Topical nuclear magnetic resonance spectrometer and method

A nuclear magnetic resonance (NMR) spectrometer includes a magnetic field profiling apparatus for producing a resulting static homogeneous magnetic field through a controllable volume and a magnetic field in an immediately adjacent surrounding volume of magnitude varying rapidly with distance. The dimension of the volume of uniform magnetic field and the immediately adjacent volume of rapidly varying magnetic field can be controlled by adjusting the current delivered by a power supply which energizes coils included in the magnetic field profiling apparatus. The generation of homogeneous magnetic fields throughout a controllable volume allows NMR techniques to be applied to a selected region which is located entirely within an inhomogeneous body, such as a particular organ in a human body. The uniformity of the magnetic field is such as to allow chemical shift information to be recovered in an NMR spectrum, and it is significant that this result is achieved in a noninvasive technique.

FIELD OF THE INVENTION 
The invention relates to NMR spectroscopy. 
BACKGROUND OF THE INVENTION 
NMR techniques have been applied in a variety of environments, for such 
purposes as well logging, flow measurement and the monitoring of 
intra-tissue conditions. 
It is well known that when a nuclear magnetic substance, such as water, is 
placed in a homogeneous static field (with a magnitude H.sub.0) its 
resonance angular frequency W.sub.0 is given by the equation: 
W.sub.0 =GH.sub.0, where G is the nuclear gyro magnetic ratio of a 
measuring substance and is a natural constant. 
Application of this phenomenon to the study of homogeneous or relatively 
homogeneous materials is well documented in the literature. On the other 
hand, application of NMR technique to inhomogeneous materials, for the 
selective study of regions of homogeneity within the inhomogeneous 
material has led to the necessity of using special techniques. For 
example, if appropriate magnetic fields are applied to an inhomogeneous 
body, the resulting nuclear magnetic resonance may include contributions 
from the various nuclear magnetic materials within the body subjected to 
the measurement. This can result in masking desired signals from one 
region by undesired signals from other regions. 
Typically, in NMR spectroscopy, material being studied is subjected to both 
a static magnetic field and a radio frequency field, and the result is the 
induction of nuclear magnetic resonance when the above-stated equation is 
satisfied. Thus, a particular nuclear magnetic resonance indicates the 
presence of selected nuclei in the sample. Typically, the static magnetic 
field is produced by a suitable coil carrying a steady current, and in 
view of the magnitude of the magnetic field required, the coil may well be 
super conducting coil, the radio frequency field is produced by a 
supplementary coil or high frequency coil, supplied with high frequency 
current. Resonance is detected by a further or receiver coil surrounding 
the sample or the supplementary coil can be time shared. 
Where the sample includes complex molecules, the localized fields produced 
by molecular electrons have a screening effect which causes identical 
nuclei in different chemical or molecular environments to resonate at 
slightly different frequencies. This effect, known as chemical shift, is 
typically of the order of 10.sup.-4 to 10.sup.-6 parts of the magnetic 
field. Provided that the magnetic field is sufficiently constant in space 
and time, these shifts, although small, can be detected and measured by 
the use of high resolution equipment and can yield valuable information 
about the chemical structure of a sample. 
Where, as has been mentioned above, the sample or body being studied is 
inhomogeneous, and it is desired to subject a particular region in the 
inhomogeneous body to study, some further techniques are required to 
attempt to isolate the nuclear magnetic resonance signal derived from the 
volume of the body desired, from other portions of the body which may 
include other nuclear magnetic materials which can mask the desired 
signals. The known techniques, however, include scanning or mapping in 
which additional coils are provided to superimpose a sequence of switched 
magnetic field gradients or else time dependent magnetic fields onto the 
static field. Damadian, for example, in U.K. patent application No. 
2,039,055A discloses a CW NMR spectrometer which requires scanning in 
frequency or magnetic field amplitude. Inevitably, the provision of 
additional fields and the analysis of the resulting signals requires 
elaborate arrangements of considerable complexity. In addition, the 
presence of gradients or time varying fields causes loss of information 
relating to chemical shift since the very gradients themselves destroy the 
homogeneity necessary to a resolution of this chemical shift information. 
SUMMARY OF THE INVENTION 
Thus, an object of the invention is to isolate selected homogeneous regions 
of an inhomogeneous body for NMR study. The static magnetic field has a 
component which is homogeneous throughout the selected region but the same 
static magnetic field has homogeneity purposefully destroyed in other 
(especially closely adjacent) regions. This destruction of the homogeneity 
of the field is such as to shift any NMR signals from these "other" 
regions to either beyond the resolution of the detecting equipment or 
sufficiently far to be easily resolvable. Furthermore, of course, to 
maximize the induced signal the homogeneous field must be centered on the 
region of interest. 
Essentially, the objects of the invention are achieved by ensuring that the 
static magnetic field is time independent and: 
1. Has a homogeneous component which is centered on the region of interest; 
2. Has a homogeneous component which is homogeneous to within a tolerance 
sufficient to preserve chemical shift effects; 
3. Is arranged to exhibit steep gradients in the vicinity of the outer 
extent of the region of interest. 
As a result, those NMR signals which are effectively received, are derived 
almost solely from the homogeneous region being studied, and other 
signals, are incapable of masking desired signals because of the steep 
gradients induced at the edges of the region of interest and beyond. 
In general, the entire body (or a major portion thereof) being examined is 
subjected to a static homogeneous field (background). In general, the 
desired field shape is achieved by application of an additional profiling 
field. The profiling field should be a field which is relatively 
homogeneous over a region and has relatively steep gradients outside said 
region. One form of a suitable field is a field centered on the region of 
interest whose intensity varies as high order of distance form said 
center. In a region near said center, the field intensity is relatively 
small notwithstanding the high order relation, because field intensity 
grows initially slowly. To extend the region of relatively homogeneous 
field intensity a further field, of opposite sense, and with an intensity 
distance relation of a lower order is applied. Preferably, the two fields 
are of orders N and M, where N-M=2X, where X is an integer .gtoreq.1. 
Thus, in accordance with a preferred arrangement the profiling field is 
obtained from essentially co-located sources of magnetic fields, one of 
which superimposes a field varying as a selected power (or order) of 
distance from a selected point, and a second magnetic field which varies 
as a higher order of power of distance from the identical point. The 
second field is, however, generated with a polarity opposite of that of 
the first field. In a controllable region both profiling field components 
have relatively little effect, and the main component of magnetic field is 
derived from the background field. At further and further distances from 
the selected point, however, the effect of two profiling field components 
increase, although their opposite polarity serves to extend the region of 
homogeneity. While the magnitude of the higher order field is initially 
less than the selected order field, its rate of increase changes more 
rapidly, and so outside of the region of interest the resultant field has 
relatively steep gradients and far from the selected point the effect of 
the higher order field completely dominates the field of selected order. 
In a preferred embodiment of the invention, the first field varies as the 
second power of distance, and the second field varies as the fourth power 
of distance, although those skilled in the art will appreciate that fields 
of varying and different orders or powers with respect to distance can be 
employed. In order to maintain the resultant field in the region of 
interest as homogeneous as possible, however, it is desirable to ensure 
that the powers with which the fields vary as a function of distance, are 
either both even or both odd. 
Of course, it is also within the scope of the invention to use more than 
two superimposed profiling magnetic fields, and three or more magnetic 
fields could also be employed so long as each differs from other fields in 
its variation of intensity with distance by powers which are even 
integers. 
Thus, in accordance with one preferred embodiment of the invention, an NMR 
spectrometer for generating an NMR spectrum from a first solid region 
located within a larger inhomogeneous body comprises: 
magnetic field generating means for generating a magnetic field including: 
(a) an RF magnetic field generator, 
(b) first static magnetic field means generating a homogeneous static 
magnetic field through a volume sufficient to encompass said body in at 
least two dimensions thereof, 
(c) second static magnetic field means for generating an inhomogeneous 
static field comprising: 
1. An innermost static homogeneous field throughout a volume sufficient to 
encompass the first solid region, 
2. A static inhomogeneous field within a second region surrounding said 
innermost homogeneous field, 
3. An outer static inhomogeneous field in a third region surrounding said 
second region with field strength varying as the Nth power of distance 
from the center of said homogeneous static field, where N is an integer 
greater than one, and 
NMR receiver means responsive to NMR signals induced therein for producing 
said NMR spectrum. 
In accordance with another aspect of the invention, a magnetic coil 
arrangement for use with an NMR spectrometer, comprises an assembly of a 
plurality of coils surrounding a volume within which an inhomogeneous body 
may be arranged; the coil assembly is arranged to enable a sample to be 
placed in the magnetic field produced in the volume when current flows 
through the coil assembly, and current supply means for the coils of the 
assembly, the coils assembly arranged and the relative magnitudes of 
current supplied thereto selected such that a predetermined or selected 
region within the volume has a substantially single valued magnetic field 
but the magnetic field in the remainder of the volume, and especially the 
field in the vicinity of the extremities of the selected region has values 
which are appreciably different from the said single value. 
In more detail, the coil assembly is arranged to provide a first component 
of a static magnetic field which has a gradient varying proportionally to 
a high order or power of distance from a center point of the selected 
region. Preferably, the high order power is even and the coil assembly is 
arranged to provide in addition, a second magnetic field component, 
opposite in sense, to the aforesaid magnetic field component and having a 
gradient which varies at a lower, even order power of distance from the 
said point. The power supply energizing the coils is arranged to supply 
relative currents to the different coils so as to ensure that the two 
different magnetic field components have magnitudes which are 
substantially equal and opposite over a controlled region around the said 
point. Thus, the resulting magnetic field around the said point, and 
substantially encompassing the region of interest is substantially zero, 
but outside the region the higher order magnetic field of the two 
predominates. The coils are arranged so that the region of zero field is 
approximately spherical in shape with the said point at its center. As a 
result of the foregoing, substantially the only magnetic field within the 
region of interest is the static homogeneous magnetic field (background), 
because in this region, the fields produced by the two aforementioned 
coils are substantially equal and opposite in magnitude. However, 
beginning at the outer extension of the region of interest and for a 
substantial distance thereafter, the higher order magnetic field first 
predominates the lower order field, and beyond the magnetic field 
intensity varies as a high order of distance. This provides a sufficient 
gradient so that any NMR signals generated in this undesired region are 
sufficiently displaced in frequency from the signals generated by the 
region of interest, so that relatively simple frequency discriminating 
circuits can be used to segregate the signals generated by the region of 
interest from the signals generated in other regions. 
As specified above, the higher order field is conveniently a fourth order 
field, whereas the lower even order field is a second order field. 
Furthermore, in preferred embodiments of the invention each of the 
aforesaid fields are generated by groups of coil pairs, each group 
producing a different one of the two fields. Each group of the coils 
includes a plurality of pairs of coils, with the coils of a pair being 
similar to each other and positioned about the center of the region to 
ensure that no net magnetic field couples out to the coil which produces 
the static homogeneous field. By using symmetrical coils in a pair the 
resulting field is of even order, if desired. 
Consider, as an example, high resolution .sup.31 P NMR spectra of 
biological molecules which can provide detailed information about the 
biochemistry in physiology of living systems. The structure, cellular 
environment and the rates of interconversion of some important 
phosphorous-containing metabolites can be examined under a range of 
physiological conditions in a variety of tissues and organs. This 
information has considerable diagnostic potential in the comparison of 
normal and diseased tissue. 
In the conventional experimental arrangement used to obtain high resolution 
.sup.31 P NMR spectra from intact organs, a radio frequency coil is 
designed to give a uniform radio frequency field B.sub.1 across the sample 
in a direction perpendicular to a static homogeneous field B.sub.0. The 
homogeneity of B.sub.0 is adjusted so that any residual inhomogeneity is 
less than the natural line width of .sup.31 P resonance and with this 
arrangement high resolution .sup.31 P NMR signals will be received from 
all parts of the body which is subjected to a combination of the radio 
frequency and static magnetic fields. 
In order to limit the volume from which this high resolution .sup.31 P NMR 
signals are received, the effect of homogeneous volume of the static 
magnetic field B.sub.0 must be reduced and centered on a region of 
interest. 
All previous NMR studies, to our knowledge with one exception was carried 
out on excised or perfused organs or required some form of surgery before 
in situ measurements. This results from the low sensitivity of .sup.31 P 
and from the lack of a suitable arrangement for spatial discrimination. 
The single exception is reported in Nature, Volume 283, pages 167-70 
(1980) by Ackerman et al. The citation reports on achievemnt of 
two-dimensional spatial resolution by the use of "surface" radio frequency 
coils. This method, however, is particularly suited to the study of 
tissues and organs that are close to the surface of a body. In contrast, 
the present invention provides a method of acquiring high resolution 
spectra from selected localized regions within a body. 
The invention does not rely upon time varying fields such as the spin 
imaging experiments on living systems which have used inhomogeneously 
broadened spectra of protons to measure spatial location and concentration 
of tissue water, see for example, "Nuclear Magnetic Resonance of a 
Biological System", Philosophical Transactions of the Royal Society (in 
Press). The difficulty with the spin imaging experiments with respect to 
high resolution NMR information is that that very information is 
deliberately washed out to avoid artifacts in the image, and spatial 
discrimination is achieved at the expense of spectral resolution. In the 
present invention, since only the static magnetic field B.sub.0 is 
modified, using a static field gradient, to select localized regions of 
homogeneous fields from which high resolution spectra are obtained, the 
biochemical information contained in the high resolution spectrum is 
retained. 
In accordance with the invention, the magnetic field B (r,.theta.) 
generated by a profile coil system with azimuthal symmetry can be 
described in the terms of a Taylor expansion about the origin, 
##EQU1## 
where B (r,.theta.) is the magnetic field at (r,.theta.); P.sub.n (cos 
.theta.) are the Legendre polynominals of order n and the field 
derivatives, .beta..sub.n are defined by the coil geometry and the DC 
current flowing through the coil system. The magnetic field B (r,.theta.) 
contains field gradients of order n, the proportions of which can be 
controlled using a multi-channel, constant current power supply. A 
sensitive volume of homogeneous field can be delineated, centered on the 
origin and surrounded by inhomogeneous field gradients. The extent of the 
sensitive volume or region of interest is selected via the constant 
current power supply. 
The parameters of the profile coil system to achieve this result are 
determined by the homogeneity of B.sub.0, the natural line width of a 
nuclear species under investigation and the bore of the magnet. 
Another aspect of the invention comprises a method of effecting high 
resolution NMR spectroscopy on selected regions (centered at a point s) of 
inhomogeneous samples, of sufficient resolution to detect chemical shift 
information on the order of 10.sup.-4 to 10.sup.-6 or smaller parts of the 
background field. In accordance with this aspect of the invention, typical 
radio frequency and homogeneous (background) magnetic fields are applied 
to the sample. To localize the experiment the sample is subjected to 
static profiling fields comprising at least two oppositely directed 
fields, each centered on s, each having an intensity-distance relation 
which is proportional to non-unity powers of distance. The order of the 
two fields are both even or odd and both the fields have null magnitude at 
said point s. The sum of the fields and the background field has a 
variation throughout said selected region .ltoreq..delta.B, wherein 
.delta.B is the natural equivalent linewidth of the desired spectrum; 
.gamma..delta.F, where .gamma. is the gyromagnetic ratio and .delta.F is 
the linewidth of the desired resonance. 
The desired profiling field is produced by a coil assembly which is wound 
on a former which is, or can be centered at the point s. The coil assembly 
preferably comprises three coil means, each having parameters (n, number 
of turns; r.sub.1 and r.sub.2, inner and outer winding ratios; 
s.sub.1,s.sub.2 distance of front and rear faces from the center point s,) 
selected to generate the desired profiling fields. The profiling fields 
are preferably second and fourth order. Each coil means comprises pairs of 
symmetrical coils wound or driven to provide zero net coupling. The coil 
means are driven by currents selected for each coil means to allow 
proportionate variation to proportionally enlarge or contract the selected 
region. 
The methods and apparatus referred to above provide for effective remote 
NMR measurements by producing a net magnetic field with cross section 
shown in FIG. 1B. Under certain circumstances it is advantageous to use a 
slightly different magnet arrangement to produce the identical field, 
i.e., one with cross section shown in FIG. 1B. 
Since the profile fields, in the vicinity of the outer extent of the 
sensitive volume must be comparable in magnitude to the background field, 
the current dissipated in the profile coils can become significant and can 
be reduced by the following technique. In the previously described 
arrangement a homogeneous background field has superimposed a profile 
field (which itself may be a composite field) which has a substantially 
single valued sensitive region and is rapidly changing, as a function of 
distance outside that region. As as alternative, especially where large 
bore magnets are used for the background field, and correspondingly where 
large volume sensitive regions are desired, the background field has a 
first homogeneous component and a second component which varies with 
position with respect to a center of the sensitive volume such that its 
maximum excursion within the sensitve region is one half the desired 
profile field. The profile field is similar to that previously described 
except that now it need only supply one half the desired profile field and 
thus can operate at reduced current. The resultant field is substantially 
identical to that previously described but the power dissipated in the 
profile coils is reduced. 
BRIEF DESCRIPTION OF THE DRAWINGS 
Preferred embodiments of the invention, and several experiments, will be 
described in connection with the attached drawings in which like reference 
characters identify identical apparatus, and in which:

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 1A illustrates the manner in which several magnetic fields, and a 
resulting field varies with respect to distance from an origin along the z 
axis. For a magnetic field which varies proportional to a high given order 
(or power) of z, curve 11 illustrates the general relationship between H 
(or B) and z for such a field. For example, curve 11 is drawn to show a 
magnetic field which varies as the fourth power of distance, that is, the 
intensity of the magnetic field is proportional to z.sup.4. A brief review 
of the curve will show that the field is of extremely small intensity for 
a finite distance from the origin, but outside this region has an 
intensity which changes extremely rapidly with distance. Thus, there is a 
small region around the origin where the magnetic field is substantially 
single valued and in fact, substantially zero (to within .delta.B) but 
outside this region the magnetic field is markedly different in its value. 
The region of substantially single valued field can be enlarged by 
providing a second magnetic field of opposite polarity to the field shown 
by the curve 11 and which varies as a lower even order power of the 
distance z. Curve 12 in FIG. 1A shows such a field which is drawn to 
illustrate a variation of intensity proportional to the square of the 
distance from the origin, that is to say, proportional to z.sup.2. 
The resultant field due to the two oppositely directed fields is merely the 
sum of these fields and has a profile as shown by curve 13, which does not 
depart from zero by an amount greater than .delta.B, through a fixed 
distance along the z axis. This value of .delta.B is reached when z=Z. For 
values of z, greater than Z, the field 13 has a rapidly increasing 
intensity since the resultant field is predominantly due to the fourth 
order field, i.e., of curve 11. 
By superimposing a field B.sub.0 which is entirely homogeneous upon the 
resultant field of FIG. 1A, a field profile such as that shown in FIG. 1B 
results. Within the region of interest about the origin (from -a to +a) 
the combined field is homogeneous (to within .delta.B), outside the region 
of interest the combined field illustrates steep gradients. More 
particularly, at very small distances from the origin both second and 
fourth order fields are negligibly small. As distance from the origin 
grows, the second order field exceeds the fourth order field and the 
resultant field achieves a zero slope at a point where the rates of 
increase of second and fourth order fields are equal. Beyond this distance 
the rate of increase of the fourth order field increases more rapidly than 
the second order field. At still a further distance from the origin the 
net fields are again zero. Beyond this point the fourth order field is, 
and remains larger than the second order field, and at some further 
distance Z the net profile field achieves its highest magnitude of 
.delta.B. Beyond this distance the net field continues to grow in 
magnitude, at some further point the second order field has a negligible 
contribution and the field has a substantially fourth power relationship 
with distance. If such a field is applied, along with the radio frequency 
field, to a substnace whose natural gyromagnetic ratio is defined by the 
frequency of the radio frequency field and the magnetic field B.sub.0, an 
NMR signal will be induced, and if the receiving equipment has a bandwidth 
defined by .DELTA.F, then the signal will have two components, a first 
component derived from the region of interest (from +a to -a) in which the 
static field is homogeneous to within .delta.B (which is selected to be 
less than the natural line of the desired resonance) plus a contribution 
from the inhomogeneously broadened induced signal from the region between 
-a and -c, and the region between +a and +c. Outside this region, i.e., 
beyond +c and -c no effective signal is received, because the signal 
induced lies outside the bandwidth of receiving equipment. 
Accordingly, the objects of the invention are achieved by providing a 
profile coil assembly to produce a magnetic field whose intensity varies 
as the curve 13 in FIG. 1A. Such a profile coil assembly is one which 
generates a magnetic field in an approximately spherical volume of radius 
R, which does not include the coil, and which, therefore, contains no 
electric current. It can be shown that such a field can be described by 
equation (1). 
If we select a magnetic field containing only components which very 
oppositely as second and fourth orders of distance, all of the terms of 
equation 1 on the right hand side are zero except for the coefficients of 
.beta..sub.2 and .beta..sub.4. 
If now we set 
EQU .beta..sub.2 =2.delta.B(R/Z).sup.2 (2) 
EQU and .beta..sub.4 =-.delta.B(R/Z).sup.4 (3) 
where .delta.B is the maximum allowed field excursion and is arranged to be 
less than .delta.F/G, where .delta.F is the half line width of the 
narrowest spectral line and G is the gyromagnetic ratio, then Z, which is 
where the magnetic field differs from B.sub.o by .delta.B, is given by Z=R 
(-.beta..sub.2 /2 .beta..sub.4).sup.1/2. (4) 
Such an arrangement of coils having the values of coefficient .beta..sub.2 
and .beta..sub.4 as set out above produce a magnetic field B which varies 
not only along the z axis, but also in all directions from the center. 
Away from the z axis the field excursion .delta.B occurs at some value of 
distance other than Z so the region of a single valued field is not 
exactly spherical. However, the departure is not significant so that Z can 
be regarded as a measure of the size of the region of single value 
magnetic field. 
More precisely, assuming the presence of fourth and second order fields, 
field intensity is given by 
EQU B=.beta..sub.2 r.sup.2 P.sub.2 (cos .theta.)+.beta..sub.4 r.sup.4 P.sub.4 
(cos .theta.) 
where 
EQU P.sub.2 (cos .theta.)=1/2 (3 cos.sup.2 .theta.-1) 
EQU P.sub.4 (cos .theta.)=1/8 (35 cos.sup.4 -30 cos.sup.2 .theta.+3) 
With these expressions the off axis field intensity can be calculated at 
r=Z. Plotting this as a function of .theta. will reveal an eight lobed, 
closed, generally circular pattern. The extent that the maxima or minima 
depart from a true circle depends on the ratio of .beta..sub.2 
/.beta..sub.4. 
If the total spectral width of the receiver which receives signals from the 
sample is W then a field excursion .DELTA.B can be defined such that 
.DELTA.B=W/G. Only those parts of the body in which the field excursion is 
less than .DELTA.B will contribute to the received signal. If 
.DELTA.B=K.delta.B then the radius of the volume contributing broadline 
signal is Z=[1+(K).sup.1/2 ].sup.1/2. FIG. 2 illustrates an exemplary coil 
which is cylindrical and wound around the axis z, with inner radius 
r.sub.1 and outer radius r.sub.2. Its ends lie at distances s.sub.1 and 
s.sub.2 from an origin 0 living on the z axis. For a number of turns n and 
current I the field B at the origin is given by: 
##EQU2## 
and .gamma.=.sup.r 2/r.sub.1, B.sub.1 =.sup.s 1/r.sub.1, B.sub.2 =.sup.s 
2/r.sub.1 ; B.sub.1 or B.sub.2 being substituted in equation 6 as called 
for by equation 5. 
The field B.sub.z at a point z along the axis is therefore: 
##EQU3## 
Equation 1 can be represented by a Taylor expansion. 
##EQU4## 
where n is a series of integers. 
By relating equation 1 to equation 8 we can write: 
##EQU5## 
The requisite values of 
##EQU6## 
can be obtained by repeated differentiation of equation 7 and these values 
are substituted into equation 9 for each value of n that is required to 
give the corresponding value of .beta..sub.n. 
The magnetic field coil arrangement which gives a magnetic field profile as 
defined by the curve 13 of FIG. 1A has no components of a magnetic field 
which are proportional to odd powers of z. A pair of coils which are 
symmetrical about an origin z=0 fulfills this requirement. Furthermore, 
since .beta..sub.n is proportional to 1/r.sup.n+1, where r is the winding 
radius of the coil arrangement, field gradients proportional to high order 
values of z can be made insignificant by winding the coil with 
sufficiently large radius. With these constraints the only field 
coefficient of significance in any pair of coils are .beta..sub.0, 
.beta..sub.2, and .beta..sub.4. These terms can be found from equation 9 
for n=0, 2, and 4. 
As result, it will be noted that .beta..sub.n for any given coil is a field 
coefficient expressed in terms of current I, turns N, inner and outer 
radii r.sub.1 and r.sub.2 and the distances s.sub.1 and s.sub.2 of the end 
faces from the origin. For any coil a series of coil coefficients h.sub.n 
can be defined equal to .beta..sub.n /I and h.sub.n is independent of 
current and depends solely on the other parameters and is therefore, 
determined solely by coil geometry and location. Thus, for any coil of 
given geometry and location a series of coil coefficients for that coil 
can be calculated. In calculating the coil coefficients of a coil the 
quantity R can be assumed to have unit value. 
With these constraints, namely a pair of symmetrical coils and a large 
winding radius, then following equation 1 the magnetic field B produced by 
such a pair of coils when carrying a current I is: 
EQU B=I [ho+h.sub.2 (z/R).sup.2 +h.sub.4 (z/R).sup.4 ] (10) 
where h.sub.0, h.sub.2 and h.sub.4 are coil coefficients calculated as 
explained and R is given a unit value. To determine the minimum number of 
separate coils making up the coil assembly which are required so that the 
desired magnetic field profile is obtained it should be recalled that 
three conditions must be fulfilled, i.e., .beta..sub.o =0, and equations 2 
and 3 should be satisfied. The first of these conditions ensures that the 
coil assembly provides a zero valued magnetic field in the selected 
region. The remaining conditions provide for opposing second and fourth 
order gradients. Fulfillment of all these three conditions simultaneously 
requires a minimum of three coils each carrying different values of 
current I.sub.1, I.sub.2, I.sub.3, respectively. Thus, 
EQU I.sub.1 h.sub.01 +I.sub.2 h.sub.02 +I.sub.3 h.sub.03 =0 (11) 
EQU I.sub.1 h.sub.21 +I.sub.2 h.sub.22 +I.sub.3 h.sub.23 =2.delta.B(R/Z).sup.2 
(12) 
EQU I.sub.1 h.sub.41 +I.sub.2 h.sub.42 +I.sub.3 h.sub.43 =-B(R/Z).sup.4 (13) 
where for each h the first suffix relates to a coil coefficient and the 
second suffix relates to a particular coil. 
It is desirable that the coils have no net coupling with the magnet coil 
which provides the background field. This is ensured by arranging that the 
total number of ampere-turns of the assembly is zero. If each coil is 
replaced by a group of coils carrying the same current and different coils 
of a group are wound in opposite sense it can be arranged that the sum of 
the turns of any group is zero and thus none of the individual coil groups 
couples to the main magnet coil. 
An example of a coil assembly that is constructed in accordance with the 
requirements set out above is illustrated in cross-section in FIG. 3. The 
coils are wound on a cylindrical former (cross-hatched in FIG. 3) the 
central axis of which corresponds to the z axis and the center of which 
lies at the center of the region of homogeneous magnetic field. There are 
three groups of coils, i.e., groups 1, 2 and 3. Each group comprises a 
number of pairs of coils. The coils of a pair are identical to each other 
and are symmetrically positioned about the center of the former. This 
ensures that there are no odd-order magnetic field gradients. Coil group 1 
comprises three pairs of coils 1a and 1a', 1b and 1b', 1c and 1c'. Coil 
group 2 comprises three pairs of coils 2a and 2a', 2b and 2b' and 2c and 
2c'. Coil group 3 comprises two pairs of coils 3a and 3a' and 3b and 3b'. 
An example of approximate relative positions of the various coils is as 
laid out in FIG. 3 and an example of a suitable number of turns for each 
coil is indicated in the lower half of FIG. 3 at each coil position. A 
negative sign adjacent a turn number indicates that the coil is wound in 
the opposite sense to the others or is connected to carry current in the 
reverse direction. All the coils of a group are connected together and 
carry the same current I.sub.1, I.sub.2, or I.sub.3 as the case may be. 
FIG. 4 is a table which list the number of turns of each coil and 
appropriate values for the coil coefficients .beta..sub.0, .beta..sub.2 
and .beta..sub.4 for every coil as calculated from equation 9. 
To determine the values of the currents I.sub.1, I.sub.2 and I.sub.3 
equations 11, 12 and 13 are solved for these unknowns from which 
EQU I.sub.1 =d.sub.1 /Z.sup.2 +e.sub.1 /Z.sup.4 (14) 
EQU I.sub.2 =d.sub.2 /Z.sup.2 +e.sub.2 /Z.sup.4 (15) 
EQU I.sub.3 =d.sub.3 /Z.sup.2 +e.sub.3 /Z.sup.4 (16) 
where d and e with appropriate suffixes are constant. 
A circuit arrangement for providing the currents I.sub.1, I.sub.2 and 
I.sub.3 in accordance with equations 14, 15 and 16 is illustrated in FIG. 
5. Voltage V is fed to a potential divider 20 and the slider of the 
potential divider is set to provide an output voltage Z which is 
adjustable proportionally to the required size of the region under 
investigation. This signal is applied to an analog divider circuit 21 
providing an output proportional to the reciprocal of its input, that is 
to say proportional to 1/Z. The output of circuit 21 is applied to two 
multipliers or squaring circuits 22 and 23 in cascade. These circuits thus 
provide outputs proportional to 1/Z.sup.2 and 1/Z.sup.4 respectively. The 
output from circuit 22 is applied to an inverting amplifier 24 feeding 
three potential dividers 25, 26 and 27 in parallel. Similarly, the output 
of circuit 23 is fed to an inverting amplifier 28 feeding three potential 
dividers 29, 30 and 31 in parallel. 
Three current generators 32, 33 and 34 provide currents I.sub.1, I.sub.2 
and I.sub.3 for the respective groups of coils. The inputs to these 
generators are obtained from respective summing amplifiers 35, 36 and 37. 
The input to summing amplifier 35 is obtained from potential dividers 25 
and 29. The input to summing amplifier 36 is obtained from potential 
dividers 26 and 30. The input to summing amplifier 37 is obtained from 
potential dividers 27 and 31. 
The sliders of the potential dividers 25, 26, 27 and 29, and 30, 31 are set 
respectively in accordance with the magnitudes of the coefficients 
d.sub.1, d.sub.2, d.sub.3 and e.sub.1, e.sub.2, e.sub.3. It will be seen 
therefore that the respective currents I.sub.1, I.sub.2 and I.sub.3 
obtained from generators 32, 33 and 34 fulfill the requirements of 
equations 14, 15, and 16. This circuit is only one of many which will 
fulfill the requirements of the invention, others will readily occur to 
those skilled in the art. 
Although the preceding discussion has described a profiling coil assembly 
to produce a profile field of intensity corresponding to the composite 
curve 13 (of FIG. 1A) those skilled in the art will understand how a coil 
assembly can be derived to produce the fourth order field of curve 11 
(FIG. 1A). While the field of curve 13 provides a larger region of 
homogeneous field than curve 11 which is preferred, the field of curve 11 
can provide the necessary steep gradients to localize a particular region, 
and thus is within the scope of the invention. 
The choice of magnetic field amplitude for an NMR experiment is determined 
by sensitivity (which increases the field intensity) and desired spectral 
resolution. These parameters fix a lower limit. An upper limit is fixed by 
economics and engineering difficulty since higher limits may require 
longer coils and higher power. Typical field strength varies from 500 
Gauss for proton NMR when high resolution is not required, from 10,000 
Gauss with less sensitive nuclei for high resolution to 120,000 Gauss for 
small magnets and 20,000 Gauss for large magnets. 
As mentioned above the background field may include a homogeneous component 
and a distance varying component when it is desirable to reduce the 
current requirements of the associated profile coil assembly. This is 
advantageous especially where the background field is generated with 
superconducting technology. In this case the background field's distance 
varying component can vary as a high order of distance from the center of 
the sensitive volume. This variation can be identical to that of an 
associated profile coil, i.e., fourth order or oppositely polarized second 
and fourth order, or some other combination which results in the desired 
profile. The profile coils is as described above except that it now need 
only provide half the non-homogeneous field previously required. In fact, 
the coil coefficients can be identical and the current halved to achieve 
the identical field shown in FIG. 1B. 
An NMR spectrometer which includes a magnet coil arrangement as described 
above with reference to FIG. 3 and FIG. 5 is generally illustrated in FIG. 
6. As shown therein the spectrometer comprises a magnet coil 41 which 
provides a constant magnetic field (background) within a central bore. 
Coil 41, which may be superconducting (alternatively can be air cored 
resistive coil, iron cored electromagnet or permanent magnet) provides a 
field which is sufficiently steady, both in space and time, to enable 
high-resolution spectroscopy to be undertaken. Within the bore a profile 
coil assembly 42 such as that shown in FIG. 3 is positioned which modifies 
the value of the magnetic field within the bore everywhere except in a 
selectable region located centrally of coil assembly 42. The background 
field and profile field are both static and their sum is homogeneous to 
less than the line-width of the desired resonance within said selectable 
region. Electric currents to the coils of coil assembly 42 are supplied 
from a current supply source 43 corresponding to the arrangement shown in 
FIG. 5. An NMR probe 44 can be inserted within the cylindrical space 
defined by coil assembly 42. Probe 44 contains rf transmitter and receiver 
coils (or only one coil, if time shared) and provision for holding a 
sample. A transmitter 45 provides rf signals to the probe 44 and a 
receiver 46 receives signals from the NMR probe 44. Receiver 46 may 
include a suitable computing arrangement for processing the received 
signals. 
In use of the spectrometer a sample is positioned in probe 44 and the probe 
is inserted into the central space within assembly 42. The region from 
which effective signals are obtained in receiver 46 has its center fixed 
by the position of assembly 42 but its size can be varied by control of 
the currents supplied by current supply source 43. 
The signals effectively received in receiver 46 will not be from the whole 
sample but only from that portion of the sample which lies in a small 
region centered on the center point of coil assembly 42. The size of this 
region can be adjusted by adjustment of potentiometer 20 forming part of 
the current supply means 43. To examine a different part of the sample the 
sample or the coil assembly 42 is moved. 
The signals received in receiver 46 will include information from which 
high-resolution spectra can be obtained from the selected region within a 
larger volume. In addition, signals will be obtained from the fringes of 
the region where the departure of the magnetic field from its steady value 
is greater than .delta.B but less than .DELTA.B. Depending on the mode in 
which the spectrometer is used this fringe region will degrade the 
received signals but this degradation can be compensated for. 
Where the spectrometer is operated in a continuous wave (CW) mode the 
spectra obtained will have a form shown in FIG. 7 and comprise 
high-resolution signals 51 superimposed on a broad line signal 52. A 
suitable function y.sub.f can be subtracted from the total signal to 
compensate for the broad line signal. y.sub.f has the form 
EQU y.sub.f =A/(1+(Bf).sup.2) (16) 
where f is the frequency and A and B are parameters which are empirically 
determined so as to give a flat base line. 
When the spectrometer is operated in a pulsed mode to provide a free 
induction decay (FID) signal which is Fourier transformed, the FID signal 
from a resonant nucleus of line width 1/r has an envelope of magnitude 
y.sub.t given by y.sub.t =exp(-t/r). The FID signal from a broad line will 
therefore decay more quickly than from a narrow line and will have the 
general form illustrated in FIG. 8. The FID signal comprises an initial 
portion 53 in which there is rapid decay followed by a later portion 54 
which decays more slowly and which contains the high resolution 
information. By delaying the accumulation of data until after the initial 
signal has decayed only high-resolution information is retained. 
As an alternative the same method as used in connection with the CW case 
can be employed. Another alternative is to use convolution differencing in 
which the free induction decay signals are multiplied by functions C of 
the form 
EQU C=exp (t-t/T.sub.1)-k exp (-t/T.sub.) (17) 
where k, T1 and T2 are chosen to suppress the broad line signal. This 
method is described in J. Mag. Res. 11,172 (1973). 
TESTS 
Two experiments were carried out, one with phantom samples and another on 
live rats in order to test the spatial discriminating or localizing 
capability of the profile coil arrangement of FIG. 3. 
In the first test a two-compartment test phantom, shown in FIG. 9 comprises 
a closed cylinder 90, 30 millimeters in diameter surrounding a closed 
spherical compartment 91 of 20 mm diameter. Both the compartments 90 and 
91 contained adenosine triphosphate (ATP), phosphocreatine (PCr) and 
inorganic phosphate (P.sub.i). The spherical compartment 91 contained 4.65 
mM ATP 9.3 mM PCr and 3.72 mM P.sub.i. The cylindrical compartment 90 
contained 4. 65 mM ATP, 18.6 mM PCr and 1.86 mM P.sub.i. These 
compositions simulate the proportions of these metabolites found in heart 
and skeletal muscle respectively. In both compartments 90 and 91 the 
solutes were dissolved in 150 mM KCL to simulate the electrical 
conductivity of tissue. The pH in the spherical compartment 91 was 
adjusted to be 0.5 less than that of the outer cylindrical compartment 90. 
The principal effect of this pH difference is to produce a chemical shift 
difference between the frequencies of the P.sub.i resonances of the two 
samples. A single turn saddle shaped radio frequency coil 92 was used, 
tuned to an operating frequency of 73.8 megahertz. The spherical 
compartment and the radio frequency coil are mounted concentrically with 
the magnetic center of B.sub.0 and .beta.(r). 
Spectra recorded from the composite samples are presented in FIG. 10a. The 
spectrum of FIG. 10a was obtained with the axial extent 2z, set to 40 
millimeters (by adjusting the potential of the voltage divider) in 300 
scans, a 6 Hz line broadening exponential multiplication was used to 
enhance S/N. The three ATP peaks and the PCr peak are unaffected by the 
difference in pH, whereas two clearly distinguishable P.sub.i peaks can be 
seen. Using the PCr peak as a reference, the positions of the two P.sub.i 
peaks from the internal and external compartments are 4.85 ppm and 5.23 
ppm, corresponding to pH values of 7.10 and 7.45 respectively. The P.sub.i 
concentration in the internal sample is twice that in the external sample, 
but since the ratio of internal to external compartment volumes is 0.2 the 
internal P.sub.i peak area should be 0.84 that of the external P.sub.i 
peak area. The value of the P.sub.i concentration ratio measured in the 
peak area is in good agreement with the expected value. 
The power supply was then adjusted so that the axial extent 2a was reduced 
to 20 millimeters and the spectrum recorded as shown in FIG. 10b and 
obtained in 600 scans with the same S/N enhancement. The broad component 
at the base of each peak is derived from the metabolites in the external 
compartment which now lie in a region of inhomogeneous magnetic field. 
This broad signal can be eliminated using convolution difference 
techniques described in the Journal of Magnetic Resonance, supra, and the 
ensuing spectrum is presented in FIG. 10c which was obtained by 6 Hz and 
60 Hz line broadenings with the vertical scale multiplied by four. The 
narrow peaks correspond to the metabolites present only in the spherical 
compartment 91 and the position of the P.sub.i peak in spectrum is 4.85 
ppm in agreement with the position measured previously. 
This experiment appeared to demonstrate the capability of the apparatus to 
acquire high resolution spectra from selected spatial location in an 
otherwise inhomogeneous body simulated by the two compartment test 
phantom. Further experiments have demonstrated a difference of 0.15 pH can 
be resolved and that the spectrum derived from an internal volume is 
almost identical to the spectrum that would be derived from the sample 
alone in the absence of other inhomogeneously broadened spectra. 
A second test, on a live animal employed a rat, the most readily 
identifiable organ being the liver. This choice was made for the reason 
that: 
a 150 gram rat fits conveniently within the radio frequency coil. The liver 
weighs about 5 grams and the rat can be positioned in such a way that a 
roughly spherical volume 1-20 mm in diameter contains liver tissue that 
can be localized with the profile coils. 
The liver contains no detectable PCr and therefore, its spectrum is easily 
distinguishable from that of muscle (see FIG. 11). 
A spin lattice relaxation times of some of the .sup.31 p resonances from 
liver are an order of magnitude shorter than those normally measured in 
other tissues and organs: this feature offers an additional means of 
identification. 
The anesthesized animal was mounted vertically in a cradle, and on the 
basis of preliminary anatomical examination was positioned so that the 
liver was centralized in the radio frequency coil. 
The spectrum obtained from the rat in the absence of any localizing field 
is presented in FIG. 11a with 128 90.degree. pulses applied at intervals 
of 2 seconds. The ATP and PCr peaks are readily identifiable, but the 
P.sub.i and the sugar phosphate regions of the spectrum is less readily 
assigned. The reason for this is that the 2,3-dipholsphoglycreate from 
blood contributes two signals at about 4.0 ppm and 6.5 ppm and the first 
of these overlaps with the P.sub.i signal. However, the small intensity of 
the signals in this region of the spectrum means that blood contributes a 
negligible amount to the ATP peaks, as the concentration of ATP and blood 
is very much less than the concentration of 2,3-diphosphoglycreate. We can 
therefore conclude that the ATP signals arise primarily from the liver and 
muscle tissue, the PCr arises exclusively from muscle, while the signals 
in the P.sub.i and sugar phosphate region may have contributions from 
liver, muscle and blood. 
Following this the sensitive volume was reduced (set to 20 mm) and the 
resulting spectrum is shown in FIG. 11b and again with 128 90.degree. 
pulses at intervals of 2 seconds. The smaller peak intensities reflect the 
fact that now high resolution signal is being acquired from a smaller 
volume. Although the spectra of FIGS. 11a and 11b were obtained with the 
same spectrometer conditions, there is a change in the relative 
proportions of the metabolite resonances, indicating an alteration in the 
region that contributes high resolution signals. In fact, the spectrum of 
FIG. 11b more closely resembles the spectrum of a perfused liver shown in 
FIG. 11e. However, there is still some PCr present, the origin of which 
will now be discussed. The spectra of FIG. 11a and 11b were obtained using 
a radio frequency pulse interval of 2 seconds, which is fairly typical for 
.sup.31 P NMR study of whole tissue. FIG. 11c shows a spectrum obtained 
with a pulse interval of 220 milliseconds, in the absence of localizing 
fields with 1024 90.degree. pulses. The PCr peak intensity is now 
significantly reduced in comparison with its intensity in FIG. 11a because 
its spin-lattice relaxation time T.sub.1, is long (about 3 seconds). The 
reduction in the ATP intensity is far less, partly because the ATP in 
tissues such as muscle has a rather shorter relaxation time (about 1 to 2 
seconds), and partly because a significant percentage of the ATP is in the 
liver, and liver ATP has very short T.sub.1 values (about 100 
milliseconds). FIG. 11d shows a spectrum obtained using 1024 90.degree. 
pulses at the short pulse interval with a reduced sense of the volume (2a 
set at 20 mm's). This spectrum contains no PCr signal and it is very 
similar to the spectrum of perfused liver shown in FIG. 11e. This 
illustrates that the signals of FIG. 11d are predominantly from the liver 
which has been successfully localized, without the necessity for surgery. 
To confirm the effectiveness of this localization, the experiment was 
continued and the animal underwent surgery to cut off the blood supply to 
the liver. That is, following the experiments whose spectra is illustrated 
in FIG. 11, the rat was removed from the probe, and surgery performed to 
ligate the hepatic artery and portal vein. The animal was then 
repositioned in the probe and the experiments of FIG. 11 were repeated and 
the results are presented in FIG. 12a-12d. The various spectrum of FIG. 
12a-12d were taken under conditions similar to those obtained in FIGS. 
11a-11d. The marked reduction of ATP and increased levels of P.sub.i, 
after ligation, shown in FIG. 12b and 12d, clearly indicate unhealthy 
liver tissue thereby verifying the origin and interpretation of the 
previous spectra. In contrast, the PCr signal intensity in FIG. 12a is 
very similar to that of FIG. 11a, since the metabolic state of the muscle 
is little affected by the operation. This confirms that the FIG. 12a 
spectrum includes muscle whereas the FIG. 12b spectrum has been localized 
to exclude contribution from muscle. 
The foregoing description is sufficient to enable those skilled in the art 
to make and use the invention claimed hereinafter. In a practical 
implementation a digital computer is used to actually control the Rf coils 
and to sample, process and display the induced signals; however, inasmuch 
as application of such a computer is not necessary to use of the 
invention, and can be effected by those of ordinary skill, disclosure of 
this particular implementation is not required.