Algorithm for adiabatic pulse design using the Shinnar Le-Roux transform

摘要

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 (F_lp(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)=F_lp(ω)e^ikω2. 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 k0.03π/(ω₅−ω_p)/(N+1) and kk_max, where k_max is a value at which the adiabatic RF pulse is truncated at 25% of a maximum RF amplitude.