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# Spin Echo

The spin-echo of nuclear magnetic resonance is one of those concepts that anyone interested in medical physics should know. Russ Hobbie and I discuss the spin-echo’s role in magnetic resonance imaging in Chapter 18 of the 4th edition of Intermediate Physics for Medicine and Biology.

“The pulse sequence shown in Fig. 18.17 can be used to determine T2 [the true or non-recoverable spin-spin relaxation time] and T*2 [the experimental spin-spin relaxation time]. Initially a π/2 [90°] pulse nutates M [the magnetization] about the x’ axis so that all spins lie along the rotating y’ axis. Figure 18.17(a) shows two such spins. Spin a continues to precess at the same frequency as the rotating coordinate system; spin b is subject to a slightly smaller magnetic field and precesses at a slightly lower frequency, so that at time TE/2 it has moved clockwise in the rotating frame by angle θ, as sown in Fig. 18.17(b). At this time a π [180°] pulse is applied that rotates all spins around the x’ axis. Spin a then points along the –y’ axis; spin b rotates to the angle shown in Fig. 18.17(c). If spin b still experiences the smaller magnetic field, it continues to precess clockwise in the rotating frame. At time TE both spins are in phase again, pointing along –y’ as shown in Fig. 18.17(d). The resulting signal is called an echo, and the process for producing it is called a spin-echo sequence.”

When I discuss this concept in class, I use the analogy of a footrace. Suppose all runners line up at the starting line, and at the sound of the starter’s gun they begin to run clockwise around a track. Because they all run at somewhat different speeds, the pack of runners spreads until eventually (after many laps) they are distributed nearly evenly, and seemingly randomly, around the track. At this time another gun is fired, commanding all runners to turn around and run counterclockwise. Now, the fast runners who were ahead of the others are suddenly behind, and the slow runners who were behind the others are miraculously ahead. As time goes on, the fast runners catch up to the slow ones, and eventually they all meet in one tight pack as they run past the starting line. This unexpected regrouping of the runners is the echo. The analogy is not perfect, because the spins always precess in the same direction. Nevertheless, the 180° pulse has the effect of placing the fast spinners behind the slow spinners, which is the essence of both the spin echo effect and the runner analogy.

The spin-echo was first observed by physicist Erwin Hahn. His paper Spin Echos (Physical Review, 80:580-594, 1950) has been cited over 3000 times. Hahn wrote a “citation classic” article about this paper, in which he describes how he made his great discovery by accident.

“One day a strange signal appeared on the oscilloscope, in the absence of a pulse pedestal, so I kicked the apparatus and breathed a sigh of relief when the signal went away. A week later, the signal returned, and this time it checked out to be a real spontaneous spin echo nuclear signal from the test sample of protons in the glycerine being used. In about three weeks, I was able to predict mathematically what I suspected to be a constructive interference of precessing nuclear magnetism components by solving the Bloch nuclear induction equations. Here for the first time, a free precession signal in the absence of driving radiation was observed first, and predicted later. The spin echo began to yield information about the local atomic environment in terms of various amplitude and frequency memory beat effects, certainly not all understood in the beginning.

As I look back at this experience, it was an awesome adventure to be alone with the apparatus showing one new effect after another at a time when there was no one at Illinois experienced in NMR with whom I could talk.”

You can learn more about Hahn and his discovery of the spin-echo from the transcript of an oral history interview published by the Niels Bohr Library and Archives, part of the American Institute of Physics.

For those of you who are visual learners, wikipedia has a nice animation of the formation of a spin-echo. Another animation is at http://mrsrl.stanford.edu/~brian/mri-movies/spinecho.mpg.

You can find an excellent video about spin-echo NMR on youtube, narrated by Sir Paul Callaghan, a New Zealand physicist (this is part of a series of videos that nicely support the discussion in Chapter 18 of Intermediate Physics for Medicine and Biology). Callaghan was a leader in MRI physics, and wrote Principles of Nuclear Magnetic Resonance Microscopy and, more recently, Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR. Tragically, Callaghan lost his battle to colon cancer this March.

Read more at Intermediate Physics for Medicine and Biology

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