Biaxial constitutive relations for the passive canine diaphragm

Abstract

Samples of the muscular sheet excised from the midcostal region of dog diaphragms were subjected to biaxial loading. That is, stresses in the direction of the muscle fibers and in the direction perpendicular to the fibers in the plane of the sheet were measured at different combinations of strains in the two directions. Stress-strain relations were obtained by fitting equations to these data. In the direction of the muscle fibers, for strains up to 0.7, stress is a modestly nonlinear function of strain and ranges up to approximately 60 g/cm. In the direction perpendicular to the fibers, the sheet is stiffer and more strongly nonlinear. At a strain in the perpendicular direction of approximately 0.35, stress increases abruptly. The stress-strain relation in the muscle direction is consistent with observations of passive muscle shortening in vivo. However, the stiffness in the perpendicular direction is not high enough to explain the observation that strains in the perpendicular direction in vivo are nearly zero. We conclude that, in the passive diaphragm in vivo, stress in the direction perpendicular to the muscle fibers is small.

Shape and tension distribution of the active canine diaphragm

“…Averaging values for these tension contours therefore provides approximations for 1 in their corresponding regions, yielding tensions of 16.9 and 14.2 for costal and crural region, respectively. Taking into account thickness of 0.30 cm in the crural muscle and 0.17 cm in the dorsal region of the costal diaphragm (4, 12), our results yield predicted stress of 56.3 and 83.5 g/cm 2 , respectively. Skeletal muscle is incompressible and does not change volume as it shortens.…”

“…Our published data on diaphragm mechanics in dogs demonstrated radius of curvature in the midcostal region of the diaphragm ranging from 4.8 to 5.3 cm with little effect of lung volume or level of muscle activation (7). Assuming a P di of 6.5 g/cm 2 , and 5 cm radius of curvature, the predicted tension along the direction of costal muscle fibers would be 32.5 g/cm, consistent with current data in Fig. 5A showing maximal tension along the direction of costal muscle fibers reaches a peak of 29 g/cm.…”

“…In contrast, the diaphragm uniquely supports stress in the direction transverse to the muscle fibers even if greater stress were present in the direction of muscle fibers. Data from uniaxial in vitro experiments may not accurately represent physiological behavior of the diaphragm muscle because it is being subjected to a pressure load in vivo, and very limited physiological data exist on the canine diaphragm under biaxial loading in vitro (2,19). Recently, we conducted biaxial loading tests of muscular sheets excised from the midcostal region of the dog diaphragm (2) and found that the muscle sheet is more compliant and considerably more extensible in the direction of the muscle fibers.…”

“…In our study we report tension values computed from the finite element analysis in grams per centimeter. We used a P di of 6.5 g/cm 2 and a uniform thickness of 0.25 cm, which is about the same thickness as that of the unloaded left midcostal region of the diaphragm. Tension in the costal muscle of the dog diaphragm was nonuniform, and tension along the fibers was severalfold greater than tension in the transverse direction.…”

“…That is, the diaphragm experiences loads both along and transverse to the direction of the fibers. Therefore, data from uniaxial loading cannot be extrapolated to accurately analyze physiological behavior of the intact diaphragm, and the data available on the mechanical properties of the diaphragm muscle under passive biaxial loading are limited (2,19). Previously, we measured shape and tension in the intact pressurized rat diaphragm, and other investigators measured these variables in the dog (6,14).…”