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# Your heart does work: A relationship of pressure and volume

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## Problem

As a pump, the heart continually is increasing and decreasing the pressure it exerts on blood. During diastole, or the relaxation phase, blood flows into the various chambers (called the atria and ventricles) of the heart, and during systole blood is pumped out. The total mechanical energy involved in this process can be calculated simply by multiplying the pressure of the blood by the volume of blood ejected from a given chamber (stroke volume). Stroke volume is distinct from the total volume of blood in a heart chamber, because not all blood is ejected from a chamber during a contraction. This amount of energy transferred by the heart during a contraction is often referred to as ‘stroke work’. Much like work done by an internal combustion engine, we can treat the heart as a thermodynamic system, and visually represent stroke work with the use of a pressure-volume diagram, as seen in Figure 1.
Figure 1. Generalized Cardiac Pressure-Volume Loop Diagram
Let’s say that this diagram describes the relationship of volume and pressure specifically for the left ventricle of a heart. Position $1$ of the graph would then mark the opening of the mitral valve, which allows blood to fill the chamber from the left atrium (diastole). Position $2$ marks the closing of the mitral valve, and the beginning of systole. The chamber begins to contract, increasing blood pressure until it raises high enough to push open the aortic valve, leading out of the heart (Position $3$). Once blood is ejected from the chamber (Position $4$), pressure will decrease and the cycle is completed, which begins diastole again.
There are various ways which we can influence how much work the heart does in a given stroke. One way we can increase stroke work is by increasing the volume of blood in the chamber during diastolic filling, known as preload. In other words, because the volume of preload is directly proportional to both stroke volume and blood pressure, an increase or decrease of preload will also increase or decrease stroke work respectively.
Which area of the graph would be equal to the amount of work done to the system after systole?