A Model of Brain Circulation and Metabolism: NIRS Signal Changes during Physiological Challenges

Abstract

We construct a model of brain circulation and energy metabolism. The model is designed to explain experimental data and predict the response of the circulation and metabolism to a variety of stimuli, in particular, changes in arterial blood pressure, CO ₂ levels, O ₂ levels, and functional activation. Significant model outputs are predictions about blood flow, metabolic rate, and quantities measurable noninvasively using near-infrared spectroscopy (NIRS), including cerebral blood volume and oxygenation and the redox state of the Cu _A centre in cytochrome c oxidase. These quantities are now frequently measured in clinical settings; however the relationship between the measurements and the underlying physiological events is in general complex. We anticipate that the model will play an important role in helping to understand the NIRS signals, in particular, the cytochrome signal, which has been hard to interpret. A range of model simulations are presented, and model outputs are compared to published data obtained from both in vivo and in vitro settings. The comparisons are encouraging, showing that the model is able to reproduce observed behaviour in response to various stimuli.

Author Summary

Monitoring the brain noninvasively is key to solving various biological and clinical problems. Near-infrared spectroscopy (NIRS) is a technique that can measure changes in the colour of the brain. The brain has an absolute requirement for oxygen; the spectroscopically observed colour changes are due to the proteins that deliver (haemoglobin) and consume (mitochondrial cytochrome c oxidase) oxygen. Haemoglobin changes colour when it binds oxygen. The changes in cytochrome c oxidase are due to the electron occupancy (reduction) of a particular copper metal centre in the enzyme. The way that the state of this enzyme changes in various situations is poorly understood. Currently there is no theoretical model that can be used to decode simultaneously all of the spectroscopic changes in these proteins, and thus limited information about the underlying biochemistry and physiology can be extracted from the NIRS signals. We therefore constructed such a model, ensuring that it is consistent with the scientific literature, in vivo data, and the underlying thermodynamic principles. The model was able to predict the physiological and spectroscopic responses to a wide range of stimuli, including changes in brain activity and oxygen delivery. It is likely to be of significant value to a wide range of clinical and life science users.