Modeling dynamic radial contrast enhanced MRI with linear time invariant systems for motion correction in quantitative assessment of kidney function.

Early identification of kidney function deterioration is essential to determine which newborn patients with congenital kidney disease should be considered for surgical intervention as opposed to observation. Kidney function can be measured by fitting a tracer kinetic (TK) model onto a series of Dynamic Contrast Enhanced (DCE) MR images and estimating the filtration rate parameter from the model. Unfortunately, breathing and large bulk motion events due to patient movement in the scanner create outliers and misalignments that introduce large errors in the TK model parameter estimates even when using a motion-robust dynamic radial VIBE sequence for DCE-MR imaging. The misalignments between the series of volumes are difficult to correct using standard registration due to 1) the large differences in geometry and contrast between volumes of the dynamic sequence and 2) the requirement of fast dynamic imaging to achieve high temporal resolution and motion deteriorates image quality. These difficulties reduce the accuracy and stability of registration over the dynamic sequence. An alternative registration approach is to generate noise and motion free templates of the original data from the TK model and use them to register each volume to its contrast-matched template. However, the TK models used to characterize DCE-MRI are tissue specific, non-linear and sensitive to the same motion and sampling artifacts that hinder registration in the first place. Hence, these can only be applied to register accurately pre-segmented regions of interest, such as kidneys, and might converge to local minima under the presence of large artifacts. Here we introduce a novel linear time invariant (LTI) model to characterize DCE-MR data for different tissue types within a volume. We approximate the LTI model as a sparse sum of first order LTI functions to introduce robustness to motion and sampling artifacts. Hence, this model is well suited for registration of the entire field of view of DCE-MR data with artifacts and outliers. We incorporate this LTI model into a registration framework and evaluate it on both synthetic data and data from 20 children. For each subject, we reconstructed the sequence of DCE-MR images, detected corrupted volumes acquired during motion, aligned the sequence of volumes and recovered the corrupted volumes using the LTI model. The results show that our approach correctly aligned the volumes, provided the most stable registration in time and improved the tracer kinetic model fit.