Superficial white matter microstructural imaging method based on time-space fractional-order diffusion

Abstract

Objective. Microstructure imaging based on diffusion magnetic resonance signal is an advanced imaging technique that enablesin vivomapping of the brain's microstructure. Superficial white matter (SWM) plays an important role in brain development, maturation, and aging, while fewer microstructure imaging methods address the SWM due to its complexity. Therefore, this study aims to develop a diffusion propagation model to investigate the microstructural characteristics of the SWM region.Approach. In this paper, we hypothesize that the effect of cell membrane permeability and the water exchange between soma and dendrites cannot be neglected for typical clinical diffusion times (20 ms <t< 80 ms). We then use SpinDoctor to simulate the diffusion magnetic resonance signals of real neurons and propose a time-space fractional-order diffusion model for SWM microstructure imaging. We evaluate the validity regime of our model using numerical simulations and compare the model parameters with several state-of-the-art methods.Main results. By analyzing the simulation signals of real neuronal cells as well as diffusion magnetic resonance data from the brains of fourteen healthy human subjects, we find that the time-space fractional-order diffusion model can be used to capture the structural complexity of the tissue, indirectly through the association of time fractional exponents with restricted diffusion and space fractional exponents with perfusion and membrane permeability.Significance. The results show that the diffusion propagation model can provide new insights into the tissue architecture of the SWM.

Keywords: anomalous diffusion; diffusion magnetic resonance imaging; fractional diffusion equation; microstructure imaging; superficial white matter.