Synopsis

We present a novel method (incorporated into FSL $$$\texttt{eddy}$$$) of estimating and correcting distortions due to dynamic changes in the susceptibility field when measuring diffusion using EPI. This method is able to track how the field changes with movement using only the diffusion data itself. We demonstrate an improvement in distortion correction, compared to using a static susceptibility field, for both simulated and actual data. Additionally, we demonstrate how computationally intensive portions of the estimation algorithm can be speeded up through GPU parallelisation. Reducing the runtime increases the likelihood of this method being widely adopted and broadens its impact potential.

Introduction

Theory

When a subject's head moves in the scanner, the susceptibility field will, to a first approximation, follow the subject. But for larger movements, particularly rotations around any axis non-parallel to the magnetic flux, that approximation becomes increasingly poor. We suggest (figure 1) modelling the changing field as a first order Taylor expansion with respect to rotation around the x-axis (pitch) and y-axis (roll). This reduces the problem from estimating a field per volume to estimating two "derivative fields", where each voxel encodes the rate of change of the field with respect to rotation. A forward model was proposed to predict the signal change in each voxel, given derivative fields with respect to pitch and roll. From this we derived an inverse model (figure 2) for estimating the derivative fields from the observed volume-to-volume changes in voxelwise intensity.

The inverse model makes use of a very large, sparse matrix $$$\mathbf{X}^T\mathbf{X}$$$ which must be estimated multiple times. This is computationally expensive, but can be divided into multiple independent computations for each value. By parallelising these calculations, the single instruction, multiple data paradigm central to GPU operation was leveraged to overcome this bottleneck³.

Experiments

The method was validated using both simulations and experimental data. The simulations (where the true field and diffusion image are known) were performed using a highly realistic MRI simulator that was recently extended to include a model for how the susceptibility-induced field changes with subject movement⁴.

The experimental data consisted of a full diffusion scan on a trained and motivated subject. They remained absolutely still during one scan, followed by an identical scan where they moved at intervals of ~ten volumes. Here the diffusion weighted volumes from the "still" scan were considered ground truth when comparing the corrected images from the "movement" scan.

For both sets of data a static field was estimated from a pair of b0 images with reversed phase-encoding using FSL $$$\texttt{topup}$$$⁵. The static fields were passed, along with the data, to FSL $$$\texttt{eddy}$$$ to estimate subject movement and eddy currents. The method described here was incorporated into $$$\texttt{eddy}$$$ and the data, estimated for everything except the dynamic susceptibility field, was used as $$$\mathbf{f}$$$ and the Gaussian Process predictions as $$$\breve{\mathbf{s}}$$$ in figure 2. Movement estimates from $$$\texttt{eddy}$$$ were used as $$$\Delta\theta$$$ and $$$\Delta\phi$$$.

Results

For both simulated and human data the estimated derivative fields looked very reasonable, with a high degree of left-right symmetry and anti-symmetry with respect to pitch and roll respectively⁶. Figure 3 demonstrates that the derivative fields estimated from the simulated data showed a high degree of similarity to the true derivative fields. Figure 4 shows the that the correlation with ground truth was vastly improved when performing the dynamic susceptibility correction compared to just using a static field.

Runtime for calculating $$$\mathbf{X}^T\mathbf{X}$$$ was approximately 30x faster for the GPU over the CPU implementation. Figure 5 shows that this result should hold for a wide range of B-spline parameterisations and volume resolutions.

Discussion

The results clearly show that we are able to estimate and correct for a susceptibility field that changes dynamically as a consequence of subject movement.

The GPU performance presented is for a fairly low-end unit (GeForce GT 750M). As each value in $$$\mathbf{X}^T\mathbf{X}$$$ in calculated by an independent thread on the GPU, performance should increase even further if run on a high-end device capable of executing more threads concurrently.

Conclusion

Acknowledgements

References

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2. Anderson J, Sotiropoulos S. An integrated approach to correction for off-resonance effects and subject movement in diffusion MR imaging. NeuroImage. 2016;125:1063-1078.

3. NVIDIA. CUDA C Programming Guide. September 22, 2017. http://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html. Accessed November 7, 2017.

4. Graham M, Drobnjak I, Jenkinson M, Zhang H. Quantitative assessment of the susceptibility artefact and its interaction with motion in diffusion MR. PLOS ONE. 2017.

5. Anderson J, Skare S, Ashburner J. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage. 2003;20:870-888.

6. Sulikowska A. Motion correction in high-field MRI. PhD Thesis. University of Nottingham. 2016.