Robert E. Mates

Left Ventricular Wall Stress Calculated from One-Plane Cineangiography

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/cm2 in the circular direction and 75 to 365 g/cm2 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.

Fluid dynamics of coronary artery stenosis.

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.

Rotational Relaxation in Nonpolar Diatomic Gases

The rotational‐translational energy transfer in collisions between homonuclear diatomic molecules and the rotational relaxation time in diatomic gases have been investigated classically. Using Parkers 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 ...

Coronary pressure-flow relationships. Controversial issues and probable implications.

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)

Vmax as an Index of Contractile State in Man

The maximal, no-load, velocity for the contractile element (V max ) was estimated in 45 patients. The patients included: 17 with normal left ventricular dynamics; eight with volume overload, compensated; 11 with volume overload, decompensated; three with pressure overload; and six with cardiomyopathy. Contractile element velocity (V CE ) during isovolumic contraction was estimated in two ways: (1) from left ventricular pressure data alone, where V CE =(1/28.8p) (dp/dt), and (2) pressure data combined with measurement of left ventricular geometry (right anterior oblique cine). V max obtained in these two ways agreed well for most patients (r = 0.82). In the normal patients, V max varied from 1.46 to 2.64 muscle lengths per sec; in contrast that of the patients with cardiomyopathy varied between 0.71 and 1.34 muscle lengths per sec. Other indices of contractility (ejection fraction, peak dp/dt, peak velocity of circumferential fiber [peak V CF ], peak V CE , and V CE at zero stress) were compared on the basis of statistical correlation and consistency of other clinical evidence (presence or absence of congestive failure). Good correlation was obtained between V max and peak V SE (r = 0.68). Ejection fraction and peak V CF were less sensitive. Neither the peak rate of pressure rise or V CE at peak stress show any significant correlation with V max or clinical state. Previous studies have shown that V max can be evaluated from pressure data alone; this study confirms this finding in patients with mitral regurgitation as well as in those with normal outflow impedance.

Analysis and Correction of Pressure Wave Distortion in Fluid-Filled Catheter Systems

Dynamic characteristics of a variety of catheters and their dependence on various operating parameters are presented. Careful flushing of the catheter with degassed water or saline considerably improves the performance of these systems. The operating temperature, number of catheter uses, and average transmural pressure difference do not have a significant effect.The error due to catheter distortion in commonly used left ventricular performance indices (end diastolic pressure, peak systolic pressure, maximum dp/dt and Vmax) was assessed. On the basis of these results, it is shown that the natural frequency of the catheter system must be greater than 40 Hz to produce results accurate to 10%.The experimental data were used to develop a semi-empirical model for the catheter transducer system. This model was used in the design of an analog compensator to further improve the dynamic characteristics of the catheter transducer system. The compensator requires only two parameter settings, catheter natural frequency and damping ratio.

A Model of Cardiac Muscle Dynamics

A mathematical model is presented describing the time- and length-dependent behavior of cardiac muscle. The model describes a wider variety of experimental data than do previously published models. It incorporates a modification of the Hill equation describing the force-velocity relation. Based on the sliding filament theory, the revised equation includes the effects of finite cross-bridge compliance proposed by A. F. Huxley. The essential simplicity of the Hill equation is retained; however, the model successfully predicts force development during both isometric and isotonic contractions, observed deactivation of the contractile element during isotonic shortening, and the apparent dependence of series elastic stiffness on time after stimulation during quick-release and quick-stretch experiments.

Rotational Temperature in an Underexpanded Jet

The axial rotational temperature distribution in an underexpanded nitrogen jet emitted from a sonic orifice has been investigated. The expansion is from room temperature and the gas possesses negligible vibrational energy. The observed difference between the rotational temperature measured with an electronbeam probe and the isentropic value can be described by a rotational relaxation analysis. The governing flow equations were integrated numerically by the classical fourth‐order Runge‐Kutta method. The rotational relaxation time developed by Lordi using Wang Chang and Uhlenbecks formal kinetic theory and Parkers molecular model was employed. Both the easy and difficult energy transfer cases were investigated and the easy case was shown to underestimate nonequilibrium affects. The numerical solutions were very sensitive to the separation between the repulsive force centers, for both energy transfer cases. The rotational temperature distributions obtained in this study are in general agreement with existi...

Models for Coronary Pressure-Flow Relationships

We have developed a mathematical model which describes pressure-inflow relationships in the coronary circulation. Model parameters have been identified during metabolic and pharmacologic vasodilation. These two stimuli appear to affect resistance and back pressure in different ways. A possible explanation involving myogenic and metabolic effects is suggested.

Evolving Concepts of Coronary Pressure-Flow Relationships

Following Bellamy’s 1978 report concerning diastolic coronary pressure-flow relationships (1), several laboratories have reinvestigated the relative roles of changes in driving pressure and resistance in physiological adjustments of coronary flow.