Modelling the effects of cerebral microvasculature morphology on oxygen transport

The cerebral microvasculature plays a vital role in adequately supplying blood to the brain. Determining the health of the cerebral microvasculature is important during pathological conditions, such as stroke and dementia. Recent studies have shown the complex relationship between cerebral metabolic rate and transit time distribution, the transit times of all the possible pathways available dependent on network topology. In this paper, we extend a recently developed technique to solve for residue function, the amount of tracer left in the vasculature at any time, and transit time distribution in an existing model of the cerebral microvasculature to calculate cerebral metabolism. We present the mathematical theory needed to solve for oxygen concentration followed by results of the simulations. It is found that oxygen extraction fraction, the fraction of oxygen removed from the blood in the capillary network by the tissue, and cerebral metabolic rate are dependent on both mean and heterogeneity of the transit time distribution. For changes in cerebral blood flow, a positive correlation can be observed between mean transit time and oxygen extraction fraction, and a negative correlation between mean transit time and metabolic rate of oxygen. A negative correlation can also be observed between transit time heterogeneity and the metabolic rate of oxygen for a constant cerebral blood flow. A sensitivity analysis on the mean and heterogeneity of the transit time distribution was able to quantify their respective contributions to oxygen extraction fraction and metabolic rate of oxygen. Mean transit time has a greater contribution than the heterogeneity for oxygen extraction fraction. This is found to be opposite for metabolic rate of oxygen. These results provide information on the role of the cerebral microvasculature and its effects on flow and metabolism. They thus open up the possibility of obtaining additional valuable clinical information for diagnosing and treating cerebrovascular diseases.