The shape of the diaphragm dome was calculated from transdiaphragmatic pressure and tension in the diaphragm. It was assumed that the muscle acts as a free membrane, attached at its edges to the inside of a vertical rib cage circular in cross section, that the attachments are inferior to the point at which the dome makes contract with the rib cage, and that the abdomen is filled with fluid with a hydrostatic gradient in pressure. The shape is different from a section of a sphere, with a radius of curvature substantially greater at the apex of the dome than at the sides. Observed shapes of human hemidiaphragm domes at functional residual capacity are not spherical but closely match the calculated shapes. Best-fitting shapes correspond to transdiaphragmatic pressures of about 3 cmH2O transdiaphragmatic pressure, suggesting that such a pressure and corresponding tension are present in the human diaphragm when it is at rest in an erect subject. In this model; as lung volume increases and the diaphragm shortens, its shape changes in such a way that the ratio between transdiaphragmatic pressure and tension in the diaphragm remains nearly constant, rather than increasing with volume. Such a model can explain the observation that the length-tension relationship of the muscle is much more important than curvature in determining the effectiveness of the diaphragm as a pressure generator.
A scalable bubble‐free membrane aerator for biosurfactant pro‐ duction