The Transmural Pressure Is the Difference in Pressure Between Two

The transmural pressure is the difference in pressure between two sides of a wall, or a separator. In the human respiratory system, the transmural pressure (trans means "across" and murus means "wall" in Latin) is a pressure difference between the lungs and the pleura. The pleura is a double-layered membrane surrounding the lungs and, with a small amount of fluid, allows frictionless movements of the lungs against the rib cage, preventing the hard ribs from puncturing the soft lung tissue. Gauge pressure is the pressure value relative to atmospheric pressure. P_alveoli represents the gauge pressure inside the lungs, and P_pleura represents the gauge pressure in the pleura. What happens with transmural pressure in the lungs an the environment where atmospheric pressure is much lower, such as on the 4205-m-high Mauna Kea volcano summit on the Big Island, Hawaii? Are there other considerations that need to be taken into account when thinking about respiration at high altitudes?