Pressure volume relationship, ventricles

Calcium accumulation and overload secondary to ischemia impair ventricular relaxation as well as contraction. This is apparently a result of impaired calcium uptake after systole from the myofilaments, leading to a less negative decline in the pressure in the ventricle over time. Impaired relaxation is associated with enhanced diastolic stiffness, decreased rate of wall thinning, and slowed pressure decay, producing an upward shift in the ventricular pressure-volume relationship put more simply, MVO2 is likely to be increased secondary to increased wall tension. Impairment of both diastolic and systolic function leads to elevation of the filling pressure of the left ventricle. 

Diamond G, Forrester JS, Hargis J, Parmley WW, Danzig R, Swan HJC (1971) Diastolic pressure volume relationship in the canine left ventricle. Circ Res 29 267-275 Feigl EO (1983) Coronary physiology. Physiol Rev 63 1-202 Gibss CF (1977) Cardiac energetics. Physiol Rev 58 1,174-254... 

Streeter DD, Vaishnav RN, Patel DJ, Spotnitz HM, Ross J Jr, Sonnenblick EH (1970). Stress distribution in the canine left ventricle during diastole and systole. Biophysical J 10 345-363 Suga H, Sagawa K (1974) Instantaneous pressure-volume relationships and their ratio in the excised, supported canine left ventricle. Circ Res 35 117-126 Tozeren A (1983) Static analysis of the left ventricle. J Biomech Eng 105 39-46 Yin FCP (1981) Ventricular wall stress. Circ Res 49 829-842... 

ANS Yes, the time varying behavior of elastance will mathematically result in an inverse force-velocity relationship of muscle. However, as I have just shown there is an additional dependence of pressure on flow that is independent of volume and it is this additional pressure loss that must be accounted for by a resistance term. Furthermore, Dr. Suga recently published the results of a study which indicated a correction term had to be added to his time varying elastance model in order for the isovolumetric and ejecting pressure-volume relationships to coincide. This correction term was of the same magnitude as our resistance term. So you cannot just use a time-varying elastance to describe the dynamics of the left ventricle. 

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 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 .

Suga H. and Sagawa K. 1974. Instantaneous pressure volume relationships and their ratio in the excised, supported canine left ventricle. Circ. Res. 35 117. 

The line plotted on a pressure-volume graph that describes the relationship between filling status and systolic pressure for an individual ventricle (ESPVR). 

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. 

Figure 1. Pressure-volume curve measured in an excised dog heart by filling an excised ventricle with saline at a constant rate. At P , the relations deviate from linear relationship. From Grantz (1980).

ANS I would disagree with your statement that elastance cannot be used to describe both the passive and active relationship between pressure and volume. If it were possible to examine the ventricle at a specific time in systole and measure the mechanical properties, you will find that that elastance has increased from its diastolic value. We could show this using our flow pulse technique where within 30 ms we were able to withdraw 1-2 ml of volume. We typically observe a large decrease in pressure, more so than we would see during diastole. That is, it is a stiffer appearing ventricle. 

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... 

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