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Validation of DSI compressed sensing reconstruction in ex vivo human brain
Robert Jones1, Giorgia Grisot1,2, Jean Augustinack1, David A. Boas1,3, Bruce Fischl1,4, Hui Wang1, Berkin Bilgic1, and Anastasia Yendiki1

1Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA, United States, 2Harvard-MIT Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, United States, 3Boston University, Boston, MA, United States, 4Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, United States

Synopsis

Compressed sensing algorithms for accelerating DSI acquisitions (DSI-CS) have helped bring DSI into the realm of clinical feasibility. Here, we assess the efficacy of dictionary-based CS methods in reconstructing high resolution ex vivo DSI of human brain blocks, and provide validation of ex vivo DSI-CS with ground truth optical imaging. We find that reconstruction accuracy, computation time and inter-subject dictionary generalizability are comparable to in vivo results, and that SNR appears influential in determining the limit of attainable reconstruction quality. We also show that fiber orientation estimates of reconstructed data are as accurate as fully-sampled estimates at a microscopic level.

Introduction

Diffusion MRI (dMRI) allows us to study white-matter architecture non-invasively in vivo. Diffusion spectrum imaging (DSI) provides detailed information helpful for delineating complex intravoxel diffusion patterns1, but requires lengthy acquisitions that limit its applicability in vivo. Recent innovations in parallel imaging2,3, MRI hardware4,5 and compressed sensing (CS) algorithms have now rendered DSI as a clinically feasible dMRI protocol6. CS applied to DSI (DSI-CS) aims to reconstruct the diffusion probability density functions (PDFs) from sub-Nyquist sampled q-space using prior knowledge. PDF recovery using adaptive dictionaries and L2 regularization was shown to yield lower reconstruction error than CS using prespecified transforms7,8 with computation times orders of magnitude faster than iterative, dictionary-based CS methods9. Here, we extend the application of DSI-CS algorithms introduced in 7 to high-resolution ex vivo DSI data obtained from human brain blocks. We investigate reconstruction accuracy with respect to q-space location and SNR, and we compare modeled diffusion orientations to fiber orientations measured directly with Polarization Sensitive Optical Coherence Tomography (PS-OCT)10,11 providing the first validation of DSI-CS with ground truth optical imaging.

Methods

dMRI: We cut two blocks (3x2x2cm) from different anatomical regions of the same ex vivo, fixed human hemisphere (Fig. 1). We imaged each block on a 9.4T Bruker magnet with |G|max=480 mT/m, using a 3D EPI sequence (δ=15ms, Δ=19ms, 514 directions, bmax=40000s/mm2, 0.25mm iso resolution) for full DSI q-space encoding with one b=0 image. A surface coil was used, leading to a dependence of SNR on distance from the coil. This allowed us to investigate the relationship between SNR and reconstruction accuracy.

PS-OCT: Following dMRI, we imaged a 2x1.5x0.5cm section of one brain block with PS-OCT. PS-OCT acquisition and analysis was performed as described previously 10,11, yielding direct measurements of in-plane axonal orientation at 10μm in-plane and 75μm through-plane resolution.

Dictionary Training & Reconstruction: We undersampled the DSI data by an acceleration factor of R=3, and used two L2-based algorithms for CS reconstruction described in 7, with dictionary training sets derived from PDFs from a single slice of fully-sampled data. We compared Principal Component Analysis (PCA) reconstruction, and Tikhonov-regularized pseudoinverse reconstruction using either dictionaries trained with the K-SVD algorithm12 [PINV(KSVD)] or the training PDFs themselves as the dictionary [PINV(PDF)]. We reconstructed slices of sample A using dictionaries trained on either sample A or sample B. We computed the normalized RMSE, in terms of both PDFs and q-space, between the fully-sampled data and those reconstructed with PINV(KSVD), PINV(PDF) and PCA.

Results

We show the accuracy of reconstructed slices of sample A, using dictionaries trained on sample A (Fig. 2a) or on sample B (Fig. 2b). For three slices, color maps depicting average RMSE in PDFs are shown (Fig. 2a,b). We examined the SNR and RMSE at each undersampled q-space location (Fig. 3c,d), and further evaluated q-space RMSE as a function of SNR (Fig. 3b). We compared in-plane fiber orientation measurements from PS-OCT to diffusion orientation estimates from fully-sampled and reconstructed datasets. We show RGB maps of in-plane orientation angles (Fig. 4a) and heat maps of angle difference between PS-OCT and dMRI orientations (Fig. 4b).

Discussion

All reconstruction methods perform similarly across slices, with PCA yielding slightly lower RMSE than the two regularized pseudoinverse methods (Fig. 2a,b). Reconstructions of sample A using dictionaries trained on sample B had errors nearly the same as dictionaries trained on sample A, especially for PINV(KSVD) and PINV(PDF) (Table 1), which supports previous in vivo results7. As expected, we find that RMSE increases with distance in q-space (Fig. 3d). We observe that, as SNR decreases below 20, accuracy deteriorates substantially for all methods (Fig. 3b). Reconstruction errors in PDFs and q-space are similar to those reported previously for lower-resolution in vivo reconstructions7 and with similar computation times (~4 seconds per slice). When compared to PS-OCT, fiber orientations from CS reconstructions show no significant difference in accuracy compared to those from fully-sampled data (Fig. 4).

Conclusion

Our ex vivo validation of dictionary-based DSI-CS methods shows that they offer acceleration without compromising the accuracy of the estimated white-matter architecture, with respect to ground truth optical imaging at microscopic resolutions. We quantified the SNR limits of our approach and have begun to investigate its robustness to differences between the training and test data. Our results are promising both for large-scale studies acquiring DSI-CS in vivo6, as well as our aim of building highly accurate models of brain circuitry from ex vivo data. In ongoing work, we are comparing the accuracy of this approach to other (non-Cartesian) q-space sampling schemes.

Acknowledgements

This work was funded by NIH grant R01-EB021265.

References

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5. McNab JA, Edlow BL, Witzel T, Huang SY, Bhat H, Heberlein K, Feiweier T, Liu K, Keil B, Cohen-Adad J, Tisdall MD. The Human Connectome Project and beyond: initial applications of 300 mT/m gradients. Neuroimage. 2013 Oct 15;80:234-45.

6. Tobisch A, Stirnberg R, Harms RL, Schultz T, Roebroeck A, Breteler MM, Stöcker T. Compressed Sensing Diffusion Spectrum Imaging for Accelerated Diffusion Microstructure MRI in Long-Term Population Imaging. Frontiers in neuroscience. 2018;12.

7. Bilgic B, Chatnuntawech I, Setsompop K, Cauley SF, Yendiki A, Wald LL, Adalsteinsson E. Fast dictionary-based reconstruction for diffusion spectrum imaging. IEEE transactions on medical imaging. 2013 Nov;32(11):2022-33.

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9. Bilgic B, Setsompop K, Cohen-Adad J, Yendiki A, Wald LL, Adalsteinsson E. Accelerated diffusion spectrum imaging with compressed sensing using adaptive dictionaries. Magn Reson Med. 2012;68(6):1747-54.

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11. Grisot G, Jones R, Augustinack J, Boas D, Fischl B, Wang H, Yendiki A. Validation of high angular resolution diffusion MRI models in the human brain with PS-OCT. International Society for Magnetic Resonance in Medicine (ISMRM). 2017.

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Figures

Figure 1. Outline of processing pipeline for DSI-CS analysis. Left: Samples are blocked, imaged with dMRI, then imaged with PS-OCT. Middle: CS dictionaries are generated from single slices of fully-sampled data, from either the sample being reconstructed (sample A) or a different sample (sample B in blue box). A subset of q-space points is extracted from fully-sampled data, upon which CS reconstruction is performed using either PINV(KSVD), PINV(PDF) or PCA methods. Reconstructed data is compared to fully-sampled data to determine reconstruction accuracy. Bottom left: dMRI fiber orientations are estimated and compared to ground truth PS-OCT orientations.

Figure 2. Top: Mean and standard error of reconstruction error across slices of sample A with training data from sample A (a.) and training data from sample B (b.). Bottom: b=0 image and color map of error from each reconstruction method for three slices of sample A with training data from sample A (a.) and training data from subject B (b.). Moving across slices, reconstruction error increases and, as visible in the b=0 images, SNR decreases.

Table 1. Summary of average PDF reconstruction error for color maps shown in Figure 2, expressed in % average RMSE.

Figure 3. (a.) b=0 images for three slices of sample A showing decrease in SNR as slice number increases. Text colors correspond to data for that slice in (b-d). (b.) Scatter plot of reconstruction error at each undersampled q-space location plotted against SNR at that location using PCA and PINV(KSVD) with training on sample A. (c.) SNR at each undersampled q–space location with increasing |q|. (d.) Reconstruction error at each undersampled q-space location with increasing |q|.

Figure 4. (a.) RGB maps of dMRI estimated in-plane orientation angles for fully-sampled (left) and reconstructed (right) data. The RGB map obtained by PS-OCT is shown at the top. (b.) Heat maps of angle difference between orientation measured with PS-OCT and orientation modeled by dMRI for fully-sampled (left) and reconstructed (right) data. All dMRI exhibit low angle difference in regions of coherent fiber structure like the internal capsule (green arrow), and higher error in regions of heterogeneous fiber organization (pink arrow).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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