大学物理 ›› 2022, Vol. 41 ›› Issue (12): 39-.doi: 10.16854/j.cnki.1000-0712.220120

• 物理.自然.技术.社会 • 上一篇    下一篇

磁共振成像K空间信号的数理模型——以自旋回波序列为例

傅洪波,陈小伟,谢国喜   

  1. 广州医科大学 生物医学工程学院,广东 广州511436
  • 收稿日期:2022-03-08 修回日期:2022-06-18 出版日期:2023-02-20 发布日期:2023-02-17
  • 通讯作者: 谢国喜,E-mail: guoxixie@163.com
  • 作者简介:傅洪波(1974—),男,湖南长沙人,广州医科大学生物医学工程学院数理系副教授,主要从事大学物理教学和数学建模和医学成像研究工作.
  • 基金资助:
    国家自然科学基金(81971607);广州医科大学学科建设项目(02-410-2206183)资助

Mathematical model of K space signal in magnetic resonance imaging: a case study of spin echo sequence

FU Hong-bo, XIAO Wei-chen, GUO Xi-xie   

  1. Institute of Biomedical Engineering, Guangzhou Medical University, Guangzhou,  511436, China

  • Received:2022-03-08 Revised:2022-06-18 Online:2023-02-20 Published:2023-02-17

摘要: K空间是磁共振成像信号空间编码的基础,准确理解K空间信号的表达式是掌握磁共振成像原理的关键和难点.本研究以常见的自旋回波脉冲序列为例,结合梯度磁场的空间编码过程,详细地推导了K空间信号的表达式. 在信号采集环节,我们利用一个简单的物理磁化模型,简化了法拉第电磁感应定律下的信号表达式. 在数学处理上,我们从微元分析出发,逐步推导出K空间数据的二维积分表达式,详细地展示了推导过程中的相关细节和依据. 本模型推导过程中有效地将一系列磁共振概念和理论联系起来,可以帮助对磁共振成像理论感兴趣的研究者深入系统地认知K空间的概念和相关理论.

关键词: 磁共振成像, K空间, 自旋回波

Abstract:  K-space is the basis of signal spatially encoding in magnetic resonance imaging. Accurately understanding signal expression of K-space is the key step to understand the principles behind magnetic resonance imaging. In this work, we take conventional spin echo pulse sequence as an example to comprehensively derive the signal expression, by combining the signal spatial encoding process. In the signal acquisition step, a physical magnetization model was used to simplify the signal expression under the Faraday,s law of electromagnetic induction. In the mathematically processing step, two-dimensional integral expression of K-space data is derived based on the micro-element analysis. The Details and the corresponding theory in each derivation step are clearly demonstrated. The model connects the key concepts and theories of magnetic resonance imaging, which can help to systematically understand the K-space concepts and the principles behind magnetic resonance imaging.

Key words:  Magnetic resonance imaging, K-space, spin echo