An Overdetermined System of Transform Equations in Support of Robust DCE-MRI Registration with Outlier Rejection

Quantitative hepatic perfusion parameters derived by fitting dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) of liver to a pharmacokinetic model are prone to errors if the dynamic images are not corrected for respiratory motion by image registration. The contrast-induced intensity variations in pre- and postcontrast phases pose challenges for the accuracy of image registration. We propose an overdetermined system of transformation equations between the image volumes in the DCE-MRI series to achieve robust alignment. In this method, we register each volume to every other volume. From the transforms produced by all pairwise registrations, we constructed an overdetermined system of transform equations that was solved robustly by minimizing the L_1/2-norm of the residuals. This method was evaluated on a set of 100 liver DCE-MRI examinations from 35 patients by examining the area under spikes appearing in the voxel time–intensity curves. The robust alignment procedure significantly reduced the area under intensity spikes compared with unregistered volumes (P < .001) and volumes registered to a single reference phase (P < .001). Our registration procedure provides a larger number of reliable time–intensity curve samples. The additional reliable samples in the precontrast baseline are important for calculating the postcontrast signal enhancement and thereby for converting intensity to contrast concentration. On the intensity ramp, retained samples help to better describe the uptake dynamics, providing a better foundation for parameter estimation. The presented method also simplifies the analysis of data sets with many patients by eliminating the need for manual intervention during registration.