Optimization And Time-frequency Analysis Of Radio Frequency Pulses In Magnetic Resonance

The radio-frequency(RF)pulse plays a key role in nuclear magnetic resonance,which can accurately manipulate spin systems and then produce the expected nuclear magnetic resonance signal.Traditional pulses have many defects in practical application,so it is necessary to optimize RF pulse.Optimal control theory can be used to optimize pulses under various constraints,and the optimized RF pulse can achieve a high fidelity state migration of the spin system,so as to obtain the ideal NMR signal.The amplitude and phase characteristics of RF pulses are closely connected with the spin system manipulation.The time-frequency analysis of RF pulse provides a more intuitive way to explain the results of pulse optimization and the underlying effect of optimized pulse on complex multi-spin system from the time-frequency distribution point of view.which proves the effectiveness of the optimization algorithm,and it also helps us better design pulse sequence.The main content of this paper can be divided into the following sections:Quasi-Newton method and stepsize search method are used to improve GRAPE algorithm,the broadband pulse and three spin cooperative pulses are designed b1 the improved algorithm.The simulation and experiment result shows that the broadband pulse optimized by improved algorithm has a higher transfer efficiency in the bandwidth range compared with traditional rectangular pulse under the amplitude limitation,and the three spin cooperative pulses can aquire a high excitation efficiency in the appropriate scanning pulse number and duration.The short time Fourier transform(STFET),continuous wavelet transform(CWT)and Wigner-Ville distribution(WVD)are introduced to analyze the time-frequency characteristics of the optimized pulses designed by the improved optimization algorithm as well as other RF pulses.The influence of different conditions on the analysis results is discussed,and the advantages and disadvantages of the three methods are also compared for the further analysis of optimized pulses.The time-frequency analysis of magnetic resonance optimized RF pulses and application software integration are studied.The optimized RF pulses obtianed earlier in the article are analyzed by time-frequency analysis and the reason why optimized pulses can achieve a better excitation is explained from the time-frequency distribution point of view,which proves the effectiveness of the optimization algorithm.Furthermore,optimized pulses are divided into a set of frequency-selective pulses by time-frequency analysis,and the nuclear magnetic moment flip angle of each spin is estimated by integrating the amplitude of each frequency-selective pulse over time,which reveals the effect of the optimized pulses on the complex multi-spin system.In addition,the time-frequency analysis C++ algorithm is convenient to integrate with the self-developed pulse sequences design software,which helps us understand the time and frequency characteristics of different pulses,so that we can design pulse sequences with better excitation.The frequency domain analysis algorithm can be improved by combining the short-time Fourier transform and the Wigner Wiley distribution,and the distribution of the pulse amplitude in time-frequency domain can be more accurately reflected while the artifact is suppressed.