Pulmonary capillary perfusion and gas exchange are physiological processes that take place at the alveolar level and that are fundamental to sustaining life. Present-day computational simulations of these phenomena are based on low-dimensional mathematical models solved in idealized alveolar geometries, where the chemical reactions between O2-CO2 and hemoglobin are simplified. While providing general insights, current modeling efforts fail to capture the complex chemical reactions that take place in pulmonary capillary blood flow on arbitrary geometries and ignore the crucial impact of microstructural morphology on pulmonary function. Here, we propose a coupled continuum perfusion and gas exchange model that captures complex gas and hemoglobin dynamics in realistic geometries of alveolar tissue. To this end, we derive appropriate governing equations incorporating a two-way Hill-like relationship between gas partial pressures and hemoglobin saturations. We numerically solve the resulting boundary-value problem using a non-linear finite-element approach to simulate and validate velocity, partial pressure, and hemoglobin saturation fields in simple geometries. We further perform sensitivity studies to understand the impact of blood speed and acidity variability on key physiological fields. Notably, we simulate perfusion and gas exchange on anatomical alveolar domains constructed from 3D μ-computed-tomography images of murine lungs. Based on these models, we show that morphological variations decrease O2 and CO2 diffusing capacity, predicting trends and values that are consistent with current medical knowledge. We envision that our model will provide an effective in silico framework to study how exercise and pathological conditions affect perfusion dynamics and the overall gas exchange function of the respiratory system. Source code is available at https://github.com/comp-medicine-uc/alveolar-perfusion-transport-modeling.

中文翻译：

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肺泡微结构中的肺灌注和气体交换建模


肺毛细血管灌注和气体交换是发生在肺泡水平的生理过程，是维持生命的基础。目前这些现象的计算模拟基于在理想化肺泡几何形状中求解的低维数学模型，其中 O2-CO2 和血红蛋白之间的化学反应得到了简化。虽然提供了一般性的见解，但目前的建模工作未能捕捉到任意几何形状上肺毛细血管血流中发生的复杂化学反应，并且忽视了微观结构形态对肺功能的关键影响。在这里，我们提出了一个耦合连续体灌注和气体交换模型，该模型在肺泡组织的真实几何形状中捕获复杂的气体和血红蛋白动力学。为此，我们推导出了适当的控制方程，其中包含气体分压和血红蛋白饱和度之间的双向 Hill 状关系。我们使用非线性有限元方法对得到的边界值问题进行数值求解，以模拟和验证简单几何中的速度、分压和血红蛋白饱和场。我们进一步进行敏感性研究，以了解血速和酸度变化对关键生理区域的影响。值得注意的是，我们模拟了由小鼠肺的 3D μ 计算断层扫描图像构建的解剖肺泡结构域上的灌注和气体交换。基于这些模型，我们表明形态变化会降低 O2 和 CO2 的扩散能力，预测的趋势和值与当前的医学知识一致。 我们设想我们的模型将提供一个有效的计算机框架来研究运动和病理条件如何影响呼吸系统的灌注动力学和整体气体交换功能。源代码可在 https://github.com/comp-medicine-uc/alveolar-perfusion-transport-modeling 获取。