Inferences on passive diaphragm mechanics from gross anatomy

The diaphragm is a relatively thin curved structure that is categorized in mechanics as a membrane. Tension in the membrane is given by the product of muscle thickness and stress parallel to the fiber bundles. If all muscle fibers were cylindrical and extended from origin to insertion, the ratio of thickness near the chest wall (CW) to thickness near the central tendon (CT) would vary inversely with the ratio of CW to CT perimeters. In freshly excised diaphragms of 36 mongrel dogs, the ratios of the perimeters (CT/CW) in the right and left costal diaphragm were 0.63 +/- 0.04 and 0.62 +/- 0.04, respectively. The means of the ratio of thickness near CW to that near CT in the right and left costal regions were 0.96 +/- 0.07 and 0.95 +/- 0.05, respectively, consistent with a nearly constant relationship between costal diaphragm membrane tension and muscle stress in the direction of the fibers. In the crural diaphragm, the average ratio of the perimeters of the insertions on CT to CW was 1.16 +/- 0.10. The average ratio of thickness of crural CW to CT was 1.25 +/- 0.11. The discrepancy between the perimeter ratio and thickness ratio in the costal diaphragm is incompatible with the muscle consisting of uniform fibers extending from CW to CT. Our data suggest that muscle fibers are either in series with a smaller number along the smaller perimeter or that they terminate by tapering within the muscle bundle. Both arrangements are consistent with previous anatomic studies (Gordon et al. J. Morphol. 201: 131-143, 1989). Having a nonuniform number of fibers mechanically in series is compatible with uniform stress in the fibers if the membrane is sufficiently curved as in a domed structure.