Modeling hemodynamic fluctuations: the brain vasculature as an excitable network

Multiple studies have examined blood oxygen level dependent (BOLD) signals of functional magnetic resonance imaging (fMRI) showing spontaneous fluctuations when the brain is at rest, sleeping or even anesthetized. These fluctuations are found at lower frequencies (around 0.1 Hz) than respiratory or cardiac functions. In addition, recent experimental works seem to rule out their relation with neural activity, suggesting a non-neural origin.

We propose a minimal model for microcirculation that only assumes a nonlinear relation between the current supported by each vessel and the pressure drop between its starting and final nodes, and a dispersive relation for volume accumulation. This simple approach qualitative reproduces the main characteristics of the observed behavior. The fluctuations emerge spontaneously under constant boundary conditions as self-sustained oscillations, forming different patterns depending on the topology of the network.

We expect that this model can shed light on the nature of spontaneous fluctuations on brain vasculature and its interplay with the properties of the network. Finally, the simplicity of the model makes it suitable for its use with different nonlinear flow networks exhibiting complex dynamical behavior.