FINITE-ELEMENT ANALYSIS OF STRESS IN THE CANINE DIAPHRAGM

Stress in the diaphragm, transdiaphragmatic pressure, and diaphragm shape are interrelated by a balance of forces. Using precise in vivo measurements of diaphragm shape and transdiaphragmatic pressure distribution in combination with finite-element analysis (ANSYS), we determined the direction and magnitude of stress in the passive diaphragm at relaxation volume. Lead spheres sutured along muscle bundles identified muscle bundle location and orientation in vivo. The x, y and z coordinates of the lead spheres and entire surface of the diaphragm, excluding the zone of apposition, were determined to within 1.4 mm. Thin shell elements were used to construct a finite-element model of the diaphragm with a 2.1- to 4.2-mm internodal spacing. The diaphragm was assumed to have a uniform thickness of 2.5 mm, and magnitude and direction of the principal stresses were computed. The results show that 1) diaphragm stress is nonuniform and anisotropic (i.e., varies both with location on diaphragm surface and direction examined), 2) largest stress (sigma(1)) is aligned with muscle bundles and is two to four times larger than sigma(2) (perpendicular to sigma(1) in diaphragm plane), and 3) stress along the muscle bundle is larger in vivo under conditions of biaxial stress than at same length in vitro under uniaxial stress. Although diaphragm stress and tension have often been assumed to be uniform, our finding that stress is oriented primarily along the muscle fibers should be considered in future models of the diaphragm. Moreover, the inequality between in vivo stress and stress in an isolated muscle bundle indicates that caution is required when extrapolating in vitro muscle data to the in vivo environment.