Estimation of shear modulus distribution in soft tissue from strain distribution

In order to obtain noninvasively quantitative static mechanical properties of living tissue, the authors propose a new type of inverse problem by which the spatial distribution of the relative elastic modulus of the tissue can be estimated only from the deformation or strain measurement. The living tissue is modeled as a linear isotropic incompressible elastic medium which has the spatial distribution of the shear modulus, and the deformation or strain is supposedly measured ultrasonically. Assuming that there is no mechanical source in the region of interest, the authors derive a set of linear equations in which unknowns are the spatial derivatives of the relative shear modulus, and the coefficients are the strain and its spatial derivatives. By solving these equations, the spatial derivatives of the relative shear modulus are determined throughout the region, from which the spatial distribution of the relative shear modulus is obtained by spatial integration. The feasibility of this method was demonstrated using the simulated deformation data of the simple inclusion problem. The proposed method seems promising for the quantitative differential diagnosis on the lesion in the tissue in vivo.