A Model for Transient Oxygen Delivery in Cerebral Cortex

Popular hemodynamic brain imaging methods, such as blood oxygen-level dependent functional magnetic resonance imaging (BOLD fMRI), would benefit from a detailed understanding of the mechanisms by which oxygen is delivered to the cortex in response to brief periods of neural activity. Tissue oxygen responses in visual cortex following brief visual stimulation exhibit rich dynamics, including an early decrease in oxygen concentration, a subsequent large increase in concentration, and substantial late-time oscillations (“ringing”). We introduce a model that explains the full time-course of these observations made by Thompson et al. (2003). The model treats oxygen transport with a set of differential equations that include a combination of flow and diffusion in a three-compartment (intravascular, extravascular, and intracellular) system. Blood flow in this system is modeled using the impulse response of a lumped linear system that includes an inertive element; this provides a simple biophysical mechanism for the ringing. The model system is solved numerically to produce excellent fits to measurements of tissue oxygen. The results give insight into the dynamics of cerebral oxygen transfer, and can serve as the starting point to understand BOLD fMRI measurements.