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Diffusion in dendritic spines: impact on permeative exchange estimation with time-dependent diffusion-weighted MRI

Kadir Şimşek^1,2 and Marco Palombo^1,2
¹Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom, ²School of Computer Science and Informatics, Cardiff University, Cardiff, United Kingdom

Synopsis

Keywords: Microstructure, Microstructure, diffusion, brain, exchange, gray matter, water, microstructure, simulation, spines, dendrites

Motivation: Diffusion exchange models NEXI and SMEX assumes permeative exchange between intra- and extra-neurite compartments. Here, we hypothesize fine microstructures, like spines in dendritic segments, without permeable membranes can mimic permeative exchange.

Goal(s): We aim to emphasize the significance of taking diffusion-mediated exchange into account when interpreting model-based estimates of exchange in intricate microstructures like the gray matter of the brain.

Approach: Monte-Carlo water diffusion simulations in spiny dendritic branches, also featuring undulations and beading

Results: Our results question the way we interpret dMRI exchange estimates, emphasizing the need to exercise caution when inferring these estimates solely as indicators of membrane permeability.

Impact: Diffusion exchange models assumes permeative exchange between intra- and extra-neurite compartments. We hypothesize fine microstructures without permeable membranes can mimic permeative exchange. We aim to emphasize considering the impact of intricate microstructures in gray matter when interpreting model-based exchange estimates

Introduction

Time-dependent diffusion-weighted MRI (dMRI) can probe exchange in complex biological tissues^1–4. While it is expected that different exchange mechanisms contribute to the time-dependent signal^5,6, measurements are often primarily interpreted in terms of transcytolemmal water exchange. The Neurite Exchange Imaging (NEXI)³ and the Standard Model with Exchange (SMEX)² are two recent examples of model-based approaches to estimate exchange in brain tissue. Both NEXI and SMEX assume that the only exchange mechanism leading to the measured time-dependent dMRI signal is permeative exchange between intra and extra-neurite compartments.
This work aims to underscore the importance of considering diffusion-mediated exchange when interpreting model-based estimates of exchange in complex microstructures such as the brain Gray Matter (GM). We hypothesize that water diffusing within spiny dendrites in the GM, without crossing the cell membrane, can originate a time-dependent signature which is indistinguishable from permeative exchange (Fig.1A); and use Monte-Carlo simulations with a basic model of spiny dendrite (Fig.1B) to validate it and evaluate the impact of different spine densities on NEXI/SMEX estimates.

Methods

Spiny Dendritic Meshes
Skeletons of spiny dendritic branches for two sets of substrates were built on MathWorks MATLAB 2022a⁷ involving functions from the Trees-Toolbox⁸ and then surface meshed using Python Blender API ^{v2.799.
Set} I: ten spiny branches ($$$\sigma$$$=[0, 2.25] μm^-1) for investigating the exchange effect of diffusion in spines without undulation and/or beading. Set II: 16 spiny branches ($$$\sigma$$$=1μm^-1), featuring combinations of 4 undulation periods ($$$N_{period}$$$=[0, 2, 4, 8]) and 4 beading amplitudes ($$$A_{bead}$$$=[0, 1, 2, 3] μm). Other details of the spine morphology can be found in Fig.1A. Notably, any of these features can be changed arbitrarily, here, we investigated realistic spine densities and realistic to extreme undulations and beading in dendritic branches.
Diffusion Simulations & Data Analysis
DisimPy¹⁰ was employed in all simulations. The number of spins and time steps were determined by the Monte-Carlo convergence^11,12:10⁶ and 2000, respectively. Five different pulsed gradient schemes, combinations of three gradient separations ($$$\Delta$$$=[10, 25, 35] ms) and two gradient durations ($$$\delta$$$=[3, 15] ms) were used with 128 directions and diffusion-weighting b up to 7ms/μm². Periodic boundary conditions were used for intra-branch diffusion simulations with diffusivities 2μm²/ms (typical value for intra-neurite water^2,13). For a fair comparison with NEXI/SMEX biophysical modelling, we simulated the total signal arising from a dMRI voxel as the weighted sum of intra and extra-neurite signals, $$$S_{neurite}$$$ and $$$S_{Gaussian}$$$, respectively: $$$S_{total}=0.7S_{neurite}+0.3S_{Gaussian}$$$. $$$S_{neurite}$$$ is derived from our simulation in spiny dendrites at different spine densities and/or undulations, while $$$S_{Gaussian}$$$ is mono-exponential decay with diffusivity of 1 µm²/ms (Fig.3,4). We assumed 70% intra-neurite signal fraction. $$$S_{total}$$$ was fitted using NEXI model³ to estimate the exchange time ($$$t_{ex}$$$) for all simulated conditions.

Results and Discussion

Fig.2 shows the time-dependence of simulated signals at different b-values and for different spine densities. Decreasing signal amplitude with increasing $$$t_d$$$ (at fixed $$$b$$$) is more marked at higher spine densities and mirrors the observed time-dependence in both ex-vivo2 and in-vivo³ measurements in the rat GM. These time-dependencies have been interpreted solely as a consequence of membrane permeability. Fig.2 documents that the presence of spines can also lead to similar observation without any permeation across the dendritic membrane.
Furthermore, Fig.3B shows the exchange time $$$t_{ex}$$$ estimated using NEXI when we assume that the total signal in the dMRI voxel comes from a weighted sum of intra and extra-neurite signals, with spiny dendrites and no membrane permeability (Fig.3A). The estimated $$$t_{ex}$$$ values (3-60 ms) for spine densities typically observed in healthy cortical GM (0.5–1.5 µm^-1) are in very good agreement with both in-vivo and ex-vivo estimates from rat GM^2,3 and human¹⁴.
Finally, we acknowledge that the simulated spiny dendrites are oversimplified. Other microstructural features, such as undulations and beading, could also confound the interpretation of exchange mechanisms. Indeed, adding undulations leads to shorter exchange times when estimated with NEXI for realistic undulation periods 0-4 (Fig.4). In contrast, Fig.5 shows that beading leads to a different time-dependence of the direction-averaged signal, indicating more restriction to the diffusion, as previously reported¹⁵.
Future work will investigate whether it is possible to disentangle permeative from diffusion-mediated exchange and how sensitive and specific our measurements can be to spine-induced diffusion-mediated exchange (e.g. with respect to undulations and beading).

Conclusion

The time-dependent signal from diffusion within impermeable spiny dendrites is indistinguishable from permeative exchange. Our findings can contribute to a more insightful interpretation of exchange estimates using dMRI, underscoring the importance of cautioning when inferring exchange estimates as indicators of membrane permeability only.

Acknowledgements

This work, KS and MP are supported by UKRI Future Leaders Fellowship (MR/T020296/2).

References

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14. Uhl Q, Pavan T, Molendowska M, Jones DK, Palombo M, Jelescu I. Quantifying human gray matter microstructure using NEXI and 300 mT/m gradients. Published online July 18, 2023. Accessed November 8, 2023. https://arxiv.org/abs/2307.09492v1

15. Budde MD, Frank JA. Neurite beading is sufficient to decrease the apparent diffusion coefficient after ischemic stroke. Proc Natl Acad Sci U S A. 2010;107(32):14472-14477. doi:10.1073/PNAS.1004841107/SUPPL_FILE/PNAS.201004841SI.PDF

Figures

Figure 1: A. Sketches of the two major exchange mechanisms investigated in this work: permeative exchange across the dendritic membrane and diffusion-mediated exchange with no permeation due to the presence of spines. B. The tunable basic model of spiny dendrites we developed to control spine morphology and density. Here we focus on spine density, so all the spines have exactly the same morphology. Future studies will explore also the impact of spine morphology on exchange measurements.

Figure 2: Simulated normalized direction-averaged signal $$$S_{avg}$$$ for different substrates presenting spines at different densities $$$\sigma$$$ for narrow (A) and fat (B) pulses. The time-dependence shows decreasing signal amplitude at fixed diffusion-weighting $$$b$$$. As a reference, the volume fraction occupied by spines, $$$\eta$$$, is also reported.

Figure 3: A. For a fair comparison with NEXI/SMEX biophysical models, we simulated the total signal arising from a dMRI voxel as the weighted sum of intra and extra-neurite signals, $$$S_{neurite}$$$ and $$$S_{Gaussian}$$$, respectively. $$$S_{neurite}$$$ is derived from our simulation in spiny dendrites at different spine densities, while $$$S_{Gaussian}$$$ is mono-exponential decay with diffusivity of 1µm²/ms. B. The estimates of exchange time using NEXI on the simulated $$$S_{total}$$$ are reported as a function of spine density for both narrow and fat pulse cases.

Figure 4: A. Demonstration of spiny dendritic meshes at spine density $$$\sigma$$$=1μm^-1 with only undulations (undulation period, $$$N_{period}$$$=[0-8]). B. Estimated exchange times ($$$t_{ex}$$$) obtained from the diffusion signal $$$S_{total}$$$ of illustrated dendritic branches in A for short $$$\delta$$$ condition. The $$$t_{ex}$$$ times decrease with increasing undulation period; however, at extreme unrealistic undulation condition, $$$N_{period}$$$=8, trend changes.

Figure 5: A. Exemplary spiny meshes at spiny density $$$\sigma$$$=1μm^-1 featuring only beading with amplitudes $$$A_{bead}$$$=[0-3] μm. B. Simulated diffusion signals of beaded substrates do not indicate intra-compartmental (i.e., from spines to dendritic branch) exchange due to increasing signal amplitudes with increasing diffusion time. This outcome highlights beading is only introduce a restriction to the molecular diffusion as reported in the literature¹⁵.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

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DOI: https://doi.org/10.58530/2024/3456