MRF undersampling optimization: Software and code for the publication: Mitigating undersampling errors in Magnetic Resonance Fingerprinting by sequence optimization

Repository to perform sequence optimization as proposed in the following paper: Mitigating undersampling errors in Magnetic Resonance Fingerprinting by sequence optimization<br> D.G.J. Heesterbeek, K. Koolstra, M.J.P. van Osch, M.B. van Gijzen, F.M. Vos and M.A. Nagtegaal <strong>Abstract:</strong> Magnetic Resonance Fingerprinting (MRF) is<br> an imaging technique for simultaneous estimation of multiple quantitative parameters in a single acquisition. The efficiency of MRF results from strong k-space undersampling, but this can go at the expense of strong aliasing artifacts. The errors due to undersampling can be predicted based on a mathematical model leveraging on perturbation<br> theory. We exploited this model to perform MRF sequence optimization by adjusting the MRF flip angle train. Numerical simulations showed that the undersampling errors can be suppressed by sequence optimization. This was further corroborated in eight in vivo scans. The results were compared to sequences with a conventionally shaped flip angle pattern and an optimized pattern based on the Cramer-Rao lower bound (CRB). A sequence optimized for improved<br> robustness against undersampling with a flip angle train of length 400 yielded significantly lower median absolute errors T1 (5.6%±2.9%) and T2 (7.9%±2.3%) compared to the conventional (T1: 8.0% ± 1.9%, T2: 14.5% ± 2.6%) and CRB-based (T1: 21.6% ± 4.1%, T2: 31.4% ± 4.4%) sequences. The proposed optimization scheme can be adapted to different<br> scan settings, reference maps and optimization parameters in a straightforward manner.

用于执行如下论文中提出的序列优化的代码库：通过序列优化缓解磁共振指纹成像中的欠采样误差<br>D.G.J. Heesterbeek, K. Koolstra, M.J.P. van Osch, M.B. van Gijzen, F.M. Vos 和 M.A. Nagtegaal <strong>摘要：</strong>磁共振指纹成像（Magnetic Resonance Fingerprinting, MRF）是<br>一种可在单次采集过程中同时估计多个定量参数的成像技术。MRF的高效性源于k空间的强欠采样，但这可能会以产生严重的混叠伪影为代价。欠采样导致的误差可基于利用微扰理论的数学模型进行预测。我们利用该模型，通过调整MRF翻转角序列来执行MRF序列优化。数值模拟表明，序列优化可抑制欠采样误差。这一点在八次在体扫描中得到了进一步证实。结果与采用传统形状翻转角模式的序列以及基于克拉美-罗下界（Cramer-Rao Lower Bound, CRB）的优化模式序列进行了比较。针对提升抗欠采样鲁棒性而优化的、翻转角序列长度为400的序列，其T1（5.6%±2.9%）和T2（7.9%±2.3%）的中位绝对误差显著低于传统序列（T1：8.0%±1.9%，T2：14.5%±2.6%）和基于CRB的序列（T1：21.6%±4.1%，T2：31.4%±4.4%）。所提出的优化方案可简便地适配不同的扫描设置、参考图谱和优化参数。