Schiavazzi D E, Arbia G, Baker C, Hlavacek A M, Hsia T Y, Marsden A L, Vignon-Clementel I E
Mechanical and Aerospace Engineering Department, University of California at San Diego, San Diego, CA, U.S.A.
INRIA Paris-Rocquencourt and Sorbonne Universités UPMC Paris 6, Paris, France.
Int J Numer Method Biomed Eng. 2016 Mar;32(3):e02737. doi: 10.1002/cnm.2737. Epub 2015 Sep 2.
The adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions. We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero-dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs.
采用模拟工具来预测手术结果，越来越引发人们对于在存在与输入临床数据相关的不确定性情况下这些预测的变异性的质疑。在本研究中，我们提出一种方法，用于将不确定性从临床数据全面传播至模型结果，与确定性模拟不同，该方法能够估计与模型预测相关的置信度。我们在虚拟的二期单心室姑息手术示例中阐述这个问题。首先，根据临床测量结果并辅以文献数据，确定右肺动脉（PA）血流分流比和平均肺动脉压的概率密度函数（PDF）。从一个零维半经验近似开始，使用贝叶斯参数估计来找到作为术前模型结果产生预期PA血流分流和平均压力PDF的边界条件分布。为降低计算成本，使用克里金近似法解决这个反问题。其次，将边界条件中的不确定性传播至模拟预测。采用稀疏网格随机配置方法，对有和没有PA狭窄的模型中的术后血流动力学模型预测进行统计表征。结果量化了虚拟手术预测中的统计变异性，从而能够在模拟输出上设置置信区间。
