使用 Gappy 适当正交分解为流体-结构模拟进行高效心血管参数估计

IF 3 2区 医学 Q3 ENGINEERING, BIOMEDICAL Annals of Biomedical Engineering Pub Date : 2024-07-05 DOI:10.1007/s10439-024-03568-z
J. Deus, E. Martin
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引用次数: 0

摘要

由于对整个血管进行全面详细的血流动力学模拟并不可行,因此数值分析应集中在心血管系统的特定区域,这就需要确定块状参数,以表示模拟计算域外的患者行为。我们提出了一种利用 gappy 适当正交分解(g-POD)估算心血管模型参数的新技术。我们利用 FSI 模拟构建了一个 POD 基础,用于计算不同的集合模型参数值,并应用线性算子保留可与现有患者测量结果进行比较的信息。然后,通过投影患者测量值或解决带有约束条件的最小化问题来计算重建解决方案的 POD 系数。然后利用 POD 重构来估计模型参数。在第一个测试案例中,使用人工患者测量值对 3 元素 Windkessel 模型的参数值进行了近似,得到的相对误差小于 4.2%。在第二个案例中,根据患者主动脉的几何形状对 4 组 3 元素 Windkessel 进行近似,结果流量误差小于 8%,压力误差小于 5%。该方法即使在病人数据嘈杂的情况下也能显示精确的结果。它能自动计算测量和模拟之间的延迟,并能灵活处理患者测量类型(特定点、空间或时间平均)。该方法易于实施,可用于通用 FSI 软件的模拟。
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Efficient Cardiovascular Parameters Estimation for Fluid-Structure Simulations Using Gappy Proper Orthogonal Decomposition

As full-scale detailed hemodynamic simulations of the entire vasculature are not feasible, numerical analysis should be focused on specific regions of the cardiovascular system, which requires the identification of lumped parameters to represent the patient behavior outside the simulated computational domain. We present a novel technique for estimating cardiovascular model parameters using gappy Proper Orthogonal Decomposition (g-POD). A POD basis is constructed with FSI simulations for different values of the lumped model parameters, and a linear operator is applied to retain information that can be compared to the available patient measurements. Then, the POD coefficients of the reconstructed solution are computed either by projecting patient measurements or by solving a minimization problem with constraints. The POD reconstruction is then used to estimate the model parameters. In the first test case, the parameter values of a 3-element Windkessel model are approximated using artificial patient measurements, obtaining a relative error of less than 4.2%. In the second case, 4 sets of 3-element Windkessel are approximated in a patient’s aorta geometry, resulting in an error of less than 8% for the flow and less than 5% for the pressure. The method shows accurate results even with noisy patient data. It automatically calculates the delay between measurements and simulations and has flexibility in the types of patient measurements that can handle (at specific points, spatial or time averaged). The method is easy to implement and can be used in simulations performed in general-purpose FSI software.

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来源期刊
Annals of Biomedical Engineering
Annals of Biomedical Engineering 工程技术-工程:生物医学
CiteScore
7.50
自引率
15.80%
发文量
212
审稿时长
3 months
期刊介绍: Annals of Biomedical Engineering is an official journal of the Biomedical Engineering Society, publishing original articles in the major fields of bioengineering and biomedical engineering. The Annals is an interdisciplinary and international journal with the aim to highlight integrated approaches to the solutions of biological and biomedical problems.
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