Ventricular Pressure Volume Relations and Energetics

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A useful alternative to Fig. 11.4 for displaying ventricular pressure and volume changes is the pressure-volume loop shown in Fig. 11.5a. During the last 20 years, the ventricular pressure-volume relationship has been explored extensively, particularly by Sagawa [1988], who wrote a comprehensive book on the approach. The isovolumic phases of the cardiac cycle can be recognized as the vertical segments of the loop, the lower limb represents ventricular filling, and the upper segment is the ejection phase. The difference on the horizontal axis between the vertical isovolumic segments is the stroke volume, which expressed as a fraction of the end-diastolic volume is the ejection fraction. The effects of altered loading on the ventricular pressure-volume relation have been studied in many preparations, but the best controlled experiments have used the isolated cross-circulated canine heart in which the ventricle fills and ejects against a computer-controlled volume servo-pump.

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Pressure Volume

FIGURE 11.5 Schematic diagram of left ventricular pressure-volume loops: (a) End-systolic pressure-volume relation (ESPVR), end-diastolic pressure volume relation (EDPVR), and stroke work. The three P-V loops show the effects of changes in preload and afterload. (b) Time-varying elastance approximation of ventricular pump function (see text).

LV Volume (ml)

FIGURE 11.5 Schematic diagram of left ventricular pressure-volume loops: (a) End-systolic pressure-volume relation (ESPVR), end-diastolic pressure volume relation (EDPVR), and stroke work. The three P-V loops show the effects of changes in preload and afterload. (b) Time-varying elastance approximation of ventricular pump function (see text).

Changes in the filling pressure of the ventricle (preload) move the end-diastolic point along the unique end-diastolic pressure-volume relation (EDPVR), which represents the passive filling mechanics of the chamber that are determined primarily by the thick-walled geometry and nonlinear elasticity of the resting ventricular wall. Alternatively, if the afterload seen by the left ventricle is increased, stroke volume decreases in a predictable manner. The locus of end-ejection points (AVC) forms the end-systolic pressure-volume relation (ESPVR), which is approximately linear in a variety of conditions and also largely independent of the ventricular load history. Hence, the ESPVR is almost the same for isovolumic beats as for ejecting beats, although consistent effects of ejection history have been well characterized [Hunter, 1989]. Connecting pressure-volume points at corresponding times in the cardiac cycle also results in a relatively linear relationship throughout systole with the intercept on the volume axis V0 remaining nearly constant (Fig. 11.5b). This leads to the valuable approximation that the ventricular volume V(t) at any instance during systole is simply proportional to the instantaneous pressure P(t) through a time-varying elastance E(t):

The maximum elastance Emax, the slope of the ESPVR, has acquired considerable significance as an index of cardiac contractility that is independent of ventricular loading conditions. As the inotropic state of the myocardium increases, for example with catecholamine infusion, Emax increases, and with a negative inotropic effect such as a reduction in coronary artery pressure it decreases.

The area of the ventricular pressure-volume loop is the external work (EW) performed by the myocardium on the ejecting blood:

Plotting this stroke work against a suitable measure of preload gives a ventricular function curve, which illustrates the single most important intrinsic mechanical property of the heart pump. In 1914, Patterson and Starling performed detailed experiments on the canine heart-lung preparation, and Starling summarized their results with his famous "Law of the Heart", which states that the work output of the heart increases with ventricular filling. The so-called Frank-Starling mechanism is now well recognized to be an intrinsic mechanical property of cardiac muscle (see Section 11.4).

External stroke work is closely related to cardiac energy utilization. Since myocardial contraction is fueled by ATP, 90 to 95% of which is normally produced by oxidative phosphorylation, cardiac energy consumption is often studied in terms of myocardial oxygen consumption, VO2 (ml O2-g-1-beat-1). Since energy is also expended during non-working contractions, Suga and colleagues [1981] defined the pressure-volume area PVA (J'g-1-beat-1) as the loop area (external stroke work) plus the end-systolic potential energy (internal work) which is the area under the ESPVR left of the isovolumic relaxation line (Fig. 11.5a),

The PVA has strong linear correlation with VO2 independent of ejection history. Equation (11.11) has typical values for the dog heart:

The intercept represents the sum of the oxygen consumption for basal metabolism and the energy associated with activation of the contractile apparatus, which is primarily used to cycle intracellular Ca2+ for excitation-contraction coupling [Suga et al., 1981]. The reciprocal of the slope is the contractile efficiency [Suga and Goto, 1991; Suga et al., 1993]. The VO2-PVA relation shifts its elevation but not its slope with increments in Emax with most positive and negative inotropic interventions [Suga et al., 1988;

Suga, 1990; Suga and Goto, 1991; Zhao et al., 1993; Namba et al., 1994]. However, ischemic-reperfused viable but "stunned" myocardium has a smaller O2 cost of PVA [Ohgoshi et al., 1991].

Although the PVA approach has also been useful in many settings, it is fundamentally phenomeno-logical. Because the time-varying elastance assumptions ignores the well-documented load-history dependence of cardiac muscle tension [Guccione and McCulloch, 1993; ter Keurs and de Tombe, 1993; Burkhoff et al., 1995], theoretical analyses that attempt to reconcile PVA with crossbridge mechanoen-ergetics [Taylor et al., 1993] are usually based on isometric or isotonic contractions. So that regional oxygen consumption in the intact heart can be related to myofiber biophysics, regional variations on the pressure-volume area have been proposed, such as the tension area [Goto et al., 1993], normalization of Emax [Sugawara et al., 1995], and the fiber stress-strain area [Delhaas et al., 1994].

In mammals, there are characteristic variations in cardiac function with heart size. In the power law relation for heart rate as a function of body mass [analogous to Eq. (11.3)], the coefficient k is 241 beats-min-1 and the power a is -0.25 [Stahl, 1967]. In the smallest mammals, like soricine shrews that weigh only a few grams, maximum heart rates exceeding 1000 beats-min-1 have been measured [Vornanen, 1992]. Ventricular cavity volume scales linearly with heart weight, and ejection fraction and blood pressure are reasonably invariant from rats to horses. Hence, stroke work also scales directly with heart size [Holt et al., 1962], and thus work rate and energy consumption would be expected to increase with decreased body size in the same manner as heart rate. However, careful studies have demonstrated only a twofold increase in myocardial heat production as body mass decreases in mammals ranging from humans to rats, despite a 4.6-fold increase in heart rate [Loiselle and Gibbs, 1979]. This suggests that cardiac energy expenditure does not scale in proportion to heart rate and that cardiac metabolism is a lower proportion of total body metabolism in the smaller species.

The primary determinants of the end-diastolic pressure-volume relation (EDPVR) are the material properties of resting myocardium, the chamber dimensions and wall thickness, and the boundary conditions at the epicardium, endocardium, and valve annulus [Gilbert and Glantz, 1989]. The EDPVR has been approximated by an exponential function of volume (see for example, Chapter 9 in Gaasch and LeWinter [1994]), though a cubic polynomial also works well. Therefore, the passive chamber stiffness dPIdV is approximately proportional to the filling pressure. Important influences on the EDPVR include the extent of relaxation, ventricular interaction and pericardial constraints, and coronary vascular engorgement. The material properties and boundary conditions in the septum are important since they determine how the septum deforms [Glantz et al., 1978; Glantz and Parmley, 1978]. Through septal interaction, the end-diastolic pressure-volume relationship of the left ventricle may be directly affected by changes in the hemodynamic loading conditions of the right ventricle. The ventricles also interact indirectly since the output of the right ventricle is returned as the input to the left ventricle via the pulmonary circulation. Slinker and Glantz [1986], using pulmonary artery and venae caval occlusions to produce direct (immediate) and indirect (delayed) interaction transients, concluded that the direct interaction is about half as significant as the indirect coupling. The pericardium provides a low friction mechanical enclosure for the beating heart that constrains ventricular overextension [Mirsky and Rankin, 1979]. Since the pericardium has stiffer elastic properties than the ventricles [Lee et al., 1987], it contributes to direct ventricular interactions. The pericardium also augments the mechanical coupling between the atria and ventricles [Maruyama et al., 1982]. Increasing coronary perfusion pressure has been seen to increase the slope of the diastolic pressure-volume relation (an "erectile" effect) [Salisbury et al., 1960; May-Newman et al., 1994].

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