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

Marte J Sætra; Andreas V Solbrå; Anna Devor; Sava Sakadžić; Anders M Dale; Gaute T Einevoll

doi:10.1117/1.NPh.7.3.035005

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

Neurophotonics. 2020 Jul;7(3):035005. doi: 10.1117/1.NPh.7.3.035005. Epub 2020 Aug 21.

Authors

Marte J Sætra^{1

2}, Andreas V Solbrå^{1

2}, Anna Devor^{3

4}, Sava Sakadžić⁴, Anders M Dale^{5

6}, Gaute T Einevoll^{1

2

7}

Affiliations

¹ University of Oslo, Centre for Integrative Neuroplasticity, Oslo, Norway.
² University of Oslo, Department of Physics, Oslo, Norway.
³ Boston University, Department of Biomedical Engineering, Boston, Massachusets, United States.
⁴ Massachusetts General Hospital, Harvard Medical School, Athinoula A. Martinos Center for Biomedical Imaging, Charlestown, Massachusetts, United States.
⁵ University of California San Diego, Department of Radiology, La Jolla, California, United States.
⁶ University of California San Diego, Department of Neurosciences, La Jolla, California, United States.
⁷ Norwegian University of Life Sciences, Faculty of Science and Technology, Ås, Norway.

Abstract

Significance: The cerebral metabolic rate of oxygen ( ${CMRO}_{2}$ ) 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 ${CMRO}_{2}$ , no gold standard exists. Traditionally, the estimation of ${CMRO}_{2}$ 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 ( ${pO}_{2}$ ) in cortex with two-photon resolution in in vivo conditions has provided a more direct way for estimating ${CMRO}_{2}$ , but has so far only been used to estimate the average ${CMRO}_{2}$ close to cortical penetrating arterioles in rats. Aim: The aim of this study was to propose a method to provide spatial maps of ${CMRO}_{2}$ based on two-photon ${pO}_{2}$ measurements. Approach: The method has two key steps. First, the ${pO}_{2}$ 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 ${pO}_{2}$ maps to obtain spatially resolved ${CMRO}_{2}$ 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 ${CMRO}_{2}$ were preset and thus known. The corresponding ${pO}_{2}$ maps were found by solving the Poisson equation, which relates ${CMRO}_{2}$ and ${pO}_{2}$ . MATLAB code for using the method is provided. Conclusion: Through this model-based study, we propose a method for estimating ${CMRO}_{2}$ with high spatial resolution based on measurements of ${pO}_{2}$ in cerebral cortex.

Keywords: analysis; estimation; metabolism; oxygen; two-photon.

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Abstract

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