The human brain is a complex organ that inherently combines multiscale structure and dynamics and translates them into the functions of the body. Because of the limitations of tools to study the brain in vivo, the understanding of these multiscale dynamics remains to be a challenge. Hence, current neuroscience research tends to investigate brain phenomena at various scales independently.
The primary aim of this thesis is to develop a quantitative approach to describe and explain mechanistic links between some multiscale dynamics of the brain, i.e., vascular hemodynamics and neural activity, and their relationships to experimental neuroimaging measurements. The main approach is to develop mathematical models, guided by the physics and physiology of the brain, that describe hemodynamics and activity in terms of physiologically realistic variables constrained by empirical observations. These models can be used to better analyze existing phenomena and also produce new quantitative predictions that can be tested in future theoretical and/or experimental explorations. In particular, the biophysical models are used to: (i) investigate the natural spatiotemporal modes of the hemodynamic response; (ii) quantify the effect of astrocytic activity to the hemodynamic response; (iii) develop a technique to deconvolve different spatiotemporal neurovascular signals from experimental BOLD-fMRI data; and (iv) explain the experimentally observed anticorrelation between EEG alpha and BOLD. The achievement of these goals contributes a significant advance to the field of neuroscience, especially in understanding and guiding neuroimaging experiments.