Resimulation of noise: A precision estimator for least square error curve-fitting tested for axial strain time constant imaging

Recent elastography techniques focus on imaging information on properties of materials which can be modeled as viscoelastic or poroelastic. These techniques often require the fitting of temporal strain data, acquired from either a creep or stress-relaxation experiment to a mathematical model using least square error (LSE) parameter estimation. It is known that the strain versus time relationships for tissues undergoing creep compression have a non-linear relationship. In non-linear cases, devising a measure of estimate reliability can be challenging. In this article, we have developed and tested a method to provide non linear LSE parameter estimate reliability: which we called Resimulation of Noise (RoN). RoN provides a measure of reliability by estimating the spread of parameter estimates from a single experiment realization. We have tested RoN specifically for the case of axial strain time constant parameter estimation in poroelastic media. Our tests show that the RoN estimated precision has a linear relationship to the actual precision of the LSE estimator. We have also compared results from the RoN derived measure of reliability against a commonly used reliability measure: the correlation coefficient (CorrCoeff). Our results show that CorrCoeff is a poor measure of estimate reliability for non-linear LSE parameter estimation. While the RoN is specifically tested only for axial strain time constant imaging, a general algorithm is provided for use in all LSE parameter estimation.