arXiv:2503.17505cs.LG2025-03

用自适应几何的波形网络预测血管血流,兼顾精度与效率。

Geometry adaptive waveformer for cardio-vascular modeling

  • 通过图运算和距离函数将不规则血管网格转为规则空间处理
  • 在多个心血管数据集上实现高精度动态血流模拟
  • 适合需要快速建模病理血管的临床研究者

心血管解剖结构复杂且常伴有病理状态,建模难度大。数值模拟虽精确但计算成本高,难以用于临床;传统机器学习方法则面临输入维度高、无法处理不规则网格、难以保持动态响应时间依赖性等难题。为此,我们提出几何自适应波形网络(Geometry Adaptive Waveformer),用于预测心血管系统中的血流动力学。该框架包含三部分:几何编码器利用基于图算子的网络与符号距离函数,将定义在不规则域上的输入转换至规则域;波形网络在转换后的场中运行;几何解码器将输出从规则网格逆变换回物理空间。我们在多组心血管数据集上验证了该方法的有效性。

原文摘要 · Abstract (English)

Modeling cardiovascular anatomies poses a significant challenge due to their complex, irregular structures and inherent pathological conditions. Numerical simulations, while accurate, are often computationally expensive, limiting their practicality in clinical settings. Traditional machine learning methods, on the other hand, often struggle with some major hurdles, including high dimensionality of the inputs, inability to effectively work with irregular grids, and preserving the time dependencies of responses in dynamic problems. In response to these challenges, we propose a geometry adaptive waveformer model to predict blood flow dynamics in the cardiovascular system. The framework is primarily composed of three components: a geometry encoder, a geometry decoder, and a waveformer. The encoder transforms input defined on the irregular domain to a regular domain using a graph operator-based network and signed distance functions. The waveformer operates on the transformed field on the irregular grid. Finally, the decoder reverses this process, transforming the output from the regular grid back to the physical space. We evaluate the efficacy of the approach on different sets of cardiovascular data.

心血管建模波形网络几何自适应血流模拟

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