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一种用于计算磁共振相位对比成像模型的欧拉公式。

An Eulerian formulation for the computational modeling of phase-contrast MRI.

机构信息

Department of Mechanical Science and Bioengineering, Osaka University Graduate School of Engineering Science, Osaka, Japan.

Department of Radiology, Nippon Medical School Musashi-Kosugi Hospital, Kanagawa, Japan.

出版信息

Magn Reson Med. 2025 Feb;93(2):828-841. doi: 10.1002/mrm.30302. Epub 2024 Sep 13.

DOI:10.1002/mrm.30302
PMID:39270130
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11604850/
Abstract

PURPOSE

Computational simulation of phase-contrast MRI (PC-MRI) is an attractive way to physically interpret properties and errors in MRI-reconstructed flow velocity fields. Recent studies have developed PC-MRI simulators that solve the Bloch equation, with the magnetization transport being modeled using a Lagrangian approach. Because this method expresses the magnetization as spatial distribution of particles, influences of particle densities and their spatial uniformities on numerical accuracy are well known. This study developed an alternative method for PC-MRI modeling using an Eulerian approach in which the magnetization is expressed as a spatially smooth continuous function.

METHODS

The magnetization motion was described using the Bloch equation with an advection term and computed on a fixed grid using a finite difference method, and k-space sampling was implemented using the spoiled gradient echo sequence. PC-MRI scans of a fully developed flow in straight and stenosed cylinders were acquired to provide numerical examples.

RESULTS

Reconstructed flow in a straight cylinder showed excellent agreement with input velocity profiles and mean errors were less than 0.5% of the maximum velocity. Numerical cases of flow in a stenosed cylinder successfully demonstrated the velocity profiles, with displacement artifacts being dependent on scan parameters and intravoxel dephasing due to flow disturbances. These results were in good agreement with those obtained using the Lagrangian approach with a sufficient particle density.

CONCLUSION

The feasibility of the Eulerian approach to PC-MRI modeling was successfully demonstrated.

摘要

目的

相位对比磁共振成像（PC-MRI）的计算模拟是一种从物理角度解释磁共振重建流速场中的特性和误差的有吸引力的方法。最近的研究已经开发出了使用拉格朗日方法对 Bloch 方程进行建模的 PC-MRI 模拟器。由于这种方法将磁化强度表示为粒子的空间分布，因此粒子密度及其空间均匀性对数值精度的影响是众所周知的。本研究开发了一种使用欧拉方法的替代方法来进行 PC-MRI 建模，其中磁化强度表示为空间平滑的连续函数。

方法

利用带有平流项的 Bloch 方程来描述磁化强度的运动，并使用有限差分法在固定网格上进行计算，同时使用扰相梯度回波序列实现 k 空间采样。对直筒和狭窄筒内充分发展的流动进行了 PC-MRI 扫描，以提供数值示例。

结果

在直筒内重建的流动与输入速度分布非常吻合，平均误差小于最大速度的 0.5%。狭窄筒内流动的数值案例成功地演示了速度分布，位移伪影取决于扫描参数，而由于流动干扰导致的体素内相位失谐。这些结果与使用拉格朗日方法并具有足够的粒子密度所获得的结果非常吻合。

结论

成功证明了欧拉方法在 PC-MRI 建模中的可行性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/35072659ad10/MRM-93-828-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/efde71050acd/MRM-93-828-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/bf6894788756/MRM-93-828-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/53b2a6492d50/MRM-93-828-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/c9d5444eab35/MRM-93-828-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/60f2a9ea33a0/MRM-93-828-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/b7bf504d087d/MRM-93-828-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/42daab80f03c/MRM-93-828-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/35072659ad10/MRM-93-828-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/efde71050acd/MRM-93-828-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/bf6894788756/MRM-93-828-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/53b2a6492d50/MRM-93-828-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/c9d5444eab35/MRM-93-828-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/60f2a9ea33a0/MRM-93-828-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/b7bf504d087d/MRM-93-828-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/42daab80f03c/MRM-93-828-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/1b37/11604850/35072659ad10/MRM-93-828-g001.jpg

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