Intramyocardial pressure: Effect of preload on transmural distribution of systolic coronary blood flow

YOUNG

INVESTIGATORS’

lntramyocardial Transmural

Pressure: Effect of Preload on

Distribution

JOSEPH P. ARCHIE, Jr., PhD, MD Birmingham,

Alabama

From the Department of Surgery, University of Alabama Medical Center. Birminoham, Ala. 35294. This study was supported in part by Program Project Grant 546550 from the National Heart and Lung Institute, National Institutes of Health, Bethesda, Md. and National Institutes of Health Trainina Grant 5 TO1 GM0 1924-03. Manuscript accepted July 12. 1974. ’ First Prize, American College of Cardiology Young Investigators’ Competition 1974. Address for reprints: Joseph P. Archie, Jr., MD Department of Surgery, Wilford Hall, U. S. Air Force Medical Center, San Antonio, Texas.

904

June 1975

AWARD

of Systolic Coronary

Blood Flow*

Impairment of systolic coronary blood flow (CBF) may be mediated by intramyocardial pressure (PI&. However, the effect of systole on the magnitude and transmural distribution of coronary blood flow has not been investigated. The purpose of this study was to measure this effect, and, indirectly, intramyocardial pressure. It is assumed that intramyocardial pressure acts on the coronary vessels as a Starling resistor, such that local coronary blood flow is determined by the equation: Coronary perfusion pressure minus intramyocardial pressure equals resistance times coronary blood flow. This equation was integrated with respect to time and solved simultaneously for intramyocardial pressure and resistance by measuring regional coronary blood flow (radioactive microsphere technique) during maximal coronary vasodilatation in two states: beating and hypocaicemic diastolic arrest. Measurements were made in 7 to 16 concentric layers of the left ventricle of 16 dogs. intramyocardial pressure ranged from near zero to twice peak left ventricular pressure. The transmural distribution of intramyocardial pressure and systolic coronary blood flow depended on preload. The transmural distribution of the ratio of intramyocardial pressure to coronary perfusion pressure was not significantly different from unity across the left ventricular wail at low levels of preload (0 to 4 mm Hg). At moderate to high levels of preload (7 to 35 mm Hg) this ratio was not different from unity (mean 1.03 and 0.96) in the two inner fifths of the left ventricular wall, but was significantly lower (mean 0.79, 0.64 and 0.41, respectively) in the middle and two outer fifths. These data show that intramyocardial pressure shuts off systolic coronary blood flow across the entire left ventricular wail at low levels of preioad, and at high levels of preload determines a gradient of decreasing systolic coronary blood flow from the subepicardium to zero in the subendocardiai layers. This finding suggests that a dilated or failing left ventricle receives systolic flow to the outer myocardial layers, whereas at low preload levels myocardial perfusion occurs entirely during diastole.

The effect of myocardial contraction on coronary blood flow has been of interest to physiologists and physicians for decades. Although it is generally agreed that systole impairs coronary flow, neither the degree of mvocardial svstolic serfusion nor the mechanism of impair” ” “ ment of flow has been elucidated. Electromagnetic flowmeter studies of large coronary arteries of .animals suggest that 15 to 40 percent of coronary blood flow occurs during systolel; however, epicardial coronary arterial compliance makes interpretation of these data difficult.” The distribution- of coronarv_I blood flow durins the cardiac cvcle i seems to depend, among other things, on preload, since the percent of systolic flow decreases early in hearts with hemorrhagic shock” but increases in the dilated, failing left ventricle.4 Intramyocardial hydrostatic pressure has been postulated as a factor in impairment of sys-

The American Journal of CARDIOLOGY

Volume 35

lNTRAMYOCARDlAL

tolic coronary blood flow, but no direct evidence of the degree of impairment has been obtained. In this study the effect of systole on left ventricular coronary blood flow and its transmural distribution was assessed by using the radioactive microsphere method 5,6 to measure local myocardial flow during diastolic arrest and the beating state. The technique used is based on the concept that developed local systolic wall stress is manifested as intramyocardial hydrostatic pressure acting locally as a Starling resistor on the myocardial vessels. Accordingly, the magnitude and transmural distribution of systolic intramyocardial hydrostatic pressure were estimated and their dependence on left ventricular end-diastolic pressure, or preload, investigated. Methods Sixteen mongrel dogs weighing 18 to 23 kg were anesthetized with pentobarbital sodium (25 mgJkg intravenously) and ventilated with room air through an endotracheal tube with use of a Harvard respirator. Polyvinyl catheters were placed in a femoral artery and vein, and 1 to 1.5 liters of 5 percent dextrose in one half normal saline solution was infused intravenously over 30 minutes. Approximately 600 cc of whole blood was withdrawn from the arterial catheter during this period, heparinized and used to prime the pump-oxygenator system. A bilateral thoracotomy was performed in the fifth intercostal space, the azygous vein ligated and the innominate artery cannulated with a short polyvinyl catheter for pressure recording. The pericardium was opened and umbilical tapes were placed around the superior and inferior venae cavae, main pulmonary artery and descending aortic arch. A Bardic arterial perfusion cannula was placed in the left subclavian artery and a Bardic venous cannula in the right ventricle by way of the right atrial appendage after systemic heparinization. A pump-oxygenator system consisting of a Travenol membrane oxygenator, a Sarns occlusive roller pump and a heat exchanger was used to establish partial bypass, which was converted to heart bypass by ligation of the aorta distal to the perfusion cannula so that only the coronary arteries were perfused by way of the aortic arch. The main pulmonary artery and venae cavae were then ligated and total isolated heart bypass was established. A 40 cc capacity latex balloon on a stiff catheter (for pressure measurement) with a 1.5 cm shoulder was placed into the left ventricular cavity and a pursestring suture secured about the shoulder so that regurgitation of the balloon through the mitral valve was not possible. The left ventricle was vented by way of the apex and the left atrium vented through a Bardic venous cannula. Pressures were measured with two Statham P23Db transducers and recorded on an Electronics for Medicine oscillograph. Zero pressure was taken at the mid left ventricular level. Heart rate was not controlled. Perfusion temperature was maintained at 37 “C throughout all experiments. Maximal pharmacologic vasodilatation was produced by injection of 10 mg of dipyridamole7 into the whole blood perfusate. Maximal vasodilatation was checked in all experiments by maintaining coronary flow constant, injecting an additional 5 mg of dipyridamole and verifying that no further decrease in coronary perfusion pressure occurred. In four experiments maximal vasodilatation was also veri-

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fied by the absence of a reactive hyperemic response as recorded by an electromagnetic flowmeter (Statham model 4000) on the left anterior descending coronary artery after 8 to 10 seconds of occlusion.8 Hypocalcemic diastolic arrest was induced by titrating the perfusate with a standard blood bank acid-citrate-dextrose solution. The left ventricular balloon volume was adjusted to a preselected level of diastolic pressure. Carbonized radioactive microspheres (mean diameter 9.2 b, standard deviation 1.2 h) labeled with scandium-46, strontium-85 or cerium-141 were injected into the arterial line upstream from the perfusion cannula. Sufficient numbers of microspheres of each type were injected to give at least 1,000 spheres/g of left ventricular tissue to ensure precision of the method.g The number of microspheres given in the first injection should occlude only 0.02 to 0.05 percent of the microcirculation and hence should not affect the distribution of spheres in the second injection. Reference samples were withdrawn at a rate of 10 cc/min for 2 minutes, beginning at the time of injection, from the aortic arch and venous return line using a Holter pump.6lg The 46Sc-labeled spheres were usually given during the arrest state. Immediately after completion of reference sample collection, 10 percent calcium gluconate was added to the perfusate until the heart beat forcefully. Maximal pharmacologic vasodilatation was again verified by addition of 10 mg of dipyridamole to the perfusate. When equilibrium was reached the pressures were recorded and either 85Sr- or 14lCe-labeled microspheres were injected. In all experiments the study during the arrest state preceded that during the beating state. In four experiments blood flow was measured by electromagnetic flowmeter on the left anterior descending coronary artery during microsphere injection in the beating state. On completion of each study the heart was fixed by injection of glutaraldehyde into the arterial perfusion line. The left ventricular balloon was removed and its volume verified. The Sarns pump was calibrated with the blood perfusate by timed volume collection. The large coronary arteries, fat, great vessels and valves were removed. The left ventricular free wall was divided into three sections: the posterior wall or inflow section (area of posterior papillary muscle), the anterolateral wall or outflow section (area of anterior papillary muscle) and the apex. These sections were trimmed perpendicular to the epicardial surface while being pressed flat and sliced into 7 to 16 concentric layers, nearly equal in thickness, parallel to the epicardial surface. Each layer, as well as the right ventricle, septum, atria and left ventricular trimmings, was weighed and the gamma radioactivity counted on a Picker Autowell spectrometer. The radioactivity of each isotope in each layer and section was computed by the method of Rudolph and Heymann. Wall thickness was normalized by computing the fractional distance of each layer from the endocardial surface using the weight of each layer and the weight of the whole section. This was possible because each layer for any section had the same surface area. Thus the location, x, for any section of the left ventricular wall ranged from zero at the endocardial surface to unity at the epicardial surface, or 1 I x 5 0, the fractional wall thickness. Total flow measured from the calibrated pump, Q,,, the radioactivity of each isotope for the total heart, IT, and each myocardial layer, Ii,.were used to compute blood flow Q or Q(x), for each layer by use of the equation: Q = Qp (Ii/ IT). Adequacy of microsphere mixing in the aortic root was checked by comparing the total myocardial flow, QT, measured by the reference sample method,“sg with known

June 1975

The American

Journal of CARDIOLOGY

Volume

35

905

INTRAMYOCARDIAL

PRESSURE AND CORONARY

FLOW-ARCHIE

1 PwED’4

P

wm=O

o

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THICKNESS

Results In 20 consecutive microsphere injections during which arterial and venous reference samples were obtained, arterial mixing and microsphere trapping were estimated. Adequacy of mixing of microspheres in the aortic arch before entry into the coronary arteries is indicated by a percent difference of 5.8 f 3.89

June 1975

. .

/

I

pump flow Q,. QT was computed using the arterial reference sample flow rate, QR, and radioactivity, 1R as follows: Qr = Qn (IT&). The percent of myocardial microsphere trapping was computed using the arterial and venous reference samples.1° The ampbtude coefficient of intramyocardia! pressure, A(x), and resistance, R(x), for each layer were computed for each myocardial layer by simultaneously solving equation 4 (Appendix) in the arrest and beating states. Values of the normalized amplitude coefficient of intramyocardial pressure, B(x), were computed from equation 5 (Appendix). The percent of systolic and diastolic flow predicted by the intramyocardial pressure data was obtained by calculating the area between the transmural distribution curves formed by the difference between coronary and intramyocardial pressure divided by resistance during both systole and diastole. These areas were multiplied by their respective time fractions of the cardiac cycle to give the percent of systolic and diastolic flow.

906

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The American Journal of CARDIOLOGY

FIGURE 1. Amplitude coefficient of intramyocardial pressure, A(x), for the anterolateral or outflow section of the free wall of the left ventricle of 16 hearts. The hearts are grouped according to preload or left ventricular end-diastolic pressure in millimeters of mercury (PLvso). The location, x, in the sections is given by the fractional wall thickness 0 5 x -< 1, from endocardium (ENDO) to epicardium (EPI). Dogs 1, 5, 9 and 13 (Table l)are indicated by closed clrcies, dogs 2, 6, 10 and 14 by closed triangles, dogs 3, 7, 11 and 15 by open clrcles, and dogs 4, 6, 12 and 16 by open Mangles.

percent (mean f standard deviation, no. = 20) between total heart flow computed by the arterial reference sample method and known pump flow. There was greater than 99 percent trapping of the 9.2 w diameter microspheres by the myocardium in most ex-

periments. The percent of nontrapped microsphere radioactivity was 0.9 f 0.82 percent (no. = 20). In general, the transmural distribution of blood flow during the arrest and beating states and, accordingly, the solutions for resistance, R, and the amplitude coefficient of intramyocardial pressure, A, were similar in the left ventricular inflow and outflow sections in each heart. However, the pattern in the apical sections varied from that of the inflow and outflow sections in most studies. The results presented here are for the outflow area or anterior wall of the left ventricle. This section is most representative of the experimental design since the inflow or posterior sections were subject to compression from the weight of the ventricle above it, and the apical sections had a variable thickness. The solutions for A(x), B(x) and R(x) for the outflow section of 16 hearts are given in Figures 1 to 4. The results are divided into four groups composed of four hearts each, on the basis of left ventricular enddiastolic pressure or preload. Measured pressures

Volume 35

INTRAMYOCARDIAL

PRESSURE AND CORONARY

P =o LVED

I

FLOW-ARCHIE

P =4 LVE D

I

I

I

I

I

PLVED=17-35

PLVED’FHI

A

0

.

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FIGURE 2. Normalized amplitude coefficient of intramyocardial hydrostatic pressure, B(x), for 16 hearts at four ranges of preload. Symbols and abbreviations as in Figure 1.

TABLE

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075

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05

075

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025

.

EP:E/VDO

70

FRACTIONAL

WALL

Ef?

THICKNESS

I

Left Ventricular

and Aortic

Pressure

and Myocardial

Blood

Flow to Left Ventricular

Outflow

Arrest State Heart no.

P,

PLV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

99 103 83 81 64 81 911 95 65 58 85 76 55 111 115 75

0

0 0 0 4 4 4 4 8 9 10 11 18 20 35 30

Sections

Beating State

Q

P,

Po

PLY

hsJ

Q

6.61 7.84 6.01 5.85 5.56 4.59 4.21 4.03 6.69 5.13 10.1 8.40 5.40 6.14 3.50 4.02

106/ 90 108/94 92173 98178 66158 100/86 88181 105197 98142 64154 90/80 78173 65144 124/107 122/99 85168

97 99 84 87 62 92 86 101 63 58 87 76 51 115 109 73

108/O 70/o 86/O 130/o 5114 11414 6214 9814 100/8 5918 7718 61/11 110/18 123/17 145135 80/28

39 21 24 30 24 35 27 50 49 22 24 28 41 68 75 44

4.18 5.72 4.83 4.72 2.37 3.69 2.40 2.34 2.86 4.39 7.65 6.65 3.69 4.06 2.68 3.04

P, and p, = phasic and mean coronary perfusion pressures (mm Hg), respectively; PLv and &,v = phasic and mean left ventricular pressures (mm Hg), respectively; Q = mean coronary flow of entire section per gram of myocardium (wet weight) (cc. min-l-g-l).

June 1075

The Amerlcen

Journal of CARDIOLOGY

Volume 35

907

INTRAMYOCARDIAL

PRESSURE AND CORONARY

FLOW-ARCHIE

and total myocardial flows to the section in each state for each heart are given in Table I. Transmural distribution of the amplitude coefficient of intramyocardial hydrostatic pressure, A(x): This is shown in Figure 1. Intramyocardial pressure (P& for any location, x, in the ventricular wall is A - PI,“. When the level at left ventricular diastolic pressure was low (0 to 4 mm Hg), and hence ventricular volume small, there was a fairly uniform A value across the wall, and a decrease at the subepicardial layer in three of eight experiments. At moderate (8 to 11 mm Hg) and high (17 to 35 mm Hg) levels of diastolic pressure, A decreased from the endocardial to the epicardial surface. Intramyocardial pressure exceeded intraventricular pressure (A >l) in some regions of the wall in some experiments, but this observation was not limited to the groups with low preload in the inner half of the left ventricular wall. Distribution of the normalized amplitude of intramyocardial pressure, B(x): This is the ratio of PIM to P,. It is shown for each heart in each group in Figure 2 and is similar to A(x). At low levels of preload B was nearly equal to or greater than unity across the ventricular wall, whereas it decreased from near unity at the endocardial surface to between 0 and 0.5 at the epicardial surface in groups with moderate and high levels of preload. In all of the hearts at zero preload, B was maximal in the outer half of the wall; and this was true in two of four hearts with a preload of 4 mm Hg. Figure 3 gives the mean and 2 standard errors of the B values (ratio of PIM to P,) for both combined low (0 to 4 mm Hg) and moderate to high (8 to 35 mm Hg) preload for five sections of left ventricular wall from endocardium to epicardium. These are the same data presented in Figure 2, but combined into two groups and five regions of the left ventricular wall. B was not significantly different from 1 at low preload in all five sections, nor were the moderate to high preload B values significantly dif-

m

12 t

TABLE

II

Percent Systolic Coronary Blood Flow by Electromagnetic Flowmeter and lntramyocardial Pressure Methods Percent Systolic Flow

Experiment 1 2 3 4

no.

Electromagnetic Flowmeter 45 24 21 10

lntramyocardial Pressure 41 20 13 8

ferent from 1 or from the low preload B values in the two inner fifths of the left ventricular wall. However, in the middle fifth and outer two fifths B was significantly less than both 1 and the low preload B values in each section. Transmural resistance: Figure 4 shows the transmural resistance for each ventricle in each group. Although there was considerable variability in magnitude and distribution among hearts there is no association with preload. Electromagnetic flowmeter vs. intramyocardial pressure calculations: The results of four experiments in which simultaneous estimates of the percent of systolic flow were made by electromagnetic flowmeter and by intramyocardial pressure calculation are given in Table II. The electromagnetic flowmeter values were slightly higher in all cases, but the differences were not large. Discussion This study has demonstrated that systole impedes coronary blood flow. The degree of impairment of regional myocardial flow was interpreted as being due to the effect of interstitial or intramyocardial hydrostatic pressure on the coronary vascular bed. The

T

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06

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a

04

s N 5

02

3 E =

: Oo

I

02

I

FRACTIONAL

908

June 1975

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0.4

1

08

WALL THIC%SS

The American Journal of CARDIOLOGY

Volume 35

FIGURE 3. The mean and 2 standard errors of the I3 values from Figure 2 for both combined low (0 to 4 mm Hg) (open circles) and moderate to high (8 to 35 mm Hg) (open triangles) preload. for each of five regions of the left ventricular wall. Probability of differences was calculated by the unpaired t test between the two groups for each of the five sections. There was no significant difference in B values in the inner two fifths of the left ventricular wall. However, for 0.4 < x < 0.6, P = 0.014; for 0.6 < x < 0.8, P = 0.0001; and for 0.8 < x < 1, P = 0.003.

INTRAMYOCARDIAL

concept that interstitial hydrostatic pressure acts as a Starling resistor in determining the perfusion pressure gradient through a vascular bed is not new. An example is the waterfall theory of pulmonary blood flow.11 Peak developed left ventricular pressure as a predictor of intramyocardial pressure: The values for systolic intramyocardial pressure measured herein are of the same magnitude as those measured by various direct techniques such as vein implants,12 arneedlesr4-l6 and micromanometerial implants,13 ters.17 The question frequently arises whether peak systolic intramyocardial pressure is greater or less than left ventricular pressure. The results of several studies12J6-18 on dog left ventricles have shown that peak systolic intramyocadial pressure is greater than peak ventricular pressure; in other studies1:m15 it has always been less than left ventricular pressure. These differences have usually been considered a result of local trauma caused by placement of the device used

PRESSURE

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CORONARY

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to measure pressure. Since the method reported herein is indirect and noninvasive, this criticism is not applicable. Baird et al.ls measured peak systolic intramyocardial pressures of 80 to 135 mm Hg in the inner half of dog left ventricles during cardiopulmonary bypass with the ventricle empty, vented and developing no pressure. Since values for peak systolic intramyocardial pressure reported herein ranged from less than to greater than left ventricular pressure, it is concluded that peak developed left ventricular pressure is not a useful predictor of intramyocardial pressure, particularly at low levels of preload. Transmural distribution of intramyocardial pressure: The amplitude coefficient of intramyocardial pressure, A(x), should in theory be accurate for regions of the ventricular wall where PIM 5 P,, or B 51. When B > 1, measured values of PIM or A may be smaller than true values for PIM, since no flow occurs when PIM > P,, and thus the amplitude is underestimated by this method.

20

.

I

0 FIGURE 4. Resistance four ranges of preload. in Figure 1.

to flow, R(x), for 16 hearts at Symbols and abbreviations as

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June 1975

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of CARDIOLOGY

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35

909

INTRAMYOCARDIAL

PRESSURE AND CORONARY

FLOW-ARCHIE

In almost all other studies in which intramyocardial hydrostatic pressure was measured at more than one depth in the ventricular wall, there was a decrease in magnitude from endocardial to epicardial surface. In this report, at high preload levels (left ventricular end-diastolic pressure greater than 7 mm Hg) similar results were obtained. However, at low preload levels (left ventricular end-diastolic pressure 0 to 4 mm Hg) the distribution of intramyocardial pressure was more uniform across the wall, with higher values usually in the outer half of the ventricular wall. Since the method used here underestimates peak intramyocardial pressure when B is greater than unity, some of these values may be higher. Transmural intramyocardial pressure as a predictor of systolic myocardial flow: Although only four estimates of percent of systolic flow by simultaneous electromagnetic flowmeter and intramyocardial pressure measurements were made (Table II), the results were consistent with the concept that transmural intramyocardial pressure can be used to predict the degree of systolic flow and vice versa. Coronary arterial compliance has been shown to play a role in overestimation of systolic flow measured by electromagnetic flowmeters, but this error should be minimal in our study because of very high flow rates and little change in coronary arterial pressure between systole and diastole. However, our electromagnetic flowmeter values for percent systolic flow were slightly higher than those computed from the intramyocardial pressure distribution, which suggests that some component of systolic flow is stored in compliant large coronary arteries. Clearly, from Figure 3, systolic myocardial flow was totally or almost totally impaired at low preload levels. This is evident from Equation 2 (Appendix), since B = P&Pc was not significantly different from 1. From Figure 3 it is seen that B was significantly less than 1 in the outer three fifths of the ventricular wall at normal and high preload levels. Thus (1 - B) was not significantly different from 0 in the inner two fifths of the ventricular wall but increased progressively to the epicardial surface in the outer three fifths of the wall. Equation 5 (Appendix) can be rewritten as Q = (1 - B)P,/R when B
June 1975

The American Journal

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CARDIOLOGY

at the middle to inner one third of the wall, whereas

at high preload levels the distribution of lengths was nearly uniform. The latter observation is consistent with a uniform circumferential stress distribution at high preload levels and, hence theoretically, a nearly linear decrease in intramyocardial pressure from left ventricular pressure at the endocardial surface to 0 at pressure the epicardial surface. 22,23 Intramyocardial distribution measurements in this study and others at high preload levels confirm this hypothesis. How to accurately estimate stress distribution at low preload levels is not known. For intramyocardial pressure to exceed left ventricular pressure there must be, in theory, some element of compressive stress.23 This is clear from the studies of Baird et al.ls in empty beating hearts in which no net wall stress developed, although intramyocardial pressures were increased. Greater forces, and hence stresses, develop in longer sarcomeres and may compress other areas of the myocardial wall. The integrated (mean) wall stress may be zero, as in the case of the empty heart on cardiopulmonary bypass, or low as with low preload levels, during hypovolemic shock, but, there may be regions of high tensile and compressive stress within the wall. The net result may be a high level of intramyocardial pressure across the entire ventricular wall and consequently little if any systolic coronary flow. Appendix Resistance to blood flow through a vascular bed is usual-

ly defined as the ratio of the mean pressure difference or gradient across the vascular bed to the mean flow. In this paper, a more precise, locally applicable, definition of coronary vascular resistance is used, namely, the resistance to flow from the aorta to any specific location in the myocardium. This resistance is determined by the viscous properties of blood and the vascular anatomy. The transmural pressure across any myocardial vessel wall is the difference between the intravascular pressure and intramyocardial hydrostatic pressure. Local myocardial blood flow will continue unless intramyocardial hydrostatic pressure exceeds intravascular hydrostatic pressure, in which case the venules or veins, or both, collapse. If intramyocardial pressure is less than intravascular pressure, the vascular bed will remain open, and intramyocardial pressure will act as a Starling resistor on the terminal venules and veins at any myocardial region. Thus, at any instant of time, the relation between local myocardial flow, resistance and intramyocardial hydrostatic pressure is given by P,. -

P,,

= RQ

Q = 0 if P,

if P,. > P,, i

P,,

(1) (2)

where P, is the coronary arterial pressure, PIM is the intramyocardial hydrostatic pressure, R is the resistance and Q is the flow. Each of these variables in turn depend on one or both of the independent variables time, t, and location in the myocardium, x. Clearly, coronary perfusion pressure, P,., is a function of time only: P, = P,(t). Intramyocardial hydrostatic pressure, PIM, may depend on both time and position, but has been shown to have the time course of left ventricular pressure. 14,15,17This means that the functional dependency of PIM on location and time, PIM(t,x), can be

Volume 35

INTRAMYOCARDIAL

separated so that PIM(t,x) = A(x) PI,v(t), where A(x) is the amplitude coefficient of intramyocardial pressure at any location x in the myocardium, and PLv(t) is the instantaneous left ventricular pressure. If A(x) = 1, intramyocardial hydrostatic pressure equals left ventricular pressure. Resistance also depends on location, x, and time, t, but if ventricular geometry or shape and blood viscosity are maintained constant, resistance, R, is time-independent; that is, R = R(x). Local myocardial blood flow depends on time and location, Q = Q(t,x). Therefore equation 1 can be rewritten in functional notation:

P,(t)

-

A(x)P,,v(t)

=

R(x)Q(t,x)

(3)

Equation 3 is valid for any instant of time and any location in the myocardium. However, there is no way to measure the instantaneous time course of Q at any specific location in the myocardium. If equation 3 is integrated with respect to time, a time average equation, valid at any location in the myocardium, is obtained. Time average regional coronary flow, B(x), can be measured by several methods, perhaps the most accurate one being the radioactive microsphere method. 4-fi Integration of equation 3 over many cardiac cycles, from tl to t2, gives: ~“P,(t)dt

11

-

~gA(x)P,,v(tjdt

t.1

=

~t*R(x)QG,xMt t1

Since A(x) and R(x) are not functions of time they can be factored out from under the integral sign, giving

I,“Pc(

t)dt -

A(x$:‘P,,vWdt

= R(x) L:’ Q(t,xMt

PRESSURE AND CORONARY

&(x) is the time average regional flow as defined in the usual way

P, = ~:_PJt)dti(t2 PLV =

t9P&dt s tl

= R(x)@x)

(4)

(tn -

tl) -

tl>

= PwI,,,/K,,

(5)

are the peak systolic values for left ventricular and coronary (aortic root) pressure, respectively. Clearly, if B(x) is greater than or equal to 1, B(x) 1 1, for any location x, no systolic flow occurs in that region.

where

where P, and &v are the mean or time average coronary arterial and left ventricular pressures, respectively, and

I

t,)

Equation 4 contains five variables, of which P,, &v and Q(x) can be measured. This leaves the local values of the amplitude coefficient of intramyocardial pressure, A(x), and resistance,R(x), for any site x which may be obtained by measuring P,, &v and Q(x) during two different states, such as during diastolic arrest and the beating state, and the resultant two equations, equation 4 at each state, solved simultaneously for A(x) and R(x). Algebraically it is required only that A(x) and R(x) be the same in both measurement states; that is, the unknowns in the two equations must be unchanged at any location x. This requirement can be met by maintaining an isovolumetric state to minimize geometric change, and pharmacologic maximal vasodilatation of the coronary vessels to remove autoregulatory changes in R(x). Thus, solutions for R(x) and A(x) as well as A(x)PLv(t), the intramyocardial hydrostatic pressure, can be obtained for any region of myocardium in which flow can be measured. Since equation 2 predicts no flow if P, _< PIM, a normalized amplitude coefficient B(x) can be computed according to the definition

B(x) = A~~)G’IJ,,,/P~,,,) A(x)&

-

G(x) = ~llLQ(x,t)dt/(t,

or E’, -

FLOW-ARCHIE

PLV,., and

PC,,,

References 1. Gregg DE: The microcirculation of the heart in reduced flow states. In, Microcirculation as Related to Shock, chap 4 (Shepro D, Fulton GF, ed). New York, Academic Press, 1968, p 52 2. Douglas JE, Greenfield JC: Epicardial coronary artery compliance in the dog. Circ Res 27:921-929. 1970 3. Granata L, Huvos A, Pasque A, et al: Left coronary hemodynamics during hemorrhagic hypotension and shock. Am J Physiol216:1583-1589, 1969 4. Buckberg GD, Flxler DE, Archie JP, et al: Experimental subendocardial ischemia in dogs with normal coronary arteries. Circ Res 30:67-81, 1972 5. Rudolph A, Heyman MA: Circulation of the fetus in utero: methods for studying distribution of blood flow, cardiac output and organ blood flow. Circ Res 21:163-184, 1967 6. Domenech RJ, Hoffman JIE, Noble MIM, et al: Total and regional coronary blood flow measured by radioactive microspheres in conscious and anesthetized dogs. Circ Res 25:581596. 1969 7. West JW, Bellet S, Manzoll VC, et al: Effects of Persantin (RA8), a new coronary vasodilatator, on coronary blood flow and cardiac dynamics in the dog. Circ Res 10:35-44. 1962 8. Coffman JD, Gregg DE: Reactive hyperemic characteristics of the myocardium. Am J Physiol 199:1143-l 149, 1960 9. Buckberg GD, Luck JC, Payne DB, et al: Some sources of error in measuring regional blood flow with radioactive microspheres. J Appl Physiol31:598-604, 1971 10. Archle JP, Flxler DE, Ullyot DJ, et al: Measurement of cardiac output with an organ trapping of radioactive microspheres. J Appl Physiol 35:148-154, 1973 11. Permutt S: Effect of interstitial pressure of the lung on pulmonary circulation. Med Thorac 22:118-131, 1965

12. van der Meer JJ, Reneman RS, Schnleder H, et al: A technique for estimation of intramyocardial pressure in acute and chornic experiments. Cardiovasc Res 4:132-140. 1970 13. Sal&bury PF, Cross CE, Rlebem PA: lntramyocradial pressure and strength of left ventricular contraction. Circ Res 10:608623, 1962 14. Brand1 G, McGregor M: lntramyocardial pressure in the left ventricle of the dog. Cardiovasc Res 3:472-475, 1969 15. Baird RJ, Manktelow RT, Shah PA, et al: lntramyocardial pressure: a study of its regional variations and its relationship to intraventricular pressure. J Thorac Cardiovasc Surg 59: 810-823, 1970 16. Kirk ES, Honlg CR: An experimental and theoretical analysis Of myocardial tissue pressure. Am J Physiol 207:361-367. 1964 17. Armour JA, Randall WC: Canine left ventricular intramyocardia! pressure. Am J Physiol220: 1833-1839. 1971 18. Baird RJ, Goldvach MM, de la Rocha A: lntramyocardial pressure: the persistence of its transmural gradient in the empty heart and its relationship to myocardial oxygen consumption. J Thorac Cardiovasc Surg 64:635-646, 1972 19. Sonnenblick EH: Implications of muscle mechanics in the heart. Fed Proc 21:975-990, 1962 20. Streeter DD, Spotnltz HM, Pate1 DP, et al: Fiber orientation in the canine left ventricle during diastole and systole. Circ Res 24:339-347, 1969 21. Yoran C, Correll JW, Ross J: Structural basis for the ascending limb of left ventricular function. Circ Res 32:297-303, 1973 22. Mlrsky I: Left ventricular stresses in the intact human heart. Biophys J 9: 189-208, 1969 23. Archie JP: Determinants of intramyocardial pressure. J Surg Res 141339-346, 1973

June 1975

The American Journal of CARDIOLOGY

Volume 35

911