This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure–area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

中文翻译：

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在肺血液循环流体动力学模型的贝叶斯不确定性量化分析中评估模型失配和模型选择

本研究使用贝叶斯推理来量化基于小鼠血液动力学和微计算机断层扫描成像数据集成的一维肺循环模型中模型参数和血液动力学预测的不确定性。我们强调了一个经常被忽视但很重要的不确定性来源：由于模型与现实之间的差异而导致的数学模型形式，以及由于错误的噪声模型（统称为“模型失配”）而导致的测量结果。我们证明，在存在模型不匹配的情况下，最小化测量数据和预测数据（传统方法）之间的均方误差会导致参数估计和血液动力学预测出现偏差和过度自信。我们表明我们提出的方法允许模型不匹配，我们用高斯过程表示，纠正偏见。此外，我们比较了线性和非线性壁模型，以及具有不同血管刚度关系的模型。我们使用基于 Watanabe Akaike 信息准则的形式模型选择分析来选择最能预测肺血流动力学的模型。结果表明，与刚度有关的非线性压力-面积关系取决于无应力半径，可以最好地预测在对照小鼠中测量的数据。