Multi-shell, multi-tissue, constrained spherical deconvolution is an appealing method for the reconstruction of fiber orientation distribution function (fODF), which is of great importance for solving complex fiber configurations to achieve reliable tractography. However, many diffusion measurements and multiple reconstruction steps are required. In this study, the deep neural network were employed to form a multi-output regression problem for establishing a fast and direct estimation of fODF. The proposed method offers a new streamlined reconstruction procedure which exhibits great potential for accelerating the reconstruction of fODF with whole-brain coverage, with satisfactory accuracy in two minutes.
We use the DNN to form a multi-output regression problem, with a spherical harmonics (SH)-based representation of fODFs as the target output, which lowers the requirement for network structure and provides a smooth representation of the data distributed on a sphere, compared to amplitude-represented fODFs. In our DNN method, down-sampled DWIs are used as input and SH coefficients as the output, directly avoiding any intermediate steps. Several options of depth and width were tested for the DNN architecture, and the 2000-1500-1000-800-500-200 setting was chosen for a balance between performance and cost of time and memory, as shown in Figure 1 and Table I.
The ethics committee of the local institute approved this human study. The DWI data were collected from three healthy subjects on a MAGNETOM Prisma 3T MR scanner (Siemens Healthcare, Erlangen, Germany) equipped with a 64-channel head-neck coil using a single-shot EPI sequence: TR/TE= 7000/67 ms, FOV= 210×210 mm2, number of slices= 50, and resolution= 2.5×2.5×2.5 mm3. Diffusion weightings of b = 1000, 2000, and 3000 s/mm2 were applied in 23, 45, and 68 directions 4 with 14 b = 0 images equally entered, resulting in a total of 150 DWIs. In addition, b = 0 images with an opposite phase-encoding direction were also acquired.
After DWI preprocessing for motion and distortion correction, 5 MSMT-CSD reconstruction was performed in MRtrix (http://www.mrtrix.org/) using an unsupervised method.6 fODF was represented by the SH series of the order lmax, amounting to (lmax +1)(lmax +2)/2 SH coefficients. Based on the highest recommended order of 8, 7 the training labels were set as the 45 fODF SH coefficients reconstructed from all 150 DWIs. One subject’s data were reserved for testing whereas 90% of the other two subjects’ data were used for training, and 10% constituted a validation set. Keras 8 was used for training and testing with Tensorflow running backend. 9 All the codes were run on a platform with an NVIDIA GTX-1080 graphics card and CUDA Deep Neural Network library10 installed.
When decreasing the DWIs, the overall root-mean-squared errors of the DNN on whole brain white matter rose gently and were lower than the MSMT-CSD reconstruction after its sharp jump from 105 to 90 DWIs, as shown in Figure 2. The first SH coefficient showed that detailed structures are still maintained for the DNN method at 15 DWIs, whereas it is mostly lost for model reconstruction, indicating its unreliable fODF estimates.
The fODFs of three typical ROIs corresponding to k=1, 2, and 3 fiber directions are depicted in Figure 3, and its statistics of angular errors are shown in Figure 4. The reducing DWIs cause a decreasing lmax in the model reconstruction results, leading to less discriminating fODF lobes and a failure of recovery of less obvious directions when the DWIs are fewer than 45 in two fiber regions and 75 in three fiber regions. In the DNN method, the morphology of fODFs remains intact, even when the DWIs decrease to 15. The steady trend of solid curves in Figure 4 suggests that the DNN method preserves the information contained in the original data very well. The smaller angular errors suggest that the DNN outperforms the model reconstruction when the DWIs are fewer than 105.
Finally, fiber tractography using extracted peaks from fODFs was conducted to validate the effectiveness of the learned fODFs. The model-reconstructed results miss several large branches of fibers, causing severe track volume loss and track length truncation when n is less than 60.
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