Theory of diaphragm structure and shape

The muscle bundles of the diaphragm form a curved sheet that extends from the chest wall to the central tendon. Each muscle bundle exerts a force in the direction of its curvature; the magnitude of this force is proportional to the curvature of the bundle. The contribution of this force to transdiaphragmatic pressure is maximal if the direction of bundle curvature is orthogonal to the surface and the curvature is maximal. That is, the contribution of muscle tension to transdiaphragmatic pressure is maximal if the muscle bundles lie along lines that are both geodesics and lines of maximal principal curvature of the surface. A theory of diaphragm shape is developed from the assumption that all muscle bundles have these optimal properties. The class of surfaces that are formed of line elements that are both geodescis and lines of principal curvature is described. This class is restricted. The lines that form the surface must lie in planes, and all lines must have the same shape. In addition, the orientation of the lines is restricted. An example of this class that is similar to the shape of the canine diaphragm is described, and the stress distribution in this example is analyzed.