Modelling Blood Flow & Oxygen Transport in the Active Brain

Abstract

The brain is critically dependent on the supply of oxygen and glucose from the bloodstream. When a brain region is activated, blood flow to that area increases; this phenomenon is termed functional hyperemia, but it remains incompletely understood. In this thesis, a novel mathematical model of blood flow and oxygen transport in the active brain is developed and used to investigate three aspects of the functional hyperemia response. First, while it is known that activation-induced dilation occurs in cerebral arteries, there is conflicting evidence about the presence of volume changes in post-arteriole vessels. A model was developed and used to reconcile these competing observations. The model predicted that arteries are responsible for the majority of volume changes during brief activation, but that dilation in capillaries and veins becomes increasingly important during longer activation. These results suggest that the apparent discrepancies between the observations were methodological—rather than physiological—in origin. Secondly, based on experimental observations and previous mathematical modelling, it is thought that functional recruitment, whereby under-utilised capillaries are enlisted during neural activation, may be an important mechanism for oxygen delivery. The model was extended to include oxygen transport, and subsequently used to test this hypothesis. The results suggested that a mechanism with effects similar to functional recruitment is required in order to produce model predictions that are consistent with in vivo data. Finally, the model was used to investigate the validity of a widely-used method to calculate activation-induced changes in the cerebral metabolic rate of oxygen consumption, an important measure of brain function, using indirect data. Predictions from the model showed a significant discrepancy between values calculated using this approach and the true rate of oxygen consumption imposed on the model. These results suggest that more sophisticated approaches are required to estimate dynamic changes in oxidative metabolism. The model presented here provides a sound basis for extension and/or application to new research questions in physiology or biomedical imaging. Furthermore, the conclusions from the model predictions may serve as the foundation for future experimental investigations.