AI 中文总结
本研究提出基于物理知识的计算框架，将Bloch方程扩展为Bloch-McConnell流动方程，通过MATLAB模拟和全局逆优化方法，从标准TOF-MRA信号剖面提取可变流体速度，为先进流量量化奠定基础，无需额外扫描时间。
AI 中文摘要
飞行时间磁共振血管造影（TOF-MRA）广泛用于血管结构成像，但提取血流速度等功能血流动力学通常需要补充相位对比扫描。本研究提出了一种新的、基于物理知识的计算框架，直接从标准TOF-MRA信号剖面中提取可变流体速度。将Bloch方程解析扩展为Bloch-McConnell流动方程，建立纵向磁化强度空间衰减与流体速度之间的数学关系。为验证此推导并克服恒速假设的局限性，开发了MATLAB模拟框架，在合成扫描仪噪声下对两种可变几何形状的流动管情况（连续变窄和局灶性狭窄）中的流体流动进行建模。采用利用双Tikhonov正则化的全局逆优化方法稳定地反演不适定的渡越时间积分，在保留结构曲线刚度的同时积极惩罚高频数值振铃。计算模拟成功恢复了逐点速度真值，准确跟踪了逐渐的血流动力学加速度和尖锐的狭窄射流。该理论框架提供了一个有力的数学概念验证，即可以从标准结构MRA成像中提取定量的、局部的功能血流动力学指标，为无需额外扫描时间的先进流量量化奠定了基础。
英文摘要
Time-of-flight magnetic resonance angiography (TOF-MRA) is widely used for nonin-vasive visualization of arterial anatomy, but extracting hemodynamics like blood velocity typically requires supplementary phase-contrast scans, tagging or multi-TE images. This study proposes a novel, physics-informed computational framework to extract variable fluid velocity directly from standard TOF-MRA signal profiles. We analytically expand the approach-to-steady-state Bloch equations to include convective flow, establishing a mathematical relationship between the spatial decay of longitudinal magnetization and fluid velocity. The velocity derivation was further extended to pointwise estimation over a 1-D centerline, overcoming the limitations of constant-velocity assumptions. To validate and solve this problem, a MATLAB (R2025b) simulation framework was developed to model fluid flow in two variable-geometry flowing tube cases, i.e., continuous narrowing and focal stenosis, under synthetic scanner noise. A global inverse optimization approach utilizing Dual-Tikhonov regularization was applied to stably invert the ill-posed transit time integral, actively penalizing high-frequency numerical ringing while preserving structural curves. The computational simulations successfully recovered ground-truth point-wise velocities, tracking gradual hemodynamic accelerations and sharp stenotic jets. This theoretical framework and the example centerline TOF-MRA signal intensity pro-vide a robust mathematical proof-of-concept that quantitative, localized functional he-modynamic metrics can be extracted from standard structural MRA imaging, establishing a foundation for advanced flow quantification without requiring additional scan time.
