Method of measuring NMR spin-spin relaxation time (T.sub.2) using spin-echos

A method is disclosed for measuring the NMR spin-spin relaxation time (T.sub.2) of nuclei using spin-echos comprising the steps of locating the nuclei in a static magnetic field, applying an RF pulse to the nuclei at the Larmor frequency of the nuclei of sufficient duration to rotate the net magnetic moment of the nuclei 90.degree., waiting a time period tau that is at least the time required for the free induction decay signal to go to zero, applying an RF pulse at the same Larmor frequency to the nuclei of sufficient duration to rotate the net magnetic moment of the nuclei 180.degree., recording the primary echo induced, waiting a time period equal to at least 3 tau, to cause the stimulated echos produced by the inhomogeneities in the RF magnetic field to fall into separate time zones from each other and the primary echo, applying an RF pulse at the same Larmor frequency to the nuclei of sufficient duration to rotate the net magnetic moment of the nuclei another 180.degree. to produce the primary and error stimulated echos, recording the primary and error stimulated echos induced thereby during a time period sufficient to allow the peaks of all of the error stimulated echos and the primary echos to appear in different time slots in the time zone, repeating the last three steps to obtain a series of frames each of which contain a primary echo and error stimulated echos, adding the primary echo and related error stimulated echos in each frame to obtain points on a decay curve indicating T2 relaxation time.

This invention relates to methods of measuring nuclear magnetic resonance 
characteristics of nuclei generally, and, in particular to a method of 
measuring the spin-spin relaxation time (T.sub.2) of nuclei using spin 
echoes. 
The spin echo technique was developed to measure spin-spin relaxation time 
(T.sub.2) because of the errors caused by inhomogeneities in the static 
and RF magnetic fields of NMR machines. It includes the steps of applying 
an RF pulse sequence at the Larmor frequency of the nuclei, whose T.sub.2 
is being measured. The first RF pulse is sufficient duration to force the 
net magnetic moment of the nuclei to rotate 90.degree.. This is followed 
by a series of RF pulses at the same Larmor frequency of sufficient 
duration to rotate the net magnetic filed 180.degree.. After each 
180.degree. pulse a spin-echo signal is produced. The T.sub.2 relaxation 
time of the nuclei is indicated by the curve drawn through the points of 
maximum amplitude of the echo signals received. 
This technique would produce an accurate measurement of T.sub.2 if the RF 
magnetic field was uniform at the same Larmor frequency because then only 
one spin-echo signal would be generated with each 180.degree. pulse. 
Unfortunately, the RF magnetic field is not uniform. For example, some 
portions of the RF field may be at the Larmor frequency but other portions 
may be at a higher or lower frequency. As a result, as suggested by Hahn 
in his paper entitled "Spin Echos" (Physical Review Vo. 80, No. 4, Nov. 
15, 1948) the inhomogeneities in the RF magnetic field produce what he 
called "stimulated echos" in addition to the primary echos. 
In the present practice of the spin-echo technique for measuring T.sub.2, 
after the 90.degree. pulse, the first 180.degree. pulse occurs after a 
time period, usually called "tau", that is at least as great as the time 
required for the free induction decay of the echo signal produced by the 
RF pulses. The second and all subsequent 180.degree. pulses occur at 2 tau 
intervals. This timing sequence is written 90--tau--180--2 tau--180 where 
the time intervals are between pulses. Starting from time, t equals zero, 
it would be 90--tau--180--3 tau--180--5 tau . . . . This sequence causes 
the primary echo signals to appear at 2 tau, 4 tau, 6 tau . . . . 
Stimulated echos, however, can appear at these same times and when they 
do, they will be masked by and mingled with the primary echos. As a 
result, the degree of error in the measured T.sub.2 is unknown.

It is an object of this invention to provide time intervals between pulses 
based on multiples of a time unit, tau, that will cause the peaks of the 
stimulated echos to appear in different time slots from the time slots in 
which the peak of the primary echos appear to allow related error signals 
to be added to the primary echos to obtain a substantially accurate 
T.sub.2 decay curve. 
It is a further object of this invention to provide a method of measuring 
NMR spin-spin relaxation time (T.sub.2) of nuclei using spin echos. 
In accordance with this invention, it has been determined that an initial 
three pulse sequence of 90--tau--180--3 tau--180 --will cause the primary 
and secondary stimulated echo signals to appear in time slots 4 tau apart. 
Therefore, subsequent 180.degree. pulses should be spaced far enough apart 
to provide time frames wide enough to receive both types of signals, which 
is a minimum of seven tau. Preferably tau is the width of the echo signals 
received for twice the free induction decay time. 
Referring now to the drawing, a typical measurement of T.sub.2 will be 
described. 
In the drawing, seven 180.degree. pulse time frames are shown following a 
90.degree. pulse. The first 180.degree. pulse occurred at time tau after 
the 90.degree. pulse. This was followed after a delay of three tau, by 
subsequent 180.degree. pulses each of which occur after a time interval of 
eight tau. As stated above, a time frame equal to seven tau' could be used 
but it is preferred to provide a time frame that is more than adequate in 
width to accommodate all echos that may be received. Tau in the drawings 
is indicated by the Greek letter r. 
We start with a 90.degree. pulse, which may or may not be exactly 
90.degree., but by using the method of this invention that is not critical 
and eliminates the time, which was often substantial, that was heretofore 
spent in tuning the NMR machine in order to get as close to exactly 
90.degree. and 180.degree. as possible with the equipment. In other words, 
in the prior art pulse sequence, much time had to be spent in attempting 
to eliminate all possible error before measuring T.sub.2. With the method 
of this invention, whatever error appears can be accounted for and it is 
not necessary to spend the time calibrating the equipment that was 
heretofore required. 
It is important, however, in the practice of this invention, that the 
timing of the pulse sequence be accurate and also the phase relationship 
of the RF signals be maintained. 
First, the nuclei are subjected to a 90.degree. pulse followed after time 
tau by an 180.degree. pulse. No echos result from the initial 90.degree. 
pulse, but there is a free induction decay so it is necessary to wait a 
time period at least long enough to allow the free induction decay to 
occur. In the middle of time frame 1, a single echo P1 will be generated 
as a result of the first 180.degree. pulse and will peak at time interval 
tau into time interval 1. This is followed by the second 180.degree. pulse 
that follows the first one by a time interval of 3 tau. 
Following this second 180.degree. pulse, echo P2 appears two tau after the 
pulse. This is another primary pulse and one will occur in each time frame 
although they will reverse their position in the time frame with each 
180.degree. pulse. They are indicated as P1-P7 in the drawing. 
If the 90.degree. and 180.degree. pulses were exactly uniform, these are 
the only echos we would get, however, since they are not, and the RF 
magnetic fields are not uniform, error stimulated echos will appear. 
Echos A and B appear on each side of echo P2 in Frame 2 at time intervals 
of tau and 3 tau. Echo A results primarily because of errors in the 
90.degree. pulse. Echo B is caused by what error there was in the 
90.degree.-180.degree. pulse combination that preceded the second 
180.degree. pulse. Neither of these echos represent the initial spin shown 
in P1 and therefore can be ignored. 
The stimulated or secondary echos that are the errors that are subtracted 
from the primary echos due to the inhomogeneity of the Rf magnetic field 
of the NMR machine are the ones that are of primary interest. They are 
designated S1-S6 in the drawing and will be referred to as secondary 
stimulated echos. They form an echo train of increasing amplitude. This 
secondary pulse train is basically the error signal created from the 
primary pulse train and as soon as the error signal appears which is 
usually in time frame 3, it will continue to propagate along with the 
primary echo. So the primary echo decays faster than the actual or true 
exponential decay while the secondary echo train increases asymptotically 
to the primary train because any error terms causing a transfer from 
primary to secondary will work in reverse taking secondary echos back into 
the primary slot. So by adding the primary and secondary signals, a true 
indication of how much phase coherent energy in each time frame remains of 
the original phase coherent energy that was in P.1 originally. 
Consequently, beginning with time frame 3, by adding primary and secondary 
signals points on the curve that indicates accurately the T.sub.2 
relaxation time will be obtained. The curve in the drawing is indicated as 
T.sub.2. 
Additional error signals C and D appear in each time slot 2 on either side 
of the secondary stimulated echos. These, like echos A and B discussed 
above, are due to 90.degree. errors and the 90.degree. to 180.degree. 
error. They are not added in the data reduction to obtain curve T.sub.2 
since they do not in any way effect the amplitude of the primary or 
secondary echos. 
From the foregoing it will be seen that this invention is one well adapted 
to attain all of the ends and objects hereinabove set forth, together with 
other advantages which are obvious and which are inherent to the apparatus 
and structure. 
It will be understood that certain features and subcombinations are of 
utility and may be employed without reference to other features and 
subcombinations. This is contemplated by and is within the scope of the 
claims. 
Because many possible embodiments may be made of the invention without 
departing from the scope thereof, it is to be understood that all matter 
herein set forth or shown in the accompanying drawings is to be 
interpreted as illustrative and not in a limiting sense.