Continuum mechanical model of the tongue and mouth floor

Abstract

In this new model, the mouth floor and the tongue body are treated as blocks represented by tri-quadratic finite elements in which the muscles are modeled as continuous directed fields of the fiber direction. Collision with the hard palate and other rigid structures is modeled by subdividing the surface into small triangles for rapid collision detection and through calculating forces by a penalty method to enforce impenetrability of the rigid structures. A similar method is provided for the more complicated case of the collision between tongue body and soft floor of the mouth. The model can be coupled with a model of the jaw and hyoid where muscles may be modeled as contracting strings. The moving hyoid and jaw provide kinematic constraints for the tongue/mouth-floor model. Active muscle stress is generated by a Hill model of muscle shortening combined with a rational extension for muscle elongation, and a polynomial curve represents the relation between muscle length and stress. The stiffness matrix and damping matrix of the system (used for the implicit time stepping method solving the equations of motion) are derived directly from the continuum mechanical muscle model. An overview of the theory and numerical examples will be presented.