0981

How to understand diffusion MRI changes in the white matter of Multiple Sclerosis patients?

Ying Liao¹, Santiago Coelho¹, Wafaa Sweidan¹, Jenny Chen¹, Dmitry S. Novikov¹, and Els Fieremans¹
¹Radiology, NYU School of Medicine, New York, NY, United States

Synopsis

Conventional diffusion MRI (dMRI) techniques, such as DTI and DKI, are sensitive to pathology but lack specificity. In brain white matter, the “Standard Model” framework of dMRI may provide specificity to microstructural changes. Generally, clinical dMRI is noisy and limited, making SM estimation challenging. Thus, different constraints and techniques have been introduced to robustly extract SM parametric maps. Here, we employ a large clinical dataset of Multiple Sclerosis patient data (N = 134) and noise propagation experiments to study the sensitivity and specificity of these techniques.

Introduction

Diffusion MRI (dMRI) and derived metrics from DTI¹ and DKI² are sensitive to pathology. To achieve microstructural specificity, the Standard Model³ (SM) framework has been proposed as an overarching dMRI model for white matter (WM) unifying many previously proposed WM models^4-16. The SM signal, measured along direction

$\hat{g}$ , is a convolution between the fiber orientation distribution function (ODF)

$\mathcal{P}(\hat{n})$ and the fiber response signal

$\mathcal{K}(b,\hat{g}\cdot\hat{n})$

$S_{\hat{g}}(b)=\int_{|\hat{n}|=1}d\hat{n}\,\mathcal{P}(\hat{n})\,\mathcal{K}(b,\hat{g}\cdot\hat{n})$ where

$\mathcal{K}(b,\xi)=S_0\,[fe^{-bD_{a}\xi^2}+(1-f)e^{-bD_{e}^{\parallel}\xi^2-bD_e^\bot(1-\xi^2)}]$ with

$\xi=\hat{g}\cdot\hat{n}$ . Here

$[f,D_{a},D_{e}^{\parallel},D_{e}^{\bot},p_2]$ are intra-axonal space (IAS) fraction, IAS axial diffusivity, extra-axonal space (EAS) axial diffusivity, EAS radial diffusivity and

$l=2$ rotational invariant of ODF, respectively.
Due to the multi-compartmental nature of the SM, the estimation of SM parameters in clinical data is degenerate¹¹. To resolve the degeneracy, WMTI¹³ and WMTI-Watson¹⁴ (denoted as Watson+ for

$D_{a}>D_{e}^{\parallel}$ and Watson- for

$D_{a}<D_{e}^{\parallel}$ ) employ relatively robust DKI metrics to derive SM parameters, while NODDI⁸ and SMT¹⁵ assume same axial diffusivity in IAS and EAS and the tortuosity approximation

$D_e^{\bot}=D_e^{\parallel}\cdot(1-f)$ . Moreover, ML-RotInv¹⁶ was employed to map

$l=0,\,2$ rotational invariants to SM parameters using a data-driven approach.
Here we compare these estimation methods by assessing WM degeneration in a clinical cohort of patients with multiple sclerosis (MS), and interpret the findings using noise propagation.

Methods

In-vivo MRI:
In a retrospective IRB-approved study, 134 MS patients (age 47.80 ± 9.60 years old, 91 females) and 124 matching controls (age 48.41 ± 9.95 years old, 84 females) were selected. These subjects underwent clinically indicated MRI using at 3T (Siemens Magnetom Prisma or Skyra). MS subjects received a clinical MS diagnosis using the McDonald criteria¹⁷, and control subjects were recruited from headache patients with normal brain MRI and no neurological disorders.
The dMRI protocol included a monopolar EPI sequence as follows: 4 b = 0, b = 250 s/mm² along 4 directions, b = 1000 s/mm² along 20 directions and b = 2000 s/mm² along 60 directions, with imaging parameters: 50 slices, 130 × 130 matrix, voxel size = 1.7 × 1.7 × 3 mm, TE = 70 ms on Prisma or TE = 95 ms on Skyra, TR = 3500 ms, GRAPPA acceleration 2, and multiband 2.
The dMRI data was processed by DESIGNER¹⁸ for denoising¹⁹, Gibbs artifact correction²⁰, motion and eddy correction²¹. SM parameters were obtained using all SM parameter estimation methods mentioned above. The genu corpus callosum (GCC) was automatically segmented by nonlinear mapping on the JHU WM label atlas²². Median values were extracted for SM and DKI metrics, and used to conduct one-way ANCOVA between control and MS groups for each parameter of interest, with group membership acting as the independent variable and controlling for patient age.

Numerical noise propagation:
Numerical noise propagation was done using synthetic dMRI signals generated with random combinations of SM parameters based on the same protocol as above. Gaussian noise at signal-to-noise ratio = 40 was added and then SM estimation methods were applied to the noisy synthetic data to predict SM parameters.
The sensitivity-specificity matrix (

$S_{ij} = \frac{\partial \hat{\theta}_{j}}{\partial \theta_{i}}$ ) is computed through linear regression of each estimated SM parameter

$\hat{\theta_{j}}$ with respect to the ground truth

$\theta_{i}$ of all five SM parameters, reflecting how changes in ground truth are picked up in the estimation.

Results and Discussion

Fig. 1 shows that DKI metrics are sensitive to MS pathology, consistent with previous studies^{23, 24}, but the underlying pathological processes remain unclear.
Table 1 reveals many SM parameter changes between control and MS, but these changes are not consistent across different SM estimation methods. Clearly, the model assumptions and fitting constraints of each estimation method impact these results. To help interpret these, we performed noise propagation for all SM estimation methods.
Fig. 2 displays the sensitivity-specificity matrix for all SM estimation methods, whereby diagonal elements measure sensitivity and off-diagonal elements show specificity. The sensitivity-specificity matrix reveals how spurious findings may arise: for axial compartmental diffusivities, Watson+ has a strong negative correlation with

$f$ , while Watson- and WMTI have strong positive correlations with

$p_2$ , which makes them unreliable in estimating axial compartmental diffusivities. Furthermore, ML-RotInv has the highest sensitivity to

$p_2$ demonstrated both by the sensitivity-specificity matrix and the detection of a significant change (p < 0.001) in

$p_2$ between controls and MS.
Overall, ML-RotInv seems the most robust and specific SM estimation method, and detects an increase in

$D_e^{\bot}$ and decrease in

$f$ (Table 1), which may reflect demyelination and axonal loss^{25, 26}, warranting further investigation. Fig. 3,4 show scatter plots of

$D_{e}^{\bot}$ versus

$f$ for noise propagation and clinical data, respectively. While the negative correlation (

$\rho=-0.46$ ) between

$f$ and

$D_e^{\bot}$ by ML-RotInv in MS (Fig. 4) could be due to estimation bias (Fig. 3), the positive correlation (

$\rho=0.36$ ) in controls seems genuine. This observation is consistent among all estimation methods, except for SMT and NODDI which have a tortuosity constraint. This is contrary to what tortuosity models^{8, 27} assume and could potentially be understood by accounting for myelin.

Conclusions

SM estimation methods introduce spurious changes in MS pathology when applied to clinical dMRI. The sensitivity-specificity matrix reveals important insight into the specificity of each estimation method. These results also warn against employing simple constraints in microstructure imaging and argue for more realistic biophysical models.

Acknowledgements

This work was performed under the rubric of the Center for Advanced Imaging Innovation and Research (CAI2R, https://www.cai2r.net), a NIBIB Biomedical Technology Resource Center (NIH P41-EB017183). Thiswork has been supported by NIH under NINDS award R01 NS088040 and NIBIB awards R01 EB027075.

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Figures

Fig. 1. Median DKI metrics in GCC. One-way ANCOVA was conducted between control and MS cases accounting for age. All DKI metrics but axial diffusivity (AD) are sensitive to the MS pathology despite lack of specificity to microstructural changes.

Table 1. SM parameter estimation by different estimation techniques in GCC of controls vs MS patients. ANCOVA accounting for age (p-value < 0.05 in bold) reveals

$f$ and

$D_e^{\bot}$ as the parameters with the most significant changes, consistent among all estimation methods. These parameters are responsible for distinct pathological mechanisms and further explored in Fig. 3 and 4.

Fig. 2. Sensitivity-specificity matrix of SM parameter estimation. Each column is calculated by a linear regression of the estimation with respect to ground truth. Diagonal elements are the measure of sensitivity while the off-diagonal elements indicates specificity. Ideally, this matrix is an identity matrix, which means the change of one SM parameter in ground truth is fully captured in its own estimation with no effect on the estimation of the other parameters. Deviation from an identity matrix suggests the entanglement between parameters, especially between diffusivities.

Fig. 3. The scatter plot between

$D_e^{\bot}$ and

$f$ in numerical noise propagation by different SM estimation methods. The correlation

$\rho$ between

$f$ and

$D_e^{\bot}$ is indicated on top of each figure.

Fig. 4. The scatter plot between median

$D_e^{\bot}$ and

$f$ in GCC by SM estimation methods. The correlation between

$D_e^{\bot}$ and

$f$ in controls and MS patients are indicated on top of each figure. The negative correlation (

$\rho=-0.46$ ) between

$D_e^{\bot}$ and

$f$ estimated by ML-RotInv in MS patients might be caused by the estimation bias (Fig. 3), whereas the positive correlation (

$\rho=0.36$ ) in controls seems genuine and consistent among all estimation methods, except for SMT and NODDI with tortuosity constraints.

Proc. Intl. Soc. Mag. Reson. Med. 30 (2022)

0981

DOI: https://doi.org/10.58530/2022/0981