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.