pretty sure they are unrelated, unless i'm missing something.
negative pressure breathing is:
when the diaphragm contracts it lowers creating a negative pressure in the thoracic region and therefore in the lungs. this leads to the inhalation of air until the pressure within the lungs and the environment are equalized.
Fluid incompressibility:
Since the molecules of a liquid are relatively close together (compared to gas) it is more difficult to compress. Gas on the other hand, since the particles are moving so quickly, they are spaced out and have room to be compressed.
Correct me if i am referring to the wrong concepts.