Work Of Breathing – Pressure-Volume Curve Integration

From a physics standpoint, work (W) = force (F) x distance (d). Similarly, pressure (P) = force (F) / area (A) and volume (V) = area (A) x distance (d). By rearranging these equations, one can show that:

work = pressure x volume

If you think about it, air pressure changes with volume based on compliance. A highly compliant lung will be able to accomodate more volume with less pressure. A stiff lung (ARDS, high extravascular lung water, interstitial lung disease) will require much more pressure to breath the same volume.

Now let’s consider that pressure is a function of volume. Knowing that and the equation above, inspiratory work will be equal to the integral of PdV integrated from the functional residual capacity (FRC, air left in the lung after a normal expiration) to the tidal volume (VT, air inspired during normal breathing).

The FRC and VT are the two volumes between which tidal breathing occurs. Integrating the area below the curve between these two volumes represents the work of breathing.

So how does this help us? Let’s take an example of a patient with cardiogenic pulmonary edema. Lung compliance will be poor due to additional extravascular lung water, interstitial edema, alveolar exudate, etc. Their pressure-volume loop would appear much more horizontal than what you see in the diagram above, and the area under the curve would also be larger suggesting increased work of breathing. By using adjuncts like bilevel positive airway pressure (BPAP), you’ll see this the curve transform into something more like what you see above. 🙂

Drop me a comment with questions! 🙂

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1 Comment
  1. Adnane Lahlou says

    Love the physics of it but a couple case scenarios would be most welcome to put this into practice.

    Thanks Rishi