(G-248) Model-Based Diffusion Microstructure Parameter Estimation Using Deep Learning

Introduction::

One of the active areas of research in diffusion MRI (DWI) is biophysical model mapping which focuses on fitting diffusion signal to the models that describe the microstructure properties of the tissue. One of the common studied models is the Standard Model (SM). This model provides high specificity, but it demands high computation power, and it is sensitive to noise, initialization, and can produce multiple degenerate results. Deep Learning (DL) methods have shown high accuracy along with fast computation time after training. They are also capable of incorporating prior information into the training which will help to acquire more accurate estimation of the model parameters and can eliminate alternative set of parameters that will result in the same diffusion signal [1]. All these features create a framework that is superior to the traditional model fitting strategies.

In this work, we propose a method to estimate SM parameters based on the rotational invariant features of the DWI in the DL architecture. The DL framework maps the rotational invariants of the diffusion signal to SM parameters. These parameters will be fed to the forward model of the SM to generate the diffusion signal. The generated DWI and estimated SM parameters are then compared with the ground truth (GT) to train the DL network. Here, we have shown the results of our method on the synthetic dataset and two in-vivo datasets are comparable to the state-of-the-art methods.

Sub-track: Magnetic Resonance Imaging and Applications (MRI)


Materials and Methods::

Computing rotational invariants of the DWI as the forward model:

The SM [2] for DWI can be modeled as the convolution of fiber orientation distribution function (fODF) P(n) and microstructural model K(b,g.n):

S(b,g) = S₀ ∫ P(n) . K(b,g.n) dn,     (1)
Where S(b,g) is the diffusion signal along gradient direction g and b-value of b, and n is fascicle direction. In a three-compartment setting, the kernel, K can be defined as:
K(b,ξ) = f_intra e^-bDaξ + f_extra e^{-bD_e(||}ξ - bD_e(⊥)(1-ξ)} + f_iso e^-bD_iso,     (2)
Where ξ = (g.n)² and [f_intra, f_extra, D_a, D_e(||), D_e(⊥), D_iso] are the intra-axonal volume fraction, extra-axonal volume fraction, intra-axonal parallel diffusivity, extra-axonal parallel and perpendicular diffusivities, and isotropic diffusivity, respectively. Here, we use rotational invariant features of the DWI as described in [3]. In this work, we considered l = 4 for the maximum order of the Legendre polynomials to calculate rotational invariants.

Training model-based neural network (NN):

Figure 1 shows our proposed model. The computed rotational invariants are the input of the network, and the output is SM parameters. These parameters are then fed to forward model to compute the rotational invariants of the estimated features.
The loss function comprises two data consistency term:
L = ||S - S^′||² + ||F - F^′||²,     (3)
Where F = [f_intra, D_a, D_e(||), D_e(⊥), p₂, p₄] is the feature vector and S is the rotational invariants of the DWI. This form of cost function guarantees the fit of model parameters along with the diffusion signal.

Results, Conclusions, and Discussions::

Synthetic experiment:

We generated 50k datapoints with randomly chosen model parameters in the following range: f_intra ∈ [0.05,0.95], {D_a,D_e(||)} ∈ [1,3]μm²/ms, D_e(⊥) ∈ [0.1,1.2]μm²/ms, p₂ ∈[0,1]. The DWI is generated based on the following protocol:two shells of 1000 and 2000s/mm2 with 85 gradient directions, and TR/TE of 6700/127ms and then made it noisy to reduce the SNR to 25. The NN is trained with the following parameters using TensorFlow: 1000 epochs with batch size of 100, ReLu activation function in hidden layers and Adam optimizer with training rate of 1e-4 and train/test ration of 0.9/0.1.

In-vivo experiment:

Two different dataset were chosen with the following acquisitions protocols:
Dataset 1: Skyra scanner, b-values=1000,2000s/mm2, TR/TE=6700/127ms, 85 diffusion directions, 3 b₀ images.
Dataset 2: Prisma scanner, b-values=1000,1500,2000,6000s/mm2, TR/TE=5300/92ms, 176 diffusion directions, 7 b₀ images.
We then trained our model separately for each setting and computed the difference map between our estimation and the results of the traditional model fitting method.

Synthetic results:

The test dataset consists of the 5k datapoints. Figure 2 shows the training loss of our proposed model. It also shows the loss of training network without the forward model included in the training. The loss of SM features for the full model is a lower than the model trained without the data consistency term for rotational invariants. Figure 3 shows the results of fitting 50 random data. Figure 4 shows the boxplot of error of all SM parameters. It indicates the loss of the proposed model is comparable to the ground truth.

In-vivo results:

We trained our framework based on the settings for each dataset and then tested it on the in-vivo data. As a reference, we also computed the SM features using SMI toolbox [4]. Figure 5 shows the reproduced DWI image based on estimated SM parameters along with each parameter map and their difference with respect to the SMI toolbox estimation. As it can be seen, the estimated results are comparable with the SMI’s counterpart. Figure 4 shows the boxplot of MAE for the in-vivo data which indicates the error of the estimation is within the comparable range.


Acknowledgements (Optional): :

References (Optional): :

[1] Jelescu, I.O., Veraart, J., Fieremans, E., Novikov, D.S. “Degeneracy in model parameter estimation for multi-compartmental diffusion in neuronal tissue.” NMR Biomed. 29 (2016): 33–47.

[2] Novikov, D.S., Fieremans, E., Jespersen, S.N., Kiselev, V.G. “Quantifying brain microstructure with diffusion MRI: theory and parameter estimation.” NMR Biomed. (2019): e3998.

[3] Novikov, Dmitry S., et al. "Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI." NeuroImage 174 (2018): 518-538.

[4] Coelho, Santiago, et al. "Reproducibility of the Standard Model of diffusion in white matter on clinical MRI systems." NeuroImage 257 (2022): 119290.