The principle of measuring left atrial pressures through the pulmonary capillaries rests on the premise that capillary resistance is very low, and with the baloon inflated there is no flow, leaving only the capillary pressure to act on the transducer.
The relationship of pressure, flow and resistance
Behold the Tube.
In it, a nameless fluid flows, with a flow rate of Q.
It flows because there is a difference in pressure from one end of the tube to the other.
This is the Delta P.
The walls of the tube offer a resistance to the flow, expressed as R.
This equation describes the rate of flow:
To rearrange it, so we describe the difference in pressure:
That is to say, the change in pressure from one end of the tube to the other is proportional to the product of the flow and the resistance.
How does this relate to the PA catheter?
In the pulmonary circulation, the Delta P we are interested in is the difference in pressure between the pulmonary capillaries and the left atrium.
Now, if you inflate the balloon and stop the pulmonary arterial flow,
Q is now zero.
This is the key feature.