Background

NEXI¹ (or SMEX²) is a two-compartment diffusion model that accounts for inter-compartment exchange. It is suited to characterize gray matter (GM) microstructure; its parameters are the inter-compartment exchange time t_ex, the intra and extra-neurite apparent diffusivities D_i and D_e and the intra-neurite signal fraction f. It has first been implemented in a preclinical setting in vivo¹ and ex vivo². Here, we aim to optimize the acquisition protocol for NEXI parameter estimation and demonstrate feasibility on a clinical 3T system.

Methods

Simulated data: Synthetic signals were generated using the NEXI model for a large number of parameter combinations, with Rician noise and SNR at b=0 ranging 80 – 120, assuming 3 different acquisition protocols. Parameter combinations included t_ex ranging [0 – 150]ms, D_i and D_e [0.1 – 3.5]µm²/ms and f [0.1 – 0.9]. Each protocol sets a total number of measurements N and the associated b-value and diffusion time (b,t) pairs. For each protocol, one multi-layer perceptron (MLP) of 3 hidden layers and 500 neurons per layer was trained on 2.10⁶ random sets and applied to a test set of 10⁴ other examples, taking as input the simulated signals and as output the corresponding NEXI parameter combinations. The first ‘Extended’ protocol was a grid of 14 b-values (1 – 7.5ms/µm²) and 12 diffusion times (20 – 47.5ms) (N=168). The Shapley values of this network were calculated on a subset of training and test sets using SHAP³ to estimate the importance of each (b,t) pair in the NEXI parameter estimations. The (b,t) pairs with highest importance were used to establish an ‘Optimized’ protocol with a realistic number of measurements (N=16). This protocol was compared to a ‘Clinical’ grid-like protocol, based on the mean absolute error (MAE) of each parameter estimation derived from these protocols. Cramer Rao Lower Bounds (CRLB) of both protocols were finally computed from simulated signals obtained from several ranges of Ground Truths. Clinical data: The study was approved by the relevant ethics board. One male healthy volunteer was scanned. Acquisition: Diffusion-weighted images were acquired on a 3T system with 80 mT/m gradients (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany), using a PGSE-EPI research sequence with the following parameters: b-values=1.00, 2.00, 3.20, 4.44 and 5.00ms/µm², 20 directions per shell, diffusion times Δ=28.3, 36.0, 45.0, 55.0 and 65.0ms, δ=16.5ms, 4 b=0 images, spatial resolution=2x2x2 mm³, total scan time: 35min. The (b,t) pairs corresponded to the “Clinical” protocol. Processing: Multi-shell multi-diffusion time data were preprocessed jointly; steps included MP-PCA magnitude denoising⁴, Gibbs ringing⁵, distortion and Eddy current corrections⁶. Parametric maps of the NEXI model parameters were estimated from the powder-average signals using non-linear least-squares (NLS) and the MLP network trained previously on the Clinical protocol.

Results and discussion

The most important (b,t) pairs for each of the NEXI parameters vary (Fig. 1): (low b, low t) and (high b, high t) combinations for t_ex, low b and full-range of t for D_i, low-medium b and medium-long t for both D_e and f. To produce an optimized protocol of N=16 (b,t) pairs, we ranked for each parameter the best (b,t) pairs by mean absolute SHAP value, weighted by the sign of the median SHAP value. Based on the RMSE on each parameter in the Extended MLP, normalized by the parameter range, we assigned 8 optimal pairs for t_ex, 4 for D_i, 2 for D_e and 2 for f (Fig. 2). In other words, the parameter with highest normalized RMSE got the largest number of optimal (b,t) pairs for its estimation. Remarkably, the MAE of the MLPs trained on the Optimized protocol was only slightly lower than that of the Clinical protocol (Table 1). The Optimized protocol also yielded slightly lower CRLB (Fig.3) for typical experimental NEXI values (see Fig.4), which suggests the variances of experimental estimates could potentially be further reduced. The marginal improvement does not however allow us to favor one protocol over the other, especially as some pairs of the Optimized protocol are difficult to achieve on a clinical system. Using the Clinical protocol, we report the first microstructure maps of the NEXI model estimated in the human brain on a conventional clinical scanner, using NLS and MLP (Fig.4). NLS results in numerous voxels hitting the permitted parameter bounds, while MLP does less. Using a cortical ribbon mask, we estimate typical NEXI parameter values in the cortex, which are consistent between NLS and MLP, as well as with previous estimates in the rat cortex¹.

Conclusion

The limit on NEXI parameter estimation precision and accuracy is largely driven by the model and the type of measurements available (linear diffusion encoding, in a combination of (b,t) pairs) and only leaves room for moderate improvement as can be estimated from CRLB. The silver lining is that a clinical acquisition protocol feasible on a 3T system with 80 mT/m gradients yields reasonable NEXI microstructure maps in the human brain. Future work will focus on estimating the robustness of these maps across subjects, as well as search for improved strategies in denoising and possibly data coverage (e.g. multi-dimensional MRI measurements) to lower the CRLB’s nonetheless. The effect of ‘fat’ diffusion pulses will also be investigated, as suggested previously².

Acknowledgements

QU, TP and IJ are supported by SNSF Eccellenza grant PCEFP2_194260. EJC-R was supported by SNSF Ambizione grant PZ00P2_185814.

References

[1] Jelescu, Neuroimage 2022 [2] Olesen, NeuroImage 2022 [3] Lundberg and Lee, NIPS 2017 [4] Veraart, NeuroImage 2016 [5] Kellner, MRM 2016 [6] Andersson, NeuroImage 2016.