Physics

Internal medicine

Inverse problem

Meteorology

Contraction (grammar)

Mathematics

Boundary (topology)

Mathematical optimization

Mathematical analysis

Optimization problem

Political science

Boundary value problem

Norm (philosophy)

Deformation (meteorology)

Applied mathematics

Medicine

The Proceedings of OPTIS

This paper presents a formulation and solution of an identification problem of the muscle activities in an organ when a deformation of the organ was observed on boundary. This study is motivated by a medical interest of wishing to know the mechanism of swallow motion and cause of aspiration. In order to elucidate the mechanism, it is necessary to identify the contraction movement of the muscles. In this study, we assume that an organ consists of hyper elastic body, and the contraction movement is a finite deformation due to the generation of the anisotropic and inelastic strain. The strain is modeled as a function of a design variable which controls the contraction rate. Based on the assumption, we formulate a state determination problem of hyper elastic deformation by the compulsory displacement on the observed boundary using a given data. Using its solution, we define an objective function by the integral of the squared norm of the reaction force over the observed boundary, and construct an optimization problem seeking the design variable that minimize the objective function. Solution of the problem is presented as an iterative scheme using the H1 gradient method for topology optimization problem of density type. Numerical examples for a cubic and cylinder bodies demonstrste that the deformations are reproduced by the identified design variables.

Formulation of muscle activity identification problem from shape observation and its solution