Abstract: The theoretical study of the signal in certain sequences is helpful to analyze the factors that affect the imaging quality and improve the imaging quality in magnetic resonance imaging. Bloch equation is one of the most universal methods to solve the dynamics behavior of nucleus in magnetic field. Bloch equation and its solutions can be written in matrix form. By acting on magnetization (the Vector M), the propagator matrix that contains some parameters, such as main magnetic field, Radio Frequency pulse (RF), relaxation time, can be used to calculate signal of magnetic resonance imaging (MRI) in different circumstances of MRI sequences.

Key words: magnetic resonance imaging (MRI), Bloch equation, the propagator matrix, IR-EPI sequences