[Paper Review] Model-based reconstruction of non-rigid 3D motion-fields from minimal $k$-space data: MR-MOTUS

Niek R. F. Huttinga, Cornelis A. T. van den Berg+2 more|arXiv (Cornell University)|Feb 15, 2019

Advanced MRI Techniques and Applications49 references4 citations

TL;DR

MR-MOTUS introduces a model-based framework for direct reconstruction of 3D non-rigid motion-fields from highly undersampled k-space data, leveraging a novel signal model that links k-space to motion-fields via deformation of a reference image. It achieves state-of-the-art motion reconstruction quality at undersampling factors up to 63 (non-rigid respiratory) and 474 (rigid head motion), enabling high spatio-temporal resolution motion estimation without image reconstruction bottlenecks.

ABSTRACT

Estimation of internal body motion with high spatio-temporal resolution can greatly benefit MR-guided radiotherapy/interventions and cardiac imaging, but remains a challenge to date. In image-based methods, where motion is indirectly estimated by reconstructing and co-registering images, a trade off between spatial and temporal resolution of the motion-fields has to be made due to the image reconstruction step. However, we observe that motion-fields are very compressible due to the spatial correlation of internal body motion. Therefore, reconstructing only motion-fields directly from surrogate signals or k-space data without the need for image reconstruction should require few data, and could eventually result in high spatio-temporal resolution motion-fields. In this work we introduce MR-MOTUS, a framework that makes exactly this possible. The two main innovations of this work are (1) a signal model that explicitly relates the k-space signal of a deforming object to general non-rigid motion-fields, and (2) model-based reconstruction of motion-fields directly from highly undersampled k-space data by solving the corresponding inverse problem. The signal model is derived by modeling a deforming object as a static reference object warped by dynamic motion-fields, such that the dynamic signal is given explicitly in terms of motion-fields. We validate the signal model through numerical experiments with an analytical phantom, and reconstruct motion-fields from retrospectively undersampled in-vivo data. Results show that the reconstruction quality is comparable to state-of-the-art image registration for undersampling factors as high as 63 for 3D non-rigid respiratory motion and as high as 474 for 3D rigid head motion.

Motivation & Objective

• To overcome the temporal-spatial resolution trade-off in dynamic MRI by bypassing image reconstruction and directly estimating motion-fields from k-space data.
• To address the challenge of high data acquisition rates in MR-guided radiotherapy and cardiac imaging by enabling high frame-rate motion estimation.
• To exploit the inherent compressibility of motion-fields to reconstruct accurate 3D non-rigid motion from minimal k-space data.
• To develop a signal model that explicitly relates k-space data to general non-rigid motion-fields, enabling direct inversion.

Proposed method

• Derive a dynamic MR signal model that expresses k-space data as a function of non-rigid motion-fields by warping a static reference image.
• Formulate the motion reconstruction as an inverse problem: recover motion-fields directly from highly undersampled k-space data using the derived signal model.
• Use a type 3 Non-Uniform Fast Fourier Transform (NUFFT) to efficiently compute the forward and adjoint operations required in the optimization.
• Apply a model-based optimization framework that enforces motion-field smoothness and consistency with the k-space measurements.
• Downsample the reference image to reduce computational cost without degrading motion-field reconstruction quality.
• Leverage the compressibility of motion-fields to enable high undersampling factors while preserving reconstruction fidelity.

Experimental results

Research questions

• RQ1 Can non-rigid 3D motion-fields be reconstructed directly from highly undersampled k-space data without intermediate image reconstruction?
• RQ2 How well does the proposed signal model based on image warping capture the relationship between k-space data and complex motion-fields?
• RQ3 What is the maximum achievable undersampling factor for accurate 3D non-rigid motion reconstruction using this model-based approach?
• RQ4 How does the reconstruction quality of MR-MOTUS compare to state-of-the-art image registration methods under extreme undersampling?
• RQ5 Can the framework be extended to real-time applications with minimal computational delay?

Key findings

• MR-MOTUS achieves motion-field reconstruction quality comparable to state-of-the-art image registration at an undersampling factor of 63 for 3D non-rigid respiratory motion.
• For 3D rigid head motion, the method maintains high reconstruction quality at an undersampling factor as high as 474.
• The reconstruction quality remains robust even when the reference image is downsampled by a factor of two, reducing computation time and memory usage.
• The type 3 NUFFT computation is the primary bottleneck, accounting for ~80% of reconstruction time, suggesting significant speedup is possible with GPU acceleration.
• The method is insensitive to minor violations of mass conservation and steady-state magnetization assumptions, especially in the central FOV, indicating robustness to physiological and field inhomogeneity effects.
• A GPU-optimized implementation is expected to accelerate reconstruction by 10–50 times, making real-time online motion reconstruction feasible.