the ischemic myocardium. Re[eyences
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