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研究生:徐義程
研究生(外文):Yi-Cheng Hsu
論文名稱:高場核磁共振造影的核自旋激發場之數學理論及工程設計
論文名稱(外文):Mathematical theory and technical designs for magnetization excitation in high field MRI
指導教授:陳宜良陳宜良引用關係
口試委員:林發暄陳界山曾文毅王偉仲鍾孝文
口試日期:2013-06-27
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:英文
論文頁數:71
中文關鍵詞:控制理論最佳化理論核磁共振影像圓偏極化射頻磁場不均勻非線性的空間編碼磁場
外文關鍵詞:Control theoryOptimization theoryMRIRF inhomogeneitynonlinear SEMs
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在眾多現代醫學影像中,核磁共振影像對於臨床醫學與基礎生物醫學研究的貢獻重大。這是由於核磁共振影像可以非侵入性的方式產生高對比、毫米等級的高空間解析度的影像。對於現代人常見的疾病診斷,例如癌症、腦血管病變等,有極大的助益。現代核磁共振影像除了針對特定的應用發展各式新的脈衝序列以外,主要的發展目標是更高的空間解析度以及更快的完成掃描。然而達成這兩項目標所面臨的共同挑戰是訊號雜訊比會下降,為了改善這個問題,核磁共振影像可利用較高(>3T)甚至達到7T的主磁場 。然而在高磁場的核磁共振影像中很難產生強度均勻的正向圓偏極化射頻磁場(B1+)來激發磁矩,使得傳統的激發方式產生的影像對比不均勻,進而影響疾病診斷。
在這篇論文裡,我們會首先介紹核磁共振影像有關激發磁矩的原理,並證明在不均勻B1+中,我們可以控制B1+波型以及梯度線圈隨時間變化的強度,以達成任意的磁矩分布。使用非線性梯度線圈以及小激發角度的條件下,我們提出了一兩步驟的脈衝序列設計方式。第一步是結合線性及非線性的空間編碼磁場(spatial encoding magnetic fields, SEMs)藉此降低問題的維度。第二步是在簡化後成為一維的問題中設計脈衝序列。我們以模擬及實驗資料證實了使用線性及二階的空間編碼磁場激發可以有效率的解決在7T高磁場中磁矩激發不均勻的問題。根據實驗資料的數值模擬結果,與其他方式相比,我們所提出的方法在脈衝序列設計上有更高的自由度,並且可以使用更少的射頻能量達成相同磁矩激發均勻度或是相同的射頻能量但更均勻的激發狀態。此外,針對激發90度磁矩的目標,我們提出了使用控制理論最佳化的多射頻脈衝激發方式。在實驗和模擬上我們證實了使用多射頻脈衝激發方式可以在B1+不均勻的情況下達成更均勻的磁矩激發分布。加上控制理論最佳化脈衝序列後,能使激發的分布更理想。在不使用平行控制射頻發射(parallel transmission)裝置情況下,使用非線性空間編碼磁場激發或者控制理論最佳化的組多射頻脈衝激發方可在高磁場核磁共振影像中降低磁矩激發不均勻的問題。


In modern medical imaging, magnetic resonance imaging (MRI) has become an indispensible tool in clinical diagnosis and neuroscience studies, because of its high contrast and millimeter resolution. In addition to the efforts in tailoring specialized pulse sequences to further advance the capability of diagnosis, modern MRI also aims to improve its spatiotemporal resolution. Both goals are challenged by the limited signal-to-noise ratio (SNR) in the MRI measurements. One approach to increase the SNR is to increase the strength of the main magnetic field. MRI with 3 T main magnetic field strength has become more and more common and 7T MRI is no longer rare. However, high-field MRI has the challenge of inhomogeneous positively oriented polarized transverse magnetic field (B1+) and consequently an inhomogeneous flip angle distribution, which causes spatially dependent contrast and makes clinical diagnosis difficult.
In this thesis, I first introduce the theory of magnetization excitation and prove that we can achieve any magnetization distribution under inhomogeneous B1+ by controlling the waveforms of radio-frequency (RF) transmission coils and linear gradient coils. By using nonlinear gradient coils with the small flip angle approximation, I propose a two-step pulse design procedure in which 1) a combination of linear and nonlinear spatial encoding magnetic fields (SEM''s) is used to remap the B1+ distribution in a lower dimension, and 2) the locations, amplitudes, and phases of spoke pulses are estimated in a lower dimension. I demonstrate that spatially selective RF excitation using generalized SEMs (SAGS) using both linear and quadratic SEMs in a multi-spoke k-space trajectory can mitigate the B1+ inhomogeneity at 7T efficiently. Numerical simulations based on experimental data suggest that, compared to other methods, SAGS provides a formulation allowing multiple-pulse design, a similar average flip angle distribution with less RF power, and/or a more homogeneous flip angle distribution. Furthermore, to achieve 90o magnetization excitation, I propose to use the optimal control method to design composite RF pulses. Based on simulations and experimental data, I demonstrate that two-pulse excitation can achieve more homogeneous flip angle distribution under inhomogeneous B1+. Applying the optimal control method can further improve the slice profile with sharper edges. Without using multiple RF coils for parallel transmission, SAGS and optimized composite pulse excitation are an effective method to mitigate the B1+ inhomogeneity in high-field MRI experiments.


摘要 i
Abstract iii
Table of content v
1 Introduction 1
2 MRI backgrounds 3
2.1 Nuclear magnetism 3
2.2 Spatial encoding and contrast preparation for MRI 5
2.3 Magnetization excitation for MRI 8
2.4 Challenges of magnetization excitation for MRI 10
2.4.1 B1+ inhomogeneity in small flip angle excitation 10
2.4.2 B1+ inohomogeneity in a large flip angle excitation 13
3 Theoretical development in magnetization excitation 15
3.1 Small flip angle approximation using parallel transmit and generalized SEMs 15
3.2 Spoke trajectory for slice selection 18
3.3 Design magnetization excitation using the optimal control theory 22
3.3.1 Controllability problem 22
3.3.2 Necessary condition for optimality and optimization algorithm 26
4 Methods of improving magnetization excitation at high field 31
4.1 Wave phenomena in MRI 31
4.2 Mitigate B1+ inhomogeneity using spatially selective RF excitation with generalized spatial encoding magnetic fields 34
4.2.1 The k-space trajectory dimension reduction using nonlinear SEMs 35
4.2.2 Design the flip angle distribution in remapped system and a spoke k-space trajectory 38
4.2.3 Simulation Results 39
4.3 Mitigate B1+ inhomogeneity by B1+ remapping with RF shimming 54
4.4 Composite pulse method 58
4.5 Using optimal control method to improve the excitation accuracy 62
5 Conclusion 66
Reference 67


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