Significance: The cerebral metabolic rate of oxygen (CMRO2) 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 CMRO2, no gold standard exists. Traditionally, the estimation of CMRO2 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 (pO2) in cortex with two-photon resolution in in vivo conditions has provided a more direct way for estimating CMRO2, but has so far only been used to estimate the average CMRO2 close to cortical penetrating arterioles in rats. Aim: The aim of this study was to propose a method to provide spatial maps of CMRO2 based on two-photon pO2 measurements. Approach: The method has two key steps. First, the pO2 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 pO2 maps to obtain spatially resolved CMRO2 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 CMRO2 were preset and thus known. The corresponding pO2 maps were found by solving the Poisson equation, which relates CMRO2 and pO2. MATLAB code for using the method is provided. Conclusion: Through this model-based study, we propose a method for estimating CMRO2 with high spatial resolution based on measurements of pO2 in cerebral cortex.

中文翻译：

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通过皮质光学测量对代谢耗氧量进行空间分辨估计。

意义：脑氧代谢率（CMRO2）是脑功能和病理的重要指标。正确解释用功能性 MRI 测量的血氧水平依赖性 (BOLD) 信号也需要了解其大小。尽管需要估计 CMRO2，但不存在黄金标准。传统上，CMRO2 的估计一直采用一些间接的方法，将几种不同类型的测量与基础生理过程的数学建模相结合。最近在体内条件下用双光子分辨率测量皮层氧 (pO2) 水平的能力为估计 CMRO2 提供了更直接的方法，但迄今为止仅用于估计接近皮层穿透小动脉的平均 CMRO2在大鼠中。目的：本研究的目的是提出一种方法，以提供基于双光子 pO2 测量的 CMRO2 空间图。方法：该方法有两个关键步骤。首先，对 pO2 图进行空间平滑处理，以减少噪声对测量的影响。接下来，将两个空间维度的拉普拉斯算子（双空间导数）应用于平滑的 pO2 图，以获得空间分辨的 CMRO2 估计值。结果：平滑引入了偏差，必须找到一个平衡点，在不引入太多偏差的情况下充分降低噪声的影响。在这项基于模型的研究中，我们使用基于模型的合成数据探索了这种平衡，即 CMRO2 的空间图被预设并因此已知的数据。通过求解与 CMRO2 和 pO2 相关的泊松方程，找到相应的 pO2 图。提供了使用该方法的 MATLAB 代码。结论：通过这项基于模型的研究，我们提出了一种基于大脑皮层 pO2 测量值的高空间分辨率估算 CMRO2 的方法。