基于a-FSI血流模型的动脉血流动力学粘弹性参数的不确定性量化
Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model
摘要：
这项工作的目的是识别和量化的不确定性有关的弹性和粘弹性参数，其特征在于动脉壁的行为，在一维人体动脉血流动力学建模。所选择的不确定性参数建模为随机高斯分布变量，使随机的控制方程系统。所提出的方法进行了初步验证模型方程，提出了一个彻底的收敛性研究，证实了随机配置方法的频谱精度和二阶精度的IMEX有限体积方案选择解决的数学模型。然后，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用例。当将流速和速度波形的变化性与压力和面积的变化性进行比较时，描绘了不同的灵敏度，后者对血管壁的机械表征的参数不确定性更加敏感。考虑简单的弹性和更现实的粘弹性本构关系进行的模拟表明，粘度参数的巨大的不确定性起着重要的作用，在预测的压力波形，扩大了这个变量的置信区间。体内记录的患者特定压力数据在使用所提出的方法获得的输出的置信区间内，并且计算压力的预期值与记录的波形相当。
英文摘要：
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.
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