Effective shear modulus reconstruction obtained with approximate mean normal stress remaining unknown.

We previously reported Methods A and B for reconstructing tissue shear modulus and density using mean normal stress as an unknown. The use of Method A enables us to obtain such reconstructions with the mean normal stress remaining unknown by using an iterative method to solve algebraic equations. However, Method A results in a low convergence speed and a low reconstruction accuracy compared with Method B that enables a reconstruction of mean normal stress together. Thus, in this report, we describe a new, rapid and accurate method, Method C, that enables the reconstructions of shear modulus and density in real time with a higher accuracy than Method A. In Method A, no reference mean normal stress is used. In Method C, an arbitrary finite value is used as a quasireference mean normal stress at an arbitrary point (i.e., a quasireference point) or an arbitrary region (i.e., a quasireference region) in the region of interest on the basis of the fact that the gradient operator implemented on the mean normal stress becomes positive-definite. When a quasireference region can be realized, Method C enables such reconstructions with a high accuracy and a high convergence speed similar to Method B. The effectiveness of Method C was verified using simulated phantom deformation data. Method C must be used instead of Method A as a practical method, in combination with Method B.