Ventricular volume elastance

SAGAWA I also disagree with Dr. Feigl. I don t see any reason why the word elastance should be used strictly as a passive property. Even the so-called passive property of muscle is quite active. It is very difficult to draw a sharp line between passive and active muscle. In addition, in engineering, the suffix ance is not used to represent a material property. Instead it represents a systems property. For example, the elastance of the balloon at a given volume is not a measure of the elasticity of the balloon material. Instead, the term elasticity, or modulus of volume elasticity, is used to describe the material property. So I think it s right to use the term elastance for the ventricular chamber regardless of its state of activation. 

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... 

The first case study of this chapter outlines the development of a model of left ventricular pumping. The model is devised from canine experiments and represents the left ventricle as a time, volume, and outflow-dependent pressure generator. In the course of model development, a new analytical method of measuring ventricular elastance emerges, with the potential of clarifying issues with previous elastance measurements. One application is a slight model expansion to study the cardiac pump theory of cardiopulmonary resuscitation (CPR). 

Mechanical performance of the heart, more specifically the left ventricle, is typically characterized by estimates of ventricular elastance. The heart is an elastic bag that stiffens and relaxes with each heartbeat. Elastance is a measure of stiffness, classically defined as the differential relation between pressure and volume ... 

Here, py and Vy denote ventricular pressure and volume, respectively. For any instant in time, ventricular elastance Ey is the differential change in pressure with respect to volume. Mathematically, this relation is clear. Measurement of Ey is much less clear. 

FIGURE 8.2 Time-varying ventricular elastance curves measured using the definition in Equation 8.3. Measured elastance curves are distinctive in shape. (Adapted from Suga, H. and Sagawa, K. 1974. Instantaneous pressure-volume relationship under various end-diastolic volume. Circ Res. 35 117-126.)... 

Sagawa, K. 1987. The ventricular pressure-volume diagram revisited. Circ. Res. 43 677-687. Campbell, K.B., Ringo, J.A., Knowlen, G., Kirkpatrick, R., and Schmidt, S.L. 1986. Validation of optional elastance-resistance left ventricular pump models. Am. J. Physiol. 251 H382-H397. 

Mathematical representation of the time-varying elastance is more complicated and is generally based on the characterization of the cardiac work cycle in the pressure-volume plane. In the P-V diagram in Figure 10.5b, the time course of the left ventricular cardiac cycle proceeds as follows. 

FIGURE 54.5 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). 

Relationship between ventricular stiffness, myocardial elasticity, coronary blood volume, cavity size and the volume mass ratio... 

Here P t), V t) and V (t) are the instantaneous ventricular pressure, volume and flow and Vd is the absolute residual volume that is associated with zero end-systolic pressure. Thus from end-diastolic volume and ventricular pressure and flow data or, equivalently, ventricular pressure and volume data one can use a least squares minimization technique to obtain A1 through A6 and such that the sum of the squared residuals between calculated and measured pressure is minimized. Maximum elastance could then be obtained from the elastance function. 

ANS As I indicated earlier, our resistance is a phenomenological descriptor of the relationship between ventricular pressure and flow. That is, ventricular flow, along with volume and time, is an independent determinant of pressure. As a result, the actual pressure within the ejecting ventricle will be less than that which would have been expected if the ventricle was purely elastic. Therefore, phenomenologically, resistance represents a loss in ventricular pressure whenever the ventricle attempts to eject blood or, equivalently, the muscle fibers are allowed to shorten. Our resistance has nothing to do with blood flow across the valve. 

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. 

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