Note: Descriptions are shown in the official language in which they were submitted.
~ ~46~,~2
-- 1 --
116456
INVESTIGATION OF S~MPLES BY N.M.R. TECHNI~UES
This inven-tioll relates to the investigation of samples hy
means of nuclear magnetic resonance (N.M.R.) -techniques.
In conventional experiments using such techniques the results
obtained relate to the average properties of a sample under investi-
05 gation, but in recent times considerahle attention has heen direc-ted
to methods hy means of which the properties of diEferent parts of
a sample may be individually distinguished, there~y making i-t
possihle for example to oh-tain information relating to the distri-
hution within an inhomogeneous sampLe of the values of parameters
such as nuclear spin density and nuclear spin relaxation time.
Broadly speaking, such methods are hased on two different principles
(which can, however, he used in comhination in specific cases).
The first of these, which may conveniently be referred to as
spatiaL selection, involves arranging the N.M.R. system so that
only signals from a selected region of the sample are received or
processed; for an example of a method hased on -the spatial
selection principle reference may he made to ~ritish Patent Specifi-
cation No, 1,508,438 and U.S. Patent No. 4,015,196. The other
principle, which may conveniently be referred to as signal coding,
involves arranging the N.M.R. system so that the signals received
from the sample contain distinguishable information about different
parts of the sample (or different parts of a region of the sample
selected ùsing the spatial selection principle).
Various methods of producing images of a sample using the
signal coding principle have been proposed, but -they generally
have the disadvantage, which is par-ticularly marked in the case of
large samples, of imposing very severe practical requirements in
respect of one or more aspects of the N.M.R. system. Thus in some
cases the methods require very rapid changes to he made in som~
component of the magnetic field appliecl to the sample, often with
a requirement that -the field throughout the sample should be
stable in a short time after the change; in other cases the
formation of a sat:Lsfactory image is dependent upon véry accurate
control of the magnetic field applied to the samp~e. The latter
consideration applies, ~or example, to the method disclosed by
Lauterbur in Nature, Vol. 242, 16 March 1973, pages 190-191, in
which N.M.R. spec-tra are derived from a sample subjected to a
magnetic field having a non-homogeneous component which gives
rise to a linear field gradient; each individual spectrum repre-
sents a one-dimensional projection of the nuclear spin density
in the sample, integrated over planes perpendicular to the direc-
tion of the gradient, and in order to obtain two-dimcnsional or
three-dimensional ~ages spectra are derived from a series of dif-
ferent directions of the field gradient and the results are subjec-
ted to a process of "image reconstruction". With this method,errors in the magnetic field result in a degradation of the image
definition.
The present invention provides a method of investigating
a sample us:inq N.M.R. techniques, in which the signal coding prin-
ciple is ut.ilised in such a way as to enable a variety of kinds
of spatially discriminated information to be obtained from the
sample, and in particular to enable images to be obtained without
incurring the disadvantage discussed above.
The essential features of a :method according to the in-
vention consist of subjecting the sample to a magnetic field havinga non-homogeneous component which exhibits a substantially linear
field gradient in a given direction relative to the sample, perfor-
ming on the sample, while it is subjected to said field, a series
of operations in each of which nuclear magnetic resonance of a
given nuclear species. is caused to occur in the sample by irradia-
ting the sample with at least one pulse of radio frequency energy
and in each of which data for a given series of epochs in a time
-2a-
domain related to the timing of the irradiating pulse(s) are de-
rived by sampling signals obtained by coherent detection of sig-
nals emitted from the sample as a result of the irradiation, the
operations of sai.d ser:ies differing substantially only by virtue
of the magnitude of said gradient having a different value for
each operation, and obtaining in respect of nuclei of said species
in the sample information which is spatially discriminated in
a dimension corresponding to said given direction by subjecting
data derived from the whole series of operations
.;1
- 3 -
to processing involvillg Fourier transforma-tion with respect -to -the
magni-tude oE said gradient~
It is to he ~mderstood that for one of the operations of the
series the magnitude of said gradi!ent may have zero value (corres-
05 ponding to the vanishing of said non-homogeneous component).
The essential features referred to ahove can he comhined in a
variety of ways with certain optional features, as is discussed
more fully helow. It is, however, appropriate first to explain in
principle the nature of the information obtainahle hy suhjec-ting
the data derived from a single series of operations as defined
above to Fourier transformation with respect to the magnitude of
~he field gradient, assuming that the magnetic field is uniform
apart from the non-homogeneous component referred to ahove. For
this purpose it is convenient to denote hy H the value of the
magnet:Lc field at a point in the sample, so that for any one
operatiion of the series H is equal to H + gx, where g is the
magnitude of the field gradient for that operation, H is the
value 1:he field would have in the absence of the non-homogeneous
component, and x is the distance of the relevan-t point from the
plane ~perpendicular to the direction of the gradient) for which
H = H " for the sake of simplicity it will be assumed for the
purpose of the present explanation that neither g nor x takes a
negative value. The N.M.R. signal resulting from the presence of
the relevant nuclear species at the point in question will thus
have an angular frequency equal to ~(FI ~ gx), where ~ is the
gyromagnetic ratio, and will give rise to a component of the form
[A cos (ygx~)J in the signals ohtained hy coheren-t detection of
the signals emLtted from the sample, Because oE the mathematical
equivalence of the variables ~ and t, it will be seen that the
value of this component for particular values of t and g can he
regarded either as a sample of a conventional signal in the time
domain (for the relevant value of ~), or as a sample of a notional
signal in a gradient magnitude domain (for the relevant value
of t), both signals of course being associated with a specific
value of x~
6~
Now consider the da-ta derived hy the saTnpling in the case
under discussion, assuming for -the sake of simplicity that the
coherent detection is effected using onLy a single phase~sensitive
detector. The data will consist of M x N numhers, where M is the
05 numher of operations and N is the numher of epochs for which
samples are taken in each operation; it is therefore convenient
to consider the data as set out in a rec-tangular matrix having
rows respectively corresponding to the different values of g for
the series of operations, and columns respectively corresponding
to the different values of t for the series of epochs. It will he
appreclated that -the numhers in each row represent the time domain
signal for the relevant value of g, while the numhers in each
column represent the gradient magnitude domain signal for the
relevant value of t. Conven.ional Fourier transformation with
respect to time would of course involve handling the data row hy
row, hut the present concern is with a method in which -the data
are handled column by column, In particular1 hy suhjecting the
data in each column to Fourier transformation -~ith respect to g
one can effectively derive, from the representation of the gradient
magnitude domain signal in each column, a representation of a
spatia:L domain signal, in the form of a set of numhers giving the
values of the spatial domain signal for different values of x~ By
appropria-te performance of the transformation, these values of x
can he made the same for each column; it should he noted that
where the well-known fast Fourier transform (F.F.T.) algorithm is
employed, this requires the processing to include a change of
variable operation, which can he carried out either hefore or
after the application of the F.F.T. algorithm. The transformed
data can then be set out in a second rectangular matrix with the
columns again corresponding to different values of t, hut with the
rows now corresponding to different values of x. Thus the rows in
the second matrix will respectively represent the time domain
signals arising from a series of slices of the sample approximating
to planes perpendicular to the direction of the field gradient.
-- 5 --
It will accordingly be seen tha-t such a procedure enables
N.M.R. measuremen-ts (which may he of many different kinds, just as
in conventional pulsed N.M.R. experiments) to be carried out with
separate results obtained for each of the slices. Merely by way
05 oE example, mention may he made of the case in which the irradiating
pulses are 90 pulses separated by intervals greater than the
spin-lattice relaxation time (Tl) and the epochs in the time
domain are chosen so that the numbers in each row of the second
matrix referred to above will represent the free induction decay
signal for the corresponding slice of the sample; in this case
the N.M.R. spectrum for each slice can he obtained by suhjecting
the data in the relevant row of the second matrix to Fourier
transformation with respect to t.
The possibility just mentioned constitutes an example of a
situation in which the overall processing of the data in a method
accordLng to the invention involves both Fourier transformation
with respect to the magnitude of the field gradient and Fourier
transformation with respect to time. In the foregoing explanatory
discussionl it was convenient to assume that in such a si-tuation
the transfonnation with respect to the magnitude of the field
gradient would be carried out first; it should be emphasised,
however, that this is not essential, since equivalent results can
be obtained with the two types of transformation reversed in
order.
The preceding discussion explains how it is possible to
obtain information which is spatially discriminated in a single
dimension. The principles involved can readily be extended to
enable spatial discrimination to be effected in two or three
dimensions in a method according to the invention, by arranging
for the magnetic field to have two or three non-homogeneous
components which respectively give rise to substantially linear
field gradients in respective directions relative to the sample
which are orthogonal to each other, ancl performing on the sample
an appropriate ensemble of operations of the same kind as involved
G~'~
- 6 -
in the one-dimensional case. [n the two-dimensional case the
ensemh:Le is arranged to consti-tute a set of series of operations
such that -the operations of each series diEfer significantly only
hy vir-tue of tlle magnitude of a first one of the gradients having
05 a different value for each operation and the respective series of
the set differ significantly only hy virtue of the magnitude of
the second of the gradients having a different value for each
series; in the three-dimensional case the ensemhle is arranged to
constitute a group of sets, each of the same kind as involved in
~he two-dimensional case, such -that the respective se-ts of the
group differ significantly only by virtue of the magnitude of the
third of the gradients having a different value for each set. It
is to be understood that the magnitude of the first gradient may
have zero value for one of the operations of each series, that the
magnitude of the second gradient may have zero value for one of
the series of the or each set and that in the three-dimensional
case th.e magnitude of the third gradient may have zero value for
one of the sets of the group. In hoth cases the processing o:E the
data derived from the whole ensemhle of operations will he similar
to that appropriate for the one-dimensional case~ but the Fourier
transformation with respect to the magnitude of the single gradient
used in the one-dimensional case will he replaced as appropriate
by either two-dimensional Fourier transformation with respect to
the magnitudes of the first and second gradients or three-dimensional
Fourier transformation with respect to the magnitudes of the
first, second and third gradients. As in the one-dimensional case
there can thus be derived information represen-ti.ng time domain
signals (or frequency domain signals if the data processing also
involves Fourier transformation with respect to time) arising from
a series of different parts of the sample; in the two-dimensional
case these parts w'Lll approximate to a two-dimensional array of
lines perpendicular to the directions o:E the two field gradients,
and in the three-dimensional case these parts will approximate to
a three-dimensional array of points.
-- 7 --
In order to use methods according to the invention for ohtaining
two-dimensional or three-dimensional images of spin density dis-tri-
hution in the sample, -the principles involved in -the techniques
discussed ahove may he used in conjunct-ion with the known principle
05 of using a ]inear field gradient wh:ile deriving a NoM~R~ spectrum
so that different spectral frequenc~es correspond to different
positions along the direction of the field gradient. For this
purpose the magnetic fie]d is arranged to have two c,r three non-
homogeneous components which respec-tively give rise to suhstan-
t:Lally linear Eield gradients in respective directions relative tothe sample which are orthogonal to each other, For two-dimensional
imaging two gradients are used and there are performed on the
sample a series of operations as in the general one-dimensional
case discussed ahove, i.e, such that the operations of the series
differ significantly only hy virtue of the magnitude of a first
one of the gradients having a different value for each operation;
the magnitude of the second of the gradients is thus kept the sarne
for all the operations. By subjecting the data derived from the
whole series of operations to processing involving both Fourier
transformation with respect to the magnitude of the first gradient
and Fourier transformation with respect to -time, one can ohtain
information separately represen-ting the spectra for each of a
series of slices of the sample approximating to planes perpendicular
to the direction of the first gradient; this informa-tion can
readily he displayed to provide a two-dimensional image of the
spin densi-ty distribution in -the sample, It should he noted that
this image will be a shadow image of the distrihution, projected
in a direction perpendicular to the directions of the first and
second gradients, For three-dimensional imaging three gradients
are used and there are performed on the samp]e a set of series of
operations as in the general two-dimensional case discussed ahove,
i.e. arranged so that the operations of each series differ signifi-
cantly only by virtue of the magnitude of a first one of the
gradien-ts having a different value for each operation and the
respective series of the set differ significantly only by virtue
of the magnitude of a second of the gradients havlng a differen-t
value for each ser-les; the magnitude oE the third of -the gradients
is thus kep-t the same for all -the opera-tions. The treatment of
the data in this case is similar to that for the case oE two-
05 dimensional imaging, but with Fourier transforma-tion with respect
to the magnitude of the first gradient replaced hy two-dimensionai
Fourier transforma-tion with respect to the magnitudes of the first
and second gradients, so that the information ohtained separa-tely
represents the spectra for each of a series of parts of the sample
approximating to a two-dimensional array of lines perpendicular to
the directions of the first and second gradients.
The imaging techniques just discussed have a significant
advantage over methods involving image reconstruction, such as
that disclosed by Lauterbur and referred to above. This arises
from the fact that when using such techniques errors in the
magnetic field give rise to geometrical distortion of the image
rather than to a degredation of its definition; for most appli-
cations the former is a much less serious fault than the latter.
In some types of method according to the invention it may be
appropriate to utilise the spatial selec-tion principle in combination
with certain of the techniques discussed above. For example in
the case of two-dimensional imaging tha-t principle can be utilised
to restrict the relevant signals to those arising from a section
of the sample approximating to a plane parallel to the directions
of the two field gradients; the image will then repersent the
spin density distribution in that section, instead of heing a
shadow image of the whole sample. The spatial selection principle
can also he employed in conjunction with the one-dimensional and
two-dimensional cases of general N.M.R. measurements discussed
above. The spatial selection may he effec-ted by known means, for
example by using l:he type of method disclosed in Bri-tish Patent
Specification No. 1,508,438 and U.S. Patent No. 4~015,196~
As with conventional pulsed N.M.R. experiments, it may be
appropriate, for the purpose of improving-the signal-to-noise
ratio, to arrange for the irradiation of the sample during each of
the operations ln a method accorcling to the invention to he in the
~onn o~ a train oF plllses or pulse se~luences, with the ~ata derived
for each operation heing ohtained hy averaging the values oF
appropriate sets of samples over -the whole train. The use o~ a
05 train of rapidly recurring pulses during each operation may also
he appropria-te in order to ohtain tl~e henefit of the multiple
sidehand technique which is utilised in the method disclosed in
sritish Patent Specifica~ion No. 1,601,816 and ~S. Patent
No. 4,184,110.
The changes in the magnitude of the magnetic fie1d gradient(s)
that must he made in a method according to the invention do not
have to he effected wi-th the same order of rapidity as is required
in certain known methods employing the signal coding principle.
While it will normally he apprDpriate to maintain the field
gradient(s) constant during the performance of each of the operations,
with discrete changes of gradient magnitude taking place hetween
successive operations, it is envisaged that in some cases it may
he possihle to utilise a continuous sweep oE gradient magnitude.
An emhodiment of -the invention will now be descrihed hy way
of exarnple with reference to the accompanying drawings, in which:-
Figure 1 is a diagrammatic representation of a N.M.R. imagingsystem in which the principles of the invention are utilised;
Figure 2 is a perspective view, partly cut away to show
internal details, of part of the structure of the system
illustrated in Figure l; and
Figures 3a, 3h, 3c and 3d are diagrams illus-trating the
layouts of four coil sets used in the imaging system,
It is assumed that in this emhodiment a san-ple to he inves-ti-
gated contains a non-uniform distrihution of water, with a single
narrow N.M.R. spectral line resulting from proton resonance. The
imaging system is designed to enahle two-dimensional images of
this distrihution to he ohtained; as explained more fully helow,
these images may he ei-ther shadow images of the whole sample or
images of a section of the sample.
- lO -
Referring to the drawings, -the sample (designated 1 in Figures 1
and 2) is disposed in a uniEorm stahle magnetic field generated hy
a magnet 2 whLch (as shown in Figure 2) is consti-tuted hy a set of
four coaxial coils 2a, 2b, 2c and 2d~ The value of the magnetic
05 field (subsequently denoted by 1~ ) is chosen to be about 1.2
kilogauss; this corresponds to a proton resonance frequency of
about five ~z~ since for proto!~s the gyro~aglletic ratio is giv2n
hy ~/2~= 4.26 kHz per gauss. ln further considering the geometry
of the arrangement, it is convenient to define a Cartesian
co-ordinate system with its z axis coincident with the axis of the
coils 2a-2d (i.e. parallel to the direction of the magne-tic field)
and the origin disposed centrally between the coils 2h and 2c.
The sample 1 is disposed substantially centrally with respect to
the z axis and with the origin lying within it; where a sectional
image is required, the sample 1 is located so that the relevant
section corresponds to the plane z=O.
Disposed within the central part of the magnet 2, so as to
surround the sample 1, is a coil set 3 for irradiating the sample 1
with radio frequency energy and for picking up N.M.R. signals from
the sample 1, The coil set 3 is designed so that the r.f. magnetic
field will be directed perpendicular to the z axis; for the sake
of definiteness, it is taken that the r.f. magnetic field is
directed parallel to the x axis. Figllre 3a more clearly il]ustrates
the layout of the coil set 3, which consists of two similar loops 3a
and 3b disposed so as to be mirror images of each o-ther with
respect to the plane x=O; each loop 3a or 3b is arranged symmetri-
cally with respect to the plane y=O, and consists of two straight
portions extending parallel to the z axis and two arcuate portions
lying in planes perpendicular to the z axis which are equidistant
from the plane z=O. The loops 3a and 3b are electrically connected
in series, with the relative senses of current flow being as
indicated by the arrows in Figure 3a.
Surrounding the coil set 3 is a tubular former 4 of non-magnetic
insulating material, on which are wound three gradient coil sets 5,
6 and 7 for subjecting the sample 1 to non-homogeneous magnetic
fields which are superimposed on the main field genera-ted hy the
magne-t 2. For the sake of clarity, the coil sets 5, 6 and 7 are
omitted from Figure 2, hut their individual layouts are respectively
illustrated in Figures 3h, 3c and 3d. These coil sets are so
05 designed that in the vicinity of the origin the field genera-ted hy
each of them will have a vector component parallel to the z axis,
this component havlng an intensity which varies monotonically with
position parallel to one of the axes (x, y and z respectively for
the coil sets 5, 6 and 7) but does not vary with position parallel
to the other two axes. In other words, the non-homogeneous fields
generated hy the coil sets 5, 6 and 7 respectively exhibit gradients
in the three mutually perpendicular directions parallel to the x,
y and z axes; the gradients are required to he substantially
linear throughout the sample 1 for the x and y directions, hut
this is not essential for the z direction. Thus, the coil set 5
consists of four similar loops 5a, 5b, 5c and 5d, each of similar
shape to the loops 3a and 3bg each of the loops 5a-5d again heing
dispose!d symmetrically with respect to the plane y=0 with their
straight portions parallel to the z axis; the loops 5a-5d are
arrange!d so that the loop 5a is a mirror image of the loop 5b with
respect to the plane z=0 and is a mirror image of the loop 5c with
respect to the plane x=0, and the coil 5d is a mirror image of the
coil 5b with respect to the plane x=0 and a mirror -Lmage of the
coil 5c with respect to the plane z=0. The loops 5a-5d are electri-
cally connected in series, with the relative senses of currentflow being as indicated by the arrows in Figure 3b. The coil
set 6 is similar to the coil set 5 but with the co-ordinates x and
y interchanged. The coil set 7 is in the form of a ~elmholtz pair
wound in opposition, the coils 7a and 7b of this set being disposed
substantially in planes perpendicular to the z axis with their
centres lying on -that axis, these planes being equidistant from
the plane z=0. It will be appreciated that the fields generated
by the coil sets 5, 6 and 7 respectively have zero value in the
planes x=0, y=0 and z=0.
In deriving an image, a ~series of operations is performed
with the coil se-ts 5 and 6 energised hy undirectionaL currents,
the value of the current supplied to the coil set 5 (and hence the
value of -the field gradient in the x direction) heing different
05 for each operation of -the series hut the value of the current
supplied to -the coil set 6 (and hence -the value of the field
gradient in the y direction) heing the same for all the operations.
The coil set 7 is utilised only in -the case where a sectional
image is to be ohtained. That case will be considered later, hut
it will be initially assumed in the following description that a
shadow image is to be obtained, so that the presence of the coil
set 7 can be ignored. Thus in the shadow image case, for any
given operation of the series the component of the total magnetic
field parallel to the z axis will have at any point in the sample 1
a value equal to H +gx+hy, where g is the magnitude of the x
gradient for the relevant operation and h is the magnitude of the
y gradient; the corresponding resonance frequency will of course
he equal to ~(~1 +gx+hy)/2~. It is convenient to take h as positive,
hut x, y, and g can he either positive or negative. Assuming that
the dimensions of the sample 1 are such that ¦x¦ and ¦Y¦ are never
greater than L, and that the highest value of ¦g¦ for any operation
of the series is ~, then the maximum and minimum possihle values
of the resonance frequency in the sample 1 are given hy (~Ho/2~)- F,
where F is equal to ~(G~h)L/2~.
Referring in particular to Figure 1 (in which the whole
assembly comprising the elements 2-7 is denoted hy the general
reference 8), -the current for the coil set 6 ls derived from a
d.c. source 9, while the current for the coil set 5 is supplied
from the output of a d.c. amplifier 10, the input of the
amplifier 10 heing connected to the output of a digital-to-
analogue converter 11 to whose input there is applied a digital
signal generated hy a computer 12. TakiLng the numher of
operations in the series as 2P, in deriving an image the value of
the digital signal is caused to assume in succession 2P different
numhers~ which together constitute the series running from P to
P-l. The value oE g can thus be taken as mAg, ~here ~ is positive
and m is a differellt one of these 2P num~ers for each operation of
the series; it will be noted that the va]ue of g is zero for one
05 operation of the series, and that the val.ue of G is equal to P~gr
The changes in value of the digital signal are arranged -to occur
at regular intervals, of dura-tion greater than the spin-lattice
relaxation time (Tl) for the protons in the sample l; i-t is of
course convenient, but not essential, to arrange for -the value of
;o m to he change~l by unity in the same sense on each occasion, For
many types of sample the duration of the intervals hetween changes
in the value of the digital signal may suitahly have a value in the
range 0.3-1 second,
As will be explained further below with reference to Figure 1,
for each operation of the series the sample 1 is irradiated with
one or more pulses of r.f. energy having a frequency equal to rH /2~,
the duration, amplitude and r.f. phase being the same for every
pulse throughout the series of operations, and the timing of the
pulse(s) relative to the intervals at which the changes in the
value of the digital signal occur heing the same for all operations
of the series. The duration of each pulse is made sufficiently
short to ensure that for all operations of the series there is
effective irra~iation at all possible values of the resonance
frequency in the sample l; this requires the duration of each
pulse to be not substantially greater than 1/2F. The duration and
amplitude of the pulses are chosen so that each pulse gives rise
to a rotation of the nuclear magnetisation in the sample 1 of the
order of 90 . The resultant N.M.R. signals picked up from the
sample 1 are subjected to coherent detection using the phase
quadrature detectiion system. The detected signals will of course
contain componentC~ at frequencies corresponding to the difference
between rH /2~ and the resonance frequencies in the sample 1; the
maximum frequency for these componen-ts is equal to F. These
components will be.transient components where the free induction
decay technique is used, i.e. where Eor each operation there is
used either a single pulse or a sequence of pulses recurring at
intervals grea-ter than T1. Grea-ter efficiency in respec-t of da-ta
collection can, however, ~e achieved if for each operation there
05 is used a sequence of pulses recurring regularly at intervals
which are short compared with the spin-spin relaxation time (T2)
for the protons in the sample 1; in this case a quasi-s-teady
state of magnetisation will be set up in the sample 1, and -the
relevant components in the detected signals wlll he suhstantially
continuous wave components. In either case, during a period
immediately following each pulse the detec-~ed signals are sampled
at a regular series of epochs defined by -t=n~t, where t represents
time measured from the centre of the duration of the pulse and n
is an integer in the series running from one to N (N heing even)O
In orcler to satisfy the sampling theorem, the sampling interval ~t
must rlot he greater than 1/2F. A corresponding constraint applies
to the magnitude of ag~ which must be small enough to ensure that
for any value of n the sampled data treated as a function of g
must not go through more than one cycle when g changes by 2o~,
this requires tha-t Qg should not he greater than ~rYLN~ti
The foregoing discussion can be appropriately illustrated hy
quoting suitable numerical values of the relevant parameters for a
specific case. It is assumed for this case that (as would commonly
be appropria-te in practice) N is chosen to he equal to 2P (i.e.
the number of epochs is equal to the number of operations in the
series) and h is chosen to be equal to G (i.e. the magnitude of
the y gradient is equal to -the highest ahsolute value of the
magnitude of the x gradient). From the expressions quoted ahove,
it can he readily deduced that in this case the conditions specified
for Qg and Qt will hoth be satisfied in the limit hy making ~gQt
equal to ~/2YPL. It is further assumed that the dimensions of the
sample 1 in any plane perpendicular to the z axis do not exceed
20 x 20 cms, so that the value of L can be taken as 10 cms. The
choice of P for a given vaLue of L is dependent on the resolution
required in the image; hy taking a value Or 128 one ohtains in
-this case an image cell size of approxima-tely 0.8 x 0~8 mm. Then
if a value of 20 microseconds is chosen Eor Qt, the specified
05 conditions for ag and ~t can he satisfied hy making the value
of ~g equal -to 2.29 milligauss/cm. The value of G and h will then
he just under ~.3 gauss/cm, with the value of F heing 25 kLIz. The
duration of each pulse can thus also suitably he made equal to 20
microseconds. It will he no-ted tha-t with these values one ob~a1ns
a reasonahle value of just over five milliseconds for the timing
of the last sampling epoch given hy N~t. In the event that Lt 15
desirecl to use a sequence of rapidly recurring pulses for each
operation, the pulse recurrence frequency may suitahly he made
equal to 1/2N~t ln this case (giving a value of JUSt under lOOHz)
Re!ferring again to Figure 1, the r.f. energy for irradiating
the samlple 1 is derived from a master oscillator 13 having a
frequency equal to yH /2~. An output from the oscillator 13 is
fed to a timing unit 14, which generates various timing signals
used in the system in response to counting of the cycles of the
oscillation. A further output from the oscillator 13 is fed to a
gate 15 which is controlled hy signals from the timing unit 14,
the gate 15 heing turned on to produce the required pulses. These
pulses are fed to a r.f. power amplifier 16 whose output is applied
to the coil set 3 via a directional coupler 17. The N.M.R. signals
picked up by the coil set 3 are fed via the directional coupler 17
to a gated low-noise amplifier 18 which is turned off during each
r.f. pulse hy means of signals derived from the -timing unit 14.
The output of the amplifier 18 is applied to two identical phase-
sensitive detectors 19 and 20, reference signals for which are
derived from the oscillator 13; thus, an output from tne
oscillator 13 is fed to a variahle phase shifter 21 and a 90
phase shifter 22 connected in cascade, outputs from the phase
shifters 21 and 22 respectively providing the reference signals
for the detectors 19 and 20 so that they operate in phase quadrature.
- 16 -
The outputs of the de-tectors 19 and 20 are respectively fed via
identical lowpass f~ ters 23 and 2~, havi.ng a cut-off frequency
somewhat above F, to a pair of identical analogue-to-digital
converters 25 and 260 The converters 25 and 26 operate, under the
05 control of strohe signals derived from the timing unit 14, to
sample the detected signals at the required epochs. The resultant
digital signals representing the sampled values are fed to the
computer 12 for processing as descrihed helow.
In cases where more than one pulse is used for each operation
of the series, the first stage of -the processing involves addition
of the sampled values epoch hy epoch for each operation, to provide
an average value for each epoch for each opera-tion. This stage is
of course not required where only a single pulse is used for each
operati.on. In any case, there will thus he available a set of 2PN
lS pairs of numbers, with the numbers of each pair respectively
cortesponding to the two signal channels; in the further processing
the numbers of each pair are respectively treated as the rea]. and
imaginclry parts of a complex number which it is convenient to
denote by S , where the suhscripts m and n respectively indicate
the relevant operation and the relevant epoch. The data constituted
by the 2PN complex numbers are subjected to Fourier transformation
with respect to the magnitude of the x gradient, To effect this
there are calculated the.values of the complex numbers f given
by the express:Lon
P-1
f = n ~ S n exp(-i~n~tm~gr~x)
m=-P
for a].l values of n from one to N and for all values of r from -P
to P-l, with ~x equal to L/P. The calculation can be speeded up
by usi.ng the fast Fourier transform algorithm, hut in this event a
change of variable operation must also be performed. The data
constituted by the 2PN complex numbers frn are then subjected to
Fourier transformation with respect to time. To effect this there
are calculated the values of the complex numhers FrS given by -the
expression
N
Frs ~ f exp(-iYn~ths~y)
n=l
Eor all values of r from ~P to P-l and for all values of s from
-N/2 to N/2-1, with ~y equal to 2L/N. The data constituted hy the
05 2P~ complex numbers F s are then processed by an algorithm, of the
type used in conventional N.M.R. experiments, to make any necessary
corrections in respect of the signal phases. The real (in-phase)
component of the final data, corresponding to an absorption mode
spectrum, is retained, while the imaginary (out-of-phase) component,
corresponding to a dispersion mode spectrum, is discarded. There
is thus obtained a set of 2PN real numbers Ar ~ which respectively
represent (each for a value of x equal to r~x and a value of y
equal to s~y) the water content of the sample 1 in-tegrated through
the sample 1 in the z direction. These numbers are utilised to
control the operation of a display device 27 so as to generate the
required shadow Lmage. The device 27 may for example incorporate
a storaLge cathode ray tube operated so as to produce a rectangular
array of 2P x ~ points whose brightnesses are respectlvely set in
accordance with the numbers A
Turning now to consider the alternative case in which a
sectional image is to be obtained, in thls case a sequence of
rapidly recurrLng pulses ls used for each operation of the series,
and the coil set 7 is energlsed with a sinusoidal audio frequency
current derived from an a.c. source 28 so as to generate a systematl
cally varylng fleld gradlent ln the z dlrectlon. It wlll be
appreclated that wlth thls arrangement for each operatlon of the
series the total magnetic field strength is substantlally lnvarlant
wlth tlme ln a thin slice of the sample 1 approximating to the
plane z=0, but varies significantly wlth tlme at all polnts ln the
sample 1 outslde this sllce, wlthln the sllce the component of
the total magnetic field parallel to the z axls wlll of course
have a value the same as that quoted above for the shadow lmage
case, i.e. equal to H +gx~hy. The effective thickness of the
slice will vary inversely with the ampLitude of the current
-- 18 -
supplied to the coi.l set 7, and Call for example he made ahout -two
mm if the c~lrren-t is such that the peak value of the z gradien-t is
of the order of 0.1 gauss/cm. The Erequency of -the current supplied
to the coil set 7 is chosen so that in the par-ts of -the sample 1
05 o-ther than the selected slice -there is a significant change hetween
consecutive ones of -the intervals between the pulses in the average
value of the magnetic field during each inter~al~ this implies
that there should not he synchronism or a low order harmonic
relationship between the pulse recurrence frequency and the frequency
of the current supplied to the coil set 7. The latter can, for
example, suitahly have a value of ahout 70 ~Iz where the pulse
recurrence frequency has a value of about lOOHz, as in the specific
case referred to above.
:[n all othe.r respects the derivation of the sectional image
is the same as is described ahove for the shadow image case, with
the f:irst stage of the data processing of course involving the
derivation of an average value of the sampled signals for each
epoch for each operation. By effecting the averaging over a
suhstantial number of periods of the systematic variation of the z
gradient field, any contrihutions to the received N.M.R. signals
arising from resonance effects in the parts of the sample 1 outside
the selected slice will he effectively smoothed out, so that the
averaged data will correspond only to the resonance effects in the
selected slice. As a result the set of numhers A will in this
case effectively represent the distrihution of water only within
the selected slice.
As noted ahove, imaging techniques such as have heen descrihed
with reference to the drawings have the advantage that field
errors will show up as shifts of position in the final image,
rather than causing a degradation of definition. The magnitude of
the positional errors that can he tolerated in the image will
determine the degree of uniformity required in the fields generated
hy the magnet 2.and the coil sets 5 and 6. For any given system,
the magnitudes of the errors can be calculated from plots of the
'~. 'i ~B L~
- 19 ~
relevant fields, and can iE required he corrected during the data
processing hy appropriate shift:Lng of values in the set oE
numhers F
I-t should he noted, however, that from a consideracion of the
05 expression given ahove for f , i-t can he seen that the spatial
resolution distance of the distrihution along the x direction
decreases as n i.ncreases. The relatively worse spatial resolution
for small values of n gives rise to an ar-tifact in the image, this
effect heing associated with the fact that in deriving the image
use is made of a field gradient which has the same magnitude for
all -the operat:ions. The artifact is similar to those ohserved
with methods involving image reconstruction, such as that disclosed
hy Lauterhur, in cases where data is collected for a range of
directions of the field gradient extending over an angle of less
than 180 . The artifact can he reduced by reducing the value of h
relative to G.
