Motion correction in Dynamic Contrast-Enhanced MRI (DCE-MRI) is challenging because of the signal intensity changes caused by the contrast-agent passage. Tracer-kinetic model-driven registration presents an attractive solution [1-3] but previous methods are limited to the 3-parameter modified-Tofts model. This model is not suitable for high-temporal resolution data aimed at a separate measurement of perfusion and permeability [4].

In this study we propose a generalisation that uses a 4-parameter 2-compartment tracer-kinetic model and image registration by free-form deformation (FFD). The methos is evaluated using 2D simulations and patient data in the kidney.

Algorithm

The breathing-induced deformation fields are initialised and the following steps are iterated:

(1) Create motion-corrected data by applying the current deformation field for each time-point to the measured source data;

(2) Create a target for registration by pixel-based fitting of the two-compartment filtration model (2CFM) to the motion-corrected data [4,5];

(3) Update the deformation fields for each time-point by FFD-based coregistration of the measured source data with these targets.

A multiresolution strategy is used to improve convergence and reduce computation time, exploiting the fact that breathing motion has comparatively low spatial resolution. The algorithm is initially performed using a 2x2 FFD and then repeated at 4x4 and 8x8. Each time the output of the previous level is interpolated to initialise the next. 8 iterations are performed at each resolution level.

Implementation details: The deformation field is applied by bilinear interpolation to the image matrix size. The 2CFM fit is performed using a measured AIF in the aorta and a fast linear fit [5]. The similarity measure for registration is the sum of squared differences between deformed source and target. It is minimized using a gradient-descent method (200 steps) with numerical estimation of the gradient and a backtracking line-search (precision of 1 image pixel).

Data generation

Patient data: A renal DCE-MRI dataset was used for evaluation: measured in free breathing using coronal 2D SR-TurboFLASH at 1.5T (4 slices, 120 dynamics, 1.1s intervals, matrix 216x216). A standard dose of contrast-agent was injected at 3ml/s.

Synthetic data: A simple synthetic phantom of the kidneys was used to generate data (120 dynamics, 1.1s intervals, matrix 128x128) with a literature-based AIF [6], a 2CFM and literature values for the tissue parameters [4]. Two types of motion applied sinusoidal vertical shifts (rigid) and nonrigid motion derived from the patient data.

Evaluation

The algorithm was implemented in IDL on a standard desktop PC (3.4GHz, 32GB). The results were evaluated by visual comparison of corrected and uncorrected images and by computing the relative error between the reconstructed and corresponding ground truth parameters.

Fig.1 shows the effect of motion correction on the data. The algorithm removes the motion without affecting the signal intensities.

Fig.2 shows the effect of motion correction on parametric maps. Organ boundaries are blurred if motion is uncorrected, but sharply delineated after registration (yellow arrow). This significantly improves delineation of smaller anatomical structures (red arrow).

Fig.3 shows the effect of motion correction in the temporal profiles. Original time-intensity curves show large respiratory signal changes which are notably reduced.

Fig.4 shows that uncorrected motion strongly reduces accuracy and precision at a wide range of noise levels.

Fig.5 shows the same results after motion correction, demonstrating that the algorithm removes the motion-induced errors almost completely.

The algorithm fully removes the motion-induced parameter error, creating a result that is virtually identical to the motion-free case. Importantly, motion correction does not increase the parameter error in motion-free data (compare top rows of fig 4 and 5). In fact, in this highly uniform phantom the small residual deformation fields have a smoothing effect that actually improves the parameter precision.

Even though a renal cortical model is used (2CFM), the method is essentially tissue-independent as any 2-compartment model will provide the same fit. This is illustrated by the patient data, as the registration works equally well in liver, spleen and renal medulla.

A key problem that remains is the long computation time: registration for the simulated dataset took 14mins using 2 resolution levels (2x2, 4x4). For the patient data this was 6hrs for 3 resolution levels (2x2, 4x4, 8x8). However, the algorithm has not been optimised for speed and there is significant room for improvement.

Tracer-kinetic model-driven registration with a 4-parameter model and FFD at low spatial resolution provides accurate motion correction without affecting signal-intensity changes. The method is essentially tissue independent and unsupervised, and is therefore applicable to other organs and tissue types. Evaluation in more patient data is needed, as well as application in 3D.