Evaluation of the Standard Error of the Regression and Coefficient of Determination as goodness-of-fit parameters for Reverberant Shear Wave Elastography

Several studies of Reverberant shear wave elastography (R-SWE) have shown its potential for clinical applications. Previous studies of R-SWE present a shear wave speed (SWS) estimation based on a curve-fitting of the regression of Bessel functions to find the wavenumber. Recently, the coefficient of determination (R
²
) was proposed as a goodness-of-fit (GoF) parameter, however, this parameter is not optimal for non-linear fit according to the literature. For this reason, this study proposes the Standard error of the regression (S) as a (GoF). Numerical simulations were performed for 10 000 plane waves to produce a reverberant field. S and R
²
parameters were evaluated using a vibration frequency from 300 to 900 Hz with steps of 200 Hz. Besides, this study suggests a threshold value to reduce estimation error with S. Experiments showed negative values for R
²
even with 10 000 plane waves. Finally, a threshold of 0.15 for S reduced the bias and coefficient of variation, preserving a major percentage of information.