Starling curve

Fig. 24.4 Starling curve of relationship between cardiac filling pressure and cardiac output. In phase A, reduction in blood volume (by diuretics) reduces filling pressure and cardiac output. In phase B, reduction in blood volume reduces filling pressure and increases cardiac output...

Diuretics increase salt and water loss, reduce blood volume and lower excessive venous filling pressure (see Ch. 26). The congestive features of oedema, in the limgs and periphery, are alleviated when the heart is grossly enlarged, cardiac output will also increase (see discussion of Starling curve, above). 

Ventricular function (Frank-Starling) curves, which plot any function of preload versus any function of cardiac work, reveal that compensatory mechanisms in untreated heart failure (mostly deleterious) may shift such curves upward and to the left. Compensation in heart failure is offset by specific drugs that can ... 

Ventricular function curve The graph that relates cardiac output, stroke volume, etc, to filling pressure or end-diastolic fiber length also known as the Prank-Starling curve... 

Figure 13-2. Ventricular function (Frank-Starling) curves. The abscissa can be any measure of preload—fiber length, filling pressure, pulmonary capillary wedge pressure, etc. The ordinate is a measure of useful external cardiac work—stroke volume, cardiac output, etc. In congestive heart failure, output is reduced at all fiber lengths and the heart expands because ejection fraction is decreased. As a result, the heart moves from point A to point B. Compensatory sympathetic discharge or effective treatment allows the heart to eject more blood, and the heart moves to point C on the middle curve.

Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],...

Figure 11-26. Vapor pressure curve for ethylene refrigerant. (Used by permission Starling, K. E. Fluid Thermodynamic Properties for Light Petroleum Systems, 1973. Gulf Publishing Co., Houston, Texas. All rights reserved.)...

There is a minor anomaly in the retention-ume distribution curve in Fig. 6. starling at r 1.2tp. This is caused by a small amount of liquid following a second flow path longer than the mainstream flow. This minor flowstream probably exited the upper spreader through the vent and then used the dead space for separation purposes, reducing the inactive volume of this vessel. 

The data designated ( ) were obtained using the pressure equation (2.9.9), those designated ( ) using the compressibility equation (2.9.10), and the smooth curve, using the Carnahan-Starling equation (2.9.11). 

Fig. 21. Entropy versus log-temperature diagram for the hard-sphere model. The solid curves give the computer simulation values for the supercooled fluid, glass, and crystal. The dashed curves have the following bases (a) a calculation from the virial equation using the known first seven coefficients and higher coefficients obtained from the conjectured closure (the plot corresponds quite closely with that calculated from the Camahan-Starling equation ) and (i>) an extrapolation of higher temperature behavior such as that used by Gordon et al., which implies a maximum in the series of virial coefficients. The entropy is defined in excess of that for the ideal gas at the same temperature and pressure. Some characteristic temperatures are identified 7, fusion point 7 , upper glass transition temperature T/, Kauzmann isoentropic point according to closure virial equation.

Figure 5.12. The compressibility factor of a hard-sphere fluid. The solid squares, circles, and diamonds indicate values obtained from the computer simulations of Erpenbeck and Wood [26], Rotenberg [27] and Woodcock [28], respectively. Curve 1 is a plot of the seventh-order virial polynomial. Curve 2 is the Shinomoto, second-order cumulant approximation of Eq. (5.204). Finally, 3 is a plot of the RG seventh-order cumulant approximation of Eq. (5.205) and of the Camahan-Starling equation (5.183) as well, since the two are indistinguishable on the scale of this figure.

Much of the criticism of the interpretation of Starling s original measured input-output relations was resolved by the introduction of a family of cardiac function curves [74], which accommodated neural and metabolic stimulation of the heart. Such influences manifest themselves in graphs of input (preload)-output (stroke volume, stroke work, etc.) as counter clockwise rotation (steeper) and stretch along the output (vertical) axis. Alteration in parameter c in Equation 18.1 and Equation 18.2 carries major responsibility for these modifications. In addition, it has recently been found that the cardiac function curve can be shifted along the horizontal (preload) axis [75]. This shift is effected by changes in air pressure, pe, external to the cardiac chambers, such as caused by the respiratory system, or by CPR, and modifies Equation 18.2 by approximation to... 

As follows from the curves in Figure 1, the models by Enskog and by Carnahan-Starling lead to somewhat different results, and the problem of a proper choice between these models arises. The theoretical curves for fluctuation temperature are compared with the experimental data of Carlos and Richardson [42] in Figure 2. These experiments were conducted with metallic balls 8.9 nun in diameter fluidized by dimetilphtalate. The maximal fluctuation temperature was experimentally observed at / = 0.32 - 0.34, which agrees well with our theoretical prediction. On the whole, the agreement between the presented theory and experiments looks quite satisfactory. 

Figure 1. Dimensionless fluctuation temperature for fluidized beds of small (1) and large (2) spherical particles according to the Carnahan-Starling and Enskog models (solid and dashed curves, respectively) u° is the terminal fall velocity of a single particle (j). = 0.6.

Figure 4. Neutral stability curves for fluidized beds as foilow from the Carnahan-Starling model at Vi = 1 and different values of IgSc (figures at the curves) in the limiting regimes of constant and varying fiuctuation temperature (solid and dashed curves, respectively) dotted curves correspond to the osmotic pressure correction function calculated with the help of the Enskog model.

The first parameter appears as a result of quasi-viscous stresses in the dispersed phase affecting the development of initial plane waves. In fact, this parameter characterizes an influence on fluidized bed stability caused by dispersed phase viscosity. The occurrence of the second parameter is due to the restriction imposed from below on permissible wave numbers for these plane waves. Actually, the second parameter descibes a so-called scaling effect of the bed dimensions on bed stability. The curves in Figure 4 correspond to the Carnahan-Starling model, save for the dotted ones which have been drawn when using Equation 4.8 to represent the osmotic pressure correction function and the Enskog factor. 

Fig. 3.1 The pressure of hard spheres. The curves are the Carnahan—Starling exjaession (3.1) for a fluid < 0.494) and the cell model result (3.12) for an fee crystal (solid curves, (j) > 0.545). The closed symbols are Monte Carlo computer simulation results [13]. The two open symbols cmrespond to the fluid-solid coexistence from simulation [11], the dotted line is the themetical result (see Sect. 3.2.3)...

In accordance with Starling s law of the heart, cardiac output is intimately dependent on In our simplified model, we have let = P. In the discussion to follow, graphs of cardiac output as a function of P (Figure 4) will be called cardiac function curves . Extrinsic regulatory influences may be expressed as shifts in such curves (Guyton et ai, 1973 Levy, 1979 Berne and Levy, 1981). 

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