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

Abstract

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.

Keywords: Dynamic contrast enhanced MRI; Model based registration; Motion compensation; Quantitative MRI.

Fig. 1.

Visual abstract depicting the basic principles of this work. The DCE-MRI data acquired from the patients is misaligned due to motion and corrupted when acquired during motion events. Aligning the dynamic sequence of volumes is challenging due to differences in contrast between volumes and the presence of artifacts lowering the quality of each image. Our approach fits an LTI model to the data and reconstructs a noise and motion free sequence of dynamic template volumes. The method then registers every volume to its template with matched contrast and interpolates the outlier volumes corrupted by motion.

Fig. 2.

Line of voxels plotted over time for a sample repetition of the synthetic data experiment. Left, coronal reference image showing the line of voxels and the mask contour in red. Right, line of voxels over time for all registration methods (REFVOL, LiMo-MoCo, gPCA and No-MoCo). Overlaid, the section of the mask that corresponds to the voxels plotted. The No-MoCo panels present sharp discontinuities at the instances of motion that are corrected by the registration methods. Both REFVOL and LiMo-MoCo correctly align all the volumes, but REFVOL presents somewhat increased variability at the beginning of the sequence.

Fig. 3.

Box plot of the nRMSE between registered and ground truth volumes in the synthetic data experiments. The mean error due to alignment before registration is 2.67 in normalized units. Registration reduces the difference to 1.514 for LiMo-MoCo, 1.519 for REFVOL and 1.632 for gPCA. Both LiMo-MoCo and REFVOL attained the smallest nRMSE of the registered images.

Fig. 4.

Consistency maps with the contours of the true kidney masks for three representative repetitions of the synthetic data experiment. The maps indicate the percentage of time that a voxel has been classified as kidney for each experiment. Voxels with values ∼ 100% indicate that these were consistently classified as kidney, while voxels with values between 0% and 100% shifted classification during the sequence. The masks registered with the different algorithms present good alignment with the ground truth masks. However, most algorithms present shifts in position of the mask in 10% of the time. LiMo-MoCo was the most consistent method in time while attaining similar accuracy values with the other competing methods (DICE coefficient 0.953).

Fig. 5.

Top: Box plots with the DICE measure between the true mask and the masks aligned using the registration transforms. Bottom: Box plots of the average consistency of the registered masks. Both LiMo-MoCo and REFVOl attained the highest DICE coefficient (0.953 and 0.958), however, the masks registered with LiMo-MoCo were more self-consistent than the rest of the algorithms.

Fig. 6.

Total Variation metric applied to the concentration curves after registration of the synthetic data experiments. The metric computes the difference in absolute value between the concentration curves before and after applying Gaussian smoothing. LiMo-MoCo presented the smallest variability of all registration methods, indicating that it reduced the discontinuities created by motion.

Fig. 7.

Parameter maps obtained after fitting the tracer kinetic model to the registered data and ground truth in one repetition of the synthetic experiment. The maps show the perfusion F_P, the tubular flow F_T and the nRMSE of the model fit (i.e. the goodness of fit). The parameter maps obtained with LiMo-MoCo present the highest similarity with the ground truth (average error in F_T = 66 ± 125 and F_P = 48 ± 62). Moreover, the residual error achieved with the proposed LiMo-MoCo was the smallest compared to other competing methods (0.94 ± 4.86).

Fig. 8.

Line of voxels plotted over time for example subjects in the patient data experiments. Left, coronal reference image showing the line of voxels in red. Right, line of plots for all registration methods and the No-MoCo baseline. Before registration, the voxel intensities present small oscillations, sharp discontinuities and outliers (indicated with red arrows). All registration methods corrected the small oscillations and most discontinuities. The “Total Variation” metric for the three subjects was (0.456, 0.232 and 0.354) for LiMo-MoCo, (0.498, 0.284 and 0.420) for REFVOL, (0.469, 0.261 and0.407) for gPCA and (0.451, 0.311 and 0.419) for No-MoCo. LiMo-MoCo consistently aligned the volumes in time and corrected the volumes corrupted by motion with the LTI model.

Fig. 9.

Illustration of the temporal behavior before and after registration of a subject. Panels (a) and (b) illustrate coronal images for No-MoCo and after applying LiMo-MoCo, respectively. Panel (c) shows the signal intensity of a single voxel for No-MoCo, LiMo-MoCo and the LTI model. The position of the voxel is indicated with the red star in the coronal images and the dashed lines in panel (c) indicate the times at which the volumes in panels (a) and (b) were acquired. Before registration, the subject changes position between frames t₂ and t₄. During the motion event, the images become corrupted and all the signal is lost. LiMo-MoCo correctly aligns the sequence of volumes and inpaints the corrupted volume with the LTI model. The Total Variation metric after registration was 0.35 compared to 0.42 in the No-MoCo case.

Fig. 10.

Results of the tracer kinetic fit. Comparison between LiMo-MoCo and No-Moco of three representative subjects of the patient data experiments. Left and middle columns correspond to the filtration parameters (F_P and F_T) and right column corresponds to the nRMSE of the model fit. The nRMSE for the three subjects was (0.172, 0.102 and 0.105) for LiMo-MoCo, (0.236, 0.010 and 0.107) for REFVOL, (0.175, 0.123 and 0.128) for gPCA, (0.241, 0.147 and 0.151) for No-MoCo.After registration with LiMo-MoCo, the residual is reduced and the parameter maps allow to distinguish the cortex from the medulla of each subject.