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A mechanical model of the dynamics of the coronary circulation in dog
J. theor. Biol. (1985) 116, 225-242
A Mechanical Model of the Dynamics of the Coronary Circulation in Dog BERNARD I. LEVY, ALAIN TEDGUI AND JEAN BAPTISTE MICHEL
Institut National de la Sante et de la Recherche Medicale, Unite 141, 41 Bd de la Chapelle 75010, Paris, France, (Received 12 November 1984, and in revised form 12 May 1985) A mechanical model of the coronary circulation, including a capacitive extramyocardial compartment and a collapsible intramyocardial vascular bed has been described. The phasic coronary blood flow (CBF) in the circumflex artery of 11 anesthetized open chest dogs was studied in control conditions and during thoracic aortic constriction and arteriovenous fistula (AVF). We measured pressures in aorta and left ventricle, phasic CBF by pulsed Doppler flowmetry and in three dogs, pressure in the left anterior descending coronary artery. After aortic and AVF unclamping, we observed a major reverse flow in the circumflex artery. This reverse flow may be explained by the displacement of the collapse point of the intramyocardial compartment, due to the relative distribution of the intramyocardial tissue pressure and the intravascular coronary pressure. The specific role of the epicardial capacitive coronary compartment and of the intramyocardial pump action has been illustrated during coronary artery clamping, ectopic beats and changes in myocardial contractility. Under all the experimental conditions, the reported results demonstrated the ability of the model to describe the patterns of the dynamic of the coronary circulation. The coronary pressure flow relationship has been considered for a long time only in term of assessing resistance characteristics. D o w n e y & Kirk (1975), Bellamy (1978), and Canty & Klocke (1979) extended Sabiston & Gregg's (1957) concept of the throttling effect o f myocardial compression on coronary blood flow during the whole cardiac cycle. They introduced the idea o f a vascular waterfall by demonstrating that the instantaneous pressure flow relationship had a zero flow pressure intercept of significant magnitude. Douglas & Greenfield (1970), Arts (1978), G o w & Hadfield (1979) and m o r e recently, Klocke et al. (1981), Eng, Jentzer & Kirk (1982) and Chilian & Marcus (1982) suggested an effect o f the coronary capacitance on the dynamics of coronary blood flow. In the meantime, Spaan, Breuls & Laird (1981) showed that the diastolicsystolic coronary flow differences could be accounted for by an intramyocardial p u m p action. 225 0022-5193/85/180225+ 18 $03.00/0
© 1985 Academic Press Inc. (London) Ltd
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The aim of this study was to present a mechanical model o f the coronary circulation, including the resistive and capacitative characteristics of epicardial and intramyocardial vessels and a collapsible intramyocardial coronary bed, the pattern of the collapse depending on the time of the course intramyocardial distribution of the tissue pressure.
Methods SURGICAL PREPARATION
Eleven mongrel dogs, weighing 22-30kg, were premedicated with intramuscular ketamine ( 1 5 m g / k g ) i.m. Anesthesia was achieved with sodium pentobarbital (30 mg/kg), i.v. Additional anesthesia was administered as needed. The dogs were ventilated with a RPR (Pesty) respirator using a 50% air oxygen mixture. The left saphenous vein was cannulated to give drugs. A left thoracotomy was performed in the fourth left intercostal space and the heart was exposed after the pericardium was incised. The proximal circumflex artery was dissected and a perivascular ultrasonic flow velocity transducer (Rudic Ltd, Trilport 77 France) was placed around the vessel. A range gated Doppler apparatus (ALVAR 8 mHz) was used; this system allowed us to measure simultaneously the internal arterial dimeter, by Doppler echography, and the instantaneous blood flow velocity, by measuring the Doppler shift. Spatial averages of the flow velocity values were calculated. Doppler instruments have no drift, consequently, mechanical zero flow determination was not necessary. Blood flow was determined by multiplying the cross sectional area and the flow velocity. After giving 10 000 units of heparin, a polyethylene catheter (3F) was inserted into one of the second or third branches of the left circumflex artery to record coronary arterial pressure (P23 DB STHATAM). A USCI 7F catheter and a Millar 5F probe were positioned in the ascending aorta and in the left ventricle respectively via the right femoral artery and the left atrial appendage. Phasic ascending aorta blood flow was measured by a perivascular electromagnetic flow transducer connected to a N Y C O T R O N (type 372S) square wave electromagnetic flowmeter. An umbilical tape was passed around the thoracic descending aorta for an occlusive snare. After a mid-line laparotomy, an arteriovenous fistula (AVF) was created between the aorta and the vena cava. A Dacron graft (internal diameter 10 mm, length 15 cm) including a cannulating electromagnetic transducer was connected to the abdominal aorta and to the inferior vena cava. The graft was connected to the vessel after partial lateral clamping by end to
DYNAMICS
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side suturing. This arteriovenous fistula (AVF) was clamped at the beginning of the experiment. Arterial blood pH, Pco2, Po2, and hemoglobin were measured every 30 minutes with a blood gas analyser (model ABL1, Radiometer) to ensure adequacy of ventilation and acid base balance. Arterial Po2 was maintained at 95-120mmHg, with arterial oxygen saturation in a range of 95-98%. The arterial pH was maintained between 7.32 and 7.49, and the Pco2 between 30 and 47 mmHg. Phasic aortic and coronary blood flow, coronary pressure, aortic and left ventricular pressure as well as the ECG were continuously recorded with a Gould ES1000 electrostatic recorder. EXPERIMENTAL
PROTOCOL
Heart rate, pressures and flows were measured in all 11 dogs in the control state. We constricted the thoracic descending aorta by tightening the tape around it (stenosis of approximately 80% ), allowing 5 minutes for hemodynamic stabilization. At other times, the arteriovenous fistula was opened for 5 minutes. In each dog, we performed two aortic constrictions and two arteriovenous fistula openings separated by more than 30 minutes to return to control values. Pressures, phasic and mean flows were measured simultaneously before, during, and 5 minutes after the aortic constriction or the AVF opening. In three dogs, the proximal left anterior descending coronary artery was clamped for 15 seconds while the distal coronary pressure was recorded. THE
PROPOSED
MECHANICAL
MODEL
Coronary arteries, capillaries and veins are divided into two separate compartments: The first is assumed to be distensible, and is only slightly or not at all directly subject to an elevation of pressure in the myocardial tissues surrounding the vessels. This compartment consists of the major epicardial coronary arteries. The second consists of the intramyocardial arterioles and capillaries. This compartment is assumed to have resistive and capacitive properties, depending on the vasomotor tone and the capillary density of the intramyocardial vascular bed. It may be partially or totally collapsed, according to the pattern of intravascular and tissue pressure. This compartment may be compared to a porous sponge which can be compressed and collapsed by the intramyocardial tissue pressure. The volume of the sponge (i.e. the intramyocardial blood volume) is determined, in the different layers of the
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myocardium, by the capillary density and recruitment. When this compartment is collapsed by the intramyocardial stresses, some of its blood volume will be driven out through the intramyocardial venules via the pores of the sponge. The pores act as elementary resistances; they are not uniformly distributed: the subendocardial layers are supposed to have greater conductance than more superficial muscle (Wusten et al., 1977, Archie, 1978; Eliasen et al., 1982). During diastole, the intramyocardial tissue pressure is minimum and the myocardial vascular bed may be assumed to be uncollapsed (Fig. 1). The
C1 Epicardium
Endocardium
FIG. 1. Schematic diagram of the model of the coronary circulation during diastole. C1 is the extramural epicardial compartment, C2, the intramyocardial compartment. The dashed line represents the pores of the second compartment; the vascular resistances are lower in the subendocardial layers.
pressure-flow relationship is therefore essentially determined by the viscous resistance of the coronary bed, by the vasomotor tone, and by the driving pressure calculated as the difference between the aortic pressure and the zero flow pressure. The intramyocardial sponge will be filled during diastole, its volume depending on the vasomotor state of the coronary bed. During the isovolumic contraction, the myocardial tissue pressure rises while the aortic blood pressure remains practically at the same level. If we assume that, at the same time, some intramyocardial blood volume moves to venules, a part of the second compartment collapses or is narrowed, due to the subendocardial tissue pressure exceeding the coronary perfusion pressure (Fig. 2) (Nematzadeh et al., 1984). The subendocardial vessels might collapse completely or more probably might merely be narrowed. During the rapid ventricular ejection, the coronary pressure has two characteristic effects: an increase in the volume of the first compliant compartment and a blood stream through the uncollapsed part of the coronary bed. The intramyocardial uncollapsed compartment, located in the subepicardial layers, is excluded from the inner capillaries. This subepicardial part of the
DYNAMICS
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I
CORONARY
~_
CIRCULATION
229
Col lapse point
Endocordium
FIG. 2. Schematic diagram of the model of the coronary circulation during systole. C1 is inflated due to high arterial blood pressure. The subendocardial part of C2, where the intramyocardial tissue pressures are higher than the intravascular blood pressures, is collapsed. The arrows represent the distribution of the tissue pressures through the ventricular wall. sponge is crushed and communicates with the major distensible coronary arteries. At the end of systole, since the blood is driven from the intramyocardial circulation to the m a j o r coronary arteries, the systolic blood pressure falls below the intravascular blood pressure in the subepicardial sponge. Figure 1 shows this mechanical model during diastole (intravascular blood pressure > intramyocardial tissue pressure) and during the end of the systole (intramyocardial pressure > intracoronary pressure in the inner layer). The coronary flow m a y be expressed as dV/dt, where V is a volume; hence, (dV/dt)/(dP/dt) has the dimension of a compliance (dV/dP) and may be considered as a pseudo compliance. During systole, if we suppose that the coronary bed behaves like a resistance and a compliance in series, instantaneous C B F is then given by: CBF(t) =
dP
(P(t) - Po)/R + (Co- C.P(t)) .-~ (t)
(1)
where R represents the total resistance of the pores, which depends on the extent o f the uncollapsed intramyocardial capillary bed, (P(t)-Po) is the driving pressure and (Co-C. P(t)) is the compliance of the first compartment, decreasing linearly with pressure, as has been shown in the isolated circumflex coronary artery (Patel & Janicki, 1970). Hence, it may be written:
dP/dt=C(t)=(P(t)-Po)
R..-~ +(Co-C.P(t))
(2)
where C ( t ) is the instantaneous pseudo compliance, expressed as the C B F ( t ) / ( d P / d t ) ratio.
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When the resistive term in equations (1) and (2) predominates, CBF(t) and C(t) are expected to increase with aortic blood pressure. The relationship is not necessarily linear, because of the possible changes in the resistance R with pressure. Conversely, when the compliance term predominates, CBF(t) and C(t) are expected to be decreasing with the aortic pressure increasing. DATA ANALYSIS
The phasic coronary flow and aortic pressure were digitized from the continuous electrostatic paper recording (sampling rate 200 Hz) with a Hewlett Packard desk top calculator (HP9825B) and a graphic digitizer (HP9874A) and stored on disk. Diastolic coronary flow was taken as beginning with the dicrotic notch of the aortic pressure tracing and ending at the time of the beginning of the upstroke of the next left ventricular pressure. The instantaneous d P / d t value was computed and the instantaneous CBF(t)/(dP/dt) ratio was plotted against the corresponding aortic pressure. TABLE 1
Hemodynamic data Aortic BP
Dog no.
HR (/min)
Syst Diast (mmHg)
Mean SD
121 26
117 22
113 119 155 127 132 114 133 140 131 136 124 107 105 105 75
216 277 211 215 130 139 147 215 259 208 215 182 174 241 148
CBF Aortic BF (ml/min)
LVEDP (mmHg)
mean syst (ml/min)
% syst
C o n t r o l ( n = 11) 89 23
3038 867
4 2
67 30
39 20
0.19 0.04
38 30 88 88 36 86 43 118 130 118 125 82 70 93 56
29 29 68 55 33 71 43 79 95 90 83 71 55 78 49
0-25 0"32 0"26 0"21 0'31 0"27 0-34 0-22 0-24 0"25 0"22 0-29 0"26 0"28 0-29
A o a i c constriction (n = 19) 1 1 2 2 3 3 4 5 5 6 6 7 7 8 9
192 169 178 158 74 70 93 168 208 158 174 117 125 170 90
2021 2227 2500 3740 3527 4036 3461 3365 3129 4158 2877 2929 1800 1808 2467
13 15 11 10 7 7 8 12 14 11 12 8 8 13 6
DYNAMICS
OF THE CORONARY TABLE 1
(cont.)
Aortic BP
Dog no.
HR (/min)
Syst Diast (mmHg)
9 10 10 11
70 134 140 132
122 175 160 148
Mean SD
122t 22
188§ 45
1 1 2 2 3 3 4 4 5 5 6 7 7 8 9 9 10 10 11 11
126 130 97 102 143 157 158 154 150 150 144 143 154 184 92 93 97 89 146 150
100 105 79 105 98 70 84 105 80 79 98 122 115 126 95 93 90 56 93 115
Mean SD
133 28
231
CIRCULATION
CBF Aortic BF (ml/min)
LVEDP (mmHg)
88 136 135 131
2201 1824 2125 1189
6 8 7 7
139§ 41
2704 849
10t 3
mean syst (ml/min) 47 125 120 100 845 34
% syst
37 78 68 50
0-26 0.21 0.19 0.17
61§ 21
0.255 0.04
Arteriovenous fistula (n = 20)
955 18
43 38 41 55 68 34 44 70 49 42 66 89 62 78 67 64 55 30 42 54
1673 1568 1653 1484 2038 2632 3220 3054 2849 2422 2270 4183 5264 4585 4261 4503 3805 3403 4146 4073
7 6 6 7 6 8 7 7 8 7 6 7 8 7 6 7 7 9 8 8
44 46 22 28 44 30 29 20 48 42 50 52 100 97 113 92 74 62 73 39
41 42 22 26 35 28 28 16 42 36 36 40 77 67 80 61 51 53 20 26
0-31 0-31 0.33 0.31 0.27 0.31 0.32 0-27 0-29 0-29 0.24 0.26 0.26 0.33 0.24 0.22 0.23 0.28 0.09 0.22
555 16
3154 1161
7 1
55 27
42 19
0.265 0.05
H R = heart rate; BP = blood pressure; syst = systolic; diast = diastolic; BF = blood flow; LVEDP = left ventricular end diastolic pressure; CBF = circumflex artery coronary blood flow. t P < 0 . 0 5 ; 5 P < 0 . 0 1 ; § P<0-001.
Results T h e c o n t r o l d a t a in T a b l e 1 s h o w the m e a n
results and the standard
d e v i a t i o n s f o r 11 d o g s . S t a t i s t i c a l c o m p a r i s o n s w e r e m a d e b y p a i r e d t t e s t between control measurements
in t h e s a m e d o g a f t e r a n i n d u c e d c h a n g e .
Figure 3 s h o w s t y p i c a l r e c o r d s in c o n t r o l c o n d i t i o n s . A f t e r 5 m i n u t e s o f t h o r a c i c a o r t i c c o n s t r i c t i o n ( T a b l e 1) t h e s y s t o l i c a n d d i a s t o l i c h y p e r t e n s i o n were a s s o c i a t e d with a 2 5 % rise in m e a n c i r c u m f l e x b l o o d flow ( P < 0-001)
232
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ECG
CBF ( cm 3. m,n- ~ ) Aortic BP
lC~r
(mmHg) Aortic BF ({ min -1 )
4
~oJ
Left ventriculor
BP (mmHg) O. 5 sec
FIG. 3. Electrocardiogram (ECG), phasic blood flow recorded in the circumflex artery (CBF), phasic aortic blood pressure (aortic BP), and blood flow (aortic BF) and left ventricular blood pressure (BP), under control conditions.
and the proportion of systolic/total CBF ratio rose 33% ( P < 0 . 0 1 ) . The peak systolic pressure and systolic circumflex blood flow were increased by 55% and 56% respectively ( P < 0 - 0 0 1 ) . The diastolic pressure rose 42% and the diastolic circumflex blood flow rose only 19% ( P < 0 . 0 1 ) . End diastolic left ventricular pressure rose from the control value 4 + 2 mmHg to 10+3 mmHg, 5 minutes after aortic constriction ( P < 0 - 0 5 ) . Figure 4 shows a typical record after aortic unclamping: the aortic pressure and the mean CBF fell, the cardiac output rose from the next beat after unclamping. The decreased mean CBF remained predominantly diastolic. Furthermore, the systolic circumflex flow became negative at the end of the systole.
ECG CBF (cm3.min -1)
1001--,
I~
I~
~
^
Aortic BP
(mrnHg) Aortic 8F
({.min -1) Left ventriculor
BP ( mmHg )
,oolA ~ A A A ( ~ ~ ~ A n ~ A
~°11,pu,u u u u u u u u u i O- 5 sec
FIG. 4. ECG, CBF, aortic BP, aortic BF and left ventricular BP, during thoracic aortic unclamping.
DYNAMICS
OF THE
CORONARY
233
CIRCULATION
ECG
CBF(crn3 min -I ) BP (mmHg) Aortic
Aortic BF ~ r/3in-i ) Left ventriculor
BP ( mrnHg )
'°°0 1J
j
0.5
sec
FIG. 5. ECG, CBF, aortic BP, aortic BF and left ventricular BP, during arteriovenous fistula
unclamping.
A similar later systolic reverse flow has been observed with AVF unclamping. When the fistulas were opened (1500 to 2000 ml/min) the systolic and diastolic pressures fell significantly (P < 0.01 ) (Table 1, Fig. 5). End diastolic left ventricular pressure rose from 4 + 2 to 7+ 1 mmHg. Mean CBF did not change significantly, but with the biggest fistulas, the CBF was almost exclusively systolic.
//~.~
CBF
',Y Pressure
FIG.
6. Schematic
representation
of
CBF
and
calculated
pseudo
compliance
(CBF/(dP/dt)), plotted against simultaneous aortic blood pressure during early systole.
Figure 6 shows a typical simultaneously computed circumflex coronary flow and instantaneous pseudo compliance C(t), plotted against the corresponding values of aortic pressure. For the same value of pressure, the circumflex blood flow and the instantaneous pseudo coronary compliance reached maximum values and decreased for high values of aortic pressure. Figure 7 shows examples of coronary flow-pressure and C(t)-pressure
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LEVY
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AL.
(a) CBF (cm3rnin -1) I
15
i I
Ioo
i
BP (mmHg)
(b)
CBF 10 dp/df (10-3cm3 mrnHq -1 ) 5
~i-t..
0 0
loo
BP (mrnHg)
FIG. 7. (a) Typical recorded BF vs aortic BP during early systole, under control conditions and during AVF unclamping. (b) Typical computed pseudo compliance vs aortic BP during early systole, under control conditions and during AVF unclamping. relationships during early systole, recorded in the same dog, under control conditions, and with AVF. The curves may all be separated into two parts: the first one with CBF, C(t) and aortic pressure, increasing in parallel, hence positive slopes of flow-pressure and pseudo compliance-pressure relationships. For high values of pressure, CBF and C(t) decreased with aortic pressure increasing, i.e. the slopes of the two curves were negative. Plotting the second part of CBF/(dP/dt) pressure curves, obtained under control conditions, aortic constriction and AVF, for the same dog, seems to fit roughly the same curve (large dashed points in Fig. 7). During proximal occlusion of the coronary artery, the decay of the distal coronary pressure and superimposed pressure pulsations were observed (Fig. 8). This decay curve shows a phasic component decreasing with time till almost complete disappearance. Discussion
Hemodynamic data, shown in Figs 3, 4, 5 and Table 1, are in agreement with those reported by Buckberg et al. (1972) in similar experiments. Briefly, our results confirm that the increased CBF remained predominantly diastolic during aortic constriction, with an increased systolic part of CBF. The morphology o f the CBF recordings was similar after aortic unclamping and AVF unclamping. The most characteristic feature was a reverse CBF at the
D Y N A M I C S OF THE C O R O N A R Y C I R C U L A T I O N
235
I see
LVBP
CBP
mmH(:j
. . . . .
,,,
,,;,
J. . . .
-,
........
Jb b b b UbbLiLJL~LJ~Jld~bbGL L~bbbbi
1°o 1 0J
FIG. 8. Aortic BF, CBF, left ventricular BP and coronary blood pressure (CBP) recorded in the left anterior descending coronary artery (LAD), during clamping of LAD.
end of systole. Furthermore, after AVF unclamping, peak systolic coronary blood flow was markedly increased (Fig. 5). Although retrograde arterial flow has been described by several investigators (Porter, 1898; Anrep & V. Saalfeld, 1933; Gregg, Green & Wiggers, 1935; Menno & Schenk, 1961; Karp & Roe, 1966; Delin, 1969; Buckberg et al., 1972; Hoffman & Buckberg, 1976), it is only recently that Spaan et al. (1981) have proved its magnitude and importance. The phasic CBF observed in different experimental conditions may be accounted for in terms of the proposed model previously described. At the end of diastole, the intramyocardial vascular bed is assumed to be filled. Its volume is possibly enhanced in aortic constriction and AVF conditions because of the metabolic vasodilatation related to the increased demand for oxygen. The intravascular pressure is assumed to decrease, during diastole, from the aortic pressure value in the epicardial superficial coronary arteries and arterioles to the zero flow pressure in the endocardial layer, ranging from 20 to 45 mmHg (Bellamy, 1978). The distribution of the intravascular pressure through the myocardial wall is determined by the vascular conductance which has been found to be greater in the subendocardial myocardium (Wusten et aL, 1977; Archie, 1978; L'Abbate et al., 1980; Verrier et al., 1980). During isovolumetric contraction, the intramyocardial tissue pressure rises as intravascular blood pressure remains at its end diastolic level. It is now well admitted that there is a roughly linear fall of the systolic tissue
236
a.
1. L E V Y
ET
AL.
pressure from endocardium to epicardium (Stein et al., 1980; Sabbah & Stein, 1982, Hoffman et al., 1982; Nematzadeh et al., 1984). The tissue pressure is generated by radial; tangential and circumferential stresses. It may be written: Pim = Pr + Pt (3) where P/m is the intramyocardial pressure. Pr and Pt represent the parts of the intramyocardial tissue pressure due to the radial stresses and to the tangential and circumferential stresses, respectively. In the endocardium, the radial part of the intramyocardial tissue pressure equals the cavity pressure. From this assumption, the tissue subendocardial pressure is higher than simultaneously measured left ventricular blood pressure (PLV) (Dieudonne, 1967; Baird, Goldbach & De La Rocha, 1972; Sabbah & Stein, 1982). In the subendocardial layers, where the tissue pressure exceeds the intravascular pressure, the coronary bed collapses. Blood is then driven out from capillaries to venules offering the least resistance (Stein et al., 1969; Steinhausen, Tillmans & Thederan, 1978). Another effect of squeezing the inner myocardial layers is an enhancement of the total coronary bed resistance, inducing a reduction in the coronary arterial inflow. This is constantly observed, during the isovolumetric contraction, in CBF recorded in all conditions (Figs. 3, 4 and 5). According to our model, the thickness of the collapsed myocardial layer is different in various experimental conditions. In the low range of pressures, the subendocardial tissue pressure/left ventricular blood pressure ratio may be expected to be higher than in control conditions. From equation (3), it may be written: P/m/PLV = 1 + P t / P L V .
(4)
The thickness of the collapsed layers can be thus expected to be more important after AVF unclamping, compared with control conditions. During aortic constriction, P/m/PLV may be assumed to be decreased, and thus, the collapse point will be probably moved toward the subendocardium. After the opening of the aortic valves, the intravascular coronary pressure rises with the aortic pressure. The coronary blood inflow, observed during early systole, is increased and may be accounted for by an inflation of the first compartment and a capillary flow through pores of the uncollapsed part of the intramyocardial compartment. This period corresponds to the part of the curves with positive slope in the CBF-aortic pressure and pseudo compliance-pressure relationships. During the aortic constriction, the uncollapsed part of the intramyocardial compartment is larger and more capillary pores are available to flux. The compliance of the epicardial coronary arteries, subjected to higher pressure, is smaller. On the other
DYNAMICS OF THE CORONARY CIRCULATION
237
hand, the more uncollapsed part of the intramyocardial compartment, larger than that in control conditions, tends to offer a lower resistance to capillary flow. As a result of the balance between these two phenomena, the CBF and the pseudo compliance increased with the pressure during the beginning of systole (Fig. 7). Conversely, during AVF unclamping, the epicardial coronary arteries, subjected to low mean pressure, may store greater blood volume during the beginning of the systole, inducing an important peak systolic CBF, observed during AVF unclamping (Fig. 5). In every instance, the CBF-pressure and the pseudo compliance-pressure relationships reached maximum values before the peak aortic blood pressure was attained. Although the blood pressure continued to increase, CBF, paradoxically, decreased (Fig. 6). Because of the tissue myocardial pressure increasing more than the intravascular pressure during early systole (Sabbah & Stein, 1982), we may assume that the collapse point moves from endocardium to epicardium. The number of capillary pores accessible to flow diminished. As the capillary density of the remained uncollapsed epicardial intramyocardial bed is lower (Wusten et al., 1977; Archie, 1978; Eliasen et al., 1982), a slight further collapse may provoke a large increase in the resistance to flow. This eiIect is more dramatic in conditions where the collapsed intramyocardial vascular compartment is larger, i.e. for more epicardial collapse point. During the AVF unclamping, the maximum value of CBF and pseudo compliance were reached before the peak systolic blood pressure was reached, earlier than in control conditions. During systole, while the aortic pressure is still increasing, and a large part of the epicardial bed collapsed, Fig. 7 seems to indicate that compliance predominates, according to equation (2). During later systole, as the aortic blood pressure decreased, a coronary reverse flow was observed after aortic unclamping and AVF unclamping (Figs..4 and 5). Under these conditions, it may be admitted that the driving pressure was in the anterograde direction, i.e. that the coronary blood pressure was higher than the simultaneous aortic blood pressure. According to the proposed model, the reverse flow recorded in the main epicardial coronary artery may be accounted for by two phenomena: (1) A blood volume stored by the compliant compartment during early systole may be restored by the elastic forces developed in the vessel walls of the epicardial coronary arteries. (2) While a part of the intramyocardial vessels collapse, blood in intramyocardial arteries is caught between a very high resistance downstream and the aortic pressure upstream. The second component of the reverse flow during later systole may be the result of the blood pressure in the subepicardial arterioles increased by an amount equal to the tissue pressure.
238
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A slight additional P/m, increasing the coronary vascular pressure, may induce a reverse flow. In both conditions where a late systolic reverse flow has been observed, these two reasons may be involved: during AVF unclamping, the uncollapsed part of the second compartment is assumed to be small, with few available pores, and the myocardial contractility is supposed to be high. Therefore, P/m may be important and a major force may be applied to the suISepicardial blood volume. The proposed model is in agreement with the results reported by Chillian & Marcus (1982), who have shown that, in normal hemodynamic conditions, a retrograde blood velocity was recorded in a small subepicardial artery, whereas blood flow velocity at this time was anterograde in an epicardial coronary artery. The retrograde component of mid-systolic blood velocity persisted in the intramyocardiai artery, despite large increase in blood flow velocity during coronary vasodilatation. After completion of the systole, the myocardial tissue pressure decreases to values lower than the diastolic arterial blood pressure. The intramyocardial vascular bed is thus uncollapsed and filled. The diastolic coronary blood flow is then driven by the difference between the aortic pressure and the zero flow pressure (Bellamy, 1978). Patterns of the diastolic flow will not be discussed in the present paper. The reverse coronary blood flow observed in certain experimental conditions may be related to the pressure pulsations detected in the distal circumflex artery after proximal occlusion of the artery (Fig. 8). This phenomenon has been previously described (Giles & Wilcken, 1977; Kroll et al., 1980; Spaan et al., 1981). Spaan et al., (1981) pointed out that this phasic component of pressure recorded after cessation of flow into the coronary system cannot be explained by a time varying resistance, but related to a phasic flow in and out the intramyocardial blood compartment. The pressure pulsation diminishes with time as the available blood volume is driven out to epicardial venules. In various experimental conditions, the partially collapsed intramyocardial vascular bed and the myocardial pump action may provoke coronary pressure or blood flow pulsations. Figure 9 shows CBF recorded during ectopic beats. It can be seen that left ventricular pressure rises induced simultaneous CBF falls, although the coronary pressure was not altered by the myocardial contractions during the ectopic beats. Furthermore, during the post extrasystolic beat, a large reverse flow was observed during the late systole. The observed phasic CBF may be accounted for by the intramyocardial tissue pressure rise. During each ectopic beat, the increased intramyocardial tissue pressure collapsed a part of the intramural vascular bed and then tended to decrease the coronary blood inflow. The myocardial potentiation
D Y N A M I C S OF THE C O R O N A R Y C I R C U L A T I O N
239
CBP ( mmHg )
CBF (cm3.min-~¿ Left ventriculor BP ( mmHg ) Aortic BF ({.min -1) !
C).5 sec
FIG. 9. Coronary blood pressure (CBP) recorded in the left anterior coronary artery, CBF recorded in the circumflex coronary artery. Left ventricular BP and aortic BF, showing phasic and opposite CBF and left ventricular BP variations, during ectopic beats without change in CBP. A reverse CBF is observed during the post ectopic systole.
during the post ectopic beat probably changed the myocardial contractility (Cranefield, 1965; Hoffman et al., 1965; Anderson et al., 1976), increased the intramyocardial tissue pressure, and thus produced a reverse flow during the late systole (Fig. 10). Dieudonne (1967) has shown that after isoproterenol injection, the point where cavity pressure equals intramyocardial tissue pressure moved towards the epicardial surface.
CB,,cm3m,o', 0Oj
'
I t
Left ventriculor 1001 '.ltlr~l~!IJINf,ll;~ ~!til~l~fPPllIl~,Ida. drP~t 8P(mm.ol
o- ~(~L£tlL~tELI~r~LLL~LLLLLLi~EI~L~L~ i._1 1 sec
lt!ii/i/lijll!lll!! I!t,l,ll, .,:
, f ~l:¢~,,,,;.,(:,;/ir,~¢c.r~;/ll
FIG. 10. CBF left ventricular BP and aortic BF, recorded a low paper speed, showing reverse CBF during every post ectopic beat.
240
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LEVY ET AL.
loo]
1
0J
OJ
100-
I00-
75
75
50
50
Aortic 8P ( mmHg )
25-
(ol
25~
FIG. 1 h C B F and aortic BP recorded at low paper speed: (a) After pentobarbital injection, showing a decrease in CBF in parallel with a decrease in BP. (b) After T N T injection, showing a decrease in aortic BP similar to that seen in (a), with maintained C B F peak, and large reverse flow.
The influence of the myocardial contractility may be illustrated by Fig. 11 which shows the effects of massive i.v. injection of trinitrine (TNT) or sodium pentobarbital on CBF and aortic blood pressure. With reduction of the contractility by the pentobarbital, the aortic blood pressure and the CBF decreased in parallel (Fig. 11 (a)). Conversely, after vasodilatation and increased contractility with TNT, the mean CBF was unchanged and enormous systolic reverse flow was observed, whereas the aortic blood pressure was markedly reduced (Fig. ll(b)). Effects of the T N T injection were to increase the intramyocardial vascular bed and possibly to enhance the myocardial tissue pressure, whereas the aortic blood pressure decreased. It may be expected that the difference between the intravascular pressure and the aortic pressure was markedly increased, provoking a reverse flow. The importance of this reverse flow is to be related to the blood volume increased by vasodilatation. Conversely, after pentobarbital injection, myocardial contractility and aortic pressure decreased in parallel, the difference between the intramyocardial tissue pressure and the aortic blood pressure remained slight; this might explain the lack of systolic reverse flow after pentobarbital injection. The proposed descriptive model may give further elements to explain the vulnerability of the subendocardial muscle to ischemia. Experimental results using microsphere methods (Buckberg et al., 1972; Downey & Kirk, 1974) showed that subendocardial ischemia is associated with a marked relative decrease in subendocardial blood flow. Conversely, recent results reported
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by Steinhausen et al. (1978) and Chillian & Marcus (1982) from direct observations and blood flow measurements in intramyocardial arterioles, concluded to little systolic flow in any part of the left venticular myocardium. According to our model, the arterial inflow may be reduced in subepicardial layers during systole, whereas the subendocardial vascular bed is collapsed. Lower systolic oxygenation may occur in the subendocardial muscle where there is neither blood flow nor blood volume, and consequently no oxygen transfer. In the subepicardial muscle, there is little inflow in the uncollapsed coronary vessels, but, the remaining blood volume in this part of the myocardium allows for oxygen transfer to muscle. The discrepancy between systolic subepicardial blood flow, as measured by microspheres or direct methods, may be due to the volume of the uncollapsed subepicardial compartment, allowing the distribution of the microspheres in this compartment and thus an overestimation of perfusion. This explanation is supported by the experiments reported by Deboer et al. (1982). These authors showed that, after experimental coronary occlusion, the infarction of the epicardium was larger in hypotensive dogs, although the percentage and the size of the infarcted endocardium did not change. During hypotension, it may be assumed that the collapse point is more epicardial, the available epicardial blood volume is decreased, and thus a larger area is more vulnerable to ischemia. A two compartment-mechanical model of the coronary circulation has been developed. This model includes capacitive epicardial arteries, not directly subjected to the intramyocardial tissue pressure, and a collapsible intramyocardial vascular bed. The collapse point position of the second compartment depends on the transmural pressure, i.e. on the relative distribution of the intramyocardial tissue pressure and the intravascular coronary pressure. The specific role of the epicardial capacitive coronary arteries and of the intramyocardial pump action has been illustrated during coronary artery clamping, ectopic beats and changes in myocardial contractility. In various experimental conditions, the reported results demonstrated the ability of the model to qualitatively describe the pattern of the dynamics of the coronary circulation. We wish to gratefully acknowledge Dr Julien I. E. Hoffman, from the Cardiovascular Research Institute, University of California, San Francisco, for reading our manuscript and for his very helpful discussion. REFERENCES ANDERSON, P. A. W., RANKIN, J. S., ARENTZEN, C. E., ANDERSON, R. W. & JOHNSON, E. A. (1976). Circ. Res. 39, 832.
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ANREP, G. V. & v. SAALEELD, E. (1933). J. Physiol. 79, 317. ARCHIE, J. P. JR. (1978). J. Surg. Res. 25, 21. ARTS, M. G. J. (1978). PhD Thesis, Rijksuniversiteit, Limburg. BAIRD, R. J., GOLDBACH, M. M. & DE LA ROCHA, A. (1972). J. Thorac. Cardiovasc. Surg. 64, 635. BELLAMY, R. F. (1978). Circ. Res. 43, 92. BUCKBERG, G. D., FIXLER, D. E., ARCHIE, J. P. & HOEFMAN, J. I. E. (1972). Circ. Res. 30, 67. CANTY, J. M. & KLOCKE, F. J. (1979). Circulation 60 (suppl 11), 101 (abstract). CHILLIAN, W. M. & MARCUS, M. L. (1982). Circ. Res. 50, 775. CRANEFIELD, P. F. (1965). Bull. N.Y.. Acad. Med. 41, 419. DEBOER, L. M. V., RUDE, R. E., DAVIS, R. F., MAROKO, P. R. & BRAUNWALD, E. (1982). Cardiovasc, Res. 16, 423. DELIN, N. A. (1969). Scand. J. Thorac. Cardiovasc. Surg. 3 (Suppl I), 1. DIEUDONNE, J. M. (1967). Am. J. Physiol. 213, 101. DOUGLAS, J. E. & GREENFIELD, J. C. JR. (1970). Circ. Res. 27, 921. DOWNEY, J. M. & KIRK, E. S. (1974). Circ. Res. 34, 251. DOWNEY, J. M. & KIRK, E. S. (1975). Circ. Res. 36, 753. ELIASEN, P., AMTORP, O., TONDEVOLD, E. & HAUNSO, S. (1982). Cardiovasc. Res. 16, 593. ENG, C., JENTZER, J. H. & KIRK, E. S. (1982). Circ. Res. 50, 334. GILES, R. W. & WILCKEN,D. E. t . (1977). Cardiovasc. Res. 11, 64. Gow, B. S. & HADFIELD, C. D. (1979). Circ. Res. 45, 588. GREGG, D. E., GREEN, H. D. & WIGGERS, C. J. (1935). Am. J. Physiol. ll2, 362. HOFFMAN, B. F., BARTELSTRON, H. J., SCHERLAG, B. J. & CRANEFIELD, P. F. (1965). Bull. IV. Y. Acad. Med. 41,498. HOFFMAN, J. I. E. & BUCKaERG, G. D. (1976). In: Progress in Cardiology. (Yu, P. & Goodwin, J. F. eds). pp 37-89. Philadelphia: Lea and Febiger. HOEFMAN, J. 1. E., BAER, R. W., UHLIG, P. N., VLAHAKES, G. J., BR1STOW, J. D., MESSIANA, L. M., HANLEY, F. L. & VERRIER, E. D. (1982). KARP, R. B. & ROE, B. B. (1966). Ann. Surg. 164, 959. KLOCKE, F. J., WEINSTEIN, I. R., KLOCKE, J. F., ELLIS, A. K., KRAUS, D. R., MATES, R. E. CANTY, J. M., ANBAR, R. D., ROMANOWSK1, R. R., WALLMEYER, K. W. & ECHT, M. P. (1981). J. Clin. Invest. 68, 970. KROLL, K., SCHIPPERHEYN, J. J., HENDRIKS, F. F. A. & LAIRD, J. D. (1980). Am. J. Physiol. 238, H214. L'ABBATE, A., MARZILLI, M., BALLESTRA, A. M., CAMI¢I, P., TRIVELLA, M. G., PELOSI, G. & KLASSEN, G. A. (1980). Cardiovasc. Res. 14, 21. MENNO, A. D. & SCHENK, W. G. (1961). Surgery 50, 82. NEMATZADEH, D., ROSE, J. C., SCHRYVER, TH. & KOT, P. A. (1984). Basic Res. Cardiol. 79, 86. PATEL, D. J. & JANICKL J. S. (1970). Circ. Res. 27, 149. PORTER, W. T. (1898). Am. J. Physiol. 1, 145. SABISTON, D. C. & GREGG, D. E. (1957). Circulation 15, 14. SABaAH, H. N. & STEIN, P. D. (1982). Am. J. Physiol. 242, H240. SPAAN, J. A. E., BREULS, N. P. W. & LAIRD, J. D. (1981). Circ. Res. 49, 584. STEIN, P. D., BADEER, H. S., SCHUE'rrE, W. H. & GLASER, J. F. (1969). Am. HeartJ. 78,331. STEIN, P. D., MARZILL1, M., SABBAH, H. N. & LEE, T. (1980). Am. J. Physiol. 238, H625. STEINHAUSEN, M., TILLMANS, H. & THEDERAN, H. (1978). Pfliigers Arch 348, 9. VERRIER, E. D., BAER, R. W., HICKEY, R. F., VLAHAKES, G. J. & HOFFMAN, J. I. E. (1980). Circulation 62 (suppl III), 62 (abstract). WUSTEN, B., BUSS, D. D., DEIST, H. & SCHAPER, W. (1977). Basic Res. Cardiol. 72, 636.
A Mechanical Model of the Dynamics of the Coronary Circulation in Dog BERNARD I. LEVY, ALAIN TEDGUI AND JEAN BAPTISTE MICHEL
Institut National de la Sante et de la Recherche Medicale, Unite 141, 41 Bd de la Chapelle 75010, Paris, France, (Received 12 November 1984, and in revised form 12 May 1985) A mechanical model of the coronary circulation, including a capacitive extramyocardial compartment and a collapsible intramyocardial vascular bed has been described. The phasic coronary blood flow (CBF) in the circumflex artery of 11 anesthetized open chest dogs was studied in control conditions and during thoracic aortic constriction and arteriovenous fistula (AVF). We measured pressures in aorta and left ventricle, phasic CBF by pulsed Doppler flowmetry and in three dogs, pressure in the left anterior descending coronary artery. After aortic and AVF unclamping, we observed a major reverse flow in the circumflex artery. This reverse flow may be explained by the displacement of the collapse point of the intramyocardial compartment, due to the relative distribution of the intramyocardial tissue pressure and the intravascular coronary pressure. The specific role of the epicardial capacitive coronary compartment and of the intramyocardial pump action has been illustrated during coronary artery clamping, ectopic beats and changes in myocardial contractility. Under all the experimental conditions, the reported results demonstrated the ability of the model to describe the patterns of the dynamic of the coronary circulation. The coronary pressure flow relationship has been considered for a long time only in term of assessing resistance characteristics. D o w n e y & Kirk (1975), Bellamy (1978), and Canty & Klocke (1979) extended Sabiston & Gregg's (1957) concept of the throttling effect o f myocardial compression on coronary blood flow during the whole cardiac cycle. They introduced the idea o f a vascular waterfall by demonstrating that the instantaneous pressure flow relationship had a zero flow pressure intercept of significant magnitude. Douglas & Greenfield (1970), Arts (1978), G o w & Hadfield (1979) and m o r e recently, Klocke et al. (1981), Eng, Jentzer & Kirk (1982) and Chilian & Marcus (1982) suggested an effect o f the coronary capacitance on the dynamics of coronary blood flow. In the meantime, Spaan, Breuls & Laird (1981) showed that the diastolicsystolic coronary flow differences could be accounted for by an intramyocardial p u m p action. 225 0022-5193/85/180225+ 18 $03.00/0
© 1985 Academic Press Inc. (London) Ltd
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The aim of this study was to present a mechanical model o f the coronary circulation, including the resistive and capacitative characteristics of epicardial and intramyocardial vessels and a collapsible intramyocardial coronary bed, the pattern of the collapse depending on the time of the course intramyocardial distribution of the tissue pressure.
Methods SURGICAL PREPARATION
Eleven mongrel dogs, weighing 22-30kg, were premedicated with intramuscular ketamine ( 1 5 m g / k g ) i.m. Anesthesia was achieved with sodium pentobarbital (30 mg/kg), i.v. Additional anesthesia was administered as needed. The dogs were ventilated with a RPR (Pesty) respirator using a 50% air oxygen mixture. The left saphenous vein was cannulated to give drugs. A left thoracotomy was performed in the fourth left intercostal space and the heart was exposed after the pericardium was incised. The proximal circumflex artery was dissected and a perivascular ultrasonic flow velocity transducer (Rudic Ltd, Trilport 77 France) was placed around the vessel. A range gated Doppler apparatus (ALVAR 8 mHz) was used; this system allowed us to measure simultaneously the internal arterial dimeter, by Doppler echography, and the instantaneous blood flow velocity, by measuring the Doppler shift. Spatial averages of the flow velocity values were calculated. Doppler instruments have no drift, consequently, mechanical zero flow determination was not necessary. Blood flow was determined by multiplying the cross sectional area and the flow velocity. After giving 10 000 units of heparin, a polyethylene catheter (3F) was inserted into one of the second or third branches of the left circumflex artery to record coronary arterial pressure (P23 DB STHATAM). A USCI 7F catheter and a Millar 5F probe were positioned in the ascending aorta and in the left ventricle respectively via the right femoral artery and the left atrial appendage. Phasic ascending aorta blood flow was measured by a perivascular electromagnetic flow transducer connected to a N Y C O T R O N (type 372S) square wave electromagnetic flowmeter. An umbilical tape was passed around the thoracic descending aorta for an occlusive snare. After a mid-line laparotomy, an arteriovenous fistula (AVF) was created between the aorta and the vena cava. A Dacron graft (internal diameter 10 mm, length 15 cm) including a cannulating electromagnetic transducer was connected to the abdominal aorta and to the inferior vena cava. The graft was connected to the vessel after partial lateral clamping by end to
DYNAMICS
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227
side suturing. This arteriovenous fistula (AVF) was clamped at the beginning of the experiment. Arterial blood pH, Pco2, Po2, and hemoglobin were measured every 30 minutes with a blood gas analyser (model ABL1, Radiometer) to ensure adequacy of ventilation and acid base balance. Arterial Po2 was maintained at 95-120mmHg, with arterial oxygen saturation in a range of 95-98%. The arterial pH was maintained between 7.32 and 7.49, and the Pco2 between 30 and 47 mmHg. Phasic aortic and coronary blood flow, coronary pressure, aortic and left ventricular pressure as well as the ECG were continuously recorded with a Gould ES1000 electrostatic recorder. EXPERIMENTAL
PROTOCOL
Heart rate, pressures and flows were measured in all 11 dogs in the control state. We constricted the thoracic descending aorta by tightening the tape around it (stenosis of approximately 80% ), allowing 5 minutes for hemodynamic stabilization. At other times, the arteriovenous fistula was opened for 5 minutes. In each dog, we performed two aortic constrictions and two arteriovenous fistula openings separated by more than 30 minutes to return to control values. Pressures, phasic and mean flows were measured simultaneously before, during, and 5 minutes after the aortic constriction or the AVF opening. In three dogs, the proximal left anterior descending coronary artery was clamped for 15 seconds while the distal coronary pressure was recorded. THE
PROPOSED
MECHANICAL
MODEL
Coronary arteries, capillaries and veins are divided into two separate compartments: The first is assumed to be distensible, and is only slightly or not at all directly subject to an elevation of pressure in the myocardial tissues surrounding the vessels. This compartment consists of the major epicardial coronary arteries. The second consists of the intramyocardial arterioles and capillaries. This compartment is assumed to have resistive and capacitive properties, depending on the vasomotor tone and the capillary density of the intramyocardial vascular bed. It may be partially or totally collapsed, according to the pattern of intravascular and tissue pressure. This compartment may be compared to a porous sponge which can be compressed and collapsed by the intramyocardial tissue pressure. The volume of the sponge (i.e. the intramyocardial blood volume) is determined, in the different layers of the
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myocardium, by the capillary density and recruitment. When this compartment is collapsed by the intramyocardial stresses, some of its blood volume will be driven out through the intramyocardial venules via the pores of the sponge. The pores act as elementary resistances; they are not uniformly distributed: the subendocardial layers are supposed to have greater conductance than more superficial muscle (Wusten et al., 1977, Archie, 1978; Eliasen et al., 1982). During diastole, the intramyocardial tissue pressure is minimum and the myocardial vascular bed may be assumed to be uncollapsed (Fig. 1). The
C1 Epicardium
Endocardium
FIG. 1. Schematic diagram of the model of the coronary circulation during diastole. C1 is the extramural epicardial compartment, C2, the intramyocardial compartment. The dashed line represents the pores of the second compartment; the vascular resistances are lower in the subendocardial layers.
pressure-flow relationship is therefore essentially determined by the viscous resistance of the coronary bed, by the vasomotor tone, and by the driving pressure calculated as the difference between the aortic pressure and the zero flow pressure. The intramyocardial sponge will be filled during diastole, its volume depending on the vasomotor state of the coronary bed. During the isovolumic contraction, the myocardial tissue pressure rises while the aortic blood pressure remains practically at the same level. If we assume that, at the same time, some intramyocardial blood volume moves to venules, a part of the second compartment collapses or is narrowed, due to the subendocardial tissue pressure exceeding the coronary perfusion pressure (Fig. 2) (Nematzadeh et al., 1984). The subendocardial vessels might collapse completely or more probably might merely be narrowed. During the rapid ventricular ejection, the coronary pressure has two characteristic effects: an increase in the volume of the first compliant compartment and a blood stream through the uncollapsed part of the coronary bed. The intramyocardial uncollapsed compartment, located in the subepicardial layers, is excluded from the inner capillaries. This subepicardial part of the
DYNAMICS
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THE
I
CORONARY
~_
CIRCULATION
229
Col lapse point
Endocordium
FIG. 2. Schematic diagram of the model of the coronary circulation during systole. C1 is inflated due to high arterial blood pressure. The subendocardial part of C2, where the intramyocardial tissue pressures are higher than the intravascular blood pressures, is collapsed. The arrows represent the distribution of the tissue pressures through the ventricular wall. sponge is crushed and communicates with the major distensible coronary arteries. At the end of systole, since the blood is driven from the intramyocardial circulation to the m a j o r coronary arteries, the systolic blood pressure falls below the intravascular blood pressure in the subepicardial sponge. Figure 1 shows this mechanical model during diastole (intravascular blood pressure > intramyocardial tissue pressure) and during the end of the systole (intramyocardial pressure > intracoronary pressure in the inner layer). The coronary flow m a y be expressed as dV/dt, where V is a volume; hence, (dV/dt)/(dP/dt) has the dimension of a compliance (dV/dP) and may be considered as a pseudo compliance. During systole, if we suppose that the coronary bed behaves like a resistance and a compliance in series, instantaneous C B F is then given by: CBF(t) =
dP
(P(t) - Po)/R + (Co- C.P(t)) .-~ (t)
(1)
where R represents the total resistance of the pores, which depends on the extent o f the uncollapsed intramyocardial capillary bed, (P(t)-Po) is the driving pressure and (Co-C. P(t)) is the compliance of the first compartment, decreasing linearly with pressure, as has been shown in the isolated circumflex coronary artery (Patel & Janicki, 1970). Hence, it may be written:
dP/dt=C(t)=(P(t)-Po)
R..-~ +(Co-C.P(t))
(2)
where C ( t ) is the instantaneous pseudo compliance, expressed as the C B F ( t ) / ( d P / d t ) ratio.
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When the resistive term in equations (1) and (2) predominates, CBF(t) and C(t) are expected to increase with aortic blood pressure. The relationship is not necessarily linear, because of the possible changes in the resistance R with pressure. Conversely, when the compliance term predominates, CBF(t) and C(t) are expected to be decreasing with the aortic pressure increasing. DATA ANALYSIS
The phasic coronary flow and aortic pressure were digitized from the continuous electrostatic paper recording (sampling rate 200 Hz) with a Hewlett Packard desk top calculator (HP9825B) and a graphic digitizer (HP9874A) and stored on disk. Diastolic coronary flow was taken as beginning with the dicrotic notch of the aortic pressure tracing and ending at the time of the beginning of the upstroke of the next left ventricular pressure. The instantaneous d P / d t value was computed and the instantaneous CBF(t)/(dP/dt) ratio was plotted against the corresponding aortic pressure. TABLE 1
Hemodynamic data Aortic BP
Dog no.
HR (/min)
Syst Diast (mmHg)
Mean SD
121 26
117 22
113 119 155 127 132 114 133 140 131 136 124 107 105 105 75
216 277 211 215 130 139 147 215 259 208 215 182 174 241 148
CBF Aortic BF (ml/min)
LVEDP (mmHg)
mean syst (ml/min)
% syst
C o n t r o l ( n = 11) 89 23
3038 867
4 2
67 30
39 20
0.19 0.04
38 30 88 88 36 86 43 118 130 118 125 82 70 93 56
29 29 68 55 33 71 43 79 95 90 83 71 55 78 49
0-25 0"32 0"26 0"21 0'31 0"27 0-34 0-22 0-24 0"25 0"22 0-29 0"26 0"28 0-29
A o a i c constriction (n = 19) 1 1 2 2 3 3 4 5 5 6 6 7 7 8 9
192 169 178 158 74 70 93 168 208 158 174 117 125 170 90
2021 2227 2500 3740 3527 4036 3461 3365 3129 4158 2877 2929 1800 1808 2467
13 15 11 10 7 7 8 12 14 11 12 8 8 13 6
DYNAMICS
OF THE CORONARY TABLE 1
(cont.)
Aortic BP
Dog no.
HR (/min)
Syst Diast (mmHg)
9 10 10 11
70 134 140 132
122 175 160 148
Mean SD
122t 22
188§ 45
1 1 2 2 3 3 4 4 5 5 6 7 7 8 9 9 10 10 11 11
126 130 97 102 143 157 158 154 150 150 144 143 154 184 92 93 97 89 146 150
100 105 79 105 98 70 84 105 80 79 98 122 115 126 95 93 90 56 93 115
Mean SD
133 28
231
CIRCULATION
CBF Aortic BF (ml/min)
LVEDP (mmHg)
88 136 135 131
2201 1824 2125 1189
6 8 7 7
139§ 41
2704 849
10t 3
mean syst (ml/min) 47 125 120 100 845 34
% syst
37 78 68 50
0-26 0.21 0.19 0.17
61§ 21
0.255 0.04
Arteriovenous fistula (n = 20)
955 18
43 38 41 55 68 34 44 70 49 42 66 89 62 78 67 64 55 30 42 54
1673 1568 1653 1484 2038 2632 3220 3054 2849 2422 2270 4183 5264 4585 4261 4503 3805 3403 4146 4073
7 6 6 7 6 8 7 7 8 7 6 7 8 7 6 7 7 9 8 8
44 46 22 28 44 30 29 20 48 42 50 52 100 97 113 92 74 62 73 39
41 42 22 26 35 28 28 16 42 36 36 40 77 67 80 61 51 53 20 26
0-31 0-31 0.33 0.31 0.27 0.31 0.32 0-27 0-29 0-29 0.24 0.26 0.26 0.33 0.24 0.22 0.23 0.28 0.09 0.22
555 16
3154 1161
7 1
55 27
42 19
0.265 0.05
H R = heart rate; BP = blood pressure; syst = systolic; diast = diastolic; BF = blood flow; LVEDP = left ventricular end diastolic pressure; CBF = circumflex artery coronary blood flow. t P < 0 . 0 5 ; 5 P < 0 . 0 1 ; § P<0-001.
Results T h e c o n t r o l d a t a in T a b l e 1 s h o w the m e a n
results and the standard
d e v i a t i o n s f o r 11 d o g s . S t a t i s t i c a l c o m p a r i s o n s w e r e m a d e b y p a i r e d t t e s t between control measurements
in t h e s a m e d o g a f t e r a n i n d u c e d c h a n g e .
Figure 3 s h o w s t y p i c a l r e c o r d s in c o n t r o l c o n d i t i o n s . A f t e r 5 m i n u t e s o f t h o r a c i c a o r t i c c o n s t r i c t i o n ( T a b l e 1) t h e s y s t o l i c a n d d i a s t o l i c h y p e r t e n s i o n were a s s o c i a t e d with a 2 5 % rise in m e a n c i r c u m f l e x b l o o d flow ( P < 0-001)
232
B.l.
LEVY E T A L .
ECG
CBF ( cm 3. m,n- ~ ) Aortic BP
lC~r
(mmHg) Aortic BF ({ min -1 )
4
~oJ
Left ventriculor
BP (mmHg) O. 5 sec
FIG. 3. Electrocardiogram (ECG), phasic blood flow recorded in the circumflex artery (CBF), phasic aortic blood pressure (aortic BP), and blood flow (aortic BF) and left ventricular blood pressure (BP), under control conditions.
and the proportion of systolic/total CBF ratio rose 33% ( P < 0 . 0 1 ) . The peak systolic pressure and systolic circumflex blood flow were increased by 55% and 56% respectively ( P < 0 - 0 0 1 ) . The diastolic pressure rose 42% and the diastolic circumflex blood flow rose only 19% ( P < 0 . 0 1 ) . End diastolic left ventricular pressure rose from the control value 4 + 2 mmHg to 10+3 mmHg, 5 minutes after aortic constriction ( P < 0 - 0 5 ) . Figure 4 shows a typical record after aortic unclamping: the aortic pressure and the mean CBF fell, the cardiac output rose from the next beat after unclamping. The decreased mean CBF remained predominantly diastolic. Furthermore, the systolic circumflex flow became negative at the end of the systole.
ECG CBF (cm3.min -1)
1001--,
I~
I~
~
^
Aortic BP
(mrnHg) Aortic 8F
({.min -1) Left ventriculor
BP ( mmHg )
,oolA ~ A A A ( ~ ~ ~ A n ~ A
~°11,pu,u u u u u u u u u i O- 5 sec
FIG. 4. ECG, CBF, aortic BP, aortic BF and left ventricular BP, during thoracic aortic unclamping.
DYNAMICS
OF THE
CORONARY
233
CIRCULATION
ECG
CBF(crn3 min -I ) BP (mmHg) Aortic
Aortic BF ~ r/3in-i ) Left ventriculor
BP ( mrnHg )
'°°0 1J
j
0.5
sec
FIG. 5. ECG, CBF, aortic BP, aortic BF and left ventricular BP, during arteriovenous fistula
unclamping.
A similar later systolic reverse flow has been observed with AVF unclamping. When the fistulas were opened (1500 to 2000 ml/min) the systolic and diastolic pressures fell significantly (P < 0.01 ) (Table 1, Fig. 5). End diastolic left ventricular pressure rose from 4 + 2 to 7+ 1 mmHg. Mean CBF did not change significantly, but with the biggest fistulas, the CBF was almost exclusively systolic.
//~.~
CBF
',Y Pressure
FIG.
6. Schematic
representation
of
CBF
and
calculated
pseudo
compliance
(CBF/(dP/dt)), plotted against simultaneous aortic blood pressure during early systole.
Figure 6 shows a typical simultaneously computed circumflex coronary flow and instantaneous pseudo compliance C(t), plotted against the corresponding values of aortic pressure. For the same value of pressure, the circumflex blood flow and the instantaneous pseudo coronary compliance reached maximum values and decreased for high values of aortic pressure. Figure 7 shows examples of coronary flow-pressure and C(t)-pressure
234
B.i.
LEVY
ET
AL.
(a) CBF (cm3rnin -1) I
15
i I
Ioo
i
BP (mmHg)
(b)
CBF 10 dp/df (10-3cm3 mrnHq -1 ) 5
~i-t..
0 0
loo
BP (mrnHg)
FIG. 7. (a) Typical recorded BF vs aortic BP during early systole, under control conditions and during AVF unclamping. (b) Typical computed pseudo compliance vs aortic BP during early systole, under control conditions and during AVF unclamping. relationships during early systole, recorded in the same dog, under control conditions, and with AVF. The curves may all be separated into two parts: the first one with CBF, C(t) and aortic pressure, increasing in parallel, hence positive slopes of flow-pressure and pseudo compliance-pressure relationships. For high values of pressure, CBF and C(t) decreased with aortic pressure increasing, i.e. the slopes of the two curves were negative. Plotting the second part of CBF/(dP/dt) pressure curves, obtained under control conditions, aortic constriction and AVF, for the same dog, seems to fit roughly the same curve (large dashed points in Fig. 7). During proximal occlusion of the coronary artery, the decay of the distal coronary pressure and superimposed pressure pulsations were observed (Fig. 8). This decay curve shows a phasic component decreasing with time till almost complete disappearance. Discussion
Hemodynamic data, shown in Figs 3, 4, 5 and Table 1, are in agreement with those reported by Buckberg et al. (1972) in similar experiments. Briefly, our results confirm that the increased CBF remained predominantly diastolic during aortic constriction, with an increased systolic part of CBF. The morphology o f the CBF recordings was similar after aortic unclamping and AVF unclamping. The most characteristic feature was a reverse CBF at the
D Y N A M I C S OF THE C O R O N A R Y C I R C U L A T I O N
235
I see
LVBP
CBP
mmH(:j
. . . . .
,,,
,,;,
J. . . .
-,
........
Jb b b b UbbLiLJL~LJ~Jld~bbGL L~bbbbi
1°o 1 0J
FIG. 8. Aortic BF, CBF, left ventricular BP and coronary blood pressure (CBP) recorded in the left anterior descending coronary artery (LAD), during clamping of LAD.
end of systole. Furthermore, after AVF unclamping, peak systolic coronary blood flow was markedly increased (Fig. 5). Although retrograde arterial flow has been described by several investigators (Porter, 1898; Anrep & V. Saalfeld, 1933; Gregg, Green & Wiggers, 1935; Menno & Schenk, 1961; Karp & Roe, 1966; Delin, 1969; Buckberg et al., 1972; Hoffman & Buckberg, 1976), it is only recently that Spaan et al. (1981) have proved its magnitude and importance. The phasic CBF observed in different experimental conditions may be accounted for in terms of the proposed model previously described. At the end of diastole, the intramyocardial vascular bed is assumed to be filled. Its volume is possibly enhanced in aortic constriction and AVF conditions because of the metabolic vasodilatation related to the increased demand for oxygen. The intravascular pressure is assumed to decrease, during diastole, from the aortic pressure value in the epicardial superficial coronary arteries and arterioles to the zero flow pressure in the endocardial layer, ranging from 20 to 45 mmHg (Bellamy, 1978). The distribution of the intravascular pressure through the myocardial wall is determined by the vascular conductance which has been found to be greater in the subendocardial myocardium (Wusten et aL, 1977; Archie, 1978; L'Abbate et al., 1980; Verrier et al., 1980). During isovolumetric contraction, the intramyocardial tissue pressure rises as intravascular blood pressure remains at its end diastolic level. It is now well admitted that there is a roughly linear fall of the systolic tissue
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pressure from endocardium to epicardium (Stein et al., 1980; Sabbah & Stein, 1982, Hoffman et al., 1982; Nematzadeh et al., 1984). The tissue pressure is generated by radial; tangential and circumferential stresses. It may be written: Pim = Pr + Pt (3) where P/m is the intramyocardial pressure. Pr and Pt represent the parts of the intramyocardial tissue pressure due to the radial stresses and to the tangential and circumferential stresses, respectively. In the endocardium, the radial part of the intramyocardial tissue pressure equals the cavity pressure. From this assumption, the tissue subendocardial pressure is higher than simultaneously measured left ventricular blood pressure (PLV) (Dieudonne, 1967; Baird, Goldbach & De La Rocha, 1972; Sabbah & Stein, 1982). In the subendocardial layers, where the tissue pressure exceeds the intravascular pressure, the coronary bed collapses. Blood is then driven out from capillaries to venules offering the least resistance (Stein et al., 1969; Steinhausen, Tillmans & Thederan, 1978). Another effect of squeezing the inner myocardial layers is an enhancement of the total coronary bed resistance, inducing a reduction in the coronary arterial inflow. This is constantly observed, during the isovolumetric contraction, in CBF recorded in all conditions (Figs. 3, 4 and 5). According to our model, the thickness of the collapsed myocardial layer is different in various experimental conditions. In the low range of pressures, the subendocardial tissue pressure/left ventricular blood pressure ratio may be expected to be higher than in control conditions. From equation (3), it may be written: P/m/PLV = 1 + P t / P L V .
(4)
The thickness of the collapsed layers can be thus expected to be more important after AVF unclamping, compared with control conditions. During aortic constriction, P/m/PLV may be assumed to be decreased, and thus, the collapse point will be probably moved toward the subendocardium. After the opening of the aortic valves, the intravascular coronary pressure rises with the aortic pressure. The coronary blood inflow, observed during early systole, is increased and may be accounted for by an inflation of the first compartment and a capillary flow through pores of the uncollapsed part of the intramyocardial compartment. This period corresponds to the part of the curves with positive slope in the CBF-aortic pressure and pseudo compliance-pressure relationships. During the aortic constriction, the uncollapsed part of the intramyocardial compartment is larger and more capillary pores are available to flux. The compliance of the epicardial coronary arteries, subjected to higher pressure, is smaller. On the other
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hand, the more uncollapsed part of the intramyocardial compartment, larger than that in control conditions, tends to offer a lower resistance to capillary flow. As a result of the balance between these two phenomena, the CBF and the pseudo compliance increased with the pressure during the beginning of systole (Fig. 7). Conversely, during AVF unclamping, the epicardial coronary arteries, subjected to low mean pressure, may store greater blood volume during the beginning of the systole, inducing an important peak systolic CBF, observed during AVF unclamping (Fig. 5). In every instance, the CBF-pressure and the pseudo compliance-pressure relationships reached maximum values before the peak aortic blood pressure was attained. Although the blood pressure continued to increase, CBF, paradoxically, decreased (Fig. 6). Because of the tissue myocardial pressure increasing more than the intravascular pressure during early systole (Sabbah & Stein, 1982), we may assume that the collapse point moves from endocardium to epicardium. The number of capillary pores accessible to flow diminished. As the capillary density of the remained uncollapsed epicardial intramyocardial bed is lower (Wusten et al., 1977; Archie, 1978; Eliasen et al., 1982), a slight further collapse may provoke a large increase in the resistance to flow. This eiIect is more dramatic in conditions where the collapsed intramyocardial vascular compartment is larger, i.e. for more epicardial collapse point. During the AVF unclamping, the maximum value of CBF and pseudo compliance were reached before the peak systolic blood pressure was reached, earlier than in control conditions. During systole, while the aortic pressure is still increasing, and a large part of the epicardial bed collapsed, Fig. 7 seems to indicate that compliance predominates, according to equation (2). During later systole, as the aortic blood pressure decreased, a coronary reverse flow was observed after aortic unclamping and AVF unclamping (Figs..4 and 5). Under these conditions, it may be admitted that the driving pressure was in the anterograde direction, i.e. that the coronary blood pressure was higher than the simultaneous aortic blood pressure. According to the proposed model, the reverse flow recorded in the main epicardial coronary artery may be accounted for by two phenomena: (1) A blood volume stored by the compliant compartment during early systole may be restored by the elastic forces developed in the vessel walls of the epicardial coronary arteries. (2) While a part of the intramyocardial vessels collapse, blood in intramyocardial arteries is caught between a very high resistance downstream and the aortic pressure upstream. The second component of the reverse flow during later systole may be the result of the blood pressure in the subepicardial arterioles increased by an amount equal to the tissue pressure.
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A slight additional P/m, increasing the coronary vascular pressure, may induce a reverse flow. In both conditions where a late systolic reverse flow has been observed, these two reasons may be involved: during AVF unclamping, the uncollapsed part of the second compartment is assumed to be small, with few available pores, and the myocardial contractility is supposed to be high. Therefore, P/m may be important and a major force may be applied to the suISepicardial blood volume. The proposed model is in agreement with the results reported by Chillian & Marcus (1982), who have shown that, in normal hemodynamic conditions, a retrograde blood velocity was recorded in a small subepicardial artery, whereas blood flow velocity at this time was anterograde in an epicardial coronary artery. The retrograde component of mid-systolic blood velocity persisted in the intramyocardiai artery, despite large increase in blood flow velocity during coronary vasodilatation. After completion of the systole, the myocardial tissue pressure decreases to values lower than the diastolic arterial blood pressure. The intramyocardial vascular bed is thus uncollapsed and filled. The diastolic coronary blood flow is then driven by the difference between the aortic pressure and the zero flow pressure (Bellamy, 1978). Patterns of the diastolic flow will not be discussed in the present paper. The reverse coronary blood flow observed in certain experimental conditions may be related to the pressure pulsations detected in the distal circumflex artery after proximal occlusion of the artery (Fig. 8). This phenomenon has been previously described (Giles & Wilcken, 1977; Kroll et al., 1980; Spaan et al., 1981). Spaan et al., (1981) pointed out that this phasic component of pressure recorded after cessation of flow into the coronary system cannot be explained by a time varying resistance, but related to a phasic flow in and out the intramyocardial blood compartment. The pressure pulsation diminishes with time as the available blood volume is driven out to epicardial venules. In various experimental conditions, the partially collapsed intramyocardial vascular bed and the myocardial pump action may provoke coronary pressure or blood flow pulsations. Figure 9 shows CBF recorded during ectopic beats. It can be seen that left ventricular pressure rises induced simultaneous CBF falls, although the coronary pressure was not altered by the myocardial contractions during the ectopic beats. Furthermore, during the post extrasystolic beat, a large reverse flow was observed during the late systole. The observed phasic CBF may be accounted for by the intramyocardial tissue pressure rise. During each ectopic beat, the increased intramyocardial tissue pressure collapsed a part of the intramural vascular bed and then tended to decrease the coronary blood inflow. The myocardial potentiation
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CBP ( mmHg )
CBF (cm3.min-~¿ Left ventriculor BP ( mmHg ) Aortic BF ({.min -1) !
C).5 sec
FIG. 9. Coronary blood pressure (CBP) recorded in the left anterior coronary artery, CBF recorded in the circumflex coronary artery. Left ventricular BP and aortic BF, showing phasic and opposite CBF and left ventricular BP variations, during ectopic beats without change in CBP. A reverse CBF is observed during the post ectopic systole.
during the post ectopic beat probably changed the myocardial contractility (Cranefield, 1965; Hoffman et al., 1965; Anderson et al., 1976), increased the intramyocardial tissue pressure, and thus produced a reverse flow during the late systole (Fig. 10). Dieudonne (1967) has shown that after isoproterenol injection, the point where cavity pressure equals intramyocardial tissue pressure moved towards the epicardial surface.
CB,,cm3m,o', 0Oj
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FIG. 10. CBF left ventricular BP and aortic BF, recorded a low paper speed, showing reverse CBF during every post ectopic beat.
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FIG. 1 h C B F and aortic BP recorded at low paper speed: (a) After pentobarbital injection, showing a decrease in CBF in parallel with a decrease in BP. (b) After T N T injection, showing a decrease in aortic BP similar to that seen in (a), with maintained C B F peak, and large reverse flow.
The influence of the myocardial contractility may be illustrated by Fig. 11 which shows the effects of massive i.v. injection of trinitrine (TNT) or sodium pentobarbital on CBF and aortic blood pressure. With reduction of the contractility by the pentobarbital, the aortic blood pressure and the CBF decreased in parallel (Fig. 11 (a)). Conversely, after vasodilatation and increased contractility with TNT, the mean CBF was unchanged and enormous systolic reverse flow was observed, whereas the aortic blood pressure was markedly reduced (Fig. ll(b)). Effects of the T N T injection were to increase the intramyocardial vascular bed and possibly to enhance the myocardial tissue pressure, whereas the aortic blood pressure decreased. It may be expected that the difference between the intravascular pressure and the aortic pressure was markedly increased, provoking a reverse flow. The importance of this reverse flow is to be related to the blood volume increased by vasodilatation. Conversely, after pentobarbital injection, myocardial contractility and aortic pressure decreased in parallel, the difference between the intramyocardial tissue pressure and the aortic blood pressure remained slight; this might explain the lack of systolic reverse flow after pentobarbital injection. The proposed descriptive model may give further elements to explain the vulnerability of the subendocardial muscle to ischemia. Experimental results using microsphere methods (Buckberg et al., 1972; Downey & Kirk, 1974) showed that subendocardial ischemia is associated with a marked relative decrease in subendocardial blood flow. Conversely, recent results reported
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by Steinhausen et al. (1978) and Chillian & Marcus (1982) from direct observations and blood flow measurements in intramyocardial arterioles, concluded to little systolic flow in any part of the left venticular myocardium. According to our model, the arterial inflow may be reduced in subepicardial layers during systole, whereas the subendocardial vascular bed is collapsed. Lower systolic oxygenation may occur in the subendocardial muscle where there is neither blood flow nor blood volume, and consequently no oxygen transfer. In the subepicardial muscle, there is little inflow in the uncollapsed coronary vessels, but, the remaining blood volume in this part of the myocardium allows for oxygen transfer to muscle. The discrepancy between systolic subepicardial blood flow, as measured by microspheres or direct methods, may be due to the volume of the uncollapsed subepicardial compartment, allowing the distribution of the microspheres in this compartment and thus an overestimation of perfusion. This explanation is supported by the experiments reported by Deboer et al. (1982). These authors showed that, after experimental coronary occlusion, the infarction of the epicardium was larger in hypotensive dogs, although the percentage and the size of the infarcted endocardium did not change. During hypotension, it may be assumed that the collapse point is more epicardial, the available epicardial blood volume is decreased, and thus a larger area is more vulnerable to ischemia. A two compartment-mechanical model of the coronary circulation has been developed. This model includes capacitive epicardial arteries, not directly subjected to the intramyocardial tissue pressure, and a collapsible intramyocardial vascular bed. The collapse point position of the second compartment depends on the transmural pressure, i.e. on the relative distribution of the intramyocardial tissue pressure and the intravascular coronary pressure. The specific role of the epicardial capacitive coronary arteries and of the intramyocardial pump action has been illustrated during coronary artery clamping, ectopic beats and changes in myocardial contractility. In various experimental conditions, the reported results demonstrated the ability of the model to qualitatively describe the pattern of the dynamics of the coronary circulation. We wish to gratefully acknowledge Dr Julien I. E. Hoffman, from the Cardiovascular Research Institute, University of California, San Francisco, for reading our manuscript and for his very helpful discussion. REFERENCES ANDERSON, P. A. W., RANKIN, J. S., ARENTZEN, C. E., ANDERSON, R. W. & JOHNSON, E. A. (1976). Circ. Res. 39, 832.
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ANREP, G. V. & v. SAALEELD, E. (1933). J. Physiol. 79, 317. ARCHIE, J. P. JR. (1978). J. Surg. Res. 25, 21. ARTS, M. G. J. (1978). PhD Thesis, Rijksuniversiteit, Limburg. BAIRD, R. J., GOLDBACH, M. M. & DE LA ROCHA, A. (1972). J. Thorac. Cardiovasc. Surg. 64, 635. BELLAMY, R. F. (1978). Circ. Res. 43, 92. BUCKBERG, G. D., FIXLER, D. E., ARCHIE, J. P. & HOEFMAN, J. I. E. (1972). Circ. Res. 30, 67. CANTY, J. M. & KLOCKE, F. J. (1979). Circulation 60 (suppl 11), 101 (abstract). CHILLIAN, W. M. & MARCUS, M. L. (1982). Circ. Res. 50, 775. CRANEFIELD, P. F. (1965). Bull. N.Y.. Acad. Med. 41, 419. DEBOER, L. M. V., RUDE, R. E., DAVIS, R. F., MAROKO, P. R. & BRAUNWALD, E. (1982). Cardiovasc, Res. 16, 423. DELIN, N. A. (1969). Scand. J. Thorac. Cardiovasc. Surg. 3 (Suppl I), 1. DIEUDONNE, J. M. (1967). Am. J. Physiol. 213, 101. DOUGLAS, J. E. & GREENFIELD, J. C. JR. (1970). Circ. Res. 27, 921. DOWNEY, J. M. & KIRK, E. S. (1974). Circ. Res. 34, 251. DOWNEY, J. M. & KIRK, E. S. (1975). Circ. Res. 36, 753. ELIASEN, P., AMTORP, O., TONDEVOLD, E. & HAUNSO, S. (1982). Cardiovasc. Res. 16, 593. ENG, C., JENTZER, J. H. & KIRK, E. S. (1982). Circ. Res. 50, 334. GILES, R. W. & WILCKEN,D. E. t . (1977). Cardiovasc. Res. 11, 64. Gow, B. S. & HADFIELD, C. D. (1979). Circ. Res. 45, 588. GREGG, D. E., GREEN, H. D. & WIGGERS, C. J. (1935). Am. J. Physiol. ll2, 362. HOFFMAN, B. F., BARTELSTRON, H. J., SCHERLAG, B. J. & CRANEFIELD, P. F. (1965). Bull. IV. Y. Acad. Med. 41,498. HOFFMAN, J. I. E. & BUCKaERG, G. D. (1976). In: Progress in Cardiology. (Yu, P. & Goodwin, J. F. eds). pp 37-89. Philadelphia: Lea and Febiger. HOEFMAN, J. 1. E., BAER, R. W., UHLIG, P. N., VLAHAKES, G. J., BR1STOW, J. D., MESSIANA, L. M., HANLEY, F. L. & VERRIER, E. D. (1982). KARP, R. B. & ROE, B. B. (1966). Ann. Surg. 164, 959. KLOCKE, F. J., WEINSTEIN, I. R., KLOCKE, J. F., ELLIS, A. K., KRAUS, D. R., MATES, R. E. CANTY, J. M., ANBAR, R. D., ROMANOWSK1, R. R., WALLMEYER, K. W. & ECHT, M. P. (1981). J. Clin. Invest. 68, 970. KROLL, K., SCHIPPERHEYN, J. J., HENDRIKS, F. F. A. & LAIRD, J. D. (1980). Am. J. Physiol. 238, H214. L'ABBATE, A., MARZILLI, M., BALLESTRA, A. M., CAMI¢I, P., TRIVELLA, M. G., PELOSI, G. & KLASSEN, G. A. (1980). Cardiovasc. Res. 14, 21. MENNO, A. D. & SCHENK, W. G. (1961). Surgery 50, 82. NEMATZADEH, D., ROSE, J. C., SCHRYVER, TH. & KOT, P. A. (1984). Basic Res. Cardiol. 79, 86. PATEL, D. J. & JANICKL J. S. (1970). Circ. Res. 27, 149. PORTER, W. T. (1898). Am. J. Physiol. 1, 145. SABISTON, D. C. & GREGG, D. E. (1957). Circulation 15, 14. SABaAH, H. N. & STEIN, P. D. (1982). Am. J. Physiol. 242, H240. SPAAN, J. A. E., BREULS, N. P. W. & LAIRD, J. D. (1981). Circ. Res. 49, 584. STEIN, P. D., BADEER, H. S., SCHUE'rrE, W. H. & GLASER, J. F. (1969). Am. HeartJ. 78,331. STEIN, P. D., MARZILL1, M., SABBAH, H. N. & LEE, T. (1980). Am. J. Physiol. 238, H625. STEINHAUSEN, M., TILLMANS, H. & THEDERAN, H. (1978). Pfliigers Arch 348, 9. VERRIER, E. D., BAER, R. W., HICKEY, R. F., VLAHAKES, G. J. & HOFFMAN, J. I. E. (1980). Circulation 62 (suppl III), 62 (abstract). WUSTEN, B., BUSS, D. D., DEIST, H. & SCHAPER, W. (1977). Basic Res. Cardiol. 72, 636.