Towards a biomechanical model of the larynx

In this paper, the development of a large-displacement large-strain 3-D finite element model of the vocal fold is reported. A fold is discretized into 720 8-node brick elements with a total of 1001 nodes and 3003 displacement degrees of freedom. The structure has realistic dimensions and geometry. The model includes geometric and material nonlinearities. The geometric nonlinearity appears in the strain-displacement relation due to the second order displacement derivatives and the material nonlinearity refers to the constitutive law. The Mooney-Rivlin rubber material formulation for an anisotropic tissue medium is used to characterize the tissue rheology. The elasticity tensor and the stress tensor for the Total Lagrangian formulation are obtained from the partial derivatives of the strain energy density function (SEDF) with respect to the Green-Lagrange strain tensor. Incompressibility constraints have been added using a mixed displacement-pressure (1 constant pressure term) finite element a hydrostatic pressure work term (Lagrange Multiplier) being added to the SEDF. The structure is subjected to a sinusoidally time-varying half cosine pressure profile applied on 117 medial surface nodes. The dynamic equilibrium equations are solved using an incremental-iterative strategy and the Newmark method of time integration for the implicit initial-boundary-value problem. The deformation of the vocal fold at various phases of the applied load was studied.