# Pressure volume curve; Is it wrong ESPVR?

ESPVR is a straight line passing through the upper left corner point of the pressure volume curve and such that the x-intercept is the dead volume of the ventricle; as far as this definition is concerned, the slope of ESPVR, i.e., Emax, refers to the contractility of the heart, and needless to say, drawing a tangent line at this point is obviously nonsense, since a discontinuous event of aortic valve closure occurs at the upper left angle point; https://ccnmtl.columbia.edu/projects/heart/exercises/MechPropHeart/lecture.html

However, the x-intercept of the Pressure volume curve on the two sites below is clearly negative, as shown in the figure cited below.

My question

Does the fact that the volume of the dead space of the left ventricle is a negative number have any special meaning? Or are these just mistakes?

The dubious pressure-volume curves cited above were taken from;

I might have resolved it myself. The details are outlined below;

Until now, I had understood that the ESPVR is fundamentally defined as "a straight line constructed to satisfy the following equation and the max value of the following E(t) is the Emax(or Ees);"

as descried in the following materials;

In other words, the concept of Def.1 is same as below

Def.1:

• The dead space volume (Vo), is known a priori and
• The ESPVR is a straight-line that "passes through (no need to tangent) the upper left corner point of the pressure-volume curve" and "with the x-intercept is volume (Vo)".

Here the definition of the "Vo" is as quoted below;

"What would happen to pressure inside a floppy balloon if we were to vary its volume. Let's start with no volume inside the balloon; naturally there would be no pressure. As we start blowing air into the balloon there is initially little resistance to our efforts as the balloon wall expands to a certain point. Up to that point, the volume increases but pressure does not change. We will refer to this volume as Vo, or the maximal volume at which pressure is still zero mmHg; this volume is also frequently referred to as the unstressed volume. " https://ccnmtl.columbia.edu/projects/heart/exercises/MechPropHeart/lecture.html

And, as quoted below, the "Vo" seems to be obtained experimentally not through ESPVR but rather during the measurement process of EDPVR.

"A typical relationship between pressure and volume in the ventricle at end-diastole is shown in Figure 5. As volume is increased initially, there is little increase in pressure until a certain point, designated "Vo". After this point, pressure increases with further increases in volume. This curve is called the "end-diastolic pressure-volume relationship" (EDPVR)." https://ccnmtl.columbia.edu/projects/heart/exercises/MechPropHeart/lecture.html

However, ESPVR seems to be conceptually understood more as the concept of Def2, below, at least from the view point of conducting the experiments.

Def.2:
Trajectory of the "upper left corner points" of each PV-loops, taken under various measurement conditions(varying preload or afterload).

For example, the following diagram seems to deal with ESPVR under the concept of Def2 rather than Def1.

In the sense of Def.2, above, it may be necessary to have PV loops measured under at least two different conditions where the contractility of the heart does not change significantly.

• If there are only two PV loops available, one might consider the straight line connecting the upper left corner points of these two PV loops as the ESPVR line.
• In cases involving more PV loops,
・it is also possible to consider a regression line that closely fits the trajectories of "upper left corner points" as ESPVR, Ees (also known as Emax) could be the slope of ESPVR, in this sense furthermore, it may even be acceptable to regard the trajectory of these upper left corner points itself as ESPVR.
・In this context, Ees (also known as Emax) could be seen as the tangent line of ESPVR, in this sense.

When viewed in the sense of Def.2, the "Vo" may no longer represent a physical entity of "the maximal volume at which pressure is still zero mmHg." Instead, it may be more appropriately perceived as an effective quantity derived from statistical processing. Consequently, it might be permissible to consider the concept of "changes in PV loops that exhibit negative dead space volume."