Biophysical modeling: Multicompartment biophysical models for brain tissue microstructure imaging

Diffusion MRI (dMRI) has evolved into a valuable tool for noninvasive brain microstructure imaging by modeling water diffusion as a linear combination of diffusion in multiple tissue compartments. The diffusion within the tissue compartments can be free, hindered, or restricted, conforming to the tissue microarchitecture. The diffusion phenomenon can be mathematically modeled to explain dMRI signals. Thus, biophysical mathematical modeling of diffusion in brain tissues can be used to characterize the underlying tissue geometry. This information is invaluable to diagnose and monitor the progression of neurodegenerative disorders and to evaluate the efficacy of intervention strategies. Microstructure imaging using biophysical mathematical models is done in three steps: (1) model selection based on tissue properties of interest, (2) optimal experiment design, by selecting MRI pulse sequence parameters ensuring maximum sensitivity of the dMRI signal to tissue microstructure, and (3) model fitting to accurately estimate the model parameters. This chapter gives a practical overview of the aforementioned process to help understand its implementation. It also describes outstanding shortcomings of the standard modeling techniques, contemporary computational models using machine learning approaches, and future research directions.