Effects of transverse fiber stiffness and central tendon on displacement and shape of a simple diaphragm model

Boriek, Aladin M., and Joseph R. Rodarte. Effects oftransverse fiber stiffness and central tendon on displacement and shapeof a simple diaphragm model. J. Appl. Physiol. 82(5): 1626-1636, 1997.Our previous experimental results (A. M. Boriek, S. Lui, and J. R. Rodarte. J. Appl. Physiol. 75:527-533, 1993 and A. M. Boriek, T. A. Wilson, and J. R. Rodarte.J. Appl. Physiol. 76: 223-229, 1994) showed that1) costal diaphragm shape is similar at functional residualcapacity and end inspiration regardless of whether the diaphragm muscleshortens actively (increased tension) or passively (decreased tension);2) diaphragmatic muscle length changes minimally in thedirection transverse to the muscle fibers, suggesting the diaphragm maybe inextensible in that direction; and 3) the central tendon isnot stretched by physiological stresses. A two-dimensional orthotropicmaterial has two different stiffnesses in orthogonal directions. In theplane tangent to the muscle surface, these directions are along thefibers and transverse to the fibers. We wondered whether orthotropicmaterial properties in the muscular region of the diaphragm andinextensibility of the central tendon might contribute to the constancyof diaphragm shape. Therefore, in the present study, we examined theeffects of stiffness transverse to muscle fibers and inextensibility ofthe central tendon on diaphragmatic displacement and shape. Finiteelement hemispherical models of the diaphragm were developed by usingpressurized isotropic and orthotropic membranes with a wide range ofstiffness ratios. We also tested heterogeneous models, in which themuscle sheet was an orthotropic material, having transverse fiberstiffness greater than that along the fibers, with the central tendonbeing an inextensible isotropic cap. These models revealed thatincreased transverse stiffness limits the shape change of thediaphragm. Furthermore, an inextensible cap simulating the centraltendon dramatically limits the change in shape as well as the membrane displacement in response to pressure. These findings provide a plausible mechanism by which the diaphragm maintains similar shapes despite different physiological loads. This study suggests that changesof diaphragm shape are restricted because the central tendon isessentially inextensible and stiffness in the direction transverse tothe muscle fibers is greater than stiffness along the fibers.