Background

NEXI¹, or SMEX², and SANDIX² are recent gray matter (GM) microstructure models that focus on either exchange time, soma radius or both estimations. While these models try to better represent the underlying (GM) microstructure, their increased complexity makes the estimation of the model parameters more challenging.
For a given model, the choice of acquisition protocol is crucial, as it allows to tune the sensitivity to some tissue parameters. However, rich protocol acquisitions are unsuited for patients due to very long scan time, as opposed to preclinical acquisitions. In clinical settings, where the protocol is less extensive, it becomes necessary to characterize its suitability for estimating microstructure parameters of a given model.
Bayesian inference methods, such as µGUIDE³, aim to estimate full posterior distributions, which allow to quantify the quality of the fitting and highlight degeneracies.
This work aims at studying the fitting quality of NEXI and SANDIX, given two acquisition protocols used in literature, using µGUIDE. We investigate the impact on the fitting of both the acquisition protocol and the noise.

Methods

Model definitions: NEXI¹ is a two-compartment model with four microstructure parameters: exchange time between neurites and extra-cellular space (ECS) t_ex, intra- and extra-neurite diffusivities D_i/D_e, and neurite signal fraction f. SANDIX² adds a third compartment of impermeable spheres to model soma, adding additional soma signal fraction fs and radius rs, making it more challenging to fit.
Protocols: We considered two PGSE protocols. First one is an extensive ex-vivo acquisition protocol, similar to the one used to validate SANDIX², while the second one is a protocol feasible for in-vivo human acquisitions, the NEXI3T Connectom protocol⁴.
Simulated data: Synthetic signals were generated following NEXI and SANDIX , using random parameter combinations sampled on biological feasible ranges, for each protocol. Rician noise levels sampled from the clinical data were added to the signals, with a median SNR of 50, to mimic real data acquisitions. 10⁶ synthetic signals were used for training µGUIDE.
Clinical data: Four healthy volunteers were scanned (2 of whom rescanned on a different day). An MPRAGE was acquired for anatomical reference (1-mm isotropic resolution). Diffusion-weighted images were acquired on a 3T Siemens Connectom system using a PGSE EPI sequence with combinations of b-values of 1 (13 directions), 2.5 (25 dir.), 4 (25 dir.), 6 (32 dir.) and 7.5ms/µm² (65 dir.) and Δ=20, 29, 39 and 49ms; δ=9ms, and 15 b=0 images per Δ at 1.8-mm isotropic resolution, TE/TR=76/ 3700 ms, for a total scan time of 45 minutes.
Processing: Multi-shell multi-diffusion time data was preprocessed jointly; steps included MP-PCA magnitude denoising⁵, Gibbs ringing correction⁶, distortion and eddy current correction⁷. The cortical ribbon was segmented on the MPRAGE image using FastSurfer⁸ and projected onto the diffusion native space using linear registration⁹. Parametric maps of both models were estimated using non-linear least squares and µGUIDE. We extract three measures from the estimated posterior distributions: maximum-a-posteriori, an ambiguity and an uncertainty measure.

Results and discussion

Fig.1&2: The extensive protocol acquisition allows to remove almost all degeneracies and substantially reduce the uncertainty of the estimates. However, this protocol is heavily impacted by noise presence , as the signal for high b-values is mostly lost. The fitting quality of the Connectom protocol is less affected by the presence of noise, as it relies on smaller b-values. However, even when considering a noise-free scenario, this protocol shows bias and variance in parameter estimates.
Estimates using NEXI with the Connectom protocol and a realistic noise level (Fig.1.D) demonstrates that t_ex estimates are mostly unreliable, while the model shows good capacity to estimate De and f. In the presence of noise, it seems impossible to jointly estimate tex and rs accurately (Fig.2.C&D).
Fig.3: High uncertainties, indicating low confidence, are obtained for t_ex in the model NEXI. De and f estimates using SANDIX show a low uncertainty, as expected from the simulations.
Fig.4 compares the estimations obtained on the cortical ribbons of all the participants using a non-linear least square fitting method and µGUIDE. Only estimates with uncertainty and ambiguity <50% were kept on µGUIDE’s estimations. Similar results are obtained on NEXI, while SANDIX shows substantial differences for t_ex, radius and Di. NEXI and SANDIX give the same estimates of extra-neurite diffusivity for all methods.

Conclusion

Our results reveal that each protocol exhibits unique strengths. The extended protocol remains resilient to noise, while the Connectom protocol also demonstrates robustness. The second protocol's limitation is its low coverage of b-values and diffusion times. Our results obtained with µGUiDE align with those obtained using Non-linear least squares, further bolstering our confidence in the former's learning capabilities.

Acknowledgements

MJ and MP are supported by UKRI Future Leaders Fellowship (MR/T020296/2).

References

[1] Jelescu, NeuroImage 2022; [2] Olesen, NeuroImage 2022; [3] Jallais et al., ISMRM 2023; [4] Uhl et al., arXiv 2023; [5] Veerart, NeuroImage 2016; [6] Kellner, MRM 2016; [7] Andersson, NeuroImage 2016; [8] Henschel, NeuroImage 2020; [9] Avants et al., Insight j, 2009