Pressure/Modulus Inversion for MR Elastography

(2) where T and E are the stress and strain tensors respectively. A simulated two-dimensional displacement field was created for a Gaussian shaped object contained in a square FOV. Normally distributed random values were added to simulate a maximum SNR of 200 in the displacement data. Low pass filtering by sine convolution was applied to smooth the effects of noise prior to inversion. The boundary conditions for the inversion were assigned to be constant pressure and constant elastic modulus. The solution of equation 1 was performed with a finite difference numerical method. Results Inverted pressure and modulus are plotted in figures la-b, and may be compared to the true values shown in c-d. In graphs e-f, line profiles through the centre of the above images are plotted to demonstrate quantitatively the performance of the inversion. These results indicate that the quality of the modulus reconstruction is similar to that for pressure. However, the pressure reconstruction is more sensitive to noise as SNR is reduced.