用物理约束神经网络，从超声数据反推血管压力波形和弹性参数。
Asymptotic-Preserving Neural Networks for Viscoelastic Parameter Identification in Multiscale Blood Flow Modeling
- 构建嵌入物理方程的自适应保持神经网络，融合多尺度血流模型。
- 仅用超声测得的截面积与血流速度，即可重建不可测的血压波形。
- 适用于临床无法直接测压的血管段，提升个性化心血管建模能力。
数学模型与数值模拟为探索心血管现象提供了非侵入性途径，可获取无法直接测量的生理量。本研究基于一维多尺度血流模型，描述动脉壁的粘弹性特性，聚焦于解决关键挑战：如何可靠地确定控制动脉在搏动压力下变形行为的粘弹性参数。为此，我们采用嵌入多尺度粘弹性血流模型物理规律的渐近保持神经网络，在学习过程中融合物理约束，实现对粘弹性参数的联合估计，并同时重构血管状态变量的时间演化过程。该方法可基于患者特异性数据（如多普勒超声获取的截面面积与速度）估算出在无直接压力测量条件下的血压波形。在合成数据与真实患者场景下的多种数值实验均验证了该方法的有效性。
原文摘要 · Abstract (English)
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood flow model that describes the viscoelastic properties of arterial walls, and we focus on improving its practical applicability by addressing a major challenge: determining, in a reliable way, the viscoelastic parameters that control how arteries deform under pulsatile pressure. To achieve this, we employ Asymptotic-Preserving Neural Networks that embed the governing physical principles of the multiscale viscoelastic blood flow model within the learning procedure. This framework allows us to infer the viscoelastic parameters while simultaneously reconstructing the time-dependent evolution of the state variables of blood vessels. With this approach, pressure waveforms are estimated from readily accessible patient-specific data, i.e., cross-sectional area and velocity measurements from Doppler ultrasound, in vascular segments where direct pressure measurements are not available. Different numerical simulations, conducted in both synthetic and patient-specific scenarios, show the effectiveness of the proposed methodology.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。