Spatially resolved estimation of metabolic oxygen consumption from optical measurements in cortex

Significance: The cerebral metabolic rate of oxygen ( $$ ) is an important indicator of brain function and pathology. Knowledge about its magnitude is also required for proper interpretation of the blood oxygenation level-dependent (BOLD) signal measured with functional MRI. Despite the need for estimating $$ , no gold standard exists. Traditionally, the estimation of $$ has been pursued with somewhat indirect approaches combining several different types of measurements with mathematical modeling of the underlying physiological processes. The recent ability to measure the level of oxygen ( $$ ) in cortex with two-photon resolution in in vivo conditions has provided a more direct way for estimating $$ , but has so far only been used to estimate the average $$ close to cortical penetrating arterioles in rats. Aim: The aim of this study was to propose a method to provide spatial maps of $$ based on two-photon $$ measurements. Approach: The method has two key steps. First, the $$ maps are spatially smoothed to reduce the effects of noise in the measurements. Next, the Laplace operator (a double spatial derivative) in two spatial dimensions is applied on the smoothed $$ maps to obtain spatially resolved $$ estimates. Result: The smoothing introduces a bias, and a balance must be found where the effects of the noise are sufficiently reduced without introducing too much bias. In this model-based study, we explored this balance using synthetic model-based data, that is, data where the spatial maps of $$ were preset and thus known. The corresponding $$ maps were found by solving the Poisson equation, which relates $$ and $$ . MATLAB code for using the method is provided. Conclusion: Through this model-based study, we propose a method for estimating $$ with high spatial resolution based on measurements of $$ in cerebral cortex.