Fast multi-compartment Microstructure Fingerprinting in brain white matter

Abstract

We proposed two deep neural network based methods to accelerate the estimation of microstructural features of crossing fascicles in the white matter. Both methods focus on the acceleration of a multi-dictionary matching problem, which is at the heart of Microstructure Fingerprinting, an extension of Magnetic Resonance Fingerprinting to diffusion MRI. The first acceleration method uses efficient sparse optimization and a dedicated feed-forward neural network to circumvent the inherent combinatorial complexity of the fingerprinting estimation. The second acceleration method relies on a feed-forward neural network that uses a spherical harmonics representation of the DW-MRI signal as input. The first method exhibits a high interpretability while the second method achieves a greater speedup factor. The accuracy of the results and the speedup factors of several orders of magnitude obtained on in vivo brain data suggest the potential of our methods for a fast quantitative estimation of microstructural features in complex white matter configurations.

Keywords: crossing bundles; deep learning; diffusion MRI; fingerprinting; microstructure; non-negative linear least-squares.

Figure 1

Our forward signal model exploits Monte Carlo numerical simulations. A voxel of white matter [artistic view borrowed from Ginsburger et al. (2018)], located here on a T1 anatomical scan of a healthy young adult from the Human Connectome Project (Van Essen et al., 2012), is represented by axon populations modeled as straight cylinders with signal contributions assumed independent. The DW-MRI signal is obtained by Monte Carlo simulations in each population (Hall and Alexander, ; Rensonnet et al., 2015).

Figure 2

(A) Microstructure Fingerprinting involves solving a large number of small NNLS problems, leading to long computation times as the dictionary size N increases. (B) In the Hybrid Method, the vector of measurements $\widehat{y}$ is decomposed by NNLS into a sparse representation in the space of physics-based fingerprints. The weights are given to a multilayer perceptron (MLP) with a split architecture to predict the tissue parameters (relative volume of axon population ν_k, fiber volume fraction fvf_k and extra-axonal diffusivity D_{ex, k}). (C) The Fully-Learned Method calculates shellwise spherical harmonics coefficients of order 12, which are fed into a DNN to predict the tissue parameters and axon populations orientation.

Figure 3

The Fully-Learned Method has better estimation accuracy than the Hybrid Method, the CSD & MF and the MF algorithm with true orientations. MAE on structured test.

Figure 4

Both accelerated method obtain estimates closer to the groundtruth for the fvf and D_ex metrics than the reference MF methods. Correlation-accuracy plots comparing the predicted values and the ground truth parameters for the four models on the test set.

Figure 5

The orientations obtained with the Fully-Learned Method outperform results from constrained spherical deconvolution in the synthetic test set. Angular Error: CSD vs. the Fully-Learned Method.

Figure 6

The accelerations methods generalize to three-way crossings, outperforming the reference MF methods in estimation accuracy for the metrics fvf and D_ex. Correlation-accuracy plots comparing the predicted values against the ground truth parameters for the four models on the test set with a three-fiber configuration. The difference between actual and estimated values are shown for the first fascicle in the two left-most columns, for the second fascicle in the two middle columns, and for the third fascicle in the two right-most columns.

Figure 7

The Hybrid Method is able to generalize to data acquired with a different experimental protocol with minimal retraining. MAE on structured test with the clinical protocol.

Figure 8

The mean differences between the reference and the accelerated Microstructure Fingerprinting follow similar trends on simulated and on in vivo data. Histogram (normalized to integrate to 1) of the signed differences between CSD & MF and the Hybrid (left) and Fully-Learned (right) Methods for fvf₁ on synthetic (top) and in vivo (bottom) data. The vertical dotted lines represent the mean of the signed difference.

Figure 9

Structural integrity between all methods seems to be maintained. Several voxels are estimated to a higher fiber volume fraction by the Fully-Learned Method. Detailed visualization on subject MGH 1001 of voxel-wise maps of fvf₁ and voxel-wise maps of the differences in fiber volume fraction for the first compartment (fvf₁) between the reference method and the Hybrid Method and the Fully-Learned Method. Constrained spherical deconvolution (CSD) was used to estimate the number of fascicles and their orientations. The analysis specifically targets voxels identified by CSD as containing two or more fascicles. (A) Voxel-wise maps of fvf₁. (B) Differences between voxel-wise fvf₁ maps.