SUMMARY A large-scale model of the coronary circulation, instrumented to permit detailed pressure and velocity measurements, has been used to study flow through isolated stenotic elements in large coronary arteries. Pulsatile aortic pressure and instantaneous peripheral resistance were simulated with servo valves. A variety of axisymmetric and asymmetric stenoses were studied and flow separation was found to occur for all but very mild stenoses. Pressure recovery downstream of the stenosis throat was limited and, in some cases, no recovery was observed. Pressure drop was primarily dependent upon the minimum area of the stenosis and relatively independent of stenosis geometry. Flow was quasi-steady at normal heart rates, and simple steady flow theory proved adequate to describe the pressure drop through the stenosis. The theory yielded results that agreed well with published data for dogs and appears promising for predicting effects of hemodynamic variables on a given stenotic lesion. Thus, principal findings of the study are that a relatively severe stenosis behaves essentially like an orifice and that a simple quasi-steady theory appears adequate to predict effects of a stenosis on coronary flow.IT HAS BEEN known for some time that a relatively severe constriction of a coronary artery is required to alter mean resting coronary flow significantly. Studies in open-chested dogs 1 "5 have delineated the following characteristics. An area occlusion of approximately 80-85% (corresponding to a diameter reduction of 60-80%) is required to reduce resting coronary flow. This value has been referred to as a "critical" occlusion. As this critical occlusion is approached, reactive hyperemia is almost entirely abolished indicating that full peripheral vasodilation has already occurred. For smaller degrees of occlusion, reactive hyperemia is reduced in comparison to the control state indicating partial vasodilation. Similar results were obtained in steady flow in vitro experiments conducted using postmortem coronary arteries with partial occlusion." In this study, in which perfusion pressure and downstream resistance could be independently controlled, it was found that at low flow rates stenotic resistance (ratio of pressure drop to flow) was essentially constant, suggesting fully developed laminar flow. At high flows resistance increased with flow, indicating the importance of turbulence, flow separation, or entrance effects. It was further observed that the resistance of the stenosis was primarily dependent on its minimum cross-sectional area rather than its length.The foregoing studies have been confined to a description of the overall behavior of coronary flow in the presence of a stenosis. Because of the small size of the arteries, it is very difficult to make any detailed pressure or flow measurements to describe in detail the flow mechanism responsible for stenotic resistance. In order to study the flow in detail, it is necessary to develop large scale laboratory models. Most studies of flow through an isolated area of...

Left ventricular dimensions from routine clinical one-plane cineangiograms were combined with left ventricular pressure measurements to permit calculation of left ventricular wall stresses. The 25 patients included 12 with normal left ventricular dynamics, 6 with volume overload, 3 with outflow obstruction, and 4 with cardiomyopathy. Average stresses calculated on the basis of an ellipsoid model agreed with average values obtained from the exact solution of a thick-walled elastic ellipsoidal shell. Peak values were 150 to 625 g/cm 2 in the circular direction and 75 to 365 g/cm 2 in the longitudinal direction. A fiber-corrected stress was defined which represents a force per muscle fiber. The variation in fiber-corrected stress during the cardiac cycle may be considerably different from the variation in simple stress.The force-velocity characteristics of circular fibers for the 25 patients are presented. The data on peak wall stress overlap in the four groups of patients. Peak velocity of circumferential fiber shortening varied from 0.44 to 0.63 lengths/sec in patients with myocardial weakness and varied from 0.74 to 2.56 lengths/sec in the other patients. Contractile element velocity was determined during ventricular ejection when the rate of force change equaled zero. Contractile element velocity of shortening was 0.22 to 0.32 lengths/sec in the cardiomyopathy group and 0.50 to 1.32 lengths/sec in the other patients. ADDITIONAL KEY WORDScontractile element velocity of shortening left ventricular wall thickness cardiac muscle mechanics B The force developed by a contracting muscle is a function of the velocity of contraction. The force-velocity relation was first determined for skeletal muscle (1, 2) and more recently has also been determined in isolated cardiac muscle (3-5). The mechanical behavior of the intact heart is a complicated function of its geometry as well as of the contractile behavior of individual muscle fibers. The performance of the heart may be determined by cineangiography

The rotational-translational energy transfer in collisions between homonuclear diatomic molecules and the rotational relaxation time in diatomic gases have been investigated classically. Using Parker's model for the intermolecular potential, numerical solutions were obtained for the rotational-energy transfer in individual collisions. The method of solution for the collision trajectories has been combined with a Monte Carlo integration procedure to evaluate the transport properties for diatomic gases. The formal kinetic-theory expressions derived by Wang Chang, Uhlenbeck, and Taxman for the transport coefficients of gases with internal energy states were used. Results are presented for the shear viscosity, thermal conductivity, and rotational relaxation time in N2 which compare favorably with experimental values. Results are included for both a coplanar and three-dimensional collision model. Approximate solutions for the rotational-energy transfer in coplanar collisions and the rotational relaxation time are also presented. The approximate expression for the relaxation time agrees well with the Monte Carlo calculation and with experimental data for N2 and O2. The effect of unequal rotational and translational temperatures was also studied and found to be significant.

On the basis of the material discussed, our current assessments of the controversial points mentioned at the beginning of this article may be summarized as follows: Pf = 0, the minimum back pressure to coronary flow associated with a measurable conductance, is indeed greater than coronary outflow pressure (and usually left ventricular diastolic pressure, as well). Pf = 0 needs to be taken into account in attempts to determine coronary driving pressure. In maximally vasodilated beds, Pf = 0 derived from diastolic pressure-flow relationships exceeds coronary outflow pressure by at least a few mm Hg. Pf = 0 varies with coronary outflow and/or diastolic ventricular cavity pressure. When left ventricular preload is elevated, Pf = 0 exceeds outflow pressure by increasing amounts. Pf = 0 appears to be systematically higher and pressure-dependent in beds in which vasomotor tone is operative. An improved understanding of the nature of, and basis for, time-dependent changes in resistance and/or Pf = 0 during long diastoles in nonvasodilated beds is needed. The contour of pressure-flow relationships which are free of reactive effects is curvilinear rather than linear. The degree of curvilinearity is substantial and can change with interventions. Curvilinearity is accentuated at lower pressures and may reflect changes in the number of perfused vascular channels as well as the caliber of individual channels. Capacitive effects need to be dealt with quantitatively in studies of pressure-flow relationships. Values of the capacitance which is involved in these effects vary with both pressure and tone. Capacitive flow also depends upon the instantaneous rate of change of pressure, which has not usually been defined in published studies. Although intramyocardial capacitance is large and plays an important role in systolic-diastolic flow interactions, a controlling role in diastolic coronary arterial pressure-flow relationships has not been established experimentally. In vasodilated beds, in-flow remains remarkably constant for several seconds after the brief transient associated with a step-change in the level of constant pressure perfusion during a long diastole. Calculations of coronary vascular resistance (by whatever method) remain of limited value, particularly when changes in response to an intervention are modest. Because of the curvilinear diastolic pressure-flow relationship, resistance is pressure-dependent and, at any given pressure, is probably best defined by establishing the slope of a diastolic pressure-flow curve which is free of reactive effects.(ABSTRACT TRUNCATED AT 400 WORDS)

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A B S T R A C T The proposal that diastolic coronary flow is regulated by an intramyocardial "back-pressure" that substantially exceeds coronary venous and ventricular diastolic pressures has been examined in an open-chest canine preparation in which instantaneous left circumflex pressure and flow could be followed to cessation of inflow during prolonged diastoles. Despite correlation coefficients consistently >0.90, pressureflow data during individual diastoles were concave to the flow axis before and during pharmacologically induced maximum coronary vasodilation. Data were better fitted (P < 0.01) by second-order equations than by linear equations in >90% of cases. Second-order pressure-axis intercepts (Pf=o)l averaged 29±+7 (SD)

We have studied the influence of left ventricular diastolic pressure (LVDP) on diastolic coronary pressure-flow relationships independently of effects of capacitive flow in an open-chest heart-blocked canine preparation in which the left circumflex (LC) bed was vasodilated with adenosine and perfused with a programmable servo valve pressure source. At the onset of long diastoles produced by cessation of ventricular pacing, LVDP was adjusted to, and maintained at, a preselected level using a blood-filled reservoir. Right atrial pressure was kept constant at approximately 8 mmHg. LC pressure (PLC) was then made to decline and rise sequentially at a constant rate (2-40 mmHg/s), with LC inflow reaching zero at the nadir of the declining pressure ramp. The capacitance-free diastolic pressure-flow relationship was considered to lie midway between the instantaneous relationships derived from each down and up ramp pair. All capacitance-free relationships were curvilinear, and the degree of curvilinearity was accentuated with increasing preload. Pressure-axis intercepts (Pf = 0) increased from 14 +/- 1.1 (SE) to 23 +/- 1.4 mmHg as preload was raised from 6-10 to 31-35 mmHg. Coronary conductance, taken as the slope of the pressure-flow relationship at any given PLC, fell progressively as preload rose, with the fall being more marked at higher levels of preload and lower values of PLC. Diastolic coronary flow also decreased as a function of preload, reflecting the increases in Pf = 0 and decreases in conductance.(ABSTRACT TRUNCATED AT 250 WORDS)

To quantify reactive elements of the coronary circulation, we have characterized in vivo diastolic coronary input impedance by introducing sinusoidal pressure oscillations of constant amplitude and varying frequency at constant mean pressure levels during prolonged diastoles in heart-blocked dogs anesthetized with pentobarbital. The behavior of coronary input impedance is similar to that observed in other peripheral vascular beds and is a function of both mean distending pressure and vasomotor tone. The behavior of impedance modulus and phase at each pressure level could be described by a lumped resistive-capacitive (RC) parallel model over a frequency range of 1-5 Hz. At higher frequencies the phase angle response could be characterized by adding a Voigt viscoelastic element to the original RC model. Calculated coronary capacitances for both models were similar in magnitude and varied inversely with mean coronary distending pressure. Values for the RC and RC viscoelastic model in the maximally dilated coronary bed were 14.1 and 21.6 X 10(-3) ml X mmHg X 100 g-1 at 30 mmHg and 2.65 and 2.70 X 10(-3) ml X mmHg-1 X 100 g-1 at 110 mmHg. With vasomotor tone intact, calculated coronary capacitance at each pressure level was reduced by a factor of two. These results indicate that an RC parallel model with pressure- and vasomotor tone-dependent capacitance adequately describes diastolic coronary input impedance at frequencies encountered during ordinary diastoles. The addition of a viscoelastic element provides adequate fits up to frequencies of 10 Hz.