Qiyuan Tian1,2, Berkin Bilgic1,2, Qiuyun Fan1,2, Congyu Liao1,2, Chanon Ngamsombat1, Yuxin Hu3, Thomas Witzel1, Kawin Setsompop1,2, Jonathan R. Polimeni1,2, and Susie Y. Huang1,2
1Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA, United States, 2Department of Radiology, Harvard Medical School, Boston, MA, United States, 3Department of Electrical Engineering, Stanford University, Stanford, CA, United States
Synopsis
Diffusion tensor imaging (DTI) is
widely used clinically but typically requires acquiring diffusion-weighted
images (DWIs) along many diffusion-encoding directions for robust model
fitting, resulting in lengthy acquisitions. Here, we propose a joint denoising
and q-space angular super-resolution method called “DeepDTI” achieved using data-driven
supervised deep learning that minimizes the data requirement for DTI to the theoretical
minimum of one b=0 image and six DWIs. Metrics derived from DeepDTI’s results
are equivalent to those obtained from three b=0 and 19 to 26 DWI volumes for
different scalar and orientational DTI metrics, and superior to those derived
from state-of-the-art denoising methods.
Introduction
Diffusion tensor imaging (DTI) is used
for probing tissue microstructure1,2
and for mapping major white matter bundles in the brain. At least 30 diffusion-weighted images
(DWIs) acquired along uniformly distributed directions are needed to robustly
derive DTI metrics that do not depend on the specific diffusion directions
acquired3,4. For DWIs with very low SNR,
the number of required DWIs may be far greater than 30. The length of such
acquisitions poses a significant barrier to performing
high-resolution DTI in routine clinical practice and large-scale research
studies.
Previous studies have demonstrated
the promise of deep learning in reducing the amount of diffusion data required
to generate scalar diffusion metrics5-7. In
this work, we propose a physics-informed supervised deep learning technique called
“DeepDTI” that minimizes the data requirement for DTI to the theoretical
minimum of one b=0 images and six DWIs and enables the generation of scalar and
orientational DTI metrics from DWIs sampled along six optimized
diffusion-encoding directions.Methods
DeepDTI
Pipeline. The
inputs to DeepDTI are: a single b=0 image, six DWIs sampled along
fixed, optimized diffusion-encoding directions (Fig.1a,b), and anatomical (T1-
and T2-weighted) images (total of nine input channels). Input
DWIs are generated by fitting the tensor model to the input data and inverting
the transformation to generate a set of DWIs sampled along six fixed, optimized
diffusion-encoding directions
extracted from routinely acquired multi-directional, single-shell diffusion MRI
data. The diffusion-encoding directions were
optimized to minimize the condition number of the diffusion tensor
transformation matrix8, hence improving robustness to experimental noise. Many
rotational variations of the six optimized diffusion-encoding directions can be
chosen, making the method applicable to a range of protocols. For example, from
90 uniform diffusion-encoding directions, ~100 sets of rotational variants can
be selected. Anatomical images are included as inputs to delineate boundaries
between tissue types and prevent blurring in the fitted results.
The outputs of DeepDTI are: the
average of all b=0 images and six ground-truth DWIs (total of seven output channels).
The ground-truth DWIs are generated by fitting the tensor model to all
available b=0 and DWIs and inverting the transformation to generate a set of
DWIs sampled along the six fixed diffusion-encoding directions such that the
input and ground-truth DWIs have the same contrast.
A deep 3-dimensional plain CNN9-11
was used to learn the mapping from the input to the residuals between the input
and output images (residual learning) (Fig.1d).
HCP Data.
Pre-processed diffusion MRI data of 70 subjects (40 for training, 10 for validation,
20 for evaluation) from the
Human Connectome Project (HCP) WU-Minn-Oxford Consortium were used12. Diffusion data were acquired at 1.25-mm isotropic
resolution along 90 uniformly-sampled diffusion-encoding directions at b=1,000
s/mm2 and 18 interspersed b=0 volumes. For each subject, five sets of one
b=0 image and six DWIs along arbitrary rotational variants of the
optimized diffusion-encoding directions were selected to obtain input data for DeepDTI.
T1-weighted
and T2-weighted images were acquired at 0.7-mm isotropic resolution.
Network
Implementation. DeepDTI was implemented using the
Keras API (https://keras.io/)
with a Tensorflow (https://www.tensorflow.org/)
backend. Training was performed with 64×64×64 voxel blocks, Adam optimizer, L2
loss using an NVidia V100 GPU for 48 epochs for ~70 hours.Results
The output DWIs from DeepDTI showed
significantly improved image quality and SNR compared to the input DWIs (Fig.2). The output DWIs were similar to the ground-truth
DWIs with a high peak SNR (PSNR) of 31.9 dB and high structural similarity
index (SSIM) of 0.97 (Fig.2h). The residuals between the output DWI and ground-truth
DWIs did not contain anatomical structure (Fig.2e,j).
DeepDTI can be viewed as a denoising
method that produces results (Fig.3iii) comparable to results using more data
(Fig.3ii, iv) or from state-of-the-art denoising algorithms BM4D13,14 (https://www.cs.tut.fi/~foi/GCF-BM3D/) (Fig.3v) and MPPCA15,16 (“dwidenoise” function in the MRtrix3 software, https://mrtrix.readthedocs.io) (Fig.3vi). Residuals between the DeepDTI-processed DWIs
and raw DWIs did not contain anatomical structure (Fig.3, rows b,d, column i).
The fractional anisotropy (FA) and primary
eigenvector (V1) from DeepDTI recovered detailed anatomical information in deep
white matter and cerebral cortex (Fig.4). The V1-encoded FA map from DeepDTI was
visually similar and only slightly blurred compared to the map fitted using all
18 b=0 and 90 DWIs.
Deviations
of the resultant FA and V1 compared to results fitted
using all 18 b=0 and 90 DWIs are
shown in (Fig.5a–d) and systematically quantified in the 20 evaluation
subjects (Fig.5e–i). The mean absolute deviation (MAD) of V1, FA, mean
diffusivity, axial diffusivity and radial diffusivity derived from the DeepDTI outputs
was 14.83°±1.51°, 0.036±0.0038, 0.0382±0.0087 mm2/s,
0.055±0.0097 mm2/s, and 0.0413±0.0081 mm2/s,
respectively, which were equivalent to the MAD of results from 3 b=0 images and
19, 21, 26, 19, and 23 DWI volumes along uniform directions (Fig.5e–i),
achieving 3.1–4.1× acceleration of scan time. Discussion and Conclusion
DeepDTI performs simultaneous
denoising and q-space angular super-resolution by leveraging the data
redundancy in the six-dimensional joint k-q space, local and global anatomy and
between different MRI contrasts.
DeepDTI can also take input DWIs at lower-resolution to generate super-resolution
DTI results at higher-resolution, and input DWIs along more than six directions
for very noisy data. Acknowledgements
This work was supported by the NIH (grants P41-EB015896, U01-EB026996, K23-NS096056) and an MGH Claflin Distinguished Scholar Award.References
[1] Basser, P. J., Mattiello, J. &
LeBihan, D. MR diffusion tensor spectroscopy and imaging. Biophysical journal 66,
259-267, doi:10.1016/S0006-3495(94)80775-1 (1994).
[2] Pierpaoli,
C., Jezzard, P., Basser, P. J., Barnett, A. & Di Chiro, G. Diffusion tensor
MR imaging of the human brain. Radiology
201, 637-648,
doi:10.1148/radiology.201.3.8939209 (1996).
[3] Jones,
D. K. The effect of gradient sampling schemes on measures derived from
diffusion tensor MRI: a Monte Carlo study†. Magnetic
Resonance in Medicine 51,
807-815 (2004).
[4] Jones,
D. K., Knösche, T. R. & Turner, R. White matter integrity, fiber count, and
other fallacies: the do's and don'ts of diffusion MRI. NeuroImage 73, 239-254
(2013).
[5] Li,
H. et al. in The Machine Learning (Part II) Workshop of the International Society
for Magnetic Resonance in Medicine, Washington, District of Columbia, USA.
[6] Gong,
T. et al. in In Proceedings of the 26th Annual Meeting of the International Society
for Magnetic Resonance in Medicine (ISMRM), Paris, France. 1653.
[7] Golkov,
V. et al. q-Space deep learning:
twelve-fold shorter and model-free diffusion MRI scans. IEEE transactions on medical imaging 35, 1344-1351 (2016).
[8] Skare,
S., Hedehus, M., Moseley, M. E. & Li, T.-Q. Condition number as a measure
of noise performance of diffusion tensor data acquisition schemes with MRI. Journal of Magnetic Resonance 147, 340-352 (2000).
[9] Zhang,
K., Zuo, W., Chen, Y., Meng, D. & Zhang, L. Beyond a gaussian denoiser:
Residual learning of deep cnn for image denoising. IEEE Transactions on Image Processing 26, 3142-3155 (2017).
[10] Kim,
J., Kwon Lee, J. & Mu Lee, K. Accurate image super-resolution using very
deep convolutional networks. In
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition,
1646-1654 (2016).
[11] Simonyan,
K. & Zisserman, A. Very deep convolutional networks for large-scale image
recognition. Preprint at: https://arxiv.org/abs/1409.1556
(2014).
[12] Glasser,
M. F. et al. The minimal
preprocessing pipelines for the Human Connectome Project. NeuroImage 80, 105-124
(2013).
[13] Maggioni,
M., Katkovnik, V., Egiazarian, K. & Foi, A. Nonlocal transform-domain
filter for volumetric data denoising and reconstruction. IEEE transactions on image processing 22, 119-133 (2012).
[14] Dabov,
K., Foi, A., Katkovnik, V. & Egiazarian, K. Image denoising by sparse 3-D
transform-domain collaborative filtering. IEEE
Transactions on image processing 16,
2080-2095 (2007).
[15] Veraart,
J., Fieremans, E. & Novikov, D. S. Diffusion MRI noise mapping using random
matrix theory. Magnetic resonance in
medicine 76, 1582-1593 (2016).
[16] Veraart,
J. et al. Denoising of diffusion MRI
using random matrix theory. NeuroImage
142, 394-406 (2016).