 Transmural pressure

Transmural pressure is the pressure inside a wall-bounded structure minus the pressure immediately outside it:It identifies the pressure difference acting across the wall. For a blood vessel, blood pressure relative to atmosphere is not automatically this difference, because surrounding tissue can exert a nonzero pressure. For an airway, the same distinction explains how surrounding pleural pressure can affect distension or compression.^[ref]

For an original comparison, an internal pressure of 100 and surrounding pressure of 20 in the same units give a transmural pressure of 80. Raising the surrounding pressure to 60 reduces it to 40 even though the internal reading has not changed. Adding the same reference offset to both pressures cancels in the difference. Independently zeroed instruments with different offsets do not obtain that cancellation automatically.

A thin-walled pressure vessel gives a useful mechanical derivation. Cut an ideal cylindrical wall longitudinally through a length $L$. The resultant pressure force on a half-cylinder is $2p_{\mathrm{tm}}rL$, while two cut edges carry total circumferential tensile force $2{\sigma }_{\theta }hL$. Force balance yields the hoop stressfor radius $r$, thickness $h$ and uniform tensile stress. A stipulated $p_{\mathrm{tm}}=10$ kPa, $r=2$ mm and $h=0.2$ mm gives ${\sigma }_{\theta }=100$ kPa. This is a thin-wall estimate, not an exact tissue constitutive law.

Pressure difference, wall stress and vascular compliance answer different questions. Pressure and geometry determine the ideal force balance, while material properties determine the resulting deformation. Negative transmural pressure can favor narrowing, but the actual shape and collapse behavior also depend on support and wall mechanics. Keeping both sides of the pressure measurement explicit prevents an atmospheric gauge reading from silently replacing the physical load across the wall.