Spiral Trajectory Design: A Flexible Numerical Algorithm and Base Analytical Equations
Spiral Trajectory Design: A Flexible Numerical Algorithm and Base Analytical Equations
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DOI：
10.1002/mrm.24675
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发表时间：
2014-01-01
影响因子：
3.3
通讯作者：
Zwart, Nicholas R.
中科院分区：
文献类型：
--
作者：
Pipe, James G.;Zwart, Nicholas R.
目的磁共振成像的螺旋轨迹可能是有利的，但通常是繁琐的设计或创建。本文提出了一种灵活的基于径向欠采样明确定义的轨迹设计数值算法，并给出了描述这些轨迹的基本（严格采样）类的几个解析表达式。理论和方法基于摆幅和振幅限制的梯度波形表达式，可以在螺旋k空间轨迹中得到所需的螺距。这个算法的源代码是用C语言编写的，是公开的。给出了近似于螺旋轨迹的解析表达式（忽略径向分量）来表征测量时间、梯度加热、最大梯度振幅和非共振相位。举例说明了几种数值计算的轨迹，并将基阿基米德螺旋与解析得到的结果进行了比较。结果几种不同的波形表明，期望的摆幅和幅度的限制，以及期望的欠采样模式，达到了使用数值方法。对于基阿基米德螺旋，数值方法和解析方法的结果是一致的。结论开发了一个通用的数值算法，并以公开的代码编写。给出了有助于描述螺旋轨迹的近似解析公式。中华医学杂志，2014,31(1):379 - 379。(c) 2013 Wiley Periodicals, Inc.；
PurposeSpiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories.Theory and MethodsExpressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results.ResultsSeveral different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement.ConclusionA versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Magn Reson Med 71:278-285, 2014. (c) 2013 Wiley Periodicals, Inc.