A model for extra-axonal diffusion spectra with frequency-dependent restriction.

PURPOSE: In the brain, there is growing interest in using the temporal diffusion spectrum to characterize axonal geometry in white matter because of the potential to be more sensitive to small pores compared to conventional time-dependent diffusion. However, analytical expressions for the diffusion spectrum of particles have only been derived for simple, restricting geometries such as cylinders, which are often used as a model for intra-axonal diffusion. The extra-axonal space is more complex, but the diffusion spectrum has largely not been modeled. We propose a model for the extra-axonal space, which can be used for interpretation of experimental data. THEORY AND METHODS: An empirical model describing the extra-axonal space diffusion spectrum was compared with simulated spectra. Spectra were simulated using Monte Carlo methods for idealized, regularly and randomly packed axons over a wide range of packing densities and spatial scales. The model parameters are related to the microstructural properties of tortuosity, axonal radius, and separation for regularly packed axons and pore size for randomly packed axons. RESULTS: Forward model predictions closely matched simulations. The model fitted the simulated spectra well and accurately estimated microstructural properties. CONCLUSIONS: This simple model provides expressions that relate the diffusion spectrum to biologically relevant microstructural properties.