全球灵敏度分析与多忠度蒙特卡洛和多项式混沌扩张用于血管血动力学
Friederike Schäfer1, Daniele E Schiavazzi2, Leif Rune Hellevik1
1Division of Biomechanics, Norwegian University of Science and Technology (NTNU), Norway.
概括
多忠实蒙特卡洛方法有效估计心血管模型的灵敏度指数,降低计算成本. 这种方法将高保真模拟与低保真模型相结合,用于准确的心血管疾病分析.
科学领域:
- 计算科学是一种计算科学.
- 生物医学工程 生物医学工程
- 心血管研究的心血管研究.
背景情况:
- 心血管系统的计算模型对于疾病诊断和治疗至关重要.
- 模型验证需要严格的验证,验证和不确定性量化.
- 灵敏度分析对于降低模型复杂性和计算成本至关重要.
研究的目的:
- 将Sobol的灵敏度指数的多忠度蒙特卡洛 (MFMC) 估计器应用于理想化的常见动脉模型.
- 为了证明减小差异,并评估MFMC方法的效率与传统方法相比.
- 评估MFMC对高维心血管模型的计算成本和有效性.
主要方法:
- 实施Sobol'敏感度指数的MFMC估计器.
- 将三维流体结构相互作用模拟与一维和零维减少顺序模型集成.
- 将MFMC结果与传统的蒙特卡洛和多项式混沌扩展 (PCE) 估计进行比较.
主要成果:
- 对于双忠度 (1D/0D) 和三忠度 (3D/1D/0D) MFMC估计器,观察到一致的灵敏度排名.
- 在相同的计算预算内,MFMC方法与单一忠实蒙特卡洛方法相比,实现了更高的差异减少.
- 由于减小了维度影响,PCE证明了理想化模型的较低计算成本,具有平滑的随机响应.
结论:
- 在心血管建模中,MFMC估计器为灵敏度分析提供了一个计算效率高的方法.
- 这些方法显著降低了复杂的心血管模拟不确定性量化的成本.
- 在MFMC和PCE之间做出选择取决于模型特性和计算约束.
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