End-systolic pressure volume relationship

Figure 1. Schematic explanation of coupling the left ventricular contraction with the systemic arterial tree. In the middle left panels, left ventricular contraction is represented by its end-systolic pressure-volume relationship. Given a particular end diastolic volume (EDV), this relationship can be converted into ventricular end-systolic pressure P s) stroke volume (5Vj relationship, which is shown by the rectilinear curve coursing from the lower left to upper right corner in the graph at the bottom. In the right middle panel, the aortic input impedance property is represented by a rectilinear arterial end-systolic pressure fF, )-stroke volume SV) relationship curve (Eq. (5)). See the text for the explanation of this representation. This arterial Pes-SV relationship is transcribed in the bottom panel in superposition with the ventricular Pe -SV relationship. The intersection of the two Pes-SV relationship curves indicates the end-systolic pressure and stroke volume which should result from coupling a left ventricle with the given EDV and the slope parameter with a systemic arterial tree with the slope parameter...

Figure 2. Flow chart of the procedures to test the ventricular model (in terms of end-systolic pressure-volume relationship) and the arterial model by end-systolic pressure-stroke volume relationship using one control set of loads (4 preloads and 1 afterload) and 8 noncontrol load sets (4 preloads and 8 afterloads).

Figure 3. Schematic illustration of the dependence of the amount of the external mechanical work (shown by shaded area) that a ventricle performs at a constant preload and under a constant contractility (i.e., a fixed slope of end-systolic pressure-volume relationship) on afterloaded arterial elastance E . Note that the shaded area becomes maximum when equals E .

Kono A., Maughan W.L., Sunagawa K., et al. 1984. The use of left ventricular end-ejection pressure and peak pressure in the estimation of the end-systolic pressure-volume relationship. Circulation 70 1057. 

Recently, the relationship between pressure-volume or force-length at the end of systole has attracted a great deal of interest as a descriptor of the contractile state of the heart. This interest stems from a series of studies in isolated, canine left ventricular preparations (Taylor et al 1969 Suga et a/., 1973 Suga and Sagawa, 1974 Weber et /., 1976 Weber and Janicki, 1977), which demonstrated the end-systolic pressure-volume relation to be quite sensitive to variations in contractile state and relatively insensitive to variations in load. In addition, the relation is linear over a wide range of volumes so that its slope can be used to quantitate the contractile state. 

Here, PVR (pressure-volume relationship) is the active P-V curve, and PVRgs and PVRd are the end systolic and diastolic P-V curves, respectively. Using this approach, the PVRgs curve would be parameterized in terms of the inotropic state of the myocardium, and fmax would be a function of inotropic state and heart rate. 

To answer the question of optimal matching between the ventricle and arterial load, we developed a framework of analysis which uses simplified models of ventricular contraction and arterial input impedance. The ventricular model consists only of a single volume (or chamber) elastance which increases to an endsystolic value with each heart beat. With this elastance, stroke volume SV is represented as a linearly decreasing function of ventricular endsystolic pressure. Arterial input impedance is represented by a 3-element Windkessel model which is in turn approximated to describe arterial end systolic pressure as a linearly increasing function of stroke volume injected per heart beat. The slope of this relationship is E. Superposition of the ventricular and arterial endsystolic pressure-stroke volume relationships yields stroke volume and stroke work expected when the ventricle and the arterial load are coupled. From theoretical consideration, a maximum energy transfer should occur from the contracting ventricle to the arterial load under the condition E = Experimental data on the external work that a ventricle performed on extensively varied arterial impedance loads supported the validity of this matched condition. The matched condition also dictated that the ventricular ejection fraction should be nearly 50%, a well-known fact under normal condition. We conclude that the ventricular contractile property, as represented by is matched to the arterial impedance property, represented by a three-element windkessel model, under normal conditions. 

Over the past decade, we (Sagawa, 1978) have measured the ventricular pressure (P)-volume (V) relationship in an isolated and blood perfused canine heart preparation and came to consider that the ventricular end-systolic P-V relationship (ESPVR) is (a) linear as opposed to the highly nonlinear P-V relationship of the frog s ventricle reported by Otto Frank a century ago, (b) rather insensitive to the preload and afterload and (c) changes its slope (E, ) sensitively with inotropic interventions without a significant shift in the volume intercept (Vq). This is to say that our model of the ventricle merely consists of a linear volume elastance E which varies with each heart beat from a smaller end-diastolic value to a larger... 

Equation (2) states that, given an end-diastolic volume 5V is inversely proportional to (the line coursing from the lower left to upper right corner of the bottom panel of Figure 1). This rectilinear relation is denoted the ventricular end-systolic pressure-stroke volume relationship (VPSVR) . 

The development of practical methods for the assessment of myocardial contractility continues and while the ESP-ESV concept provides one approach for quantitating changes in the contractile state, it requires further modification in order that it may be employed for patient to patient comparison. The preliminary studies described here on the basis of the developed stress concept shows some promise, however, further studies are required to examine the relationships between peak systolic pressure and end diastolic volume in order to explore an alternative definition for developed stress. 

---