Reconstructions of shear modulus, poisson´s ratio, and density using approximate mean normal stress /spl lambda//spl epsiv//sub /spl alpha//spl alpha// as unknown

As a differential diagnosis technique for living soft tissues, we are developing ultrasonic-strain-measurement-based shear modulus reconstruction methods. Previously, we reported three-dimensional (3D) and 2D reconstruction methods utilizing a typical Poisson´s ratio very close to 0.5 (nearly incompressible). However, because a decrease in the accuracy of the reconstructed value was confirmed to be due to the difference between the original value and the set value, we proposed 3D and 2D methods of reconstructing Poisson´s ratio as well. Furthermore, we proposed methods of reconstructing density and dealing with dynamic deformation. However, due to tissue incompressibility, the reconstructions of shear modulus, Poisson´s ratio, and density became unstable. In this report, to obtain stable, unique reconstructions, we describe a new reconstruction method using mean normal stress approximated by the product of one of Lame´s constants lambda and volume strain epsiv_alphaalpha as an unknown. Regularization is simultaneously applied to the respective distributions to decrease the instability of the reconstructions due to measurement errors of the deformation. This method also enables stable, unique reconstructions of shear modulus and density under the condition that the mean normal stress remains unknown. We also verify the effectiveness of this method through 3D simulations, while showing erroneous artifacts occurring when 2D and 1D reconstructions are performed