Method for focusing of magnetic resonance images

Apparati and methods for magnetic resonance imaging a selected interrogation volume in a tissue of a human or animal body, to provide increased signal-to-noise ratios for fixed data acquisition times. The method involves excitation of magnetic resonance in a selected interrogation volume that may be as small as 500-3,000 cm.sup.3, through controllable focusing or steering of a rotating magnetic field signal used to induce magnetic resonance. The response signals issued by the excited volume element are then collected by focusing of these response signals, using a phased array of antennae for this purpose. Use of the invention with well known nuclear magnetic resonance excitation procedures, such as spin echo, echo planar, gradient recalled and backprojection, are discussed.

FIELD OF THE INVENTION 
This invention relates to medical imaging of a human or animal body, and 
particularly of the cardiac region, using RF focusing techniques together 
with nuclear magnetic resonance imaging in high magnetic fields, to 
improve the signal-to-noise ratio per unit data acquisition time and to 
improve the spatial resolution, spectroscopic sensitivity and/or data 
throughput rate of such imaging. 
BACKGROUND OF THE INVENTION 
Medical imaging techniques for organs and tissues in a human or animal body 
have changed considerably over the last 20 years, in good measure because 
of adoption of nuclear magnetic resonance imaging for medical imaging. 
Damadian(Science 171(1971) 1151-1153), Weisman(Science 178 (1972) 
1288-1290), Lauterbur(Nature 242(1973) 190-191), Eggleston et al(Cancer 
Research 33 (1973) 2156-2160) and Damadian et al (Proc. Nat. Acad. Sci. 71 
(1974) 1471-1473; Science 194 (1976) 1430-1431) were among the first to 
recognize the value of, and to apply the techniques of, NMR to distinguish 
between normal and abnormal developments in human and animal bodies. 
Nuclear magnetic resonance ("NMR") is a relatively young research area and 
was first discussed and experimentally investigated by Bloch and his 
co-workers in 1946 (Phys. Rev. 70 (1946) 460-474 and 474-485). The Bloch 
articles are incorporated herein by reference. In NMR, an approximately 
constant magnetic field B.sub.0 =B.sub.0Hi.sub.z is applied in a fixed 
direction, which defines the z-axis of the associated coordinate system, 
to the target(organ, tissue, etc.), and a time-varying field B.sub.1 
=B.sub.1 (i.sub.x cos .omega.t+i.sub.y sin .omega.t) is applied in a plane 
perpendicular to the z-direction, where the amplitude B.sub.1 is also 
approximately constant. The magnetic polarization vector M satisfies the 
magnetization torque equation 
EQU dM/dt=.gamma.(M.times.B)+(M.sub.0 /T1)i.sub.z -.OMEGA..multidot.M (1) 
where .gamma. is the gyromagnetic ratio, B=B.sub.0 +B.sub.1 is the total 
impressed magnetic field, M.sub.0 is an equilibrium magnetization 
established by the polarization field, T1 is a characteristic time 
interval for return to equilibrium of the transverse component of 
magnetization, T2 is a characteristic time interval describing de-phasing 
of the magnetization, and .OMEGA. is a diagonal second rank tensor or 
dyadic that phenomenologically accounts for relaxation of the three 
magnetization components that is of the form 
##EQU1## 
For protons, the ratio .epsilon. is 42.57 MHz per Tesla. The spin-lattice 
relaxation time T1 and the spin-spin relaxation time T2 are often of the 
order of 600-1,000 msec and 20-100 msec, respectively. The observable 
quantities are M.sub.x and M.sub.y. 
These equations can be solved under various driving and receiving field 
conditions to obtain the magnetization components for the system. When the 
system is excited by a radiofrequency ("RF") magnetic field intensity 
B.sub.1 at or near the resonant frequency f.sub.0 =.omega..sub.0 
/2.pi.=.gamma.B.sub.0, the spin system will draw energy from the RF 
exciting field. Conversely, if the spin system is near resonance, energy 
can be returned to a structure positioned to receive this RF energy. 
Analysis of the system of equations is Eq. (1) is discussed by A. Abragam, 
The Principles of Nuclear Magnetism, Oxford University Clarendon Press, 
1961, pp. 37-75, and is incorporated herein by reference. Medical imaging 
is concerned generally with receipt and interpretation of the fields 
produced by this given-back energy. 
In subsequent discussions, it will be assumed that the frame of reference 
is one that rotates with the RF rotating magnetic field B.sub.1 at the 
resonant frequency f.sub.0. The magnetization components M.sub.x' and 
M.sub.y' are of particular interest here. In a frame rotating with the 
field, the magnetic field directed along the x'-axis in the rotating frame 
produces a magnetization only along the y'-axis. In this frame, the 
broadband RF pulse and various gradient magnetic fields (discussed below) 
that perturb the spin system are easily visualized and analyzed. 
One problem that faces any approach to excitation, selective or otherwise, 
of a tissue, organ or other biological component of a human or animal body 
(herein referred to simply as "tissue" for convenience), or parts thereof, 
is that the "noise", which arises from tissue not within the desired 
volume element, is often substantial because of the relatively large 
surrounding tissue volume that produces such noise. A time-varying 
magnetic field B.sub.1 in the tissue produces a corresponding electric 
field E.sub.1 by Maxwell's equations, and because the tissue has non-zero 
conductivity, this produces a corresponding non-zero current vector J. The 
volume integral of the scalar product of J and E gives rise to power 
dissipation in the entire tissue volume element, and this produces noise 
at the signal sensing apparatus unless the field of view of the tissue 
volume element can be somehow limited. This process can be represented by 
a "body noise" resistor whose contribution is proportional to tissue 
conductivity. Noise sets a lower limit on the resolution, expressed as the 
smallest volume of tissue that can be sensed by the receiver, and sets a 
lower limit on the length of the time interval over which signal 
acquisition is possible. Noise is produced by uncontrolled electronic 
action in the receiver circuits ("Johnson noise"), by the "body noise" 
resistor noise source, and by thermally induced magnetization in the 
tissue being imaged. 
Three volume elements, of quite different sizes, are involved here: (1) 
tissue volume, which can be a few hundred to a few hundred thousand 
cm.sup.3 in size; (2) RF signal interrogation volume from which the 
receiver receives the sensed response signals; and (3) magnetic resonance 
excitation volume or "voxel volume" within the tissue, which can be much 
less than 1 mm.sup.3 in size. The interrogation volume is defined by the 
volume surrounded by the coil, applicator or other transmitter used to 
generate the RF magnetic field and by the extend of the unwanted electric 
field generated in the body itself. In conventional approaches, this 
interrogation volume can be 50,000-100,000 cm.sup.3, which is much larger 
than the tissue volume for cardiac monitoring. Preferably, the 
interrogation volume should be about the same size as the tissue volume, 
or smaller. 
According to one well known relation in magnetic resonance physics, the 
signal-to-noise ratio (SNR) is proportional to the product of B.sub.0 and 
a volume ratio: 
EQU SNR.varies.B.sub.0 [voxel volume/interrogation volume][.DELTA.t].sup.1/2, 
where .DELTA.t is the data acquisition time and B.sub.0 is the primary 
magnetic field strength. Increase of B.sub.0 causes a proportional 
increase in the system's resonant frequency. Increase of .DELTA.t is often 
constrained by throughput requirements. Increase of B.sub.0 and/or 
reduction of the interrogation volume is thus a primary concern, if the 
signal-to-noise ratio is to be increased. 
What is needed here is an approach that (1) minimizes or suppresses the 
body noise per unit acquisition time that issues from the tissue volume, 
and (2) increases the available signal per unit acquisition time. 
SUMMARY OF THE INVENTION 
These needs are met by the invention which, in one embodiment, provides a 
method for limiting the field of view, and thus the noise contribution, by 
reducing the interrogation volume element to a size no larger than 3,000 
cm.sup.3 in a tissue in a human or animal body. The method provides for 
increased signal by use of a primary magnetic field B.sub.0 of larger 
magnitude (2-10 Tesla). In order to limit the field of view within the 
body or tissue, a high frequency RF magnetic field, with f.sub.0 =85-340 
MHz, is chosen for the rotating field. The corresponding or effective 
wavelength .lambda. within the tissue is relatively short (11-41 cm), due 
to the high dielectric permittivity of tissue at such frequencies. This 
short effective wavelength allows one to focus the RF energy within a 
modest size interrogation volume element in the tissue, thus markedly 
limiting the field of view. 
According to this method, a first or primary magnetic field (intensity) 
B.sub.0 =B.sub.0 i.sub.z is applied in a first (z) direction and a second 
focused magnetic field B.sub.1 (x,y,z,t), sometimes referred to herein as 
B.sub.1 for convenience of notation, is applied in a perpendicular (xy) 
plane, where B.sub.1 has constant magnitude, rotates in the xy-plane with 
approximately constant angular frequency .omega., and is applied only over 
a first time interval t.sub.1 &gt;t&gt;t.sub.1 +.DELTA.t.sub.1 for predetermined 
quantities t.sub.1 and .DELTA.t.sub.1. Application of the field B.sub.1 
provides a "theta pulse" that tips the magnetization vector M away from 
the z-axis toward the xy-plane by a predetermined reorientation angle 
.theta., and two popular choices are .theta.=90.degree. and 
.theta.=10.degree.-20.degree., as discussed below. For convenience of 
notation, the primes on the coordinates x, y, z in the rotating frame for 
dropped in the following discussion. 
A slice select gradient magnetic field B.sub.2 (z) is applied to the 
tissue, either simultaneously with or preceding application of the field 
B.sub.1, to convert a portion of the longitudinal magnetization M.sub.0 in 
a selected z-slice into xy-plane magnetization M.sub.x and/or M.sub.y over 
a predetermined time interval given by t.sub.2 &lt;t&lt;t.sub.2 +.DELTA.t.sub.2, 
where t.sub.2 .ltoreq.t.sub.1. 
One or more additional gradient magnetic fields B.sub.3 (x,y) is then 
applied to put the magnetization in selected tissue voxel volume elements 
within the chosen z-slice into differential magnetic resonance over a 
predetermined time interval, in order to "tag" the (x,y) spatial locations 
of these voxels. The gradient magnetic fields B.sub.2 (z) and B.sub.3 
(x,y) all have field vectors parallel to the field vector of the primary 
magnetic field B.sub.0. A "read" cycle is then initiated by application of 
an RF magnetic field B.sub.5 (x,y,z,t) plus another gradient magnetic 
field B.sub.6 (x,y), or of the gradient magnetic field B.sub.6 (x,y) 
alone, to the tissue voxel volume elements within the z-slice. The 
magnetization thus produced excites electromagnetic signals that issue 
from the selected tissue voxel volume elements within a determinable tim 
interval given by t.sub.sig &lt;t&lt;t.sub.sig +.DELTA.t.sub.sig. The spatial 
locations of these voxel volume elements, from which the electromagnetic 
signals issue, are thus "tagged" by the choice of the gradient magnetic 
fields. 
An array of sampling antennae, numbered n=1, 2, . . . , N, which senses the 
direction and amplitude of electromagnetic response signals issued by the 
selected nuclei, is provided, where antenna number n in the array is 
activated to sense these signals only over a predetermined time interval, 
given by t.sub.sig,n &lt;t&lt;t.sub.sig,n +.DELTA.t.sub.sig,n, that depends upon 
n. This particular nth time interval corresponds to receipt, at antenna 
number n, of the response signal that was issued by the excited selected 
nuclei in the predetermined time interval t.sub.sig &lt;t&lt;t.sub.sig 
+.DELTA.t.sub.sig. Differences among these N time intervals may be 
compensated for by use of phase shifts, time delays or other similar 
adjustments in the response signals received. 
Excitation of magnetization in the selected voxel volume elements can be 
accomplished by a number of approaches, including but not limited to the 
spin echo method, the echo planar method, the gradient recalled method, a 
backprojection method and various spectroscopic imaging techniques. All of 
these provide spatially resolved discrimination of this magnetization. 
Selective sensing of the electromagnetic signals issued by the selected 
nuclei in the voxel volume elements is implemented by an array of antennae 
surrounding the tissue volume. The sequence of antenna activation time 
intervals t.sub.sig,n &lt;t&lt;t.sub.sig,n +.DELTA.t.sub.sig,n is chosen so that 
the sensing antenna number n is activated and senses the received or 
response signal RS (FID, spin echo or other resultant signal) that was 
issued by the selected magnetization in the tissue during the antenna's 
own activation time interval t.sub.sig,n &lt;t&lt;t.sub.sig,n 
+.DELTA.t.sub.sig,n, within which it receives this response signal RS. 
Because the RS signal thus issued by the selected magnetization may 
require different amounts of time to reach each of the sensing antennae in 
the array, the times t.sub.sig,n and/or the time interval lengths 
.DELTA.t.sub.sig,n may differ from one antenna to another. If the sensing 
antennae are arrayed approximately on the circumference of a circle with 
the selected voxel volume elements positioned at the center, the 
parameters t.sub.sig,n and, separately, the parameters .DELTA.t.sub.sig,n 
may be approximately equal within each parameter set. If the sensing 
antennae are arrayed on two or more planes adjacent to the tissue these 
parameters may be quite different from one another with each parameter 
set. 
The sensing antenna also serve as the source of the transmitted magnetic 
field B.sub.1 in one group of embodiments of the invention. In alternative 
embodiments, the transmitted magnetic field B.sub.1 is provided by a first 
array of antennae or other sources and the sensing antennae form a second, 
separate array to recover the response signal RS. 
In all embodiments, the invention includes apparatus for producing nuclear 
magnetic resonance in a tissue and for sensing the RS signals induced in 
the selected nuclei in the tissue. In a first embodiment, the apparatus 
includes a dipole magnet, excited by current-carrying coils. The magnet 
substantially surrounds the patient's body and produces an approximately 
homogeneous magnetic field of specific field strength in the range 2-10 
Tesla in a first (z) direction in the body. The apparatus includes an RF 
magnetic field source that produces a rotating magnetic field with 
approximately constant magnitude, with the magnetic field vector rotating 
in an xy-plane perpendicular to the z-direction with approximately 
constant angular frequency. The apparatus further includes a switched 
power source for the rotating magnetic field source so that this rotating 
magnetic field can be activated and deactivated during predetermined time 
intervals. The apparatus also has gradient magnetic field means for 
applying one or more additional gradient magnetic fields, over 
predetermined time intervals, to the tissue to excite selected 
magnetization in selected voxel volume elements in the tissue. The 
apparatus also includes an array of sensing antennae, positioned as a 
phased array adjacent to the tissue, to sense the RS signals issued by the 
selected magnetization. Several embodiments of these arrays are available. 
The apparatus further includes switching means connected to each sensing 
antenna to independently activate each antenna over a predetermined time 
interval so that each antenna senses the RS signals only over its own time 
interval. 
Recall that the z-axis of the associated coordinate system is determined by 
the direction of the primary magnetic field B.sub.0 and that the magnetic 
field B.sub.1 (x,y,z,t) rotates in a plane that is perpendicular to the 
direction of B.sub.0. A second coordinate system is defined by three 
distinct planes relative to the human or animal body being examined: (1) a 
"transverse plane" TP that is oriented perpendicular to a longitudinal 
line that runs approximately parallel to the backbone of the body; (2) a 
"sagittal plane" SP that includes a longitudinal line of the body and 
includes a line that passes from the back to the front of the body; and 
(3) a "coronal plane" CP that includes a longitudinal line of the body and 
includes a line that passes from the right side of the body to the left 
side of the body. These three planes are illustrated in FIG. 1 and are 
defined by the body b itself. A transverse plane, sagittal plane or 
coronal plane may pass through the body or be positioned outside and 
adjacent to the body to which it refers. 
In a first embodiment of the phased array of antennae, the primary magnetic 
field B.sub.0 is oriented perpendicular to a coronal plane and the RF 
magnetic field B.sub.1 (x,y,z,t) rotates in this coronal plane. Two 
antennae arrays, positioned in coronal planes located in front of and 
behind the body, provide an RF magnetic field B.sub.1. In a second 
embodiment, the primary magnetic field B.sub.0 and the RF magnetic field 
B.sub.1 are oriented as in the first embodiment, but the RF magnetic field 
B.sub.1 is produced by a differently positioned array of antenna, located 
at the right side and left side of the body. In a third embodiment of the 
phased array of antennae, the primary magnetic field B.sub.0 is oriented 
perpendicular to a transverse plane and the RF magnetic field B.sub.1 
rotates in this transverse plane. In a forth embodiment of the phased 
array of antennae, the primary magnetic field B.sub.0 is oriented 
perpendicular to a sagittal plane and the RF magnetic field B.sub.1 
rotates in the sagittal plane. 
In a general embodiment of the method invention, an approximately static, 
approximately homogeneous, primary magnetic field B.sub.0 oriented in a 
predetermined (z) direction is applied to the tissue, or to the 
interrogation volume of the tissue, and an RF magnetic field B.sub.1 
(x,y,z,t), which rotates in a plane that is approximately perpendicular to 
the field vector B.sub.0, is applied over a first predetermined time 
interval given by t.sub.1 &lt;t&lt;t.sub.1 +.DELTA.t.sub.1. A slice-select, 
gradient magnetic field B.sub.2 (z) is applied over a predetermined time 
interval given by t.sub.2 &lt;t&lt;t.sub.2 +.DELTA.t.sub.2, in order to select a 
particular slice of the tissue. This gradient magnetic field B.sub.2 (z) 
is oriented parallel to the primary magnetic field B.sub.0 but has much 
smaller magnitude and varies strictly monotonically with change in 
position in the z-direction. One or more additional gradient magnetic 
fields B.sub.3 (x,y), with field vector oriented parallel to the 
z-direction but changing with position in directions x and y in a plane 
perpendicular to the z-direction, is applied over a predetermined time 
interval given by t.sub.3 &lt;t&lt;t.sub.3 +.DELTA.t.sub.3, in order to 
selectively excite voxel volumes within the chosen z-slice for study. The 
selected volume is excited by another RF rotating magnetic field and 
another gradient magnetic field, or by a gradient field alone, and a 
response signal is sensed at one or more phase arrays of antennae. The 
individual antennae receive the response signals RS at different times and 
compensate for this by means of internal phase shifts, time delays or 
other adjustments at the individual antennae that make up the array; these 
adjustments are used to focus the antenna array on the interrogation 
volume of interest. The resulting signals are then processed in order to 
properly analyze and display the response signals RS produced within the 
interrogation volume. 
To evaluate and diagnose cardiac and other diseases of the heart and other 
organs and tissues non-invasively, a device that can image the anatomical 
structures with sub-millimeter resolution and that can view biochemical 
functions such as perfusion and metabolism with sub-centimeter resolution 
is provided. Diagnostic magnetic resonance imaging and spectroscopy, using 
RF focusing techniques and a high strength primary magnetic field, provide 
the improved signal-to-noise ratios that are required to achieve 
sub-millimeter spatial resolution and sub-centimeter localized 
spectroscopic signals. Focusing of the transmit and receive radiofrequency 
electromagnetic fields allows the volume of tissue from which response 
signals are sensed to be limited to a much smaller interrogation volume of 
interest, in order to reduce the energy deposited in the tissue by this 
radiation. Use of a plurality of sensing antennae, positioned in a phased 
array, allows an increase in the signal to noise ratio and allows a 
concomitant improvement in the data acquisition rate for the system.

DESCRIPTION OF BEST MODE 
FIG. 2 is a flow chart illustrating the general method of the invention. 
The tissue, identified as 31 in FIG. 3, is placed in a static, homogeneous 
primary magnetic field B.sub.0, oriented in a first (z) direction in the 
laboratory frame, in the first step 11. A rotating magnetic field B.sub.1 
(x,y,z,t) is applied in an xy-plane that is approximately perpendicular to 
the z-direction in the third step 13. The rotating magnetic field B.sub.1 
has approximately constant magnitude and rotates with approximately 
constant angular frequency .omega. in the xy-plane. The primary and 
rotating magnetic fields may be represented approximately as 
EQU B.sub.0 =B.sub.0i.sub.z, (3) 
EQU B.sub.1 (x,y,z,t)=B.sub.1 (x,y,z) (i.sub.x cos.omega.t+i.sub.y 
sin.omega.t), (4) 
where i.sub.x, i.sub.y and i.sub.z form a mutually orthogonal triad of unit 
length vectors, oriented in the x-, y- and z-directions in the rotating 
frame, respectively, where the z-direction coincides with the direction of 
the static primary field B.sub.0. The equations (1)-(4) are most easily 
analyzed in a rotating frame that rotates with the rotating magnetic field 
B.sub.1 (x,y,z,t), as discussed by Abragam, ibid. A slice-select gradient 
magnetic field B.sub.2 (z)=B.sub.2 (z)i.sub.z (amplitude varying with a 
coordinate, here z) is applied to the tissue approximately simultaneously 
with the RF magnetic field B.sub.1, to excite magnetization in selected 
voxel volume elements 33 in the interrogation volume (FIG. 2, step 12), 
shown in FIG. 3. The RF magnetic field B.sub.1 (x,y,z,t) is applied in a 
time interval given by t1&lt;t&lt;t1+.DELTA.t1. 
FIG 3 illustrates the general configuration of the magnetic fields B.sub.0, 
B.sub.1 and B.sub.2 used to collectively excite magnetization in the 
selected slice or volume elements 33 in the tissue 31. The magnetic field 
vector B.sub.2 (z) is oriented in the z-direction, with amplitude B.sub.2 
(z) increasing (or decreasing) strictly monotonically as the coordinate z 
increases. The amplitude B.sub.2 (z) may increase linearly with z, as a 
power law in z with B.sub.2 (z) .varies.z.sup.a (a.noteq.0), or in some 
other manner. The range of amplitudes of this third magnetic field B.sub.2 
(z) is chosen so that the conditions for nuclear magnetic resonance are 
satisfied in a narrow z-slice, given by z.sub.2 &lt;z&lt;z.sub.2 
+.DELTA.z.sub.2, and this occurs over a predetermined time interval given 
by t.sub.2 &lt;t&lt;t.sub.2 +.DELTA.t.sub.2. 
Returning to FIG. 3, selective excitation of the selected particles in the 
selected voxel volume elements 33 of the tissue 31 is caused to occur over 
a predetermined time interval given by t.sub.1 &lt;t&lt;t.sub.1 +.DELTA.t.sub.1, 
with t.sub.2 .ltoreq.t.sub.1, after which external excitation of the 
selected voxel volume elements by the field(s) B.sub.1 (x,y,z,t) ceases. 
In step 15, a time sequence of one or more gradient magnetic fields 
B.sub.3 (x,y), all with field vectors oriented in the z-direction, is 
applied to spatially encode the magnetization in the voxel volume elements 
33, according to a desired phase shift or resonance frequency 
perturbation, as a function of the x- and/or y-coordinates. This occurs 
over a time interval given by t.sub.3 &lt;t&lt;t.sub.3 +.DELTA.t.sub.3. 
Another rotating magnetic field, B.sub.5 (x,y,z,t) (not required in some of 
the approaches discussed below), having the same angular frequency as 
B.sub.1 (x,y,z,t) but applied for a longer time interval or with a greater 
field amplitude, is then applied in step 16 to the tissue, in the presence 
of a gradient magnetic field. Magnetization in the voxel volume elements 
that were prepared by application of the preceding magnetic fields will 
cause issuance of electromagnetic response signals RS, in a time interval 
given by t.sub.sig &lt;t&lt;t.sub.sig +.DELTA.t.sub.sig (step 17). These voxel 
volume elements will provide the predominant response signals RS. A phased 
array of sensing antennae is then provided adjacent to the tissue 31 (FIG. 
3) to sense the response signals RS issued by the selectively excited 
nuclei, as indicated by step 19. Each sensing antenna, numbered n=1, 2, . 
. . , N, in the phased array is activated for a particular time interval 
or "sense window" W.sub.n, given by t.sub.sig,n &lt;t&lt;t.sub.sig,n 
+.DELTA.t.sub.sig,n, during which the response signals RS produced in the 
selected interrogation volume element 33 (FIG. 3) in the time interval 
t.sub.sig &lt;t&lt;t.sub.sig +.DELTA.t.sub.sig, arrive at antenna number n. 
Devices that provide controllable phase shifts or time delays of one 
signal relative to another, for example, electronically alterable phase 
shifters or mixers with variable local oscillator phases or time delays, 
may be used to controllably alter the signals transmitted by, or received 
at, the phased array of antennae. This allows focusing or steering of the 
signals in the interrogation volume, in a manner well known in propagation 
of electromagnetic signals, as part of the signal processing in step 21 in 
FIG. 2. 
The interior of a human or animal body has many organs, tissues, fluids and 
other components, each with a characteristic set of material parameters, 
such as dielectric and magnetic permittivity, electrical conductivity, 
etc. Analysis of propagation of electromagnetic signals within such a body 
often uses a set of average parameters for purposes of evaluating signal 
attenuation and other material responses. Here, material response data on 
canine muscle, obtained from the publication by E. C. Burdette et al, 
"In-Situ Tissue Permittivity at Microwave Frequencies: Perspective, 
Techniques, Results", appearing in Medical Applications of Microwave 
Imaging, ed. by L. E. Larsen, I.E.E.E. Press, New York, 1986, pp. 13-40, 
were used to determined a suitable resonant frequency range for NMR 
imaging in such materials. Analysis of the Maxwell equations in a linear, 
isotropic, lossy, electromagnetic medium leads to solutions for the 
electric and magnetic field amplitudes E and B in one spatial dimension 
(r) of the form: 
EQU E,B.varies.exp[-(.alpha.+j.beta.)r+j.omega.t], (5) 
EQU (.alpha.+j.beta.).sup.2 =-.omega..sup.2 .mu..epsilon.'+j.omega..sigma..mu., 
(6) 
EQU .mu.=magnetic permeability in tissue .congruent..mu..sub.0 
=4.pi..times.10.sup.-7 Henry/meter, (7) 
EQU .epsilon.'=real part of complex dielectric permittivity in tissue, (8) 
EQU .sigma.=electrical conductivity (mho/meter) in tissue, (9) 
EQU r=spatial coordinate measured in wave propagation direction, (10) 
where .epsilon.' and .sigma. may be frequency-dependent. Physically 
realistic solutions of Eq. (4) are: 
EQU .alpha.=[.omega..sup.2 .mu..epsilon.'/2].sup.1/2 [[1+tan.sup.2 
.delta.].sup.1/2 -1].sup.1/2, (11) 
EQU .beta.=[.omega..sup.2 .mu..epsilon.'/2].sup.1/2 [[1+tan.sup.2 
.delta.].sup.1/2 +1].sup.1/2, (12) 
EQU tan .delta.=.sigma./.omega..epsilon.'. (13) 
The quantity .lambda.=2.pi./.beta. serves as an effective wavelength for an 
undulating wave in the spatial coordinate r, the quantity v=.omega./.beta. 
services as the phase velocity for this wave, and the quantity .alpha.'=20 
log.sub.10 [.alpha.] (in dB/cm) serves as an exponential attenuation 
coefficient for a wave of temporal frequency f=.omega./2.pi. propagating 
through the material. FIG. 4 and 5 present the results of calculations of 
.alpha.' and .lambda., using interpolations of the experimental data of 
Burdette et al, supra, for 17 frequencies shown in Table 1, ranging from 
14.9 MHz to 340.6 MHz. For NMR imaging of protons with .gamma.=42.57 
MHz/Tesla, these 17 frequencies correspond to primary magnetic field 
strengths B.sub.0 of 0.35 Tesla to 8 Tesla, as indicated in Table 1. For 
proton NMR, primary magnetic field strengths B.sub.0 of 3 Tesla to 8 Tesla 
produce wavelengths .lambda. in the range of 11.3 cm (B.sub.0 =8 Tesla) to 
30 cm (B.sub.0 =3 Tesla), with corresponding signal attenuation 
coefficients .alpha.' of 1.95 dB/cm (8 Tesla) down to 1.4 dB/cm (3 Tesla). 
This is an attractive range of wavelengths .lambda. for NMR imaging of 
protons, and the corresponding range of signal attenuation coefficients 
.alpha.' is acceptable for path lengths in the body of no more than 20 cm. 
Thus, for NMR imaging of protons in material such as canine muscle, 
primary field strengths B.sub.0 =3-8 Tesla, corresponding to resonant 
frequencies f.sub.0 =.gamma.B.sub.0 of 127.7 MHz-340.6 MHz, are quite 
attractive for this purpose. For studies in humans or animals, the range 
of primary magnetic field strengths will be similar, but not necessarily 
identical, and will cover a total range of primary magnetic field 
strengths B.sub.0 =2-10 Tesla. 
TABLE 1 
______________________________________ 
Material Parameters For Canine Muscle Versus Frequency 
B0 .alpha.' 
(Tesla) 
Frequency (dB/cm) .lambda.(cm) 
.epsilon.'/.epsilon..sub..omicron. 
.sigma.(mho/meter) 
______________________________________ 
0.35 14.9 MHz 0.53 88.2 161 0.72 
0.5 21.3 0.66 71.6 125 0.75 
1.0 42.6 0.92 46.6 90.1 0.83 
1.5 63.9 1.08 36.2 80.2 0.88 
2.0 85.1 1.21 30.9 73.1 0.88 
2.5 106.4 1.31 26.4 65.7 0.85 
3.0 127.7 1.40 23.6 60.2 0.82 
3.5 149.0 1.47 21.4 56.9 0.81 
4.0 170.3 1.54 19.6 54.9 0.81 
4.5 191.6 1.61 18.6 53.6 0.83 
5.0 234.1 1.67 16.8 52.7 0.85 
5.5 234.1 1.72 15.7 52.7 0.87 
6.0 255.4 1.77 14.7 51.5 0.88 
6.5 276.7 1.82 13.5 51.1 0.90 
7.0 298.0 1.87 12.7 50.8 0.91 
7.5 319.3 1.91 12.0 50.5 0.92 
8.0 340.6 1.95 11.3 50.2 0.93 
______________________________________ 
To form medical images of targets such as organs and tissues within a 
living being, magnetic resonance imagining techniques will be used. A 
description of some of these techniques follows. A selected voxel volume 
element of the tissue can be excited in a predetermined time interval by 
use of certain time-dependent gradient magnetic fields to produce the 
conditions required for such resonance in, or adjacent to, that volume 
element. One such method, the spin echo method, is discussed by L. E. 
Crooks in "An Introduction to Magnetic Resonance Imaging", I.E.E.E. Engrg. 
in Med. and Biol., vol. 4 (1985) pp. 8-15, incorporated herein by 
reference, and proceeds as follows. 
With reference to FIG. 6A, the tissue to be imaged is prepared by placing 
it in a static, approximately homogeneous magnetic field B.sub.0 and 
simultaneously applying an RF rotating magnetic field B.sub.1 (x,y,z,t) in 
the xy-plane and a z-slice select gradient magnetic field B.sub.2 (z), 
which may have the form B.sub.2 (z)=G.sub.z zi.sub.z or any other form 
that is monotonically increasing in z. The field B.sub.1 is often referred 
to as a "90.degree. pulse" in the spin echo method. 
Another gradient magnetic field B.sub.3 (y) is introduced, with field 
vector oriented along the z-direction and field strength increasing 
monotonically (e.g. linearly) in the y-direction. The range of field 
strengths of this fourth magnetic field B.sub.3 is chosen so that the 
conditions for resonance within the z-slice are the same within narrow 
y-slices given by y.sub.3 &lt;y&lt;y.sub.3 +.DELTA.y.sub.3, and this occurs only 
over a predetermined time interval given by t.sub.3 &lt;t&lt;t.sub.3 
+.DELTA.t.sub.3. Each of these narrow y-slices has a different 
characteristic phase shift associated with it because the local magnetic 
field at each voxel volume element is slightly different. This phase shift 
changes monotonically (e.g., linearly) with change in the position 
coordinate y. Another gradient magnetic field B.sub.4 (x) is introduced, 
with field vector in the z-direction and field strength increasing 
monotonically (e.g., linearly) in the x-direction. The conditions for 
resonance are satisfied within narrow x-slices given by x.sub.4 &lt;x&lt;x.sub.4 
+.DELTA.x.sub.4, and this occurs only over a predetermined time interval 
given by t.sub.4 &lt;t&lt;t.sub.4 +.DELTA.t.sub.4, with t3+.DELTA.t3.ltoreq.t4. 
The appropriate frequency associated with each narrow x-slice changes with 
change of the position coordinate x. The amplitudes B.sub.3 (y) and 
B.sub.4 (x) of the fourth and fifth gradient magnetic fields are strictly 
monotonically increasing (or decreasing) in the indicated coordinates y 
and x, respectively. 
A sixth rotating magnetic field B.sub.5 (x,y,z,t), with longer duration or 
a greater amplitude than the field B.sub.1, is applied at a predetermined 
time T.sub.E /2 after application of the fifth magnetic field B.sub.4 (x) 
and is often referred to as a "180 degree pulse". Application of the field 
B.sub.5 reverses the sense of increasing phase in the selected nuclei. At 
a determinable time T.sub.E after application of the field B.sub.1, a 
response signal RS issues from the previously excited selected nuclei 
within the original z-slice. This response signal is often referred to as 
a spin echo signal. 
The fourth, fifth and sixth magnetic fields are repeatedly applied a 
predetermined total of M times, with the magnitude of the fourth or phase 
encode magnetic field .vertline.B.sub.3 (y).vertline. being incremented by 
a fixed amount with each repetition. After the fourth, fifth and sixth 
magnetic fields have been applied, response signals RS issue from the 
selectively excited volume element, and these signals can be sensed by an 
adjacent phased array of coils or antennae. 
The product of the magnitude of the rotating magnetic field B.sub.1 and the 
time over which this field is applied is chosen so that the magnetization 
vector M is "tipped" from its initial orientation along the z-axis by a 
reorientation or tipping angle .theta.. The magnetization vector M lies in 
the xy-plane after application of the field B.sub.1 (x,y,z,t), 
corresponding to the tipping angle .theta.=90.degree.. In a similar 
manner, the RF field B.sub.5 (x,y,z,t) is chosen to achieve a tipping 
angle of 180.degree.. The spin echo method, used together with the method 
of the invention, is illustrated in a flow chart in FIG. 6A, with the 
sequence of magnetic fields applied being illustrated in FIG. 6B. The 
manifold of spin echo signals is processed into a useful image using 
two-dimensional Fourier transforms of response signals RS. 
In the echo planar method, first discussed by P. Mansfield and I. L. Pykett 
in Jour. of Mag. Resonance, vol. 29 (1978) pp. 355-373 and incorporated 
herein by reference, the rotating RF magnetic field B.sub.1 for a 
.theta.=90.degree. pulse and the z-gradient magnetic field B.sub.2 (z) are 
switched on during the same time interval, then switched off. FIG. 7A 
shows in flow chart form the steps followed in this version of the echo 
planar method. A steady x-gradient magnetic field B.sub.4 (x) is 
established for a second time interval of length 4 m (m=1, 2, 3, . . . ), 
where .tau. is predetermined, and the y-gradient magnetic field B.sub.3 
(y) is established and periodically reversed during this second time 
interval, as shown in the graphical views of the echo planar magnetic 
pulse sequences in FIG. 7B. This sequence may be repeated to improve 
signal definition, but a single such sequence allegedly provides all 
information for a two-dimensional scan of a slice defined by the 
z-gradient magnetic field B.sub. 2 (z). In anther version, 180.degree. 
pulses are provided to produce spin echos by periodically reversing the 
x-gradient magnetic field B.sub.4 (x). 
The gradient recalled method, illustrated in flow chart form in FIG. 8A, 
proceeds in a manner similar to that of the spin echo method with the 
following differences. First, the amplitude of the slice-select gradient 
magnetic field B.sub.2 =B.sub.2 (z,t) is initially positive (or negative) 
and then changes sign before the field disappears, with the time integral 
of the field B.sub.2 over the time interval of application being zero. 
Second, the amplitude of the frequency encode gradient magnetic field 
B.sub.4 =B.sub.4 (x,t) also changes sign at a predetermined time, and the 
integral over the time for which this field is applied is zero. Third, the 
product of the magnitude of the rotating magnetic field B.sub.1 and the 
time over which this field is applied is such that the magnetization 
vector is not tipped by .theta.=90.degree. into the xy-plane, but is 
tipped by a smaller angle that is usually no more than .theta.=20.degree.. 
FIG. 8B illustrates the sequence of magnetic field amplitudes used to 
implement the invention, when used together with the gradient recalled 
method. The gradient recalled method is discussed by A. Haase et al in 
"FLASH Imaging. Rapid NMR Imaging Using Low Flip-Angle Pulses", Jour. of 
Mag. Resonance, vol. 67 (1986) pp. 258-266, which is incorporated herein 
by reference. 
Another useful method is the convolution/backprojection method, discussed 
by P. D. Lauterbur in "Imaging Formation by Induced Local Interactions; 
Examples Employing Nuclear Magnetic Resonance", Nature, vol. 292 (1973) 
pp. 190-191, and by L. Axel et al in "Linogram Reconstruction for Magnetic 
Resonance Imaging", I.E.E.E. Trans. in Medical Imaging, vol. 9 (1990) pp. 
447-449, incorporated by reference herein. 
FIGS. 9A and 9B illustrate a top view and side view, respectively, of one 
embodiment of the source (the "applicator") of the rotating or oscillating 
RF second magnetic field B.sub.1 (x,y,z,t) according to the invention. In 
these figures, the tissue 71 is shown in outline as a human form for 
definiteness, but any other reasonable form could also be used. The 
primary magnetic field B.sub.0 is oriented perpendicular to the coronal 
plane in the top view in FIG. 9A so that the field vector points from back 
to front (or from front to back), as shown in FIG. 9B. The applicator 
includes two plates 73 and 75, each containing an array of open 
waveguides, stripline antenna or similar sources ("antennae") that produce 
a focused sum of magnetic fields B.sub.1 that rotates approximately in a 
plane parallel to the applicator plates at approximately constant angular 
frequency. 
The rotating magnetic field B.sub.1 may be replaced in any of the 
embodiments discussed herein by a magnetic field B.sub.1 that oscillates 
in a single direction lying in the rotation plane. For convenient 
reference, a rotating magnetic field B.sub.1 (corresponding to circular 
polarization) and a uni-directional oscillating magnetic field B.sub.1 
(corresponding to linear polarization) will be collectively referred to 
here as a "rotating magnetic field". 
Referring again to FIG. 9A, the two sections 73 and 75 of the applicator 
may each have a fluid or solid 77, positioned between the applicator 
section and the outer boundary of the tissue 71, that approximately 
matches the average complex impedance of the tissue material at the 
angular frequency .omega. applied by the focused rotating magnetic field 
B.sub.1. This "impedance-matching material" 77 may be water, 
physicological saline, gels or other suitable material. Alternatively, the 
tissue 71 could be completely immersed in the impedance-matching material, 
as discussed by S. J. Foti et al in "A Water Immersed Phased Array System 
for Interrogation of Biological Targets", published in Medical 
Applications of Medical Imaging, ed. by L. E. Larsen, I.E.E.E. Press, 
1986, New York, pp. 148-166. Preferably, the applicator sections should be 
positioned as close to the tissue 71 as possible, within 5 cm thereof or 
even contacting the target, in order to reduce the signal loss that occurs 
in transmission of an electromagnetic signal between applicator and tissue 
71. 
The applicator sections 73 and 75 are connected to a switched power supply 
78 that activates and deactivates the applicator during predetermined time 
intervals, as discussed above. A source of the primary magnetic field 
B.sub.0 and of the gradient magnetic fields, all oriented in the same 
direction as B.sub.0, may be provided as shown in FIGS. 13, 14A/14B, 15 
and 16 for the respective embodiments shown in FIGS. 9A/9B, 10A/10B, 
11A/11B and 12A/12B. The source of the gradient magnetic fields in FIGS. 
9A/9B may be connected to a switched power supply 79 that activates and 
deactivates the gradient magnetic fields during predetermined time 
intervals. The array of antennae that serves as source of the focused 
rotating magnetic field B.sub.1 may also serve as the array of focused 
sensing antennae used to sense the RS signals issued by nuclei in the 
selected voxel volume elements of the tissue 71. A plurality of phased 
transmitters to individually phase shift the signals B.sub.1 (x,y,z,t) 
transmitted from the antenna would be required here. 
FIGS. 10A and 10B illustrate another embodiment of the applicator, in top 
view and side view, respectively. The tissue 81 is partly surrounded by 
two components 83 and 85 of the applicator, both of which are connected to 
one or a plurality of switched power sources 88. The primary magnetic 
field B.sub.0 is again perpendicular to the coronal plane and is directed 
from back to front, or from front to back, as shown. The two applicator 
components 83 and 85 together provide a rotating magnetic field B.sub.1 
(x,y,z,t) that rotates with approximately constant angular frequency 
.omega. parallel to a coronal plane passing through the tissue from the 
left side to the right side. Optionally, the volume between the tissue 81 
and the applicator components 83 and 85 may be filled with an 
impedance-matching fluid or solid 87 that matches the relevant 
electromagnetic properties of the tissue material. A switched power supply 
88 provides power for the rotating magnetic field sources 83 and 85. 
Another switched power source 89 provides power for the gradient fields, 
whose field vectors are parallel to B.sub.0. Optionally, the sources for 
the focused magnetic field B.sub.1 may also serve as the sensing antennae 
for the RS signals issued by selectively excited nuclei in the selected 
voxel volume elements in the tissue. 
FIGS. 11A and 11B illustrate a third embodiment, in top view and end view, 
respectively, of one applicator according to the invention. The tissue 91 
is surrounded by a plurality of coils or other RF magnetic field sources 
93A, 93B, . . . , 93F, 93G, etc. that are part of the applicator. These 
sources together produce a focused rotating magnetic field B.sub.1, best 
shown in the end view in FIG. 11B, that rotates in a transverse plane with 
approximately constant angular frequency .omega.. Another magnetic field 
source (not shown) produces the primary magnetic field B.sub.0 that is 
oriented perpendicular to this transverse plane in this embodiment. The 
sources for the rotating magnetic field B.sub.1 and for the gradient 
magnetic fields are powered by a plurality of switched power supplies 98 
and a switched power supply 99, respectively. Optionally, the volume 
between the applicator components and the edge of the tissue may be filled 
with an impedance-matching fluid or solid 97, as in the embodiments 
illustrated in FIGS. 9A, 9B, 10A and 10B. Optionally, the array of 
components 93A, 93B, etc. that serve as the sources for the focused 
magnetic field B.sub.1 may also serve as sensing antennae for sensing the 
RS signals issued by the selectively excited particles in the selected 
voxel elements of the tissue 91. 
FIGS. 12A and 12B are top and side views, respectively, of a fourth 
embodiment of the applicator according to the invention. The tissue 101 
has two plates 103 and 105, positioned near the front and back surfaces of 
the patient or tissue, that serve as part of the applicator. The plates 
103 and 105 contain a plurality of antennae that produce a focused 
magnetic field B.sub.1 that rotates in a sagittal plane within the tissue 
101. The primary magnetic field B.sub.0 has its field vector directed 
perpendicular to this sagittal plane within the tissue. A plurality of 
switched power supplies 108 and 109 provides power for the focused 
rotating magnetic field B.sub.1 and for the gradient magnetic fields, 
respectively, as discussed above. Optionally, an impedance-matching fluid 
or solid 107 may fill the volume between the plates 103 and 105 and the 
target 101, as done in the embodiments of the applicator shown in FIGS. 
9A, 9B, 10A, 10B, 11A and 11B. Optionally, the plurality of coils or other 
sources contained in the plates 103 and 105 may also serve as the sensing 
antennae for the RS signals issued by the selectively excited nuclei 
within the selected voxel volume elements of the tissue 101. 
FIG. 13 illustrates a front view of one embodiment of apparatus useful in 
producing the magnetic fields required by the invention shown in FIGS. 9A 
and 9B. The useful interrogation volume that can be selectively excited by 
this apparatus, operating at a primary field strength of 2-10 Tesla, is 
about 500-3,000 cm.sup.3 but may be made larger if desired. A dipole 
magnet having a yoke 41 of suitable material is provided with a sequence 
of coils 43a and 43b, preferably superconducting, to produce the primary 
magnetic field B.sub.0, which is perpendicular to a coronal plane in this 
embodiment. The focused rotating magnetic field is provided by a phased 
array 44 of antennae, positioned in two coronal planes adjacent to the 
body or tissue 53, that produce a magnetic field vector B.sub.1 (x,y,z,t) 
that rotates at an approximately constant angular frequency .omega. in a 
coronal plane, as seen in top view in FIG. 9A. Power for producing the 
magnetic field B.sub.1 is provided by one or a plurality of switched power 
supplies 45. Gradient coils 47, 48 and 49 provide the supplemental 
magnetic field or fields B.sub.2, B.sub.3 and/or B.sub.4 for excitation of 
the selected voxel volume elements and are connected to another switched 
power supply 46. An optional pole piece 51 provides flux concentration for 
the primary magnetic field B.sub.0. The body or tissue 53 is optionally 
supported on a tissue support 55 that can be transported into and out of 
the primary field region 57 for the apparatus. 
FIGS. 14A and 14B are front and top views of an embodiment of apparatus 
useful in producing the magnetic fields required by the invention shown in 
FIGS. 10A and 10B. The apparatus shown in FIGS. 14A and 14B operates in a 
manner similar to the apparatus shown in FIG. 13. The primary magnetic 
field B.sub.0 is again perpendicular to a coronal plane in this 
embodiment. The focused rotating or other time-dependent magnetic field 
B.sub.1 (x,y,z,t) is provided by a phased array 44' of coils or antennae, 
positioned in two sagittal planes adjacent to the body or tissue 53, that 
produce a magnetic field vector B.sub.1 that rotates at an approximately 
constant angular frequency .omega. in a coronal plane, as seen in the top 
view in FIG. 10A. Power for producing the magnetic field B.sub.1 is 
provided by a plurality of switched power supplies 45. Gradient coils 47, 
48 and 49 provide the supplemental magnetic field or fields B.sub.2, 
B.sub.3 and/or B.sub.4 for excitation of the selected voxel volume 
elements and are connected to other switched power supplies 46. An 
optional pole piece 51 provides flux concentration for the primary 
magnetic field B.sub.0. The body or tissue 53 is optionally supported on a 
tissue support 55 that can be transported into and out of the primary 
field region for the apparatus. 
Another embodiment is illustrated in the top view of FIG. 15, in which the 
magnetic coils 43a and 43b produce a primary magnetic field B.sub.0 that 
is perpendicular to a transverse plane within the body or tissue 53. A 
focused rotating magnetic field B.sub.1 (x,y,z,t) that rotates in this 
transverse plane is produced by a circumferential assembly of 
longitudinally-oriented coils or antennae 59. This embodiment corresponds 
to the applicator embodiment shown in FIGS. 11A and 11B. Power for the 
rotating and gradient magnetic fields comes from switched power supplies 
45 and 46. 
FIG. 16 illustrates an embodiment of the magnetic field apparatus that is 
useful in providing the fields used in the embodiment of the applicator 
shown in FIGS. 12A and 12B. The coils 43a' and 43b' have been rotated by 
90.degree. from their orientation in FIGS. 13 and 14A to produce a primary 
magnetic field B.sub.0 that is perpendicular to a sagittal plane of the 
patient. The sources 47', 48' and 49' of the gradient magnetic fields have 
also been rotated by 90.degree. to produce gradient magnetic fields 
parallel to B.sub.0. The focused rotating magnetic field B.sub.1 is 
provided by the antennae 44". 
FIG. 17 illustrates the desired focusing or steering of excitation signals 
transmitted by a linear array of transmitters A.sub.1, A.sub.2, . . . , 
A.sub.N, located at positions that need not be equidistantly spaced. The 
distanced of interrogation volume element S to its perpendicular "foot", 
indicated as F, on the line containing the linear array of transmitters is 
taken to be h, and the distance from the foot F to the nth transmitter 
A.sub.n is taken to be d.sub.n. The total phase shift .psi..sub.n, 
including propagation delay for a signal of effective wavelength .lambda. 
that travels from the transmitter, through a phase shifter, to an array 
element A.sub.n, to the interrogation volume element S, or in the reverse 
direction, becomes 
EQU .psi..sub.n =2.pi.R.sub.n .lambda.+.phi..sub.n, (14) 
EQU R.sub.n =[h.sup.2 +d.sub.n.sup.2 ].sup.1/2, (15) 
EQU .phi..sub.n =phase shift introduced internally at transmitter number n. 
(16) 
In order to achieve focusing or steering at the interrogation element S, it 
is desirable that 
EQU .psi..sub.1 =.psi..sub.2 =. . . =.psi..sub.N (mod 2.pi.), (17) 
which can be achieved by arranging that the internal phase shift 
.phi..sub.n introduced at the array element A.sub.n satisfies the relation 
EQU .phi..sub.n -.phi..sub.m =(2.pi./.lambda.)(R.sub.m -R.sub.n) (mod 2.pi.) 
(m,n=1, 2, . . . , N) (18) 
If a signal, issued at the interrogation volume element S, is to be 
coherently received rather than transmitted at an array of antenna 
receivers, also indicated as A.sub.1, A.sub.2, . . . , A.sub.N in FIG. 17, 
the associated phase shifts .phi.'.sub.m and .phi.'.sub.n impressed at the 
receivers A.sub.m and A.sub.n, respectively, should also satisfy Eq. (18). 
The phase shifts .phi.'.sub.n (=.phi..sub.n) for transmission and/or 
reception for the phased array of antennae {A.sub.n }, shown in FIG. 17, 
can be introduced electronically and will vary with the location of the 
interrogation volume element S. However, these phase shifts can also be 
introduced in the software used to process signals to be transmitted or 
received at the antenna {A.sub.n }, and this is the preferred approach for 
the invention. 
S. J. Foti et al, supra, have discussed provision of a phased array of 
transmitters or receivers at frequencies 20 times as high (.about.3 GHz) 
as those of interest here, with the transmitting or receiving elements 
spaced equal distances apart and with the interrogation volume element S 
effectively located at infinity (h infinite). The mathematics used with 
the invention disclosed here is somewhat more complex because h is finite, 
and the same electronic components can be used for both transmitting the 
rotating magnetic field signals B.sub.1 (x,y,z,t) and for sensing the RS 
signals received from the interrogation volume element S that is 
selectively excited. 
FIG. 17 illustrates focusing on the interrogation volume by a 
one-dimensional array of transmitting and/or receiving elements, arranged 
along a line LL'. A one-dimensional array of such elements may also be 
positioned along a curvilinear path, such as a circle, ellipse, hyperbola 
or parabola. More often, use of a two-dimensional array of transmitting 
and/or receiving elements is appropriate; and in this instance the 
elements may be positioned at the vertices of: (1) a rectangular lattice; 
(2) a regular hexagonal lattice; (3) an equilateral triangular lattice; 
(4) a lattice of non-equilateral triangles; or (5) some other appropriate 
two-dimensional lattice, on a planar or curved surface. The transmitting 
and/or receiving elements can also be formed as two or more annular arrays 
of such elements AR1, AR2 and AR3, as shown in FIG. 18, in order to 
provide focusing of the excitation RF signals or response signals RS at a 
position along a line LL' that passes through the body. 
In performing magnetic resonance imaging by focusing of the selective 
excitation signal or focused pick-up of the RS signal, use of the gradient 
magnetic fields allow resolution of structures of the size of voxel 
volumes. Focusing the array of RF signals allows resolution of a structure 
the size of the interrogation volume. Movement of the transmitter or 
receiver plane in an axial direction, as recommended by Foti et al, supra 
is not required for three-dimensional selective excitation or signal 
pick-up according to the invention. 
FIG. 19 illustrates one embodiment of a signal processor that can be used 
to process the response signals RS received by the array of antennae 
A.sub.n shown in FIG. 17. When the apparatus operates in the receiver 
mode, response signals RS1, RS2, RS3, . . . , RSN arrive on their 
respective signal lines at N transmitter/receiver switches T/R1, T/R2, . . 
. , T/RN and are passed along N receiver path signal lines to N signal 
amplifiers 201, 202, . . . , 20N, respectively. The transmitter/receiver 
switches T/Rn are used to protect sensitive circuits from damage by high 
power pulses. The output signals that issue from each of the N amplifiers 
201, 202, . . . , 20N are split and sent along N signal lines to an 
assembly of heterodyne receivers 21n-m (n=1, 2, . . . , N; m=1, 2, . . . , 
M, with M=3 in this example), each with its own associated local 
oscillator ("LO"), 22n-m. Each heterodyne receiver 21n-m produces an 
output signal with much lower output frequency but with phase angle 
preserved, after appropriate filtering, and the heterodyne output signals 
are passed to phase shift devices 23n-m. The phase shift device 23n-m 
introduces a controllable phase shift .phi..sub.n,m into the received 
response signal passing through that phase shift device. Thus, for 
example, the phase shift devices 231-1, 232-1 and 233-1 introduce phase 
shifts .phi..sub.1,1, .phi..sub.2,1 and .phi..sub.3,1 into the respective 
output signals that issue from these three devices; and these three output 
signals are combined in a summing device 251 whose output signal is the 
sum of the N input signals RS1, RS2, . . . , RSN, suitably phase shifted. 
Alternatively, the phase shift devices 21n-m may be deleted and the 
desired phase shifts may be introduced through the controllable phase 
shifts in the local oscillator signals from the LOs. The phase-shifted 
output signals from the summing devices 251, 252 and 253 are received by 
analog-to-digital converters ("ADCs") 261, 262 and 263, respectively, and 
the output signals from these ADCs, after appropriate post-processing, 
represent a particular physically determinable parameter associated with 
the interrogation volume of the tissue, such as density of the selected 
nuclei, the spin-lattice relaxation time T1, the spin-spin relaxation time 
T2, a local diffusion constant for a voxel volume element, or some 
spectroscopic parameter. Such a physically determinable parameters can be 
represented as a spatially resolved quantity. Any parameter associated 
with a voxel volume element that can be measured using this approach will 
be referred to as a "characterizing parameter" here. The embodiment of 
phased array signal processing may be used with any array of two or more 
receivers for the response signals RS. 
When the apparatus shown in FIG. 19 is used as a transmitter rather than as 
a receiver, a master oscillator ("MO") 280 with a predetermined output 
signal frequency produces an oscillating output signal that is received by 
each of N phase shift devices 281, 282, . . . , 28N that introduce N 
predetermined phase shifts .phi..sub.1,j, .phi..sub.2,j, . . . , 
.phi..sub.N,j into the MO signal. These phase shifted signals are then 
directed through N signal amplifiers 291, 292, . . . , 29N, the amplified 
output signals are sent through the respective transmitter/receiver 
switches T/R1, T/R2, . . . , T/RN, and the transmitter/receiver output 
signals are transmitted by the respective antennae A.sub.1, A.sub.2, . . . 
, A.sub.N. This process is repeated for J-1 additional sets of phase 
shifts .phi.=.phi..sub.n,j (j=2, . . . , J) to selectively excite J 
different interrogation volumes. 
The phase shifted antenna output signals are focused on a particular 
interrogation volume in this transmitter mode, in order to selectively 
excite that selected volume. Alternatively, the phase shifts .phi..sub.n,j 
(n=1, 2 , . . . , N) may be deleted and the body or tissue may be bathed 
in magnetic radiation, to non-selectively excite the whole body. Selective 
excitation of an interrogation volume is preferred here, for two reasons. 
First, irradiation of the whole body or tissue should be limited to the 
specific portion being examined, in order to limit the energy deposition 
and consequent heating to that specific portion. Second, indiscriminate 
excitation of nuclear magnetic resonance in the body as a whole will 
produce undesired response signals from regions that are of no interest, 
and these unwanted response signals must be filtered or otherwise canceled 
in order to examine the response signals from the interrogation volume of 
interest. 
Additional computer processing, including signal storage, computation of 
two-dimensional Fourier transforms and other image processing in a memory 
and Fourier transform module 271 is optionally provided to complete the 
signal processing. A suitable image display 273 may also be provided to 
visually display the processed images. 
The signals configuration of FIG. 19 is useful if the phase shift devices 
23n-m and the summing devices 25m are relatively inexpensive and if most 
of the processing is to be done for signals in analog form. If, in the 
other hand, most of the processing is to be done for signals in digital 
form, or if a phase device or signal summing device is relatively 
expensive, another configuration, shown in FIG. 20, may be used for 
processing of the responsive signals RS. In the receiver mode, the 
response signals RS1, RS2, . . . , RSN arrive at the respective antennae 
A.sub.1, A.sub.2, . . . , A.sub.N and are sent along their respective 
signal output lines to signal amplifiers 301, 302, . . . , 30N, 
respectively. The amplified response signals RS1, RS2, . . . , RSN are 
received and processed by heterodyne receivers 311, 312, . . . , 31N and 
their associated local oscillators 321, 322, . . . , 32N, respectively, to 
reduce the effective carrier frequencies to the dc-to-kHz range. The 
heterodyne receiver output signals are passed through ADCs 331, 332, . . . 
, 33N, respectively. The output signals of the ADCs 331, 332, . . . , 33N 
are received by memory modules 341, 342, . . . , 34N, respectively, of a 
memory unit. The memory module 341 receives and temporarily stores a 
sequence of samples of the response signal RS1, taken at different times, 
for subsequent processing. In a similar manner, the memory modules 34n 
(n=2, 3, . . . , N) each receive and temporarily store a sequence of 
samples of the response signal RSn. 
A first sequence of phase shifts .phi.=100 .sub.n,1 (n=1, 2, . . . , N) is 
determined and loaded into phase shift compensation devices 35n that may 
be part of the memory units 34n, and each sequence of response signal 
samples RSn held in the memory modules 34n is sent through the phase shift 
compensation device 35n to impress a selected phase shift 
.phi.=.phi..sub.n,1 or a corresponding time delay on that sequence. 
Alternatively, these phase shifts can be impressed on the response signals 
RSn being processed by deleting the phase shift compensation devices 35n 
and introducing the desired phase shifts through controllable phase shifts 
in the local oscillator signals. The phase-shifted output signals are then 
sent to a signal summing device 361, and a first sum signal OS1 issues 
that represents a magnetic resonance response signal received from a first 
selected interrogation volume. This process is repeated with J-1 
additional sets of determined phase shifts .phi.=.phi..sub.n,j (j=2, 3, . 
. . , J; n=1, 2, . . . , N) to produce J&lt;1 additional sum signals OSj, 
representing J-1 other selected interrogation volumes. The collection of 
sum signals OS1, OS2, . . . , OSJ represents the response signals issued 
by the different selected interrogation volumes. Note that, beyond the 
memory unit, signal processing may be done "off-line" because the response 
signal samples are fixed in the memory modules. The signal processing 
embodiment shown in FIG. 20 allows off-line signal processing, requires 
only N phase shift devices 35n and one signal sum device 361 to be 
provided for the processing, and allows most of the processing to be 
performed on the signals in digital form. If the response signals RS are 
to be phase shifted and processed in parallel, the entire signal 
processing module 367 shown in FIG. 20 may be reproduced a suitable number 
of times and these signal processing modules may be operated 
simultaneously to produce the desired images of the interrogation volumes. 
Operating in the transmitter mode, the apparatus of FIG. 20 begins with an 
oscillatory signal produced by a master oscillator 370 and deliver the MO 
output signal to an array of phase shift devices 371, 372, . . . , 37N 
that impresses a first sequence of predetermined phase shifts 
.phi..sub.n,1 on these output signals. The phase shifted MO output signals 
are amplified by a power amplifier 38n and are then passed to the 
respective antennae A.sub.1, A.sub.2, . . . , A.sub.N for transmission as 
a focused beam. This process continues for each sequence of chosen 
transmission phase shifts .phi.=.phi..sub.n,j (n=1, 2, . . . , N; j=1, 2, 
. . . , J), with each such sequence of phase shifts causing the 
transmitted magnetic field signals to focus on a selected interrogation 
volume. Again, if the body or tissue is to be uniformly bathed in the 
rotating magnetic field signal, the phase shift devices 371, 372, . . . , 
37N may be deleted.