Identification of muscle activity in tongue motion during swallowing through medical image data

Abstract

This paper presents a formulation to identify muscle activities from the variation in shapes of organs during swallowing. We assume that each organ consists of a three-dimensional hyperelastic body, and the contraction movement of the muscle is caused by a contractive inelastic stress in the organ. A function distributed in the organ domain to control the magnitude of the inelastic stress is chosen as a design variable in the same manner as the density in the topology optimization problem of density variation type. The identification problem is formulated as a problem of determining the design variable that minimizes an objective cost function defined by the squared L² norm of the reaction force in the normal direction on the boundary when an enforced displacement to fit the varied boundary of the organ and the inelastic stress modeling the muscle activity are applied. The finite deformation problem of the hyperelastic body is analyzed using the finite element method. The direction of the muscle fiber is assumed to be the direction of the minimum principal stress obtained as the solution to the finite deformation problem. The solution to the identification problem is presented based on a scheme using the H¹ gradient method for the topology optimization problem of density variation type. A numerical example using a previously developed model of the tongue is introduced to demonstrate the effectiveness of the proposed approach.