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Laboratory for Physiology and Department of Anesthesiology, Institute for Cardiovascular Research Vrije Universiteit, VU University Medical Center, Amsterdam, The Netherlands
ABSTRACT I. INTRODUCTION II. THE CARDIAC MUSCLE AND THE CORONARY VASCULATURE A. Functional Arrangement of the Cardiac Muscle and the Coronary Circulation B. Coronary Pressure-Flow Relationships 1. Autoregulation 2. Myogenic control 3. Metabolic control 4. Endothelium-based control 5. Autoregulation gain 6. Flow reserve 7. Coronary flow reserve 8. Fractional flow reserve 9. Supply-to-demand ratio C. Summary III. THE CARDIAC MUSCLE AFFECTS THE CORONARY VASCULATURE A. Cardiac Muscle and Coronary Flow in Diastole 1. Instantaneous pressure-flow relationship and zero-flow pressure intercept 2. Summary 3. Effect of ventricular volume changes on coronary flow in diastole 4. Summary B. Cardiac Contraction and Coronary Flow in Systole 1. Arterial inflow and venous outflow 2. Coronary arterial input impedance 3. Summary C. Models Explaining the Diastolic-Systolic Changes of the Vasculature 1. The waterfall model 2. The intramyocardial pump model 3. The varying elastance model 4. The muscle shortening and thickening model 5. The vascular deformation model 6. Summary D. Applications and Limitations of the Models 1. Arterial inflow and venous outflow 2. Static versus dynamic systole 3. Coronary arterial input impedance 4. Effect of contraction in layers of the heart wall 5. Cardiac contraction and the coronary microcirculation A) FLOW AND VELOCITY IN THE MICROCIRCULATION. B) DIAMETERS IN THE MICROCIRCULATION. C) HETEROGENEITY OF FLOW. D) VENULES PROTECT ARTERIOLES FROM COLLAPSE. 6. Intramyocardial pressure A) MEASUREMENT OF INTRAMYOCARDIAL PRESSURE. B) INTRAMYOCARDIAL PRESSURE EXPLAINED. 7. Flow reserve and supply-to-demand ratio E. Cardiac Contraction Augments Coronary Flow F. Effects of Cardiac Muscle on the Coronary Vasculature: Summary IV. THE CORONARY VASCULATURE AFFECTS THE CARDIAC MUSCLE A. Coronary Flow and Cardiac Muscle in Diastole B. Coronary Flow and Cardiac Muscle in Systole 1. The Gregg effect A) SYSTOLIC STIFFNESS. 2. Coronary vascular emptying augments cardiac contraction C. Effects of Coronary Vasculature on Cardiac Muscle: Summary V. ROLE OF THE EXTRACELLULAR MATRIX IN CROSS-TALK A. Theoretical Suggestions B. Experimental Findings C. Summary VI. CONCLUSIONS A. Cardiac Muscle Affects the Coronary Vasculature B. Coronary Vasculature Affects the Cardiac Muscle C. Extracellular Matrix GRANTS ACKNOWLEDGMENTS REFERENCES
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ABSTRACT |
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I. INTRODUCTION |
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Earlier reviews of coronary hemodynamics have provided substantial information about the coronary circulation (124, 151, 175, 226, 233, 235, 376, 377, 448, 458). However, limited attention has been given to the mutual interaction (cross-talk) of the cardiac muscle and the coronary vasculature. Modern measurement techniques, presently allowing for the noninvasive determination of human cardiac perfusion and cardiac muscle contraction (35, 176, 182, 269), now make it possible to study cross-talk in the clinical setting. These novel techniques together with a better knowledge of cross-talk will help to improve the understanding of pathological changes, adaptations, and the effects of therapeutic interventions (3, 105, 135, 136, 180, 222, 258, 300, 319, 328, 455).
The multiple mutual interactions between the coronary vasculature and the cardiac muscle can be divided into mechanical (including the role of the extracellular matrix) and mediator-based mechanisms (Fig. 1). This review concentrates on the acute mechanical factors that contribute to the two-way interactions between cardiac muscle and vasculature, which we will call mechanical cross-talk. On the one hand, the contracting cardiac muscle generates force and ventricular pressure, shortens and thickens, and increases in stiffness. These changes affect the coronary vasculature and coronary flow. On the other hand, increased vascular filling increases the vascular diameters that affect the neighboring cardiac muscle cells. Furthermore, when the smooth muscle tone changes it affects the mechanical properties of the vascular wall. Both vascular effects influence cardiac muscle contraction.
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Most examples in this review pertain to the left ventricle; the right ventricle is mentioned, when pertinent.
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II. THE CARDIAC MUSCLE AND THE CORONARY VASCULATURE |
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The coronary circulation is a system of branching vessels that can be divided into the epicardial arteries and veins and the intramyocardial vessels. The mechanical cross-talk between cardiac muscle and vessels mainly takes place at the level of the intramyocardial vessels. The intramyocardial vessels can be further divided into the transmural vessels and the microcirculation. Information about the anatomy of the coronary vasculature and its integration in the muscular network can be found in a number of publications (46, 150, 217, 331, 360, 376, 401, 404, 409a). The detailed structure of coronary arteries, the capillary network, and the venular system and their relation to function has been described by Kassab and co-workers (213–219, 409a). Currently, Spaan et al. (381) are developing a new method where the coronary microcirculatory morphology in situ can be visualized, including the relationship with the cardiac muscle. Pressure measurements in differently sized arteries and arterioles have indicated that under normal conditions, 45–50% of total coronary vascular resistance resides in vessels larger than 100 µm (279). Details about the coronary arterial microcirculation and its regulation can be found elsewhere (71, 75). The important role of the coronary microcirculation in coronary disease has been reviewed by Cecchi et al. (65).
The number of resistance vessels in the subendocardium is somewhat higher than in the subepicardium (402). As a result of this anatomical difference, the flow in diastole is 
10% higher in subendocardial than in subepicardial layers. The greater impeding effect of cardiac muscle contraction on arterial flow in subendocardial compared with subepicardial layers is thus, partly, compensated for by the difference in the number of resistance vessels. Differences in mean flow in the layers are generally small under physiological conditions, but may exist (137).
A homogeneous distribution of flow, cardiac metabolism, and muscle function as proposed earlier (414) is probably too simple a view. Local coronary perfusion differs, and this heterogeneity increases towards the microcirculation (22, 23, 29, 31, 170, 236, 239, 349, 410, 409a), but this is not related to certain fixed regions (30, 209). Heterogeneity in flow between control and moderate dilation differs little (99) but is different during maximal vasodilation (23). This heterogeneity depends on perfusion pressure (127) and on the perfusate (285); therefore, it is only partially dependent on the anatomy. Heterogeneity of flow is present in ischemia in the patient (344). Oxygen consumption, glucose uptake, glycolytic enzyme activity, and oxygen delivery are related and also heterogeneously distributed (6, 158, 179, 252, 372). In addition to flow heterogeneity, flow regulation (193), metabolic control of flow (98), vasomotion (400), microvascular coronary 
-adrenergic vasoconstriction (77), and responses to drugs (78, 236, 265) are all heterogeneously distributed. Heterogeneity is greatest at the submillimeter scale (30), but it has not been established if, on this scale, cardiac muscle contraction is also heterogeneously distributed in the heart wall (33). Magnetic resonance imaging (MRI) and positron emission tomography (PET), and even ultrasound, can provide insight into heterogeneity of flow, muscle function, local oxygen consumption, etc. (165, 344). There is also variation in flow with time called "twinkling" (29, 228), resulting from vasomotion. It may therefore be expected that heterogeneity also exists in mechanical cross-talk.
B. Coronary Pressure-Flow Relationships
Coronary pressure-flow relationships are strongly determined by autoregulation. Furthermore, flow reserve depends on autoregulation, and the supply-to-demand ratio assumes that flow is related to muscle metabolism and is negligible in systole. All three characterizations depend on vasomotor tone and cardiac contractility and thus on the mechanical properties of the vasculature and the cardiac muscle. We show below that the mechanical properties of the vasculature and cardiac muscle affect mechanical cross-talk.
Autoregulation (Fig. 2) is the capacity of an organ to regulate its own blood flow when perfusion pressure is challenged (293, 338). Cardiac muscle plays an important role in coronary autoregulation: blood flow adjusts to muscle metabolism, and in the physiological range flow is rather independent of perfusion pressure. The level of the plateau of the autoregulation curve is related to the metabolic state of the heart (293, 306). There are several local autoregulatory control mechanisms that match blood flow to activity of the tissue. By changes in the diameter of mainly the arterioles, where vascular resistance resides (74, 306, 338, 446), flow can be adjusted within a typical response time of a few seconds (365, 416). Changes in the diameter of the microvessels in part result from the smooth muscle properties per se, myogenic control, and in part result from factors released from the cardiac muscle, metabolic control, and the endothelium-based control.
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The vascular transmural blood pressure leads to stress in the circumferential direction of the vessel wall and is called "hoop stress." This pressure-induced vascular control forms the basis of the myogenic response and results in a change in vessel diameter to maintain a constant hoop stress, as shown in the coronary arterioles of the pig and the human (191, 192, 255, 256, 298). After an increase in the intraluminal pressure (Fig. 3), the diameter initially follows passively, and subsequently active smooth muscle contraction causes the diameter to decrease, leading to normalization of the wall stress. In response to decreased pressure, the opposite effect takes place. The myogenic response resides in the smooth muscle itself, since it is present in vessels without endothelium (254). The effect of myogenic regulation on the resistance distribution of the coronary system has been modeled (86). The myogenic autoregulation is based on hoop stress determining vascular tone and is not the result of mechanical cross-talk. However, vasomotor tone does affect cross-talk.
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Where the vasculature is in close contact with the cardiac muscle, mediators released from the cardiac muscle can affect smooth muscle tone. A single responsible mediator cannot be distinguished. Metabolites such as adenosine and carbon dioxide play a role, while pH and ions, oxygen, and K+-ATP channels also appear to be involved, depending on the conditions (38, 39, 56, 91–93, 112, 116, 124, 181, 225, 294). Metabolic autoregulation is an aspect of cross-talk. However, the mechanical aspect is indirect, since a change in vasomotor tone affects vascular mechanics and thus mechanical cross-talk.
Shear stress is caused by friction between the flow of blood and the vascular wall, and it acts in the axial (longitudinal) direction on the endothelial cells. The main mediator released from the endothelium affecting the smooth muscle cells is NO. This flow-induced control of vascular tone adjusts the diameters such that the shear stress is maintained constant, e.g., increased flow causes an increase in vessel diameter (240–242, 253, 257). A relationship exists between myogenic and endothelium-based control (255). It was recently shown that an endothelium-derived hyperpolarizing factor also plays a role in vivo (453). In addition, there is metabolic communication between cardiac muscle and endothelial cells (56). Chilian et al. (74) concluded that a significant part of the arterial tree, with vessels larger than the smallest arterioles, also contributes to total coronary vascular resistance, implying a role of endothelium-based regulation in coronary vascular tone and resistance. The vascular bed acts as a functional syncytium through electrical coupling of vascular cells (100, 335, 357), and changes in coronary resistance take place through "coordinated" action. An elegant concept integrating myogenic, metabolic, and flow-dependent regulation was published by Jones et al. (192), and this was modeled by Cornelissen et al. (85).
We conclude that endothelium-based control, by affecting smooth muscle tone and vascular mechanics, plays a role in mechanical cross-talk.
All three autoregulatory mechanisms, which to a certain extent are redundant, act together, and the interaction is complex. However, an order of action can be distinguished. If perfusion pressure changes, the endothelium-mediated regulation and the myogenic response will be activated first, and then, if cardiac muscle contractility and metabolism increase, the metabolic regulation will follow. With a change in cardiac metabolism, the metabolic regulation will be initiated first. The myogenic response will then follow, and the increased flow will result in flow-mediated dilation through increased shear stress.
Autoregulation gain (G) is a measure of the strength of autoregulation and can be calculated as (see Fig. 4)
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Q/P being the slope of the regulated mean pressure-mean flow relationship and Q/P the slope of the line connecting the point of determination and the origin of the graph, as a (theoretical) measure of the resistance. It can be seen that for perfect autoregulation, the gain equals one and for no autoregulation, assuming the pressure-flow relationship would go through the origin, the gain equals zero. Autoregulation gain can be plotted as a function of pressure to obtain the range of regulation and its dependence on perfusion pressure. The assumption that the not-regulated pressure-flow relationship (dashed line of Fig. 4) goes through the origin has been challenged (see sect. IIIA1).
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Flow reserve at any given pressure is the difference between regulated and not-regulated flow. As such, it is influenced by changes in metabolism (which change the autoregulatory plateau) as well as by a stenosis, which changes the maximal flow. The functional behavior of a coronary artery stenosis is difficult to estimate from images (angiography, MRI, and even multislice computed tomography). Therefore, interventions combined with measurements of pressure or pressure gradient and/or flow have been proposed to quantify the functional severity of a stenosis (145–148, 281, 310). Since this characterization requires pressure and/or flow measurements, including the pressure distal of the stenosis, simpler characterizations such as coronary flow reserve and fractional flow reserve have been introduced.
Flow reserve is the ratio of maximal flow obtained by coronary vasodilation and the resting or reference flow [see Fig. 2, ratio (A+B)/A] (97, 145–148, 234, 236, 271). This ratio is reduced when a stenosis is present. The microcirculatory resistance and the maximal dilatory capacity of the microcirculation, together with the severity of the stenosis, determine the resting flow and the maximal flow. Thus the coronary flow reserve (CFR) depends not only on the severity of the stenosis but also on the state of the microcirculation. A short coronary occlusion may be used to obtain vasodilation. However, this physiological dilation may be less than when vasodilation is obtained pharmacologically (113, 137, 259). With a larger flow than in physiological dilation, a larger estimate of CFR is obtained (see Fig. 2). Since the myogenic response takes place in 15 or more seconds (365), and the metabolic control starts even later, this sets the minimally required duration of the occlusion (83). A value of CFR >2 is used as cut-off value; a CFR <2 implies a functional stenosis.
In the beating heart, mean flow and mean maximal flow are affected by cardiac muscle contraction. When the CFR is determined in diastole only (280), the confounding effect of cardiac contraction is not included in the results. However, vascular emptying and compliance (capacitance) may then play a role, but their effects can be corrected (24).
Bishop and Samady (45) recently reviewed the subject of CFR. Hoffman (171, 172) discussed the limitations of and the difficulties with CFR. The main limitations are that the function of the microcirculation is not accounted for, e.g., maximal dilation is often not achieved (113, 149). Furthermore, the CFR only gives global information, whereas flow is heterogeneously distributed (22).
We conclude that the CFR depends on the microcirculation, which is affected by cardiac muscle contraction and thus depends on mechanical cross-talk.
Another functional estimate of the severity of a stenosis is the fractional flow reserve (FFR) (320). The FFR is the ratio of the maximal flow (Qmax,s) in the bed perfused by the stenosed artery and the maximal flow in a normal, unstenosed area (Qmax,n). Therefore
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The main advantage of the FFR is that it can be derived from flow measurements only that can be carried out noninvasively using ultrasound Doppler or MRI. The measurement of distal pressure would obviate a flow measurement but may, even using a thin pressure wire, increase apparent stenosis severity.
The relationship between flow velocity and the pressure drop over a stenosis is an accurate and direct quantification of the functional properties of the stenosis, but more difficult to obtain because measurement of proximal and distal pressures, together with flow, is required (26, 280, 361).
It has not been established whether the maximal flow in muscle areas distal of a stenosis is similar to maximal flow in a normal area. Furthermore, it is not known whether the effect of cardiac contraction on the coronary vasculature is similar in these two areas.
When the CFR and FFR are studied in diastole, the microcirculation is studied without the confounding effect of the cardiac contraction (see below) (120, 248), and cross-talk will be minimal.
Flow during maximal dilation is, in part, determined by cardiac contraction, and FFR may thus depend on cross-talk.
Oxygen delivery to the cardiac muscle should be in equilibrium with the oxygen use or demand. Supply is related to arterial inflow because coronary oxygen extraction is close to its maximal value. If it is assumed that the effect of cardiac contraction on the subendocardial layers is such that coronary perfusion is negligible in systole, arterial inflow only takes place in diastole. The supply then can be calculated as the area under the perfusion pressure in diastole. When there is no stenosis present, this equals the area under the diastolic aortic pressure. Thus, under these assumptions, diastolic pressure and the duration of diastole are the determinants of oxygen supply. Oxygen demand mainly depends on ventricular wall stress or systolic pressure and heart rate (337, 345, 386). When expressed per heart beat, the area under the systolic part of ventricular or aortic pressure can be used as an estimate of oxygen demand. In this way, we can apply the so-called supply-to-demand ratio (173), which is directly related to the ratio of the areas under diastolic and systolic pressure.
The supply-to-demand ratio depends on the duration of diastole with respect to the heart period, i.e., the diastolic time fraction. This time fraction has recently received attention (82, 123, 129, 295, 412). The supply-to-demand ratio also depends on the ratio of systolic and diastolic pressure, which decreases with age (448) and exercise (114), and can give information about (pharmacological) interventions (207, 208).
The supply-to-demand ratio is determined by cross-talk because tissue perfusion in systole depends on cardiac muscle contraction.
Autoregulation of flow is an integrated and coordinated control by an apparently redundant system based on three interacting mechanisms: myogenic control, metabolic control, and endothelium-based control. The gain of autoregulation can be quantified. Autoregulation modulates the mechanics of the vasculature and thus affects mechanical cross-talk. The supply of oxygen mainly depends on diastolic flow, and thus on the diastolic time fraction. However, even a small flow in systole, e.g., at high heart rates, can contribute to perfusion and is affected by cardiac contraction. Thus the supply-to-demand ratio depends on mechanical cross-talk. Quantification of a stenosis is often based on CFR and FFR. However, CFR depends on the microcirculation as well, and thus on the effect of cardiac muscle contraction. The FFR assumes that the bed distal of the stenosis and the normal representative bed are similarly influenced by cardiac muscle contraction. Therefore, both CFR and FFR are affected by cross-talk.
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III. THE CARDIAC MUSCLE AFFECTS THE CORONARY VASCULATURE |
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A. Cardiac Muscle and Coronary Flow in Diastole
1. Instantaneous pressure-flow relationship and zero-flow pressure intercept
A vascular bed, in our case the coronary system, can be characterized in terms of steady-state and instantaneous pressure-flow relationships (36, 37, 50). The steady-state relationship is the one that is measured after regulation has taken place (see autoregulation curve of Fig. 2). The instantaneous relationship is determined over a short time period (1 s), and the vasculature is assumed to be in a "fixed" vasoactive state (106, 416). The instantaneous relationship between pressure and flow of the coronary circulation can be determined during a long diastole (e.g., obtained through vagal stimulation) so that the coronary vasculature is characterized without the confounding effect of cardiac muscle contraction, i.e., with minimal mechanical cross-talk (Fig. 5). The instantaneous pressure-flow relationship, therefore, describes the momentary state of the vascular bed. Figure 6 shows the steady state, or autoregulation curve, together with instantaneous pressure-flow relationships as determined from a range of steady-state pressures (36). The instantaneous relationships in general appear to be straight (36) or curvilinear (237, 238) with a so-called zero-flow pressure intercept, Pf=0, i.e., with negligible flow, pressure is still present. The inverse of the slope of the instantaneous pressure-flow relationship is the instantaneous resistance (Ri). The instantaneous resistance and the intercept pressure both depend on the vasoactive state of the coronary bed. For increased perfusion pressure, the vasculature constricts as a result of autoregulation, and the resistance and intercept of the instantaneous pressure-flow relation increase, thereby keeping mean flow in the steady-state constant (107, 238). In humans, the zero-flow pressure intercept of the instantaneous pressure-flow relation is 40 mmHg in control and 15 mmHg in vasodilation (307). A Pf=0 is not only found in the left heart but also in the right heart in diastole (430). These intercept pressures are significantly higher than coronary sinus pressure, left ventricular end-diastolic pressure, and right atrial pressure.
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0.07 ml · mmHg–1 · 100 g tissue–1 (375, 376) to 0.38 ml · mmHg–1 · 100 g tissue–1 (380)], depending on heart rate (91, 92) and vasoactive state (423), may explain the intercept. An intravascular volume of 12 ml/100 g muscle has been reported (196, 411). This large microcirculatory compliance indeed appears to be present, because venous outflow, from blood stored in the microvascular reservoir (compliance), persists after a sudden stop of arterial inflow (80, 201, 347). After arterial inflow is resumed in a stepwise manner, venous outflow is delayed, suggesting an unstressed vascular volume or large compliance, estimated to be 4 ml/100 g muscle (407). Several authors (142, 201) showed, in the in situ dog heart during maximal vasodilation, evidence for the existence of a microvascular unstressed volume, which results in delayed venous outflow after sudden resumption of stopped arterial inflow. The filling of the intramyocardial compartment above its unstressed volume affects the diastolic pressure-flow relationships (142), but not their intercept, indicating that arterial inflow depends on the compliance in the microcirculation. In cardiac arrest, the blood stored in the microcirculation is discharged to the venous side keeping venules open while arterioles decrease in size (167).
Sipkema and Westerhof (364) showed that the apparent intercept of the pressure-flow relationship of a thin-walled latex microtube (Fig. 8) depends on the plateau of its pressure-cross-sectional area relationship, which, in turn, depends on vasomotor tone. Both explanations as given by Spaan and Sipkema support the hypothesis that (microvascular) compliance plays a major role in the explanation of the zero-flow pressure intercept (364, 375, 376). An additional suggestion that the intercept is related to vessel wall properties is that when the coronary perfusion fluid is changed from blood to a crystalloid medium, an intercept pressure remains (342, 415). However, others have shown that the perfusion medium does affect the intercept, suggesting that the rheological properties of blood may play a role as well (205, 352). It has also been suggested that surface tension between blood and vessel wall (358, 359) and the glycocalyx (84, 325, 425) might contribute to the intercept pressure.
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Versluis et al. (424) showed, in isolated perfused rat papillary muscle, that the waterfall is located in arterioles larger than 110 µm.
It has still not been proven beyond doubt that the intercept is a real intercept and not an apparent intercept, i.e., an intercept obtained by extrapolation of the data. Kanatsuka et al. (210) analyzed in detail the momentary value of the diameter of arterioles in the coronary bed while pressure was decreasing. It was found that the diameters of arterial microvessels gradually decline as aortic pressure falls. This suggests that the coronary resistance does not remain constant during a long diastole, even when the bed is maximally dilated (210). The finding that even during maximal vasodilation a zero-flow pressure intercept is present suggests that a venous waterfall may exist. A distal, venous, waterfall was indeed shown to exist in the epicardial coronary veins (409), and also in the skeletal muscle veins (51). Such a separate venous waterfall can be seen and studied by cannulation of the venous system (409). Increased coronary sinus pressure was shown to decrease flow, but this was less than the decrease in perfusion pressure (arterial minus venous pressure), suggesting a waterfall mechanism (303). A large coronary venous compliance may also explain this waterfall.
The instantaneous pressure-flow relationship should be considered with caution. It has been shown that the relationship may not be linear (238). The relationships may include a contribution of arterial compliance, because the flow that fills the arterial compliance depends on the rate of change of perfusion. Thus, when the pressure and flow change occur too rapidly, errors result. These errors and suggestions for correction have been reported (24, 61, 237, 282, 283).
Instantaneous pressure-flow relationships are determined over such a short period of time that they describe the bed in a particular state at the working point. It may therefore be suggested that the ratio of the slopes of the autoregulation curve and the slope of the instantaneous pressure-flow relationship, the regulatory index, are a better measure of gain of autoregulation than the formula given in the section on autoregulation gain (416).
The instantaneous pressure-flow relationships are determined in diastole and so rapidly that vasomotor tone may be assumed constant. The relationships describe the coronary vasculature in "fixed state" of the vasculature and without the confounding effects of the cardiac muscle and are therefore not affected by mechanical cross-talk. The slope and intercept of the relationships both depend on smooth muscle tone. The intercept is most likely the result of a large microvascular compliance.
3. Effect of ventricular volume changes on coronary flow in diastole
Several groups have reported diastolic pressure-flow relationships during maximal vasodilation. Figure 9 shows a representative example of coronary pressure-flow relationships in the isolated maximally vasodilated rabbit heart in diastolic arrest for two filling pressures, corresponding to a ventricular volume change of about a factor of 2 (362). The effect is only slightly dependent on the muscle layer, i.e., subendocardial or subepicardial (264). In the open-chest dog, an increase in left ventricular volume from 20 to 50 ml (diastolic left ventricular pressure from 5 to 20 mmHg) did not significantly affect diastolic coronary arterial inflow (132, 134). However, when volume was increased to 60 ml (diastolic left ventricular pressure of 28 mmHg), flow decreased by 16%. In other studies using the isolated dog heart (436) or the in situ dog heart (119), the pressure-flow relationships in diastole show a change in the intercept but little change in slope with ventricular volume changes. After pericardiectomy, the effect of ventricular filling on the relationships is decreased possibly explaining the differences between the in situ (117, 119) and isolated heart (362). Aldea et al. (5) studied the effects of changes in ventricular lumen pressure and extraventricular pressure on coronary flow in diastolic arrest. They found an almost parallel shift to higher intercept pressures of the coronary pressure-flow relationships, when either lumen pressure or external pressure was increased. However, they also found an increase in venous pressure.
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20%, at a perfusion pressure of 70 mmHg, shows changes in microvascular resistance, calculated on the basis of a model, of about a factor of 2 (87, 380). However, this study applied stretch starting from short lengths, namely, "slack length." Model calculations predict that when muscle length increases from 70 to 90% of Lmax, corresponding to a ventricular lumen volume increase by a factor of 2, diastolic flow is decreased by 30% (426). When the pressure-area relationship of an isolated vessel and the pressure-area relationship of the muscle cavity in which the vessel fits are added, the pressure-area relationship of the vessel embedded in muscle is obtained (159, 427). It was shown that increased diastolic chamber stiffness does affect coronary vascular compliance (435). In diastole, the cardiac muscle contributes little to the pressure-area relationship of an embedded arteriole, while the pressure-area relationship of an embedded vein is almost entirely determined by the surrounding muscle (Fig. 10). Because the small arteries and the arterioles, but not the venules, mainly determine coronary resistance, the diastolic cardiac muscle influences coronary resistance only marginally.
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In the dilated heart in diastole, with increased cardiac muscle stiffness and higher diastolic ventricular pressure, the cardiac muscle has a larger effect on the embedded arteries and arterioles. Thus, in the dilated heart, and with most flow taking place in diastole, vasodilatory capacity of the coronary circulation is reduced and flow reserve is decreased (59).
The data in the literature regarding the contribution of the diastolic cardiac muscle on the coronary vasculature are not consistent. Some publications report a small effect on resistance vessels, while others show a substantial effect. The differences may, in part, result from differences in initial cardiac muscle length and amount of stretch. However, it appears that if there is an effect it is stronger on the intercept than on the slope of the pressure-flow relationships. A model accounting for vessels embedded in cardiac muscle predicts little effect on arterioles but a strong effect on venules. The pericardium, and therefore the venous waterfall, may also account for part of the differences reported. However, reconsideration of the models and more experiments under well-defined conditions are necessary. In the dilated heart, maximal flow and therefore CFR is limited.
B. Cardiac Contraction and Coronary Flow in Systole
The coronary arterial inflow is impeded and venous outflow is augmented during cardiac muscle contraction. In contraction the total vascular volume is decreased, which means that the resistance of the vasculature is increased. The cardiac muscle is also stiffer so that compliance of the embedded vasculature is decreased, also resulting in a decrease in vascular volume. The vascular volume decrease causes blood to be pumped out. This results in the arterial inflow impediment and venous outflow augmentation. Here we discuss these phenomena as an introduction to the models reported in the literature.
1. Arterial inflow and venous outflow
Anrep and co-workers (12, 13) and Gregg and co-workers (153–156) have already shown that coronary arterial inflow is impeded and venous outflow is augmented during cardiac contraction. When the coronary bed is vasodilated and cardiac muscle contractility is high, arterial inflow may even reverse in early systole (see Fig. 11). This so-called systolic arterial flow impediment has been confirmed by many research groups in isolated heart studies (48, 175, 245–249) and in the in situ heart (5, 73, 111, 115, 128, 152, 154, 175, 197, 200, 267, 412), and it has been observed in humans as well (26, 128, 198, 278, 286). It is also observed in the circumflex coronary artery in control and in increased cardiac contractility (200) and has been seen in septal coronary artery stenosis (141, 204, 227). Coronary mean pressure-mean flow relationships measured in the heart in situ during maximal vasodilation show that mean flow decreases with exercise as a result of the decreased duration of diastole. This finding emphasizes that the major contribution to mean flow is during diastole and that systolic flow is small (115). Increased venous outflow in systole is found in the great cardiac vein, and the magnitude is greater with increased contractility [202; see for discussion also the publications by Olson and Bugni (314), Hoffman and Spaan (175), and Spaan et al. (378)].
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Many researchers assumed that the cardiac muscle contraction generates a ventricular lumen pressure that is communicated to the interstitium, thereby causing an intramyocardial pressure (20, 111). The increased intramyocardial pressure subsequently causes a decrease in the transmural vascular pressure and thus a decrease in vascular diameter. The decrease in vascular diameters in systole causes a decrease in vascular volume, and this volume is "pumped" to venous and arterial sides of the coronary circulation. The diameter decrease also causes an increase in coronary resistance. However, there is not only an effect of intramyocardial pressure on the vasculature but also a direct contribution of the cardiac muscle on the vasculature. The cardiac muscle becomes stiffer in systole; it may shorten and thicken leading to a decrease in vascular diameters and volume. Shortening of the cardiac muscle cells will also deform the vasculature (change branching angles at bifurcations and increase vascular tortuosity). The two mechanisms, the indirect effect through ventricular pressure and the direct effects of the cardiac muscle, both play a role depending on the conditions. For example, the contribution of ventricular pressure depends on the elastance of the ventricular wall, i.e., in systole, when the ventricular muscle is stiff, the effect of ventricular pressure is shielded off by muscle stiffness (243). The concepts and models are discussed below.
2. Coronary arterial input impedance
The decrease in coronary arterial inflow in systole is based on changes in the coronary vascular system. The changes in the arterial part of the circulation can be studied by the derivation of arterial input impedance, which is a comprehensive description of the entire coronary arterial system. While peripheral resistance mainly characterizes the peripheral vasculature, the input impedance gives a description including both the proximal part of the vasculature, the arterial conduit vessels, and the periphery (448). Input impedance cannot be determined in the standard way by applying Fourier analysis on the pressure and flow signals, because during a heart beat the contracting cardiac muscle affects the system, i.e., we are studying a time-varying system (448). Therefore, the so-called impulse response method has been applied in systole and diastole (266, 366, 417). It was shown that the response is rather short in duration so that it can be determined in systole and diastole separately. In the left panels of Figure 12A, the impulse responses are shown, superimposed on the pressure waveform. By subtracting the waveform without impulse response from the one containing the impulse response, the response alone is calculated.
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As a result of cardiac contraction, flow in large arteries is impeded in systole and flow in large veins is augmented in systole. The magnitude of coronary arterial flow impediment depends on perfusion pressure and cardiac muscle contractility. Venous outflow depends on cardiac contractility and venous pressure.
Two mechanisms exist to explain the findings. First, cardiac contraction causes, via the generation of ventricular pressure, an intramyocardial pressure. This decreases vascular transmural pressure and vascular diameter and volume and increases resistance. Second, cardiac contraction results in changes in the muscle properties such as stiffness, and the muscle length and thickness vary over the cardiac cycle. These phenomena directly affect the vasculature. The cardiac muscle contraction results in vascular volume and resistance changes, which mainly take place in the microcirculation.
C. Models Explaining the Diastolic-Systolic Changes of the Vasculature
The contracting cardiac muscle exerts an impeding effect on arterial inflow and augments venous outflow. The coronary arterial input impedance data show that this effect of contraction on coronary flow mainly results from changes in the vasculature.
The effect of cardiac muscle contraction on the coronary vasculature is based on two mechanisms.
The cardiac muscle contraction increases ventricular lumen pressure, which results in an increase in interstitial or intramyocardial pressure. This pressure is proportional to ventricular pressure and decreases the vascular transmural pressure, and thereby vessel diameter. This concept forms the basis of the waterfall model (111), and the intramyocardial pump model (19, 379). Experiments have shown that pressure, applied in the lumen of the ventricle and externally by means of a pressure chamber (5) or through the pericardium (395), has an effect on coronary pressure-flow relationships.
The contraction of the cardiac muscle causes a decrease in vascular diameters and deformation of the blood vessels by a direct effect. This concept is formulated by the varying elastance model. An increase in stiffness of the cardiac muscle (vessel environment) decreases vessel lumen similar to what happens in the ventricular lumen during contraction (245, 387, 447); in the muscle shortening and thickening model, the shortening and related thickening of the muscle fibers during contraction cause a decrease in vessel diameters (426, 450); and in the vascular deformation model, deformation of the vasculature, vessel shortening, changes in bifurcation angles, and changes in tortuosity result from muscle contraction (169).
Contractility has an effect on coronary pressure-flow relationships independent of ventricular lumen pressure (247, 420).
It turns out that neither of these concepts, alone, completely describes what happens to the coronary vasculature during cardiac muscle contraction. Also the contribution of their effects depends on the contractile state of the heart, the mode of cardiac contraction (isobaric, isovolumic), and the layer in the heart wall (subepicardial, subendocardial).
The first well-described and accepted model to explain coronary arterial inflow impediment in systole is based on the "vascular" waterfall (111) (Fig. 7). As mentioned above, the vasculature alone exhibits a zero-flow pressure intercept, which is a vascular waterfall dependent on smooth muscle tone but independent of the surrounding (cardiac) muscle. In this section we discuss the waterfall that results from cardiac muscle contraction. We therefore prefer the term waterfall model instead of the term vascular waterfall model as is most often used in the literature. Farhi et al. (122) elegantly showed that in ventricular fibrillation a cardiac muscle- and smooth muscle-based waterfall exists and that vasodilation could lower the waterfall pressure. The main aspect of the waterfall model is that the flow is not determined by the arterial minus venous pressure and vascular resistance, but by arterial minus waterfall pressure and vascular resistance (51, 122). This means that calculations of resistance, by dividing the arteriovenous pressure difference by flow (or since venous pressure is much lower than arterial pressure, simply arterial pressure divided by flow) are not correct (see sect. IIB5).
The waterfall model as proposed by Downey and Kirk (111) states that ventricular pressure generates a so-called intramyocardial or interstitial pressure Pim, which acts on the outer surface of the blood vessels (Fig. 13A, left). This intramyocardial pressure is transmitted to the vascular lumen and forms the basis of the waterfall pressure. The intramyocardial pressure is assumed to be equal to ventricular pressure Plv at the subendocardium, and negligible at the subepicardium (111): Pim = kxPlv, with k = 1 at the subendocardium and k = 0 at the subepicardium. The intramyocardial pressure is largest in subendocardial layers, and thus the effect of contraction is strongest there. This model explains that with decreased perfusion pressure, as distal to a stenosis, ischemia is mostly subendocardial.
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2. The intramyocardial pump model
Spaan et al. (376, 378, 379) introduced the intramyocardial pump model, originally suggested by Arts and Reneman (19, 20), which is based on the pumping action of the cardiac muscle in analogy to the ventricular pump. The intramyocardial pump model improved the waterfall model such that reversal of arterial inflow in systole (Fig. 11) can be explained and the increase in venous outflow in systole is accounted for (Fig. 14). However, the compliance in the model prevents changes in mean flow between the heart arrested in diastole and systole. The electrical representation of the model contains a capacitor, implying this same limitation in static conditions. The model has been extended to include the changes in flow in the steady state of contraction, by making the resistances dependent on intramyocardial pressure (53, 376). Several lumped and distributed models have been based on the intramyocardial pump concept (19, 20, 42, 58, 66, 369–371, 461, 462). The modified intramyocardial pump model (53, 175, 376) does include changes in vascular volume and resistance but does not include vascular compliance changes.
