Adiabatic RF Pulse Design via Quadratic Phase Modulation
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Solution Overview
Problem
Magnetic resonance imaging (MRI) systems face challenges in achieving uniform flip angles in the presence of nonuniform B1 fields, particularly at high magnetic field strengths, where adiabatic pulses are needed to provide immunity to B1 inhomogeneities but require high peak RF amplitudes.
Innovation Solution
A systematic method using the Shinnar Le-Roux (SLR) algorithm to design high-bandwidth, low-peak-amplitude adiabatic RF pulses by overlaying quadratic phase across the spectral profile, ensuring adiabatic behavior and distributing RF energy uniformly, thus reducing peak RF amplitude while maintaining spectral characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If adiabatic pulses are used to provide immunity to B1 inhomogeneities, then reliability is improved, but peak RF amplitude increases
Solution Approach 1:
The patent applies quadratic phase modulation to the RF pulse spectrum, changing the phase parameter distribution across frequency. This transforms the time-domain pulse shape and amplitude envelope, enabling adiabatic behavior with reduced peak amplitude. The quadratic phase term e^(ikω²) modifies the spectral profile to achieve both adiabaticity and lower peak power requirements.
Solution Approach 2:
The patent designs RF pulses with time-varying amplitude and frequency characteristics that dynamically satisfy the adiabatic condition. The pulse envelope and instantaneous frequency are modulated according to quadratic phase relationships, creating a dynamic pulse structure that maintains adiabaticity throughout the pulse duration while controlling peak amplitude.
2Adaptability or versatility
If high bandwidth is achieved for adiabatic pulses, then spectral coverage is improved, but peak RF amplitude increases
Solution Approach 1:
The patent uses quadratic phase modulation to reshape the spectral profile across the desired bandwidth. By applying the phase term e^(ikω²) to the linear phase frequency profile, the method redistributes spectral energy to achieve high bandwidth coverage while maintaining reduced peak amplitude through optimized energy distribution across frequencies.
3Productivity
If pulse duration is reduced for faster imaging, then productivity is improved, but adiabatic behavior deteriorates
Solution Approach 1:
The patent creates dynamically modulated pulses where amplitude and frequency vary in coordinated fashion according to quadratic phase relationships. This dynamic structure allows the pulse to maintain adiabatic conditions throughout its shorter duration by continuously adjusting parameters to satisfy the adiabatic criterion, enabling fast imaging without sacrificing adiabaticity.
Data Source
AI summary
A method for providing an adiabatic RF pulse that is an inversion or refocusing pulse for a RF pulse sequence is provided. A linear phase frequency profile (Flp(ω)) is determined for the adiabatic RF pulse. A quadratic phase is applied to the linear phase frequency profile for the adiabatic RF pulse to obtain F(ω), wherein the applying the quadratic phase comprises setting F(ω)=Flp(ω)eikω<sup2>2</sup2>. A polynomial β is set to equal a Fourier Transform (F(ω)). A corresponding minimum phase α polynomial is determined for the β polynomial. (α,β) are set as inputs to an inverse Shinnar Le-Roux transform to generate an adiabatic RF waveform. The adiabatic RF waveform is truncated to produce the adiabatic RF pulse, wherein k>0.03π/(ω5−ωp)/(N+1) and k<kmax, where kmax is a value at which the adiabatic RF pulse is truncated at 25% of a maximum RF amplitude.