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Time dependence of the diffusion and kurtosis tensors in strongly filtered diffusion signals

Noam Shemesh¹, Andrada Ianus¹, and Sune N Jespersen^2,3
¹Champalimaud Centre for the Unknown, Lisbon, Portugal, ²Center for Functionally Integrative Neuroscience, Department of Clinical Medicine, Aarhus University, Aarhus, Denmark, ³Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark

Synopsis

The sensitivity of diffusion MRI (dMRI) towards microstructural features is quite high, but its specificity is low due to the ubiquity of water in biological tissues. Here, we harness a strongly filtered diffusion kurtosis imaging (DKI) approach to (i) suppress fast diffusion spins typically associated with extracellular space and (ii) measure the time dependencies of the full filtered diffusion and kurtosis tensors in an ex-vivo mouse brain at 16.4T. Following the application of a very strong filter of b₁=15ms/µm² perpendicular to axon fibers, we find signatures for restricted diffusion that are tentatively associated with intracellular space.

Introduction

Diffusion MRI (dMRI) can provide detailed information on micron-scale dimensions even when the voxel size is very large^1,2. The sensitivity of dMRI methods, including Diffusion Tensor MRI (DTI) and Diffusion Kurtosis MRI (DKI) towards microstructural features in, e.g., disease³ or plasticity⁴, is well documented but specificity remains low in biological tissues⁵. The diffusion tensor⁶ and more recently, kurtosis tensor^7,8 time dependencies^9–11, along with the Standard Model for diffusion^2,12, have been proposed as more specific markers for in tissue microstructure. However, D(t) and K(t) experiments inherently conflate information from all tissue components.

Filtered dMRI experiments are typically used for measuring exchange by varying mixing time^13,14. More recently, filtered dMRI was used with an initial diffusion weighting designed to suppress more rapidly diffusing spins, followed by a conventional dMRI block probing the remaining components by varying the orientations and b-values of the second wavevector^15–17. The suppressed spins are typically considered “extra-axonal” or “extracellular”; however, effective suppression of extra-axonal components in white matter (WM) requires b>15 [ms/µm²]^18, and previous studies extracted direction-averaged properties rather than full tensors. Thus, the true time dependencies of the intracellular diffusivity and kurtosis still remain unknown.

Here, we harness a very high b-value filtered-DKI(t) approach to characterise detailed D(t) and K(t) profiles of the unsuppressed (restricted) water components in brain tissue.

Methods

All animal experiments were preapproved by the competent national and international authorities and were carried out according to EU Directive 2010/63.

Sample: A mouse brain was extracted from a healthy adult via intracardiac PFA perfusion and preserved in a PBS solution. The brain was then mounted in a 10 mm NMR tube filled with Fluorinert® and scanned at 37°C on a 16.4T scanner equipped with a microimaging probe capable of producing up to 3000 mT/m (isotropic).

MRI Experiments: A Double Diffusion Encoding^19,20 pulse sequence was modified (Fig. 1) such that the first gradient pulse pair provided strong constant diffusion weighting of b₁=15 ms/µm² (Δ₁/δ₁=10/3 ms) perpendicular to corpus callosum, followed by a 10 ms mixing time and another gradient pulse pair with δ₂=2 ms and variable Δ₂ of 4,5,6,7.5,10,12.5 and 15 ms. The b₂-values for the second pair were 0,1,1.5,2,2.5 ms/µm² for each and 30 directions per b₂-value were acquired, allowing for the extraction of the full diffusion and kurtosis tensors from the filtered diffusion component. A total of 8 S(0,0) and 10 S(15 ms/µm²,0) images were acquired per b-value. Other parameters were TR/TE = 3000/51 ms, EPI bandwidth = 400 kHz (single shot, no partial FT), FOV = 18×10 mm2, in-plane resolution 180×180 µm2, slice thickness 0.7 mm (3 slices), and 16 averages.

Data Analysis: Pre-processing included MP-PCA denoising^21, ghost correction²², phase-unwrapping and extraction of real(data)²³, and Gibbs unringing²⁴. The pre-processed data were then fit to a simple DKI model²⁵ yielding mean, axial and radial diffusivities (MD, AD, and RD, respectively), and mean, axial and radial kurtosis (MK, AK, and RK, respectively).

Results

We first examine the quality of the data after imparting a very strong filter of b1=15 ms/µm². Figure 2 shows the preprocessed data with S(0,0) (Fig. 2A), and filtered data S(b₁=15 ms/µm², b₂) b₂ = 0-2.5 ms/µm² (Fig. 2B). The scalebar of Fig. 2A is x10 of 2B. Images are of sufficient quality for analysis even when strong diffusion filtering was applied. The median signal to noise ratios for S(0,0) and S(15,0) images were 126 and 37 respectively. Fig. 2C shows the entire decay curve, including the 5-fold attenuation due to the filter; the inset zooms onto the decay of the filtered data only S(b₁=15 ms/µm², b₂), evidencing a high quality non-gaussian signal decay.

Individual filtered maps for the two extreme diffusion time regimes (4 ms and 15 ms) are shown in Fig. 3 and Fig. 4, the former for diffusion tensor properties (and S(15,0)) and the latter for the kurtosis parameters, respectively. Fig. 5 shows the time dependence in ROIs comprising corpus callosum and cortical gray matter. Notice the non-monotonic RK, which likely reflects restriction in WM.

Discussion

The filtered DKI(t) sequence effectively suppresses signals from components with higher diffusivity, presumably extracellular^15,17in general and extra-axonal in WM. Thereby, diffusion of intracellular components can be probed with higher specificity. The striking RK(t) curve in corpus callosum suggests that given the radial diffusivity and the time to peak, the restricted component diffuses a characteristic length scale of l_c = ~2.1 µm (calculated from the Einstein equation). This observation is consistent with the apparent early decrease in RD(t), but not with its behaviour at later times, perhaps due to microscopic orientation dispersion effects (e.g., undulation along the fiber). Notably, the calculated correlation length is larger than typical axonal diameters in mouse corpus callosum (~1 µm), suggesting that the time-dependence arises from signal in the larger axons¹⁸ and consistent with recent findings of microscopic kurtosis in Correlation Tensor MRI^26,27. Our findings thus suggest that intra-cellular water components experience restricted diffusion, as also shown by experiments probing the time-dependent diffusion coefficient of intracellular metabolites²⁸.

Conclusions

The intra-axonal component (at least in mouse corpus callosum ex-vivo) exhibits time-dependent restricted diffusion. These filter-DKI(t) experiments shed light into the basic diffusion properties in the brain and enhance dMRI’s specificity.

Acknowledgements

This work was supported in part by “la Caixa” Foundation (ID 100010434) and European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 847648, fellowship code CF/BQ/PI20/11760029.

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Figures

Figure 1. Pulse sequence and model. A DDE waveform is used with and as independent blocks separated by a mixing time (τ_m). In the filtered DKI experiment, >>D_e(n₁) thereby significantly attenuating the signal from this component. The remaining signal is then probed for time dependence using applied along 30 directions (n₂), enabling a full DKI analysis for every diffusion time. TE is always constant. The interpretation of the signal for fibers perpendicular to the filter is shown on the right, and is an extension of the Standard Model.

Figure 2. Data quality. (A) S(b₁=0, b₂=0) reveals a typical signal to noise (S/N) of >120. (B) As b₁ is set to 15 ms/µm², a strong attenuation is observed but the typical S/N remains high, > ~30. As b₂ is increased from 0-2.5 ms/µm², signals are further attenuated. (C) Quantification in an ROI comprising corpus callosum (different markers in each b-value represent different G₂ directions) reveals clear non-gaussian signals –the linear (red) fits do not describe the data while DKI (black) fits are adequate (only the highest, lowest and middle fits are shown for clarity).

Figure 3. Diffusion Tensor maps for the filtered experiment. (Top) Maps for Δ=4ms. (Bottom) Maps for Δ=15ms. Despite the very strong filter, high quality maps are obtained. S(15,0) is the fitted signal for b₁=15 ms/µm² and b₂=0; note how the white matter signal is larger than gray matter, inverting the typical contrast for b=0 data due to the strong filter. AD- Axial Diffusivity; RD – Radial diffusivity; MD – Mean diffusivity; FA – Fractional Anisotropy

Figure 4. Diffusion kurtosis maps for the filtered experiment. (Top) Maps for Δ=4ms. (Bottom) Maps for Δ=15ms. Despite the very strong filter, high quality maps are obtained. Note that in WM, as expected, RK<AK. MK – Mean Kurtosis; AK – Axial Kurtosis; RK – Radial Kurtosis.

Figure 5. Quantification of the time dependent experiments for corpus callosum and cortical gray matter ROIs. S0’s are stable, while diffusivities slowly decrease. The radial kurtosis (RK) shows a marked peak for the corpus callosum voxel, suggesting restriction.

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

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DOI: https://doi.org/10.58530/2022/2428