发表机构
School of Biomedical Engineering, Faculty of Medicine, Dalian University of Technology; College of Biomedical Engineering, Fudan University（大连理工大学医学院生物医学工程系; 复旦大学生物医学工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高佩克莱数下经典泰勒-阿里斯弥散模型失效的问题，提出一种基于显式闭合系数与修正KAN网络的一维有效弥散模型，准确捕捉对流主导弥散转变，并提升流速反演精度。
AI 中文摘要
佩克莱数表征了从经典泰勒-阿里斯弥散到对流主导的纵向溶质输运的转变，在极高的径向佩克莱数 $Pe_r$ 下，经典模型变得不再适用。我们针对这一高 $Pe_r$ 区间，通过引入两个闭合系数 $\ heta_u$ 和 $\ heta_d$，开发了一种新颖的显式闭合一维（1-D）有效弥散模型，其函数结构通过低频传递函数匹配和修正的科尔莫戈罗夫-阿诺德网络（KAN）识别。所得模型捕捉了从低 $Pe_r$ 下的经典泰勒-阿里斯弥散到高 $Pe_r$ 下对流主导弥散的转变。分析表明，在高 $Pe_r$ 区间，轴向输运在有效对流通量与弥散通量之间重新分配，导致宏观对流速度降低。数值验证表明，在所研究的高 $Pe_r$ 条件下，该模型与对流-扩散模型高度一致，而经典泰勒-阿里斯模型则表现出显著偏差。将所提模型应用于平均流速反演进一步证明了速度估计的改进，尤其是在高 $Pe_r$ 区间。这些结果凸显了考虑非经典弥散对于基于对比剂的动脉血流速度测量的可靠性至关重要，并为高 $Pe_r$ 质量输运提供了新的见解。
英文摘要
At high Peclet number, the classical Taylor-Aris dispersion model becomes inadequate for early-time contrast-agent transport in arteries, while an explicit closure model and a clear physical interpretation of this regime remain lacking. In this study, we develop a novel explicit-closure one-dimensional (1-D) effective dispersion model for this regime, with its functional structures identified through symbolic regression. Analysis of the resulting model reveals that, in the high-Peclet-number regime, axial transport is redistributed between the effective convection flux and the dispersive flux, resulting in a reduction of the effective convective transport velocity in the dispersion model. This redistribution gives rise to a transition from the classical quadratic scaling to a linear scaling of the effective diffusivity with radial Peclet number. Numerical validation demonstrates close agreement with the convection-diffusion model over the investigated high-Peclet-number conditions, while the classical Taylor-Aris model exhibits substantial deviations. Application of the proposed model to averaged flow velocity inversion further demonstrates improved velocity estimation, particularly in the high-Peclet-number regime. These results highlight the importance of accounting for non-classical dispersion for reliable contrast-agent-based arterial blood flow velocimetry and provide new insight into high-Peclet-number mass transport.
Comments42 pages, 9 figures
