A FEM-based direct method for material reconstruction inverse problem in soft tissue elastography

A novel finite element method (FEM) based direct method is developed for the material reconstruction inverse problem in soft tissue elastography. The solution is obtained by minimising an objective function, defined as the sum of the square of the residual norms at all nodes, where the nodal residual norm is defined as a linear function of elasticity parameters of the associated elements. The measured deformation is enforced directly and satisfying the equilibrium at every node is utilised as the optimisation objective. As a result, the soft tissue elastography can be obtained directly by solving the resulting set of linear equations.