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Spin and Gradient Echoes
Publication Name:
Current Protocols in Magnetic Resonance Imaging
Unit Number:
Unit B4.1
DOI:
10.1002/0471142719.mib0401s00
Online Posting Date:
May, 2001
Abstract
This unit discusses the basic concept of an echo. The phase of the spins plays the fundamental role in this process. A general description as to how an echo occurs is followed by a discussion on both spin echoes and gradient echoes.
Figures
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Figure B4.1.1 (A) The FID signal in the laboratory frame for all spins precessing at the same Larmor frequency. The laboratory RF transmit field oscillates at that frequency. (B) The same experiment but as measured in the Larmor rotating frame (i.e., demodulated). The rotating frame RF field is at “rest.” (C) The demodulated FID signal when the demodulation is not exactly at the Larmor frequency. (D) The total demodulated FID signal from several isochromats, each with slightly different Larmor frequencies, exhibiting a decay, with slow oscillations, that is faster than T 2 decay alone, due to dephasing. The demodulation in (D) is determined by the average (fast) frequency. Note that the laboratory signal in (A) is only suggestive since the oscillations seen in practice are too rapid to display. The T2¢ effects have not been included in any of the curves; note that the differences in case (D) could be considered, alternatively, to be due to field inhomogeneities. -
Figure B4.1.2 A /2 pulse is applied along the positive x¢ axis at t = 0, and a pulse is applied along the positive y¢ axis at t = to invert the phase that the spins have accumulated. The spins then “rephase”, producing what is called an “echo.” Notice that the signal strength is still limited by the T 2 envelope at the echo time TE = 2, as measured from the center of the RF pulse. The corresponding exponentials for the decay envelopes are found in Equation1 field to get twice the angle of spin rotation. The echo shows a positive local maximum, instead of a negative local minimum, since the magnetization is rephased along + y¢. The subscripts on the RF pulse brackets denote the axis along which the RF field is applied. -
Figure B4.1.3 A simulation of an ensemble of spins in the rotating reference frame during a spin echo experiment. A /2 pulse rotates the spins, around the x¢ axis, into the transverse plane where they begin to precess. The spins accumulate extra phase, until this accumulation is inverted by the pulse. The spins continue to collect extra phase at the same rate and, at a later time, all spins return to the positive +y¢ axis together, forming an echo. The echo amplitude is still reduced, however, by the intrinsic T 2 decay. -
Figure B4.1.4 Immediately after the application of the RF pulse, a negative gradient is applied between t 1 and t2 . (A) The transverse magnetization starts to dephase owing to the magnetic field that spins experienced at different positions. (B) At t = t3 , a positive gradient is then applied to reverse the phase of the spins. At t = t ¢, all spins will be refocused and a gradient echo is formed.
Videos
Literature Cited
| Key References | |
| Haacke, E.M., Brown, R.W., Thompson, M.R., and Venkatesan, R. 1999. Magnetic Resonance Imaging: Physical Principles and Sequence Design. John Wiley & Sons, New York. | |
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This book covers the technical discussion here as well as other advanced materials in detail. | |
| Hahn, E.L. 1950. Spin echoes. Phys. Rev. 80:580. | |
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This paper introduces the fundamental concepts of spin echo. | |
