This work aims at identifying and quantifying uncertainties related to elastic and viscoelastic parameters, which characterize the arterial wall behavior, in one-dimensional modeling of the human arterial hemodynamics. The chosen uncertain parameters are modeled as random Gaussian-distributed variables, making stochastic the system of governing equations. The proposed methodology is initially validated on a model equation, presenting a thorough convergence study which confirms the spectral accuracy of the stochastic collocation method and the second-order accuracy of the IMEX finite volume scheme chosen to solve the mathematical model. Then, univariate and multivariate uncertain quantification analyses are applied to the a-FSI blood flow model, concerning baseline and patient-specific single-artery test cases. A different sensitivity is depicted when comparing the variability of flow rate and velocity waveforms to the variability of pressure and area, the latter ones resulting much more sensitive to the parametric uncertainties underlying the mechanical characterization of vessel walls. Simulations performed considering both the simple elastic and the more realistic viscoelastic constitutive law show that the great uncertainty of the viscosity parameter plays a major role in the prediction of pressure waveforms, enlarging the confidence interval of this variable. In-vivo recorded patient-specific pressure data falls within the confidence interval of the output obtained with the proposed methodology and expectations of the computed pressures are comparable to the recorded waveforms.

这项工作旨在识别和量化与弹性和粘弹性参数有关的不确定性，这些参数在人体动脉血流动力学的一维建模中表征了动脉壁的行为。选定的不确定参数被建模为随机的高斯分布变量，从而使控制方程系统成为随机的。所提出的方法最初在模型方程式上进行了验证，并进行了全面的收敛性研究，该研究证实了随机配置方法的频谱精度以及为求解数学模型而选择的IMEX有限体积方案的二阶精度。然后，将单变量和多变量不确定性定量分析应用于a-FSI血流模型，涉及基线和患者特定的单动脉测试案例。将流量和速度波形的变化与压力和面积的变化进行比较时，描绘出了不同的灵敏度，后者导致对容器壁机械特性背后的参数不确定性更加敏感。考虑到简单弹性和更现实的粘弹性本构律进行的模拟表明，粘度参数的巨大不确定性在预测压力波形中起着重要作用，从而扩大了该变量的置信区间。体内记录的患者特定压力数据落在通过建议的方法获得的输出的置信区间内，并且所计算压力的期望值与记录的波形相当。