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Accelerated Microstructure Quantification by Q-Space Trajectory Imaging Using Machine Learning
Oliver Goedicke1, Frederik B. Laun2, Jan Martin3, Julian Rauch1,4, Peter Neher5, Maximilian R. Rokuss5,6, Mark E. Ladd1,4,7, and Tristan A. Kuder1,4
1Division of Medical Physics in Radiology, German Cancer Research Center (DKFZ) Heidelberg, Heidelberg, Germany, 2Institute of Radiology, University Hospital Erlangen, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany, 3Siemens Healthineers, Erlangen, Germany, 4Faculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany, 5Division of Medical Image Computing, German Cancer Research Center (DKFZ) Heidelberg, Heidelberg, Germany, 6Faculty of Mathematics and Computer Science, Heidelberg University, Heidelberg, Germany, 7Faculty of Medicine, Heidelberg University, Heidelberg, Germany

Synopsis

Keywords: Microstructure, Machine Learning/Artificial Intelligence, Q-space, QTI, Microscopic Anisotropy, µFA

Motivation: Tensor-encoded diffusion MRI (dMRI) methods for tissue microstructure elucidation typically require lengthy dMRI acquisitions and computationally costly, SNR-sensitive data analysis.

Goal(s): Employing q-space trajectory imaging (QTI), we seek to greatly reduce both the number of required measurements and computational burden in analysis for robust estimation of parameters quantifying brain tissue microstructure.

Approach: A machine learning-based estimator is trained on a 10-fold reduced subset of an extensive dMRI protocol acquired in 18 healthy volunteers.

Results: The proposed method outperforms a state-of-the-art model fitting framework, yielding smoother parameter maps and showing lower deviation from the chosen ground truth, even at reduced SNR/increased resolution.

Impact: Quantitative measures of brain microstructure are obtained by accelerated tensor-encoded diffusion MRI, employing a voxel-wise regression neural network. Observed resilience at reduced voxel size (1.7mm)3 appears promising regarding measurement of parameters such as microscopic fractional anisotropy in a clinical setting.

Introduction

In QTI, microstructure contained within a voxel is described by a diffusion tensor distribution (DTD)1. Its 2nd-order cumulant expansion relates the dMRI signal $$$S$$$ to statistical moments of the DTD, namely the 2nd-order mean and 4th-order covariance tensor $$$\mathbf{D}$$$ and $$$\mathbb{C}$$$, respectively1:$$S\left(\mathbf{B}\right)=S_0\exp\left(-B_{ij}D_{ij}+\frac{1}{2} B_{ij}B_{kl}C_{ijkl}\right)$$with the signal in absence of diffusion encoding $$$S_0$$$ and measurement tensors $$$\mathbf{B}$$$. Conventional model fitting of $$$S\left(\mathbf{B}\right)$$$ gives access to $$$\mathbf{D}$$$ and $$$\mathbb{C}$$$, from which scalar parameters can be computed that provide insight on size variation, orientation coherence and shape anisotropy of microstructural domains, such as the microscopic fractional anisotropy2 $$$\mathrm{\mu\,\!FA}$$$.

As demonstrated for other dMRI modalities3-6, machine learning approaches allow for computationally efficient direct parameter estimation, while easing the requirement on the number of diffusion-weighted measurements.

We show that a regression neural network can reliably estimate the sought-after parameters from strongly abbreviated measurement protocols, producing smoother maps with lower deviation from the chosen ground truth when compared against conventional model fitting.

Methods

Dataset:

After written informed consent, brain dMRI data of 18 healthy volunteers (IRB-approved study S-184/2018) were acquired, covering an extensive "full protocol" comprising $$$\mathbf{B}$$$ tensors of varying shapes, sizes and orientations7 displayed in Tab. 1. A custom pulse sequence8 capable of general waveform diffusion encoding was deployed on a 3T Siemens Prisma system, with measurement parameters outlined in Tab. 2.
Preprocessing included denoising and correction for motion, distortion and Gibbs ringing using elastix9, FSL10 and MRtrix11 libraries. Ground truth (GT) parameters were established by model fitting the "full protocol" data via a non-linear least-squares constrained optimization (NLLS) routine12 (QTI+, enforcing relevant positivity conditions to $$$\mathbf{D}$$$ and $$$\mathbb{C}$$$).

Neural Network:

A feed-forward, fully connected Multi-Layer Perceptron (MLP) was implemented in PyTorch13 (Fig. 1). It takes voxel-wise sequences of dMRI signal values as inputs and estimates the scalar parameters of interest, bypassing DTD model parameters $$$\mathbf{D}$$$ and $$$\mathbb{C}$$$.
The MLP was trained to estimate GT parameters from a highly abbreviated and separately preprocessed "short protocol" subset of the "full protocol" acquisition (Tab. 1).

Performance Evaluation:

MLP predictions were evaluated against the GT by computing the brain-wise normalized root mean squared error (nRMSE) and compared to NLLS model fitting the "short protocol" data. For the comparison, 18-fold leave-one-out cross validation was performed, enabling evaluation of the MLP’s performance across the entire available dataset.
Lastly, both protocols were acquired at reduced voxel sizes for a separate volunteer, probing the MLP's robustness to decreased SNR.

Results

MLP training completed in 8 minutes, with inference times of 0.14 seconds for one brain compared to 17 minutes for NLLS fitting (Apple M1 Pro 10‑Core CPU).

Output produced by the MLP shows little deterioration in visual quality when compared to the GT in Fig. 2. Difference maps are consistent with perceived higher deviations and noise present in the NLLS maps. Quantitatively, nRMSEs of the MLP predictions are consequently lower than those of the NLLS output (Fig. 3 (a)).

Results for the high-resolution acquisition in Fig. 4 show a similar pattern, with overall larger deviations for both estimators and increased perceived noise, which is present in GT maps as well. While notably higher, nRMSEs in Fig. 3 (b) indicate superior performance of the MLP.

Discussion and Conclusion

We observe microstructural parameter maps of considerably higher quality from the MLP when compared to model fitting on reduced input data, especially at high resolution (1.7mm)³.

Direct parameter estimation bypasses DTD model parameters $$$\mathbf{D}$$$ and $$$\mathbb{C}$$$, thus not allowing the enforcement of positivity conditions, as implemented in the QTI+ framework12. However, with estimations of $$$\mathbb{C}$$$ offering difficulties arriving at acceptable and unique solutions12, the simplicity of our approach yields marked robustness. This becomes evident from the MLP’s resilience to significantly reduced SNR in the high-resolution acquisition. Especially in this regard, future work could aim to compare direct estimators to a recently proposed self-supervised, physics-informed approach14.

It must be noted that in the high-resolution acquisition, TE was increased by 6 ms compared to the GT measurement, which may pose challenges regarding generalization. Considering good agreement with the “full protocol” model fit at (1.7mm)³, the slight TE increase seems unproblematic for our voxel-wise approach, but requires further investigation.

In conclusion, voxel-wise regression MLPs enable direct and robust microstructure quantification from accelerated dMRI acquisitions and markedly faster analysis. By training on QTI data of, to our knowledge, previously unavailable extent and quality, our MLP provides notably higher-fidelity parameter maps than model fitting, with 24 slices acquired in 5 minutes. This seems encouraging regarding possible clinical investigation of the obtained microstructural parameters, e.g. in localized pathologies.

Acknowledgements

No acknowledgement found.

References

  1. Westin CF, Knutsson H, Pasternak O et al. Q-space trajectory imaging for multidimensional diffusion MRI of the human brain. Neuroimage 2016;135:345-362.
  2. Lasič S, Szczepankiewicz F, Eriksson S et al. Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the q-vector. Frontiers in Physics 2014;2.
  3. Golkov V, Dosovitskiy A, Sperl JI et al. q-Space Deep Learning: Twelve-Fold Shorter and Model-Free Diffusion MRI Scans. IEEE Trans Med Imaging 2016;35(5):1344-1351.
  4. Li H, Liang Z, Zhang C et al. SuperDTI: Ultrafast DTI and fiber tractography with deep learning. Magn Reson Med 2021;86(6):3334-3347.
  5. de Almeida Martins JP, Nilsson M, Lampinen B et al. Neural networks for parameter estimation in microstructural MRI: Application to a diffusion-relaxation model of white matter. NeuroImage 2021;244:118601.
  6. HashemizadehKolowri S, Chen RR, Adluru G et al. Jointly estimating parametric maps of multiple diffusion models from undersampled q-space data: A comparison of three deep learning approaches. Magn Reson Med 2022;87(6):2957-2971.
  7. Westin CF, Pasternak O, Knutsson H. Rotationally Invariant Gradient Schemes for Diffusion MRI. Proc Intl Soc Mag Reson Med 20 2012: 3537.
  8. Martin J, Endt S, Wetscherek A et al. Contrast-to-noise ratio analysis of microscopic diffusion anisotropy indices in q-space trajectory imaging. Z Med Phys 2020;30(1):4-16.
  9. Klein S, Staring M, Murphy K et al. elastix: A Toolbox for Intensity-Based Medical Image Registration. IEEE Transactions on Medical Imaging 2010;29(1):196-205.
  10. Andersson JLR, Skare S, Ashburner J. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage 2003;20(2):870-888.
  11. Tournier JD, Smith R, Raffelt D et al. MRtrix3: A fast, flexible and open software framework for medical image processing and visualisation. NeuroImage 2019;202:116137.
  12. Herberthson M, Boito D, Haije TD et al. Q-space trajectory imaging with positivity constraints (QTI+). Neuroimage 2021;238:118198.
  13. Paszke A, Gross S, Massa F et al. Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems 2019;32.
  14. Boito D, Özarslan E. Q-space trajectory imaging with positivity constraints: a machine learning approach. Proc Intl Soc Mag Reson Med 31 2023: 3780.

Figures

Tab. 1: (a) "Full" and (b) "short protocol" composition: number of tensor orientations measured at each b-value ($$$\mathrm{trace}\left(\mathbf{B}\right)$$$). Each orientation set was chosen rotationally invariant7. Spherical tensors were rotated onto 3 orthogonal axes and averaged over multiple repetitions as indicated by square brackets and subscripts.


Tab. 2: Measurement parameters for ground truth (18 volunteers: 5 female, 13 male, age: 20-29, median: 25) and high-resolution acquisitions (one male volunteer, age: 26).


Fig. 1: MLP architecture: For each voxel separately, the input layer receives sequences of dMRI signal values in a predefined order corresponding to the "short protocol". After 4 hidden layers (hl) with ReLU activation and varying numbers of nodes $$$\mathrm{n}$$$, the output layer returns the microstructural parameters of interest.

During training, the learning rate was decreased by 7.5% for every new epoch between epochs 15 and 75.


Fig. 2: Scalar microstructural parameters (mean diffusivity $$$\mathrm{MD}$$$, fractional anisotropy $$$\mathrm{FA}$$$, microscopic fractional anisotropy $$$\mathrm{\mu\,\!FA}$$$, orientation coherence $$$\mathrm{C_c}$$$ and mean diffusivity variation coefficient $$$\mathrm{C_{MD}}$$$ obtained from the GT and "short protocol" NLLS fit, as well as the MLP prediction. Difference maps reveal the highest deviations in the ventricles, where $$$\mathrm{\mu\,\!FA}$$$ values appear increased for NLLS maps.

Fig. 3: (a) nRMSEs of all parameters for NLLS and MLP predictions. RMSEs were computed over all brain voxels of a given volunteer and normalized by the mean parameter value over those same voxels. Boxes indicate the innerquartile range (IQR) with whiskers extending to 1.5 IQR and data outside that range shown as circular markers.


(b) nRMSEs computed for the high-resolution acquisition reveal the same pattern as found in (a).


Fig. 4: Parameter and difference maps for the high-resolution acquisition. Here, the average prediction of the 18-fold MLP ensemble was computed. Increased perceived noise is present in all parameter maps including the GT, most notably in the NLLS results.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)
3464
DOI: https://doi.org/10.58530/2024/3464