First Advisor

Lee Casperson

Term of Graduation

Spring 1994

Date of Publication


Document Type


Degree Name

Master of Science (M.S.) in Electrical Engineering


Electrical Engineering




Magnetic resonance imaging -- Mathematical models



Physical Description

1 online resource (ix, 79 pages)


The steady-state free precession (SSFP) is one type of the fast scanning technique in MRI. So far most of its analysis are concentrated on the gradient echo SSFP (GR SSFP), very few paper discuss the spin echo SSFP (SE SSFP), and they are usually based on the simplified the hard pulse assumption. The advantage of the SE SSFP is that it can refocus the dephasing caused by the magnetic field inhomogeneity, which is the disadvantage of the GR SSFP. Also the hard pulse model can provide very limited information.

The purpose of this paper is to establish the soft pulse model for both GR SSFP and SE SSFP. By using the spinor method to describe the interaction between the RF pulse, magnetic field, and the spin's magnetization, we create the steady state equations of the GR SSFP and SE SSFP, and give their analytical solutions.

Because the SE SSFP's mathematical model is very complicated, we introduce a new concept, the linked-pulse, to simplify the problem, and provide the valuable results.

Based on both traditional hard pulse model and our soft pulse model, we did a series of simulations, and compared both results. First of all, the soft pulse model can provide the slice profile and gradient effects, which is impossible for the hard pulse model. Second, in both models, the signal intensities are all depended on the T1/T2 ratio, which is the characterization of the SSFP image. Third, we also observed how the pulse shape and the flip angles affect the slice profile and the signal intensity.

In conclusion, the soft pulse model can give more information than hard pulse model can, such as slice profile and gradient effects, etc., provide more aspects for analyzing the SSFP image.


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