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Towards quantifying Gray Matter “micro-connectivity”: the measurable impact of dendritic spines on metabolite diffusion

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, brain, diffusion, microstructure, metabolites, DW-MRS, spines, gray matter, simulation

Motivation: Dendritic spines are fine microstructures increase the complexity of brain cells. Spines are characteristic morphological feature of neurons and their density can change with pathological conditions.

Goal(s): Quantification of dendritic spines in gray matter in human brain using diffusion-weighted MR spectroscopy

Approach: Using Monte-Carlo diffusion simulations for metabolites, to investigate how a dMRS signal is sensitive to the dendritic spines.

Results: Our findings suggests potential biomarkers for characterizing dendritic spines in human brain gray matter using diffusion-weighted MR spectroscopy

Impact: This work establishes a benchmark for spine sensitivity and quantification. Also it offers potential dMRS acquisition parameters for spine detection in human brain.

Introduction

The brain gray matter (GM) exhibits highly heterogeneous and complex microstructures that can be probed by diffusion-weighted MRS (dMRS) in-vivo^1–4. Several works have already investigated the effect of cell body size/density^5,6; cell processes branching^6–8, undulation⁹, beading¹⁰ and orientation dispersion^7,11 on dMRS measurements.
However, only a few works^12,13 have investigated the potential effects of secondary structures like dendritic spines. Dendritic spines play a crucial role in synapse development and plasticity in both healthy and pathological conditions^14–16. But it is still unclear what the impact of dendritic spine is on metabolites dMRS signal and whether we can measure it in typical human acquisitions.
Here we aim to answer these questions by investigating the impact of dendritic spine density on dMRS measurements using numerical simulations.

Methods

Spiny Dendritic Meshes
Skeletons for ten spiny branches were built on MATLAB R2022a¹⁷ (MathWorks) involving functions from the Trees-Toolbox¹⁸ and then surface meshed using Python Blender API v2.79¹⁹. Spine density $$$σ$$$ was varied from 0 to 2.25μm^-1. The branch length was 250μm with a diameter of 1μm. The spines having diameter of 1μm, were connected to the main branch with a cylindrical neck having a diameter of 0.25μm and a length of 1.5μm. Notably, any of these features can be changed arbitrarily, but here we focused on spine density and purposely varied only that. Moreover, to investigate the impact of undulation and beading in addition to spine, we also added undulation and beading with period [0-8] and amplitude [0-3]μm, respectively.
Diffusion Simulations & Data Analysis
All diffusion Monte-Carlo simulations were performed using DisimPy²⁰ with periodic boundary conditions. The number of spins 10⁶ and time steps 2000 were determined by the Monte-Carlo^21,22; intra-branch diffusivity was 0.35μm²/ms (typical value for N-acetyl-aspartate, NAA²³).
We simulated 15 different pulsed gradient schemes with combinations of eight gradients separations($$$\Delta$$$= [10, 25, 35, 55, 85, 160, 235, 310] ms), two gradients ($$$\delta$$$= [3, 15] ms), 128 directions and b-values up to 25ms/μm².
To characterize the hindering/restricting effect of spines on metabolites diffusion, we used a modified astro-sticks model (mAS)^2,24,25. This model is based on randomly-oriented sticks with effective intra-stick axial diffusivity $$$D_{eff}(D_{intra},K_{intra},b,\theta)=D_{intra}(1-K_{intra}D_{intra}b\cos^2\theta)$$$, where $$$\theta$$$ is the angle between the branch direction and the diffusion gradient direction, $$$D_{intra}$$$ is the metabolite intra-stick apparent axial diffusivity, and $$$K_{intra} is the metabolite intra-stick apparent axial kurtosis, accommodating non-Gaussian diffusion due to spines hindering/restriction^24,25. The numerical integration yields the corresponding powder-averaged signal^13,26,27:
$$S/S_0 = \int^1_0e^{bD_{eff}\cos^2\theta}d(\cos\theta)$$

Results

Exemplary pyramidal cells from adult rat brain cortex²⁸ are illustrated in Fig.1A alongside a typical spiny dendritic segment. For comparison, our spiny dendrite substrates are shown in Fig.1B, including the geometric properties.
Fig.2 depicts the simulated diffusion signals for all diffusion times, $$$t_d$$$, with both $$$\delta$$$ conditions. The mAS model fits perfectly the metabolite signals, as illustrated in Fig.2. The horizontal lines are the spine volume fractions ($$$\eta$$$) illustrated to highlight intracellular exchange between compartments (i.e. spines and main dendrite), which is prominent for $$$\sigma$$$>0.75.
Fig.3 presents estimated $$$D_{intra}$$$ and $$$K_{intra}$$$ values as a function of (and corresponding $$$\eta$$$ values).
The sensitivity analysis of spines on the dendritic branches is reported in Fig.4 for ideal (A) and clinically feasible (B) acquisitions. At the top of each panel, the mean values of $$$D_{intra}$$$ & $$$K_{intra}$$$ obtained from noise-induced signals at different SNR levels are illustrated as a function of $$$\sigma$$$. At the bottom, the relative changes in $$$D_{intra}$$$ & $$$K_{intra}$$$ driven by corresponding percentage changes of (i.e. +-25%; +-50%) from a given reference value of $$$\sigma$$$=1μm^-1 are reported.
Fig.5 shows the relative changes in $$$D_{intra}$$$ & $$$K_{intra}$$$ obtained as in Fig.4 but from undulated and beaded spiny branches for the reference =1μm^-1 for short (B) and fat (C) pulse schemes; ideal (top row) and clinically feasible (bottom row) cases.

Discussion

For changes in $$$\sigma$$$ from the typical value 1μm^-1 observed in pathologies like essential tremor (~-25%)¹⁴ and autism (~+50%)¹⁶, $$$D_{intra}$$$ & $$$K_{intra}$$$ from the mAS model show measurable changes for the ideal acquisition at $$$t_d$$$=9ms. For the pulse scheme used in clinical human studies^13,26, only changes in $$$D_{intra}$$$ remain measurable, while changes in $$$K_{intra}$$$ require SNR>100 to be measurable.
Noteworthy, undulations and beading overall lead to further decreasing $$$D_{intra}$$$ and increasing $$$K_{intra}$$$. However, this effect is minimal (~+-10%) for realistic values of beading amplitude (1-2μm) and undulation period (0-4), and even less (~+-5%) for clinically feasible pulse schemes.

Conclusion

This study suggests that metabolite diffusion as measured by dMRS can be sensitive to spine density and that $$$D_{intra}$$$ & $$$K_{intra}$$$ from the mAS model can be promising imaging markers of GM ‘micro-connectivity’ in healthy and diseased brain.

Acknowledgements

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

References

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Figures

Figure 1: (A) Pyramidal cells from adult mouse cortex are illustrated as an example of spines in real cells on the left. A typical dendritic segment in a neuronal cell is presented on the right that can have spine density varying from 0.5 to 2 spines per micron. (B) Illustration of tuneable basic spiny segments with a chart inscribing geometric properties of the branches, including spine densities ($$$\sigma$$$) and spine volume fractions ($$$\eta$$$).

Figure 2: Simulated metabolite diffusion signals for all spiny branches with spine densities, $$$\sigma$$$, up to 2.25µm^-1 are depicted as dots for short and fat gradient pulses (A and B, respectively). The lines represent the fit with the modified astro-sticks model^24–26 (mAS Model) for spine quantification. The horizontal lines show the spine volume fraction level ($$$\eta$$$) which has impact on $$$\sigma$$$>0.75 μm^-1. The missing $$$\eta$$$ lines are hidden due to the scaling on the y axis.

Figure 3: Estimated model parameters ($$$D_{intra}$$$ & $$$K_{intra}$$$) are illustrated as a function of $$$\sigma$$$ for short (A) and fat (B) gradient pulse schemes. The colour coding indicates diffusion signals at different $$$t_d$$$s up to 310ms, for $$$\delta$$$=3ms (A) and $$$\delta$$$=15ms (B), respectively.

Figure 4: Spine sensitivity analysis - 100 diffusion signals with different signal-to-noise (SNR) levels were generated. The mean $$$D_{intra}$$$ & $$$K_{intra}$$$ and their standard deviations are compared with $$$\sigma$$$ (A: ideal; B: clinically feasible gradient scheme). At the bottom of each panel, the change in $$$D_{intra}$$$ & $$$K_{intra}$$$, are shown with errors for typical changes [±25%, ±50%] in $$$\sigma$$$=1μm^-1 due to pathology^14–16. Cohen’s d-values report stronger effect sizes are observed for $$$D_{intra}$$$ when a decrease occurs in the $$$\sigma$$$.

Figure 5: Matrix-plots demonstrate the computed percentage changes in $$$D_{intra}$$$ & $$$K_{intra}$$$ with respect to the case of no undulation and beading for $$$\sigma$$$=1μm^-1, obtained from undulated and beaded spiny branch simulation estimates. $$$D_{intra}$$$ & $$$K_{intra}$$$ percentage differences are shown for ideal (top) and clinically feasible (bottom) pulse schemes. Exemplary beaded and undulated spiny branches are illustrated on each axes (x and y, respectively).

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

0933

DOI: https://doi.org/10.58530/2024/0933