Is fitting error a reliable metric for assessing deformable motion correction in quantitative MRI?

Quantitative MR (qMR) can provide numerical values representing the physical and chemical properties of the tissues. To collect a series of frames under varying settings, retrospective motion correction is essential to align the corresponding anatomical points or features. Under the assumption that the misalignment makes the discrepancy between the corresponding features larger, fitting error is a commonly used evaluation metric for motion correction in qMR. This study evaluates the reliability of the fitting error metric in cardiac diffusion tensor imaging (cDTI) after deformable registration. We found that while fitting error correlates with the negative eigenvalues, the negative Jacobian Determinant increases with broken cardiomyocytes, indicated by helix angle gradient line profiles. Since fitting error measures the distance between moved points and their re-rendered counterparts, the fitting parameter itself may be adjusted due to poor registration. Therefore, fitting error in deformable registration itself is a necessary but not sufficient metric and should be combined with other metrics.