肺循环一维模型的灵敏度分析和不确定性量化
Sensitivity analysis and uncertainty quantification of 1D models of the pulmonary circulation
摘要：
本研究结合了一维（1D）模型与micro-CT成像和血流动力学数据，以量化控制和缺氧诱导的高血压小鼠肺动脉中的流量和压力预测的不确定性。我们使用局部和全局敏感性和相关性分析来确定可以从模型和可用数据推断的参数。最小二乘优化用于估计小鼠特定参数，贝叶斯以及渐近不确定性量化技术用于确定模型参数和响应的置信区间、可信区间和预测区间。这些技术用于检查网络大小的影响，并了解参数如何随疾病（高血压）而变化。结果表明，外周血管阻力是最敏感的，随着网络尺寸的增加，参数的行为发生变化。相关性分析表明，高血压大血管的刚度与边界的近端阻力相关。我们能够使用确定性和贝叶斯技术来估计可识别的参数（使用贝叶斯分析确定的参数分布的最大值与局部最优值对齐）。根据这些估计，我们确定了置信区间和预测区间，这些区间都在生理预期范围内。本文研究的代表性小鼠的估计参数值的分析表明，高血压小鼠具有更硬（但更大）的血管，并且近端和外周血管系统的顺应性均降低。
英文摘要：
This study combines a one-dimensional (1D) model with micro-CT imaging and hemodynamic data to quantify uncertainty of flow and pressure predictions in the pulmonary arteries in a control and hypoxia induced hypertensive mouse. We use local and global sensitivity and correlation analysis to determine parameters that can be inferred from the model and available data. Least squares optimization is used to estimate mouse specific parameters, and Bayesian as well as asymptotic uncertainty quantification techniques are employed to determine confidence, credible, and prediction intervals for the model parameters and response. These techniques are used to examine the effects of network size and to understand how parameters change with disease (hypertension). Results showed that the peripheral vascular resistance is the most sensitive, and as the network size increases the parameter behavior changes. Correlation analysis revealed that in hypertension large vessel stiffness is correlated with proximal resistance in the boundary. We were able to estimate identifiable parameters using both deterministic and Bayesian techniques (the maxima of the parameter distributions determined using Bayesian analysis aligned with local optima). From these estimates we determined confidence and prediction intervals, which all were within physiological expectation. Analysis of estimated parameter values for the representative mice studied here showed that the hypertensive mouse has stiffer (but larger) vessels and that compliance is decreased both in the proximal and peripheral vasculature.
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