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Extended multi-shell diffusion acceleration with Gaussian processes estimated reconstruction (ems-DAGER)1Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, UK, Oxford, United Kingdom
Synopsis
Keywords: Image Reconstruction, Diffusion/other diffusion imaging techniques, Signal modelling
Diffusion-weighted MRI suffers from relatively long acquisition time, especially for high spatial- resolution and/or high angular- resolution acquisitions. Thus, methods to increase the acquisition speed are urgently needed. Recently, increasing attention has been paid to utilize the relations between k- and q-space points for further acceleration. Here, we extend the Diffusion Acceleration with Gaussian process Estimated Reconstruction (DAGER) to leverage shared information in multi-shell acquisitions and incorporate eddy-induced distortion correction.Introduction
High spatial- and angular- resolution dMRI can benefit neuroscience with more accurate characterization of tissue properties at the cost of longer scan times1-2. A range of methods to accelerate dMRI acquisition have been proposed including traditional k-space acceleration3-5, q-space acceleration6-7 and joint k-q acceleration methods8-10. Diffusion Acceleration with Gaussian process Estimated Reconstruction (DAGER)11 achieves highly accelerated dMRI by exploiting q-space smoothness with Gaussian processes12 to inform undersampled k-space reconstruction.Currently, DAGER has two major limitations. First, it can only reconstruct single-shell dMRI data, which is not compatible with advanced biophysical models13-14. Second, to minimize the impact of eddy current distortions, antipodal symmetric property of q-space signal has not been utilized, which limits the potential of DAGER for achieving higher accelerations. In this work, we extend DAGER for multi-shell acquisition (ems-DAGER) and incorporate eddy-current distortion correction into a joint k-q reconstruction. We demonstrate improvements of ems-DAGER for multi-shell data using highly-realistic simulations.
Method
Multi-shell DAGERDAGER uses Gaussian Processes (GP) to model dMRI signals15. For single-shell dMRI data, the covariance of signals on the q sphere is characterised using a spherical covariance function :
$$c(x,x′)=C_\theta (arccos|⟨g,g′⟩|;a) (1)$$
with
$$C(\theta)=\begin{array}{l} \\ \left\{\begin{matrix} 1-\frac{3\theta }{2a} +\frac{\theta ^{3} }{2a^{3} } \ \theta < a\\ 0\ \theta \ge a\end{matrix}\right. \end{array} (2)$$
where $$$x$$$ refer to dMRI signals from different diffusion directions, $$$g$$$ refers to the diffusion direction, $$$\theta$$$ represents the angular difference and $$$a$$$ is a hyperparameter controlling signal smoothness within a shell.
To exploit shared information cross shells, we extend the single-shell DAGER to multi-shell by adding a squared-exponential function to the GP covariance function:
$$c(x,x′)=C_\theta (arccos|⟨g,g′⟩|;a)exp(-\frac{(logb-logb')^2}{2l^2} ) (3)$$
where $$$b$$$ is the b value, $$$l$$$ is a hyperparameter controlling signal smoothness between shells. With this formulation, sharable information between different shells can be incorporated into the reconstruction as shown in Fig.1 (a).
ems-DAGER incorporates GP estimated multi-shell dMRI signal as a prior and solves the following reconstruction problem:
$$u=\min_{u} (\frac{1}{2\sigma _k^2}\left \| Au-d \right \|^2_2+\frac{1}{2}(u-\mu )^H(\sum \otimes I_N)^{-1}(u-\mu ) ) (4)$$
where $$$u$$$ is the unknown image, $$$\sigma _k$$$ is the noise standard deviation, $$$A$$$ is the encoding matrix, $$$d$$$ is the acquired signal, $$$\mu$$$ is the mean value of GP prediction, $$$\sum$$$ represents the covariance matrix generated from $$$C$$$ and $$$ N$$$ is the number of voxels. The problem is solved using gradient descent method.
Eddy current-corrected reconstruction
Eddy current-induced distortions lead to mismatch between diffusion directions. At opposite sides of the sphere, the q-space points share the same diffusion contrasts yet eddy currents induce opposite distortions, which undermines the locally coherent assumption in DAGER. In this work, we propose a 2-step reconstruction to tackle this problem. In step 1, we use single-shell DAGER without using antipodal symmetric property to reconstruct the data shell-by-shell. This initial reconstruction is used to estimate eddy current induced B0 field inhomogeneity with FSL’s Eddy16. These eddy current terms are then incorporated into the encoding matrix $$$A$$$ that maps the undistorted image $$$u$$$ to distorted k-space data $$$d$$$. In step 2, we perform ems-DAGER reconstruction using antipodal symmetric property. The full pipeline for ems-DAGER is shown in Fig.1 (b).
Dataset
Simulations were constructed based on HCP17 dMRI data using a ball-and-stick model. A 100-direction dataset was generated with 50 b=1000s/mm2 and 50 b=2000s/mm2 images uniformly sampled in q-space, representing a widely used multi-shell dMRI protocol (e.g., UKBiobank18). A 64-direction dataset consisting of 32 b=1000s/mm2 and 32 b=2000s/mm2 images uniformly sampled in q-space was also generated to evaluate the performance of ems-DAGER with a small number of diffusion directions. Eddy-current-induced field inhomogeneity was measured from a phantom using the same diffusion directions and b values on a 3T Siemens scanner. A graph model based approach11 was applied to design a k-q undersampling where a local q-space neighbourhood across two shells has diverse k-space undersampling patterns. Under-sampled multi-channel datasets were simulated with sensitivity maps from an 8-channel head coil and R=4/6.
Results
Fig.2 compares the proposed ems-DAGER with the single-shell DAGER for the 100-direction data, which both include eddy correction. The use of multi-shell information substantially improves the image quality, outperforming original DAGER method which only exploits information from a single-shell.The reconstruction results and corresponding residual maps for the 64-direction data are shown in Fig. 3 and Fig. 4, respectively. Single-shell DAGER breaks down with large aliasing due to the limited number of directions per shell. In comparison, ems-DAGER provides higher reconstruction accuracy. Notably, for R=6 with only 8 coils, ems-DAGER is still able to reconstruct images without major errors, indicating the efficacy of utilizing multi-shell information.
The improvement in image quality translates to the color-coded fractional anisotropy (cFA) (Fig. 5) maps. Due to the residual aliasing artifacts, the cFA maps obtained from SENSE show strong artifacts. While the single-shell DAGER method can improve the image quality, the result still shows higher noise levels and inconsistent color patterns from the reference. ems-DAGER produces cFA maps which best delineate brain structure.
Conclusion
We extended the DAGER method to jointly reconstruct multi-shell dMRI images with eddy-current correction. We demonstrated that the introduction of multi-shell information can improve the reconstruction performance regarding SNR and artifact suppression. Our future research will investigate the performance of ems-DAGER in vivo.Acknowledgements
W.W. is supported by the Royal Academy of Engineering (RF\201819\18\92). K.L.M. is supported by the Wellcome Trust (WT202788/Z/16/A). The Wellcome Centre for Integrative Neuroimaging is supported by core funding from the Wellcome Trust (203139/Z/16/Z).References
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