Background: The rate of adaptation of coronary blood flow in response to stepwise changes in heart rate (HR) has been extensively studied in dogs and goats to improve our understanding of the dynamics of coronary regulation processes and their pathophysiology and to obtain time constants for mathematical modeling of the coronary regulation. However, little is known about the dynamic characteristics of coronary flow adaptation in humans. In patients undergoing coronary artery surgery, we investigated the rate of coronary adaptation in response to stepwise changes in HR, in the awake and anesthetized states. Methods: In 11 patients with stable coronary artery disease, arterial blood pressure, right atrial pressure, and coronary sinus blood flow, measured by continuous thermodilution, were calculated per beat. The ratio of beat-averaged arterial blood pressure minus right atrial pressure and coronary sinus blood flow was calculated to obtain an index of coronary resistance. The rate of change of coronary resistance index was quantified by t 50, defined as the time required to establish 50% of the total change in coronary resistance index. Responses of coronary resistance index after HR changes, before and after induction of anesthesia, were compared. The anesthesia technique consisted of 100 μg · kg -1 fentanyl and 0.1 mg · kg -1 pancuronium bromide in combination with oxygen in air ventilation (FI(O 2) = 0.5). Results: In the awake situation, t 50 values of the dilating and constricting responses, induced by an increase and a decrease in HR were 5.0 ± 2.1 (SD) s (range 2.6-9.0 s) and 5.7 ± 1.2 s (range 4.1-7.8 s), respectively. During fentanyl/pancuronium anesthesia, the rate of coronary flow adaptation was significantly slower, with t 50 values of 10.2 ± 2.1 s (range 7.7-13.1 s) after an HR step-up and 9.8 ± 2.1 s (range 6.6-13.2 s) after an HR step-down. Compared to the awake situation, arterial blood pressure was significantly reduced during anesthesia, but coronary vascular resistance remained unchanged. This implies that the steady-state static regulation of coronary blood flow had not changed. Conclusions: These preliminary data suggest that, in patients with coronary artery disease, the rate of change in coronary vascular resistance in response to pacing-induced changes in HR is mitigated by fentanyl/pancuronium anesthesia during positive pressure ventilation. A further qualification of our findings in a larger number of patients is warranted.@en

Common parameters to describe the coronary circulation are resistances (Rs) and capacitances (Cs). In six isolated, maximally dilated, perfused, non contracting canine interventricular septa, the Rs and Cs at different pressure levels were estimated by obtaining the inflow-pressure transfer functions (Q/P) and volume-pressure transfer functions (T/P). To interpret the data, simple lumped two compartment RCR models were fitted. Models with fixed resistances could not fit simultaneously Q/P and T/P. Therefore models with volume dependent parameters were tested as well. However, these models had more parameters, which could not be uniquely identified from the data. Many parameter sets, which predicted adequate transfer functions, were created. After comparing these parameter sets, it was concluded that the first resistance and the first capacitance could be estimated, furthermore a relation between the distal capacitance and the volume sensitivity of the third resistance was found: the higher the capacitance, the lower the sensitivity.

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Changes in coronary perfusion pressure affect coronary arterial resistance (autoregulation) as well as myocardial oxygen consumption (Gregg's phenomenon). The interaction between the effects of perfusion pressure and myocardial oxygen consumption on coronary flow control was investigated using a model. This model analysis predicts that autoregulation and Gregg's phenomenon compete with each other in controlling coronary flow. The negative feedback system of the metabolic control system can become a positive feedback system when the level of arterial tone decreases and Gregg's phenomenon becomes more important.

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The effect of flow steps in coronary arterial flow (Qa) on myocardial oxygen consumption (MVo2) was investigated at different heart rates (HR) to further elucidate the dependency of myocardial oxygen consumption on perfusion. In six anesthetized goats the left main coronary artery and the great cardiac vein were cannulated. The hearts were paced alternately at 60 and 130 beats per min. Flow steps were applied at both HR during control and maximal vasodilation by adenosine. MVo2, in steady state before and after the flow step, was calculated by multiplication of Qa and arterio-venous oxygen content difference (Fick's law). Heart rate affected the MVo2 dependency on flow during control as well as during maximal vasodilation. With vascular tone present, the MVo2 dependency on flow (ΔMVo2/ΔQa), in μl O2/ml, was 16.0 ± 3.6 at HR 60 and 21.7 ± 3.9 at HR 130. During maximal vasodilation, these values were 9.5 ± 2.9 and 17.0 ± 5.3 at HR 60 and 130, respectively. The higher MVo2 dependency on flow at high HR may be explained via a dependency of MVo2 on microvascular pressure. The pressure change in the microvessels induced by a flow step is probably larger at high HR than at low HR because of increased venous resistance at high HR, due to increased compression by the heart contraction.@en

By fitting of simulations with an oxygen exchange model to measured responses of the arteriovenous oxygen content difference after a flow step, coronary volumes can be estimated. In this study the dependence of the volume estimates on the choice of the oxygen exchange model for the coronary circulation was investigated. A model consisting of a single well-mixed compartment results in smaller volume estimates than a series array of mixed compartments in which Po₂ declines gradually (Krogh-like model). Use of the former model for data analysis resulted in realistic volume estimates. Thus, these results indicate that the oxygen exchange vessels are better represented by a single mixed compartment than by a cylinder having Krogh characteristics. This conclusion agrees with capillary Po₂ being equal to or smaller than venous Po₂ which cannot be explained by a Krogh model. From these arguments we conclude that though both models are rough representations of the coronary circulation, the coronary O₂ exchange vessels of the beating heart can be represented better by a single mixed compartment than by a series array of mixed compartments which has Krogh characteristics.

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In six open-thorax-anaesthetized dogs with paced hearts and a retrogradely cannulated epicardial lymph vessel, the sensitivity of myocardial lymph pres- sure to left ventricular pressure during systole and during diastole was determined. The lymph vessels were can- nulated using PE-90 tubing, and lymph pressure was measured by connecting the cannula to a microtip press- ure transducer. To obtain the systolic sensitivity, left ven- tricular pressure was changed by clamping the de- scending aorta, which caused left ventricular pressure to increase. The diastolic sensitivity was obtained from natural variation to left ventricular pressure caused by atrial contractions during induced long diastoles. The mean ratio of the pulse in lymph pressure to the pulse in left ventricular pressure was determined: systole: 0.069 + 0.013, n = 213, diastole: 0.76 -+ 0.16, n = 249 and, if possible, linear regression analysis between lymph and left ventricular pressure was performed. The systolic regression coefficients could be determined in six dogs and the diastolic coefficients in three dogs. Dur- ing long diastoles lymph pressure variations are on aver- age 76 per cent of those in the left ventricle. However, during systole, the sensitivity of lymph pressure to left ventricular pressure is more than ten times lower. It is not unlikely that the structural embedment of lymph ves- sels within the myocardium is such that volume vari- ations by cardiac contraction are limited. @en

Coronary blood flow is tightly coupled to the myocardial oxygen consumption. We have presented a control model based on the assumption that the tissue oxygen pressure is the controlled variable. The coronary blood flow in itself is not a controlled variable but merely the result of a different control system: the tissue oxygen pressure. From our control equation there is no relation between the slope of the autoregulation curve and the gain of the tissue P02 control system. The slope is independent of the level of oxygen consumption.@en

he rate of change of coronary adjustment in the anesthetized dog to a step change in heart rate (HR) and in perfusion was analyzed. The left main coronary artery was perfused either at constant pressure (CP) or at constant flow (CF). Coronary arterial pressure and flow were continuously measured and averaged per beat, after which their ratio, being an index of coronary resistance in steady state, was calculated. The rate of change of pressure-to-flow ratio was quantified by t50, the time required to establish half of the completed response. The t50 values for the dilating responses at CP were 5.5 +/- 0.4 (SE) s for an increase in HR and 5.5 +/- 0.1 s for a decrease in perfusion. At CF these values were 9.3 +/- 0.9 and 9.7 +/- 1.6 s, respectively. The t50 values for the constricting responses with CP were 6.6 +/- 0.5 s for a decrease in HR and 6.2 +/- 0.2 s for an increase in perfusion. At CF these values were 12.2 +/- 1.5 and 10.8 +/- 2.2 s. The responses in the dog are faster than in the goat. Furthermore, the directional sensitivity in responses with perfusion changes, observed earlier in goats, is normally absent in dogs. @en

Coronary flow is controlled by the myocardium at the tissue level. This local control can be characterized by two manifestations: the adaptation of blood flow to the level of oxygen consumption and the relative independence of blood flow from coronary arterial pressure. The former manifestation is referred to as flow adaptation to metabolism, the latter one as autoregulation. Alternative terms for flow adaptation to metabolism found in the literature are metabolic regulation and functional hyperemia. However, autoregulation may also be mediated by metabolic processes and therefore metabolic regulation is an ambiguous term. Hyperemia means ‘increased blood flow’ and consequently hyperemia implies the definition of a standard control value of flow. The term flow adaptation to metabolism, or simply flow adaptation, expresses the ability of the coronary system to adapt flow to metabolic needs of the heart, and is the term further used here.@en

In this study the response of driving pressure/flow ratio on an abrupt change in heart rate was analysed. The difference between the response obtained with constant pressure and constant flow perfusion was also studied. The responses show a fast initial reversed phase followed by a slow phase caused by regulation. To test whether the initial phase could be the result of mechanical changes in the coronary circulation, a model for regulation was extended by the addition of four different mechanical models originating from the literature. These extended models were able to explain the fast initial phase. However, the mechanical model consisting of an intramyocardial compliance (C=0·08 ml mm Hg-1 100 g-1) with a variable venous resistance, and the model consisting of a waterfall and a small compliance (C=0·007 ml mm Hg-1 100 g-1) both explained these responses best. The analysis showed that there is no direct relationship between rate of change of vascular tone and rate of change of pressure/flow ratio. However, on the basis of the two extended models, it can be predicted that the half-time for the response of regulation to be complete is about 9s with constant pressure perfusion and 15 s with constant flow perfusion.@en

We have previously shown that steady‐state coronary flow during auto‐regulation and metabolic rate changes is predicted by a mathematically expressed theory which assigns control of coronary vascular resistance to tissue PO2. Our present purpose was to test the applicability of this theory to the non‐steady state as exemplified by a sudden step change in heart rate. 2. The theory predicted that the response time of change of resistance in these circumstances would be slower with constant‐flow perfusion of the coronary bed than with constant‐pressure perfusion, and that with constant‐pressure perfusion only, the rate of adaption of resistance would be dependent on the level of pressure used. 3. These predictions were tested in open‐chest goats with cannulation of the left main coronary artery and perfusion with alternately constant pressure or constant flow. Sudden step changes in heart rate were induced by pacing to induce rapid transients in myocardial metabolic rate. 4. The half‐time of subsequent change in perfusion pressure‐flow ratio, which in the dynamical state is not equal to resistance, was 15.7 +/‐ 0.4 s (mean +/‐ S.E.M.), which was statistically shorter than for constant flow (22.2 +/‐ 0.5 s, P less than 0.001). 5. The half‐time of subsequent change in perfusion pressure‐flow ratio with constant‐pressure perfusion was 14.4 +/‐ 0.6 s at low pressure and 17.0 +/‐ 0.6 s at high pressure (P less than 0.001). 6. The results differed from those predicted by the theory, in that the changes described above were preceded by a rapid (5 s) step change in pressure‐flow ratio, up with an increase in heart rate and down with a decrease in heart rate. We postulated that this was a mechanical effect due to greater compression of the coronary microvasculature with more frequent contractions. 7. To test this hypothesis, we measured changes in coronary blood volume by integrating the difference between arterial inflow and venous outflow. These experiments showed a decrease in coronary blood volume with heart rate increase and vice versa. 8. Abolition of autoregulation and metabolic regulation was achieved with maximum vasodilatation of the coronary bed with adenosine. A sudden switch in heart rate then produced the initial step change in pressure‐flow ratio, but not the subsequent adaptation over 13‐25 s. This confirmed that the former effect is attributable to a passive mechanical mechanism.@en