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

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Abstract
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 that 1) costal diaphragm shape is similar at functional residual capacity and end inspiration regardless of whether the diaphragm muscle shortens actively (increased tension) or passively (decreased tension); 2) diaphragmatic muscle length changes minimally in the direction transverse to the muscle fibers, suggesting the diaphragm may be inextensible in that direction; and 3) the central tendon is not stretched by physiological stresses. A two-dimensional orthotropic material has two different stiffnesses in orthogonal directions. In the plane tangent to the muscle surface, these directions are along the fibers and transverse to the fibers. We wondered whether orthotropic material properties in the muscular region of the diaphragm and inextensibility of the central tendon might contribute to the constancy of diaphragm shape. Therefore, in the present study, we examined the effects of stiffness transverse to muscle fibers and inextensibility of the central tendon on diaphragmatic displacement and shape. Finite element hemispherical models of the diaphragm were developed by using pressurized isotropic and orthotropic membranes with a wide range of stiffness ratios. We also tested heterogeneous models, in which the muscle sheet was an orthotropic material, having transverse fiber stiffness greater than that along the fibers, with the central tendon being an inextensible isotropic cap. These models revealed that increased transverse stiffness limits the shape change of the diaphragm. Furthermore, an inextensible cap simulating the central tendon 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 changes of diaphragm shape are restricted because the central tendon is essentially inextensible and stiffness in the direction transverse to the muscle fibers is greater than stiffness along the fibers.

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