A model of oxygen dynamics in the cerebral microvasculature and the effects of morphology on flow and metabolism

Abstract

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 behaviour of cerebral metabolic rate with transit time distribution. In this paper, we extend a recently developed technique to solve for residue function and transit time distribution in an existing physiologically accurate model of the cerebral microvasculature to calculate cerebral metabolism. We present the mathematical theory based on solving the mass transport equation followed by results of the simulations. It is found that oxygen extraction fraction 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. The metabolic rate is thus affected more significantly by cerebral blood flow than oxygen extraction fraction. A negative correlation can also be observed between transit time heterogeneity and the metabolic rate of oxygen for a constant cerebral blood flow. The heterogeneity of the transit time distribution also has an effect on the response of oxygen extraction fraction and cerebral metabolic rate to sudden changes. 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.