Estimation of Metabolic Oxygen Consumption From Optical Measurements in Cortex

Abstract

We seek a standardized method for estimating cerebral metabolic rate of oxygen (CMRO2) from optical measurements of partial pressure of oxygen (pO2). This parameter is critical for understanding how the brain responds to changes in metabolism and oxygen delivery. Such changes are associated with clinical conditions like stroke and Alzheimer’s disease. The oxygen consumption rate is further important for the interpretation of functional magnetic resonance imaging. We approach two different methods for estimating CMRO2: The Krogh method and the Laplace method. They are based on Fick's law of diffusion and carried out using different assumptions. When oxygenated blood flows through the veins in your brain tissue, oxygen molecules cross the vessel wall, spread throughout the brain matter and are consumed by active neurons. For the Krogh method we assume an axisymmetric, cylindrical geometry of the vessel-tissue region. The assumption leads to a model describing pO2 as a function of the distance to vessel. In order to apply this model to data we implement a general optimization solver in C++. The code is verified with unit testing and made available on Github. The Krogh method, mostly used to study muscles, show disconcerting results when applied to data from brain tissue. The results indicate that the method is not robust. This is remarkable for such a well-known and established method. We introduce the Laplace method as an alternative way of estimating CMRO2. The method states that CMRO2 can be estimated by taking the second derivative of pO2 measurements. It has the advantaged of not relying on geometrical or biophysical assumptions. In order to validate the method we construct a dataset with known ground truth and apply the Laplace method. For this data the method is able to estimate CMRO2 with a precision of the relative error much less than 1. Finally we apply the method to the experimental data. Based on the work with this thesis, I conlude that the Laplace method represents a more useful tool for measuring oxygen consumption than the Krogh mehtod. The thesis lays an important foundation for further study of the implications the Laplace method provides.