An analytical model of restricted diffusion in dendritic spines.

Motivation: Recent studies show that diffusion-weighted MRI (dMRI) and spectroscopy (dMRS) measurements of water and brain metabolites are sensitive to spine density. However, these studies relied on simulations, and an analytical biophysical model for dMRI/dMRS signals from spiny dendrites is still lacking. Goal(s): To present a first step toward developing such a model. Approach: We provide the analytical solution for the signal in the short gradient pulse (SGP) approximation, validation with Monte-Carlo simulations, and investigation of wide pulses impact. Results: In typical preclinical settings, sensitivity to spine density, but not morphology, is present and measurable with ultra-strong gradients. Impact: We developed a biophysical model for characterizing diffusion MR signal from spiny dendrites, providing a foundation for designing dMRI/dMRS methods to non-invasively quantify changes in spine density and morphology, hallmarks of neuroplasticity, and several neurodegenerative diseases, and neurological disorders.