Shape of the canine diaphragm

Abstract

In an earlier study (Angelillo M, Boriek AM, Rodarte JR, and Wilson TA. J Appl Physiol83: 1486–1491, 1997), we proposed a mathematical theory for the structure and shape of the diaphragm. Muscle bundles were assumed to lie on lines that are simultaneously geodesics and lines of principal curvature of the diaphragm surface, and the class of surfaces that are formed by line elements that are both geodesics and lines of principal curvature was described. Here we present data on the shape of the canine diaphragm that were obtained by the radiopaque marker technique, and we describe a surface that fits the data and satisfies the requirements of the theory. The costal and crural diaphragms are fit by cyclides with radii of 3.7 and 2.3 cm, respectively. In addition, the theory is extended to include the description of a joint between cyclides, and the observed properties of the joint between the costal and crural diaphragms at the dorsal end of the costal diaphragm match those required by the theory.