Can we detect the effect of spines and leaflets on the diffusion of brain intracellular metabolites?

Abstract

Prior models used to clarify which aspects of tissue microstructure mostly affect intracellular diffusion and corresponding diffusion-weighted magnetic resonance (DW-MR) signal have focused on relatively simple geometrical descriptions of the cellular microenvironment (spheres, randomly oriented cylinders, etc…), neglecting finer morphological details which may have an important role. Some types of neurons present high density of spines; and astrocytes and macroglial cells processes present leaflets, which may all impact the diffusion process. Here, we use Monte-Carlo simulations of many particles diffusing in cylindrical compartments with secondary structures mimicking spines and leaflets of neuronal and glial cell fibers, to investigate to what extent the diffusion-weighted signal of intracellular molecules is sensitive to spines/leaflets density and length. In order to study the specificity of DW-MR signal to these kinds of secondary structures, beading-like geometry is simulated as "control" deviation from smooth cylinder too. Results suggest that: a) the estimated intracellular tortuosity increases as spines/leaflets density or length (beading amplitude) increase; b) the tortuosity limit is reached for diffusion time t>200 ms for metabolites and t>70 ms for water molecules, suggesting that the effects of these finer morphological details are negligible at t longer than these threshold values; c) fiber diameter is overestimated, while intracellular diffusivity is underestimated, when simple geometrical models based on hollow smooth cylinders are used; d) apparent surface-to-volume, S/V, ratio estimated by linear fit of high frequency OG data appears to be an excellent estimation of the actual S/V ratio, even in the presence of secondary structures, and it increases as spines and leaflets density or length increase (while decreasing as beadings amplitude increases). Comparison between numerical simulations and multimodal metabolites DW-MRS experiments in vivo in mouse brain shows that these fine structures may affect the DW-MRS signal and the derived diffusion metrics consistently with their expected density and geometrical features. This work suggests that finer structures of cell morphology have non-negligible effects on intracellular molecules' diffusion that may be measured by using multimodal DW-MRS approaches, stimulating future developments and applications.

ActiveAxADD: Toward non‐parametric and orientationally invariant axon diameter distribution mapping using PGSE

“…43 In vivo metabolites have diffusivities similar to ex vivo water, which matches our simulations. 43 Other WM features should be taken into consideration when applying ActiveAx ADD on real data. First, our simulations did not include dispersion and/or undulation of axons.…”

“…The protocol should nevertheless be adapted to in vivo diffusivity and careful experiments should be conducted to ensure that the EA compartment can effectively be ignored (e.g., Monte Carlo simulations). On the other hand, dMRS sequences allow isolating the diffusion signal for specific metabolites like N ‐acetyl‐aspartate and glutamate, which are physically restrained to the IA space . In vivo metabolites have diffusivities similar to ex vivo water, which matches our simulations …”

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

“…33 The same relation for the p = −1 universality class of random permeable membranes in d = 2 was verified by Novikov et al 49 The borderline ''log" case of = 1 for p = 0 in d = 2 dimensions (Equation Monte Carlo along synthetic model neurites, dimension d = 1, featuring realistic spines, leaflets and beads placed randomly according to the Poissonian statistics, p = 0. 150 The deviation from the = 1∕2 power law at the longest t may be attributed to the periodic boundary conditions for a relatively short sample. In the same setting, Equation 33 transverse to the neurites was verified for sub-ms times, regime (i).…”

Improving the Realism of White Matter Numerical Phantoms: A Step toward a Better Understanding of the Influence of Structural Disorders in Diffusion MRI

“…The effect of beadings on the intra-cellular diffusion process -which is not studied in this work-might also be quantitatively substantial, as suggested in Marco et al [31]. In this work, the sensitivity of the diffusion signal of intracellular metabolites with respect to beaded structures was studied using MonteCarlo simulation of brain metabolites dynamics, which can be compared, from the numerical simulation point of view, with the waters one after proper scaling.…”

“…Indeed, beadings are supposed to primarily affect the diffusion process along the fibers and a 1/ √ t ∼ √ ω frequency-dependence of the parallel diffusivity in the intra-cellular space of beaded axons is expected. Similarly to what was done in Marco et al [31] for intracellular metabolites, an interesting approach would be to capture directly the effect of beading on the intra-cellular parallel diffusivity √ ω term, by performing 3D Monte-Carlo simulations of spin dynamics in the intra-cellular space and fitting the scaling factor of the √ ω term for various beaded geometrical configurations. The amount of variation of this "intra-cellular disorder" scaling factor in the presence of beading could be compared to the variation of the scaling factor A studied in this work.…”