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Motion Modelling and Analysis Group

School of Biomedical Engineering and Imaging Sciences,

King's College London

Imaging Motion

Dynamic MR Imaging Using Manifold Alignment

(Funded by EPSRC grants EP/H046410/1 and EP/M009319/1)

Estimating respiratory motion inside the lungs is useful for a range of clinical applications. However, estimating lung motion using MR has known problems: dynamic 3D images have poor contrast and resolution, so motion estimates tend to be interpolated from the high contrast areas at the lung boundary. However, dynamic 2D MR imaging has good resolution and excellent vessel contrast, due to the in-flow effect of unpolarised blood (see movies below)

Dynamic 3D MR imaging of the lungs.
Dynamic 2D MR imaging of the lungs.

This work aimed to combine the contrast/resolution advantages of 2D MR with the coverage of 3D MR. The technique used dynamic 2D coronal images acquired at shifting slice positions. A novel simultaneous groupwise manifold alignment scheme was then used to find motion state correspondences between the slices from different positions. This enabled them to be stacked into high resolution, high contrast 3D volumes (see movie below).

Retrospectively stacked dynamic 3D MR imaging of the lungs using manifold alignment.


This work was subsequently extended, resulting in a manifold alignment scheme that did not require any inter-dataset comparisons between the high-dimensional data. Normally, such comparisons are an essential part of manifold alignment schemes, but in medical imaging it is often not feasible. For example, MR slices acquired at different positions image different parts of the anatomy, so direct comparison of the images is not meaningful. We developed a scheme based on graph theory that enabled signature vectors to be assigned to each node (i.e. 2D image). These signatures were characteristic of the local graph structure of the node, and were used in place of the imaging data as the high-dimensional data in the inter-dataset comparison. The resulting technique, which we term self-aligning manifolds, was one of very few manifold alignment techniques to work in this way, and it enabled the application of manifold alignment for the first time in applications featuring highly dissimilar medical image datasets.

Ultrasound gating
Respiratory gated compounded ultrasound volumes of the liver using self-aligning manifolds: (left) gates 1-8 shown in aligned manifold space of two ultrasound views; (right) animation of compounded gates with number in top-left corresponding to gate number in left figure.

Dynamic 3D MR volumes of the thorax, retrospectively stacked from dynamic 2D MR: (left) animation of coronal slice through volumes; (right) low dimensional embedding of 2D slices with colour indicating slice position. Circle indicates current input slice.


The work described above performed manifold alignment of reconstructed 2D imaging data. This places a fundamental limit on the achievable temporal resolution to the amount of time it takes to acquire enough k-space data to reconstruct each image. In subsequent work we extended the concept to perform manifold alignment of the 3D k-space data themselves, which enables much higher temporal resolution. This work built on the self-aligning manifolds work, and resulted in a scheme capable of retrospectively reconstructing dynamic images with high spatial and temporal resolution.

Retrospectively reconstructed 3D dynamic MR images using manifold alignment of k-space data: 3rd, 4th, 5th and 6th sagittal slices through the volume and the maximum intensity projection.


The graph-based signatures employed by the self-aligning manifolds work have since been developed, resulting in a new technique based on wave kernel signatures which also permits the contributions of the different datasets to the aligned manifold to be individually weighted. This has been demonstrated to produce superior performance on the problem of 4D MR slice stacking and was also demonstrated on semi-supervised alignment of simultaneously acquired PET and MR data.