[论文解读] Relaxation in Spherical Coordinates: Analysis and Optimization of pseudo-SSFP based MR-Fingerprinting

Jakob Assländer, Riccardo Lattanzi+2 more|arXiv (Cornell University)|Mar 1, 2017

Advanced MRI Techniques and Applications被引用 12

一句话总结

本文提出了一种在球坐标系下优化的自旋轨迹，用于基于伪-SSFP的MR-Fingerprinting，以高效率同时编码T₁和T₂弛豫时间。通过利用混合态公式和数值优化，该方法在两种参数上均实现了接近最优的信噪比效率，优于Look-Locker和多自旋回波技术，并在体内实验中得到验证。

ABSTRACT

Purpose: The analysis of optimized spin ensemble trajectories for relaxometry in the hybrid state. Methods: First, we constructed visual representations to elucidate the differential equation that governs spin dynamics in hybrid state. Subsequently, numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramer-Rao bound for $T_1$-encoding, $T_2$-encoding, and their weighted sum, respectively, followed by a comparison of the Cramer-Rao bounds obtained with our optimized spin-trajectories, as well as Look-Locker and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. Results: After a nonrecurring inversion segment on the southern hemisphere of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern half of the sphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance $T_1$- and $T_2$-encoding still result in near optimal signal-to-noise efficiency. Thus, the second parameter can be encoded at virtually no extra cost. Conclusion: We provide insights regarding the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We find that joint acquisitions of $T_1$ and $T_2$ in the hybrid state are substantially more efficient than sequential encoding techniques.

研究动机与目标

• 分析在Bloch球上混合态下的自旋动力学，使用微分方程进行弛豫时间测量。
• 设计最优的自旋集合轨迹，以最小化T₁编码、T₂编码及其加权和的Cramer-Rao界。
• 将优化后的轨迹与传统方法（如Look-Locker和多自旋回波）的性能进行比较。
• 通过人体脑部扫描的体内实验验证优化轨迹的性能。
• 指导设计鲁棒且高效的脉冲序列，用于同时映射T₁和T₂弛豫时间。

提出的方法

• 在Bloch球上构建了混合态下自旋动力学控制微分方程的可视化表示。
• 通过数值优化，在混合态约束下最小化T₁、T₂及其加权和的Cramer-Rao界。
• 设计了从南半球非重复反转开始、并在北半球遵循重复环路的轨迹。
• 通过将第一个环路的起点与最后一个环路的终点对齐，确保轨迹的连续性，仅初始偏差除外。
• 在人体脑部的体内MR-Fingerprinting扫描中应用优化轨迹以验证性能。
• 将优化序列的信噪比效率与Look-Locker和多自旋回波方法进行比较。

实验结果

研究问题

• RQ1 混合态下的自旋轨迹如何影响T₁和T₂弛豫时间编码的Cramer-Rao界？
• RQ2 在Bloch球上何种轨迹模式能同时最小化T₁和T₂的估计方差？
• RQ3 在混合态下联合T₁/T₂编码能否在几乎不增加某一参数代价的情况下实现接近最优的信噪比效率？
• RQ4 与传统方法（如Look-Locker和多自旋回波）相比，优化后的混合态序列在估计精度方面表现如何？
• RQ5 南半球初始反转段在整体编码效率中起到多大影响？

主要发现

• 优化后的自旋轨迹从南半球的非重复反转开始，随后在北半球形成重复环路。
• 轨迹在第一个环路的起点和最后一个环路的终点表现出明显偏差，表明初始段具有非周期性特征。
• 数值结果与基于自旋动力学控制微分方程推导出的直观洞察高度一致。
• 混合态序列在估计效率方面显著优于Look-Locker和多自旋回波等传统方法。
• 在混合态下实现的联合T₁和T₂编码达到了接近最优的信噪比效率，使T₂编码的附加成本几乎可忽略。
• 人体脑部扫描证实了优化轨迹在真实成像条件下的可行性与鲁棒性。