Dynamic contrast enhanced (DCE) MRI is a widely used method to determine functional parameters in different organs such as the kidney or the heart. Fast MRI sequences are used to obtain a time-series of images during and after the administration of constrast agent. The time course of the contrast-media dynamic is then the basis for pharmacokinetic modelling. However, acquisition times in order of minutes cause an inter-frame misalignment due to physiological motion such as breathing which obstructs a pixel by pixel analysis of DCE data. Motion correction with conventional registration methods typically fails as the mixing of breathing motion and contrast agent related changes does not satisfy the related cost-function.¹

A promising approach to overcome this problem is to generate a virtual time series with reduced motion but sustained contrast dynamic to use as a virtual template (VT) in an iterative registration process (see Figure 1). Pairs of the motion corrupted time series and the VT then exhibit similar intensity, which suits conventional registration methods.

This approach was already explored^2,3,4 differing in the way to generate the VT. In this work we investigated different approaches in VT-generation and evaluated the results on a synthetic kidney phantom and in-vivo cardiac perfusion data.

The method of VTR uses an iterative registration of the time corrupted sequence onto a motion-less template. The registered time-series is then again used to generate a VT, which results in a more precice registration-template at each step. We used a fixed number of 10 iterations and the free-form-deformation registration with the bending energy regularization set to 0.1.⁵

The first approach in generating a VT $$$I_{vt}$$$ was to temporally smooth (TS) the motion corrupted sequence $$$I_{mc}$$$ for each fixed spatial location by solving³:

$$I_{vt}=\arg\min_I\int_0^T[|I(x,t)-I_{mc}(x,t)|^2]+\alpha|\delta_tI(x,t)|^2dt$$

The second approach was to use the Low-Rank component $$$L$$$ of the motion-corrupted sequence as a template, by solving the Low-Rank Sparse decomposition, given as⁶:

$$\min||L||_*+\lambda||S||_1\quad\text{s.t.}\quad~L+S=I_{mc}$$

The low-rank component contains the slow changing components (background and little contrast dynamic), movement and contrast dynamic are stored in the sparse component. The last approach uses an Independent-Component Analysis (ICA) to remove breathing motion.² Motion related components were automatically detected and removed by determining the variation in the IC-Mixing Matrix.

The methods were tested on a synthetic kidney phantom consisting of three compartements with known contrast dynamic. Accuracy of the VTR-results was computed in two ways: First, we compared the ground-truth contrast-media dynamic to the VTR-results by computing the mean RMSE over all pixel to show the global accuracy of the contrast-media dynamic. Second, we computed the Structural Similarity Index Measure (SSIM) to the ground truth at every time-step and averaged over time to get a measure of structural accuracy.

All VTR-methods were tested using in-vivo contrast-enhanced myocardial perfusion data acquired during an incomplete breathold. Imaging was done on a 3T-MR-system with a Turbo Flash sequence and the following parameter: TR/TE/FA=2.12ms/1.05ms/12$$$^\circ$$$, resolution: 2.8x2.8mm$$$^2$$$, 80 frames and an acquisition length of 56s.

VTR-results of the synthetic kidney phantom are shown in Figure 2. The ICA-approach is able to handle not only the strong contrast dynamic at the beginning, where the TS-approach fails, but also the slow variation in the end, where the LS-approach fails. This result is in accordance with the similarity measures shown in Table 1. Template-generation with ICA delivers the most accurate contrast-media dynamic (lowest mean RMSE), however, the structural similarity is slightly higher in the LS approach. The TS-approach yields more inaccurate results because the temporal smoothing deforms the morphology of the virtual templates to a certain extent, hence the registration result is also deformed compared to the ground truth.

The proposed methods are also suitable for breathing correction of cardiac perfusion data as can be seen in Figure 4: According to the results of the kidney phantom template generation with ICA globally yields the most accurate contrast-media dynamic, whereas morphological structure is best preserved with the LS-method.

By generating a synthetic kidney phantom with known constrast-media dynamic we were able to asses the accuracy of different VTR-registration approaches and identified the method of ICA-template-generation as the most accurate method. The numerical findings were succesfully adopted for the clinically relevant situation of cardiac perfusion imaging with incomplete breathold.