Friday, March 19, 2021

The Carr-Purcell-Meiboom-Gill Pulse Sequence

The most exciting phrase to hear in science, the one that heralds new discoveries, is not “Eureka!” but “That’s funny...” 

Isaac Asimov

In Section 18.8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I describe the Carr-Purcell pulse sequence, used in magnetic resonance imaging.

When a sequence of π [180° radio-frequency] pulses that nutate M [the magnetization vector] about the x' axis are applied at TE/2, 3TE/2, 5TE/2, etc., a sequence of echoes are formed [in the Mx signal], the amplitudes of which decay with relaxation time T2. This is shown in Fig. 18.19.
The Carr-Purcell pulse sequence, as shown in Fig. 18.19 of Intermediate Physics for Medicine and Biology.
Fig. 18.19  The Carr-Purcell pulse sequence.
All π pulses nutate about the x' axis.
The envelope of echoes decays as et/T2.

Russ and I then discuss the Carr-Purcell-Meiboom-Gill pulse sequence.
One disadvantage of the CP [Carr-Purcell] sequence is that the π pulse must be very accurate or a cumulative error builds up in the successive pulses. The Carr-Purcell-Meiboom-Gill sequence overcomes this problem. The initial π/2 [90° radio-frequency] pulse nutates M about the x' axis as before, but the subsequent [π] pulses are shifted a quarter cycle in time, which causes them to rotate about the y' axis.
The Carr-Purcell-Meiboom-Gill pulse sequence, as shown in Fig. 18.21 of Intermediate Physics for Medicine and Biology.
Fig. 18.21  The Carr-Purcell-Meiboom-Gill pulse sequence.

The first page of Meiboom, S. and Gill, D. (1958) “Modified Spin-Echo Method for Measuring Nuclear Relaxation Times.” Rev. Sci. Instr. 29:688–691, superimposed on Intermediate Physics for Medicine and Biology.
Meiboom, S. and Gill, D. (1958)
“Modified Spin-Echo Method for
Measuring Nuclear Relaxation Times.”
Rev. Sci. Instr.
Students might enjoy reading the abstract of Saul Meiboom and David Gill’s 1958 article published in the Review of Scientific Instruments (Volume 29, Pages 688-691).
A spin echo method adapted to the measurement of long nuclear relaxation times (T2) in liquids is described. The pulse sequence is identical to the one proposed by Carr and Purcell, but the rf [radio-frequency] of the successive pulses is coherent, and a phase shift of 90° is introduced in the first pulse. Very long T2 values can be measured without appreciable effect of diffusion.
This short paper is so highly cited that it was featured in a 1980 Citation Classic commentary, in which Meiboom reflected on the significance of the research.
The work leading to this paper was done nearly 25 years ago at the Weizmann Institute of Science, Rehovot, Israel. David Gill, who was then a graduate student… , set out to measure NMR T2-relaxation times in liquids, using the well-known Carr-Purcell pulse train scheme. He soon found that at high pulse repetition rates adjustments became very critical, and echo decays, which ideally should be exponential, often exhibited beats and other irregularities. But he also saw that on rare and unpredictable occasions a beautiful exponential decay was observed... Somehow the recognition emerged that the chance occurrence of a 90° phase shift of the nuclear polarization [magnetization] must underlie the observations. It became clear that in the presence of such a shift a stable, self-correcting state of the nuclear polarization is produced, while the original scheme results in an unstable state, for which deviations are cumulative. From here it was an easy step to the introduction of an intentional phase shift in the applied pulse train, and the consistent production of good decays.
The key point is that the delay between the initial π/2 pulse (to flip the spins into the xy plane) and the string of π pulses (to create the echoes) must be timed carefully (the pulses must be coherent). Even adding a delay corresponding to a quarter of a single oscillation changes everything. In a two-tesla MRI scanner, the Larmor frequency is 83 MHz, so one period is 12 nanoseconds. Therefore, if the timing is off by just a few nanoseconds, the method won’t work.

Initially Gill didn’t worry about timing the pulses precisely, so usually he was using the error-prone Carr-Purcell sequence. Occasionally he got lucky and the timing was just right; he was using what’s now called the Carr-Purcell-Meiboom-Gill sequence. Meiboom and Gill “somehow” were able to deduce what was happening and fix the problem. Meiboom believes their paper is cited so often because it was the first to recognize the importance of maintaining phase relations between the different pulses in an MRI pulse sequence.

In his commentary, Meiboom notes that
Although in hindsight the 90° phase shift seems the logical and almost obvious thing to do, its introduction was triggered by a chance observation, rather than by clever a priori reasoning. I suspect (though I have no proof) that this applies to many scientific developments, even if the actual birth process of a new idea is seldom described in the introduction to the relevant paper.
If you’re a grad student working on a difficult experiment that’s behaving oddly, don’t be discouraged if you hear yourself saying “that’s funny...” A discovery might be sitting right in front of you!  

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