Movement correction in DCE-MRI through windowed and reconstruction dynamic mode decomposition

Abstract

Images of the kidneys using dynamic contrast-enhanced magnetic resonance renography (DCE-MRR) contains unwanted complex organ motion due to respiration. This gives rise to motion artefacts that hinder the clinical assessment of kidney function. However, due to the rapid change in contrast agent within the DCE-MR image sequence, commonly used intensity-based image registration techniques are likely to fail. While semi-automated approaches involving human experts are a possible alternative, they pose significant drawbacks including inter-observer variability, and the bottleneck introduced through manual inspection of the multiplicity of images produced during a DCE-MRR study. To address this issue, we present a novel automated, registration-free movement correction approach based on windowed and reconstruction variants of dynamic mode decomposition (WR-DMD). Our proposed method is validated on ten different healthy volunteers' kidney DCE-MRI data sets. The results, using block-matching-block evaluation on the image sequence produced by WR-DMD, show the elimination of $99\%$ of mean motion magnitude when compared to the original data sets, thereby demonstrating the viability of automatic movement correction using WR-DMD.

Keywords: DCE-MRI; DMD; Movement correction; R-DMD; W-DMD; WR-DMD.

Fig. 1

(Top) 5 frames at time = {30,50,74,82,100}s selected from a DCE-MRI sequence of a healthy volunteer. The yellow and red reference lines show the alignment of the kidney and liver regions. The first image shows the peak stage of contrast agent inside the kidney region. The regions of kidney and liver clearly depict the translation of movements in the vertical direction, arising due to the patient movements. (Bottom) The yellow and red reference lines clearly showing the proper alignment of the kidney and liver regions after processing with WR-DMD. The video-based results can be viewed at https://youtu.be/TWq34TFGNcU and https://youtu.be/UT7f4ch4H-I (colour figure online)

Fig. 2

Flow chart showing the steps involved in the methodological framework. First, a DCE-MRI sequence consisting of N images is processed using the W-DMD algorithm in order to output each $N-2$ W-DMD components C1 and C2. At this stage, the W-DMD(C1) produces the low-rank images and W-DMD(C2) produces sparse images. W-DMD(C1) is given as an input to DMD which produces $N-3$ DMD modes. The first three DMD modes are then selected for reconstructing the motion-stabilised image sequence

Fig. 3

Methodological pipeline showing the working mechanism of W-DMD. DMD runs over the window containing first three images in the sequence, obtaining two dynamic modes. The first dynamic mode ‘c1’ capturing the low-rank image across the window and second dynamic mode c2 capturing the sparse representation. The next step exclude the first image and consider images $\{2,3,4\}$, followed by $\{3,4,5\}$ and $\{4,5,6\}$ producing c1 and c2 components. Finally, all of the c1s and c2s across all the windows are concatenated to obtain W-DMD component-1 (W-DMD (C1)) and W-DMD component-2 (W-DMD (C2))

Fig. 4

Exemplars of dynamic MR images from 10 healthy volunteers’ kidney slice produced by DCE-MRI sequence considered as 10 different data sets in this study. The images here show the central kidney slice at time 120s aortic peak enhancement after the contrast agent is injected. The yellow boundary on the kidneys is a result of manual delineation from a human expert. The mean intensity values are calculated in this region across the time producing time–intensity plots (colour figure online)

Fig. 5

Motion magnitude with respect to first image in the sequence across the data set-1

Fig. 6

(Top) five images from data set-1’s W-DMD(C1) at time = {30,50,74,82,100}s showing the low-rank images. The first image shows the peak stage of contrast agent inside the kidney region. (Bottom) Corresponding images from the W-DMD(C2) showing their sparse representation

Fig. 7

Time–intensity curves across 10 data sets (sequentially from left to right)

Fig. 8

(Top) The top six most significant DMD modes on W-DMD(C1) from data set-1. (Bottom) bottom six least significant DMD modes on W-DMD(C1)

Fig. 9

A comparison of mean motion magnitude between original and W-DMD-, R-DMD- and WR-DMD-processed image sequences. The results are shown across 10 data sets calculated using block-matching-block algorithm. A smaller mean motion magnitude indicates a more stable sequence

Fig. 10

Mean motion magnitude across 10 data sets calculated using block-matching-block algorithm utilising WR-DMD. A smaller mean motion magnitude indicates a more stable sequence. Here, M is the number of modes that were used in the reconstruction process. As the number of modes increases, the mean motion magnitude also increases

Fig. 11

Comparison with intensity-based image registration methods. Each box-plot has 10 values corresponding to 10 data sets. A smaller value in the X-axis indicates greater smoothness; so smaller is better