Rapid MRI using multiple receivers producing multiply phase-encoded data derived from a single NMR response

Method and apparatus for more rapidly capturing MRI data by receiving and recording NMR RF responses in plural substantially independent RF signal receiving and processing channels during the occurrence of an NMR RF response. The resulting plural data sets respectively provided by the plural RF channels are then used to produce multiply phase-encoded MRI data from the single NMR RF response. Practical examples are disclosed for reducing required MRI data capturing time by factors of at least about one-half.

This invention is generally related to magnetic resonance imaging (MRI) 
using nuclear magnetic resonance (NMR) phenomena. It is particularly 
directed to method and apparatus for more efficiently capturing and 
providing MRI data suitable for use in multi-dimensional Fourier 
transformation MRI imaging processes. 
MRI is by now a widely accepted and commercially viable technique for 
obtaining digitized video images representative of internal body 
structures. There are many commercially available approaches and there 
have been numerous publications describing these and other approaches to 
MRI. Many of these use multi-dimensional Fourier transformation techniques 
which are, by now, well-known to those skilled in this art. 
For example, in one commercially available MRI system, a slice selective 
G.sub.z magnetic gradient pulse is utilized in conjunction with RF 
nutation pulses (including a 180.degree. nutation pulse) to produce true 
spin echo NMR RF pulses from only a relatively narrow "planar" or "slice" 
volume perpendicular to the Z axis. During readout and recordation of the 
NMR spin echo RF response, a G.sub.x magnetic gradient pulse is employed 
to provide spatially dependent frequency/phase-encoding in the X axis 
dimension. Accordingly, by a first one-dimensional Fourier Transformation 
process, one can obtain Fourier coefficients representing the NMR spin 
echo response at different X locations emanating from a correspondingly 
located "column" volumes parallel to the Y axis. By rapidly repeating this 
same process using different slice selective G.sub.z gradient pulses 
during a single T1 NMR interval, it is known that one can significantly 
enhance the efficiency of obtaining data for a number of planar volumes 
(sometimes called "multi-slice" MRI). 
However, one cannot produce the requisite two-dimensional visual image from 
only a single dimension of Fourier transformation (per slice) as just 
described. To obtain the second dimension of Fourier coefficients for 
resolution in the Y axis dimension, a different G.sub.y phase-encoding 
pulse (e.g., different in magnitude and/or time duration) is utilized 
during the NMR excitation process such that the NMR spin echo responses 
during different data gathering cycles will produce Fourier coefficients 
phase-encoded with respect to spatial location in the Y axis dimension. 
Accordingly, if one wants to obtain, for example, a resolution of 256 
pixels along the Y axis dimension, then one must go through 256 data 
gathering cycles (per slice) with correspondingly different Y axis 
phase-encoding in each cycle to assemble the requisite data required for 
the second dimension of Fourier transformation. 
Because the normally encountered T1 NMR parameter is on the order of a 
second or so in many human tissues, and because one typically does not (in 
this exemplary system) repeat a data taking cycle within the same volume 
until the previous NMR nuclei have substantially returned to their 
quiescent conditions, it will be appreciated that the need to repeat a 
data taking cycle literally hundreds of times translates into an overall 
MRI data capturing process that requires several minutes to complete. And 
some of the more interesting future MRI applications may even require 
thousands of data taking cycles and several tens of minutes using current 
technology. At the same time, as is well known in the art, MRI systems, 
facilities and operating personnel represent a significant expense which 
can only be economic if the time required for capturing NMR data per 
patient is minimized. 
In addition to the rather basic economic improvement that can be obtained 
by reducing MRI data capture time, it may also make practical some rather 
sophisticated new MRI possibilities. For example, three dimensional MRI 
may be useful for permitting one to obtain oblique reconstruction images 
on any desired (oblique) plane. For this application, one should use 
isotropic resolution which implies the creation of an MRI data set having 
256 voxels (volume picture elements) in each of three mutually 
orthogonally dimensions. Even if partial flip imaging techniques are used 
to minimize intervals between NMR excitation sequences, current MRI 
techniques might still require imaging times on the order of a half 
hour--which is probably beyond a reasonable imaging time for most 
patients. If this time requirement could be reduced by at least a factor 
of one-half, it might become a much more attractive possibility. 
Similarly, echo planar imaging techniques (which permit all data required 
for a single image to be obtained after a single excitation) would become 
more practical if higher resolution data could be obtained during the 
ensuing train of NMR RF responses (which is necessarily limited by the T2 
decay parameter). 
The enhanced diagnostic possibilities that may someday be provided by 
spectroscopic MRI imaging might also become more practical if some 
technique is developed for shortening the time required to collect 
requisite spectroscopic imaging data. MRI angiography is another technique 
which presently requires unusually long MRI imaging times and which may 
become considerably more practical if a reduced imaging time technique 
could be employed. 
Furthermore, it is perhaps self-evident that motion artifact can be reduced 
if one can somehow shorten the time interval over which requisite MRI data 
is collected. 
In short, standard techniques of two-dimensional Fourier transform magnetic 
resonance imaging are already highly efficient in two out of three 
dimensions. Through the use of selective excitation and data acquisition 
with a readout gradient, the Fourier transform of the acquired data 
effectively localizes signal in two dimensions. However, there remains a 
time consuming aspect of MRI insofar as it is still necessary to obtain 
multiple phase-encoded data acquisitions to localize the signal in the 
third (Y axis) dimension in many standard MRI processes. 
The need for reducing MRI image time requirements has been recognized by 
many others. There are other techniques for more rapidly obtaining 
requisite MRI data. For example, other techniques for rapid MRI imaging 
have attempted to reduce the time spent on acquiring phase-encoded 
acquisitions. For example, data conjugation techniques (exploiting the 
symmetries of the Fourier transform) are already employed in some 
commercial processes to reduce the number of required acquisitions by a 
factor of two. Partial flip angle nutation (instead of a full 90.degree. 
initial RF nutation angle) may also be employed to eliminate signal loss 
normally encountered with rapid acquisitions (e.g., as in short repetition 
time techniques). In principle, the most efficient means of signal 
acquisition for MRI may involve the use of only partial initial RF 
nutation angles or "partial flip" combined with a very short TR interval 
between repetitions of the NMR excitation-response processes used in the 
data gathering phase of MRI. For example, this latter partial flip 
technique has aided in the development of three dimensional Fourier 
transform techniques for imaging a large number of sections within a very 
short TR. 
Some publications generally relevant to such MRI techniques as have just 
been discussed may be noted as follows: 
Kumar A., Welti D. and Ernst R. R. NMR Fourier Zeugmatography. Journal of 
Mangetic Resonance 1975; 18:69-83. 
Sutherland R. J. and Hutchison J. M. S. Three-Dimensional NMR Imaging Using 
Selective Excitation. Journal of Physics E 1978; 11:79-83. 
Lauterbur P. C. Image Formation By Induced Local Interactions: Examples 
Employing Nuclear Magnetic Resonance Nature 1973; 16:242-243. 
den Boef J. H., van Vijen C. M. T. and Holzscherer C. D. Multiple-Slice NMR 
Imaging by Three-Dimensional Fourier Zeugmatography. Physics in Medicine 
and Biology 1984; 29:857-867. 
Feinberg D. A., Hale J. D., Watts J. C. Kaufman L. and 
Mark A. Halving MR Imaging Time By Conjugation: Demonstration at 3.5KG. 
Radiology 1986; 161:527-531. 
Ernst R. R. Sensitivity Enhancement in Mangetic Resonance In: Waugh J. S., 
ed. Advances in Mangetic Resonance Vol. 2, N.Y.: Academic Press, 
1966:1-135. 
Carlson J., Crooks L. E., Ortendahl D. A., Kramer D. M. and Kaufman L. 
Technical Note: Comparing S/N and Section Thickness in 2-D and 3-DFT MRI. 
Radiology 1988;166:266-270 
I have discovered a new MRI reconstruction algorithm which permits a 
reduction in the number of required phase-encoding data acquisitions in an 
MRI imaging sequence without reducing either resolution or field of view. 
One principle of this technique involves the use of two (or more) 
non-interacting receiver coils (and corresponding independent RF receiving 
and signal processing channels) so as to each simultaneously detect an NMR 
response signal from the same tissue. An imaging sequence may use 
phase-encoded spin echoes or gradient echoes in the usual way; however, 
the reconstruction algorithm effectively calculates multiple Fourier 
projections of the tissue from but a single NMR response (e.g., a spin 
echo). 
A full implementation of this discovery using but two receiver coils (and 
associated RF signal processing channels) can reduce the number of needed 
phase-encoded data acquisitions by 50% as compared to the fewest number 
otherwise (e.g,. previously) required. 
In essence, my new technique is a variation of standard two-dimensional or 
three-dimensional MRI but, instead of using a single RF receiver coil and 
its associated RF signal processing channel, I use at least two (or more) 
different non-interacting receiver coils and associated RF signal 
processing channels to simultaneously detect an NMR response signal 
emanating from a given tissue. The coils are constructed and/or oriented 
so that their respective responses to the same NMR signal are 
different--i.e., the coil responses respectively depend upon the relative 
spatial location of the nuclei emitting the NMR RF response. This added 
spatial dependency provides additional information from the same single 
NMR RF response which can be effectively used to reduce the number of NMR 
data acquisition cycles required for a given resolution of MRI image 
reconstruction. In short, the MRI reconstruction algorithm is permitted to 
calculate multiple Fourier projections from but a single NMR RF response 
(e.g., a single spin echo) resulting in a significant time savings in 
required MRI data acquisition time. 
Some aspects of my invention have already been published ("An Algorithm for 
NMR Imaging Reconstruction Based on Multiple RF Receiver Coils," Journal 
of Magnetic Resonance J. Mag. Res., Vol 74, pp 376-380, 1987). And others, 
subsequent to my invention, have now proposed the general concept of using 
multiple detectors for MRI data acquisition so as to save data acquisition 
time--but without any apparent practical implementations in mind (see 
Hutchinson et al, "Fast MRI Data Acquisition Using Multiple Detectors," 
Magnetic Resonance in Medicine, Vol. 6, 1988, pp 87-91). 
This invention is especially useful in MRI data capturing sequences where a 
dimension transverse to the static magnetic field is phase-encoded over a 
plurality of data gathering sequences to obtain requisite MRI data for a 
single image. It may be used with both two and three-dimensional Fourier 
Transform Magnetic Resonance Imaging processes. Preferably, in the 
exemplary embodiments, the static magnetic field is horizontal (as in a 
super conducting solenoidal magnet) so that the exemplary RF receiving 
coils permit the most convenient patient access. 
In this invention, a system of multiple RF receiving coils provides some 
localization of NMR RF signal responses in at least the phase-encoded 
dimensions. By using spatial dependence of the phase (primarily) and the 
amplitude (secondarily) of the NMR RF response signal induced in a set of 
non-interacting RF receive coils, it is possible to calculate multiple 
phase-encoded signals from but a single NMR RF response (e.g., a single 
NMR spin echo response). This technique is compatible with existing two 
and three dimensional imaging techniques and may also find use in 
conjunction with other rapid MRI imaging techniques. The exemplary 
embodiments provide for a reduction in the required minimum number of NMR 
RF responses by a factor of at least about two. 
It is worth noting some specific imaging protocols to which this rapid 
technique may be applied. These examples are not intended to be 
comprehensive, but rather, protocols chosen to illustrate sequences which 
are presently limited by the number of necessary phase-encoded 
acquisitions: 
(1) 3D partial flip imaging can achieve a realistic minimum TR of 
approximately 50 msec. Below this value data acquisition time, i.e., echo 
length, must be decreased, resulting in an increased bandwidth with a 
consequent increase in noise. One promising utility of 3D MRI is oblique 
reconstruction to form images on any plane. For this one should use 
isotropic resolution which would imply a high resolution data set of 
256.sup.3 voxels. Using a 50 msec TR, this gives a minimum imaging time of 
55 minutes. Data conjugation may reduce this to 27 minutes, but this is 
still beyond reasonable imaging time for most patients. A reduction to 14 
minutes through the use of multiple receivers makes this an attractive 
possibility. 
(2) Echo planar imaging collects all data for a single image after one 
excitation. Data acquisition time is therefore limited by T2 of the 
tissue. Presently resolution is limited by the number of projections 
available within this time. One laboratory's limitation on resolution is 
128 phase-encoded projections. Multiple receiver coil reconstruction will 
allow for higher resolution (e.g., 256 projection) echo planar imaging. 
(3) Short TR partial flip imaging has been seen to be inappropriate for 
some imaging protocols. Tissue contrast generally decreases in short TR 
partial flip images, which can be a disadvantage in some diagnoses. 
Metallic implants and magnetic field inhomogeneities give rise to 
artifacts that further degrade the images. (Since it relies on gradient 
echoes, 2D partial flip MRI is much more susceptible to these artifacts.) 
Multiple receiver coil reconstruction may allow for new flexibility in 
protocols which manipulate image contrast in rapid scan. 
Further expansion of the ability of MRI to serve clinical needs relies on 
reduction of imaging time. This new approach towards rapid MRI can be used 
with existing methods and can further reduce imaging time. Other possible 
applications involve imaging times longer than those of standard MRI. For 
example, spectroscopic imaging is hindered in patient acceptance by the 
very long imaging times required. A reduction by 50% in imaging time can 
certainly improve its clinical usefulness. MRI angiography generally 
requires two to four times the usual imaging time. In this case, a 
reduction in time will aid not only in acceptance, but also in improving 
the image registration by reducing patient motion during the scan time. 
Motion artifacts produced by respiratory motion decrease with signal 
averaging. Thus, multiple coil image reconstruction may be used as a way 
to reduce artifacts in a fixed imaging time. Multiple coil reconstruction 
will add to the flexibility of implementing many MRI procedures. 
These examples are described to illustrate how a reduction in phase-encoded 
data acquisition time can provide new possibilities in imaging protocols. 
A distinct use of this reconstruction is as a technique that increases the 
number of data set acquisitions effected in the same amount of time. While 
this will probably not result in an improvement in the signal to noise 
ratio, it may be useful in reducing motion artifacts. A discussion of 
signal to noise in the exemplary embodiment will be presented later. 
Further improvements can be had by adding additional receiver coils. In 
general one may consider a set of N receivers. Using the exemplary 
reconstruction algorithm, one may then calculate N phase encoded 
projections per echo. Introducing more receiver coils adds to the 
technical difficulty of implementation due to the necessity of maintaining 
electrical isolation between the receiving coils. 
In one exemplary embodiment, a pair of essentially co-located "birdcage" 
coils is utilized. One of the coils is tuned to a fundamental frequency 
corresponding to the desired NMR frequency band (e.g., about 15 MHz) while 
the second coil is tuned so that its second harmonic is at the same 
frequency (e.g., about 15 MHz). As will be shown in more detail below, 
this results in the requisite current/voltage distribution on the axially 
extending coil wires to take on the form of sin .theta. and sin 2.theta., 
respectively, where .theta. is a relative wire location angle in the x,y 
plane. Standard MRI RF coil construction techniques are used to minimize 
mutual inductance or capacitive coupling between the two coils so as to 
keep them substantially independent of one another. Saddle coil 
constructions may also be utilized to obtain the requisite respective sin 
.theta. . . . sin N.theta. current/voltage distributions in the N 
receiving coils.

In FIG. 1 an MRI system 100 is schematically depicted as including the 
usual static magnet, gradient coils, shim coils, transmit RF coils, 102 
under control of processor 104 (which typically communicates with an 
operator via a conventional keyboard/control display module 106). 
Although, it is conceivable that a single processor might both control the 
system and also carry out the actual MRI imaging processes, it is perhaps 
more conventional to employ a system of multiple processors for carrying 
out specialized functions within the MRI system 100 as will be 
appreciated. Accordingly, as depicted in FIG. 1, an MRI image processor 
108 receives digitized data representing RF NMR responses from an object 
under examination (e.g., a human body 110) and, typically via multiple 
Fourier transformation processes well-known in the art, calculates a 
digitized visual image (e.g., a two-dimensional array of picture elements 
or pixels, each of which may have different gradations of gray values or 
color values, or the like) which may then be conventionally displayed at 
112. 
In accordance with this invention, a plurality of receive coils 1 . . . N 
are independently coupled to a common imaging volume (e.g., a desired 
portion of body 110). The RF signals emanating from these coils are 
respectively processed in independent RF channels 1 through N. As depicted 
in FIG. 1, each such RF channel may comprise a considerable amount of 
conventional analog RF signal processing circuits as well as an eventual 
analog to digital conversion before being input to the MRI processor 108 
(which may typically include means for digitally storing the acquired data 
during a data acquisition sequence until the image processor 108 uses such 
acquired data to produce an image at 112). 
Although the RF channel circuitry may typically include a rather complex 
(and expensive) amount of circuitry, it is not believed necessary to 
describe it in any detail since conventional RF signal processing 
circuitry per se may be employed with this invention. However, the extra 
expense of using extra receive coils and associated RF signal processing 
channels does have to be balanced against the improvement in data 
capturing time when considering the overall economics of this approach. 
Accordingly, to practice this invention, modifications need be made in 
essentially only three areas of a conventional MRI processing system: 
1. additional receive coils need to be employed and their construction is 
preferably such that they are substantially independent (i.e., effectively 
without substantial mutual inductive coupling or capacitive coupling); 
2. an additional RF signal processing channel needs to be added for each of 
the additonal receive coils; and 
3. the MRI reconstruction algorithm programmed into and implemented by the 
image processor 108 needs to be slightly modified so as to use the 
additional incoming data to calculate multiply phase-encoded MRI data in 
an appropriate way. 
Since the RF signal processing channels are, per se, simply replications of 
existing conventional RF channels, it is not believed that any further 
detailed description of such additional channels need be given in this 
application. Rather, the following disclosure will concentrate on 
practical exemplary embodiments for the receive coil and for the new 
calculations to be made in the image processor 108. 
Present reconstruction techniques in two dimensional NMR imaging are highly 
efficient in two of the three dimensions. One limitation is the large 
number of phase-encoded echoes which must be acquired in order to 
reconstruct a full image. In an attempt to facilitate the development of 
very fast NMR imaging techniques, it is useful to consider reconstruction 
techniques which do not rely on multiple acquisitions of phase-encoded 
spin echo signals. 
One approach for reducing the number of phase-encoded spin echoes required 
for a reconstruction of an image is described below. It uses multiple 
coils for the acquisition of signals, then uses the resulting additional 
information to speed the reconstruction process. The reconstruction 
algorithm is, initially, in the following discussion, based on an 
idealized NMR detector. Thus, theoretically, one can conceive a situation 
in which it may be possible to reconstruct an entire image from but a 
single NMR spin echo! However, as one might expect, realities of 
signal-to-noise make this a highly unrealistic situation. Nonetheless, the 
description is presented since it is the easiest way to initially 
demonstrate the algorithm. A more practical implementation of this 
algorithm is described later in which a set of two coil "building blocks" 
is used to reduce the number of required spin echoes by a factor of two. 
As an introduction to the technique, consider the idealized NMR detector in 
FIG. 2. Long, straight wires 200 (parallel to the static magnetic field 
H.sub.o) run along the surface of a (non conductive) cylinder 202. The 
ends of these loops are closed at infinity. Only a few wires are shown. In 
the idealized coil, wires would densely surround the cylinder. Assume that 
the voltages on each of these loops induced by a precessing magnetic NMR 
dipole can be monitored separately. Denote the voltage induced on the loop 
whose wire is at an angle .theta. from the vertical by V(.theta.). 
Standard two dimensional reconstruction allows a straightforward procedure 
for localizing magnetization in two dimensions by means of slice selection 
and read-out gradients (G.sub.z and G.sub.x, respectively). The time 
consuming processes are the number of required repetitions of the basic 
cycle to acquire the requisite phase-encoded data for resolving nuclei 
along the y-axis dimension. The problem at hand is to devise an algorithm 
to reconstruct a column 300 of magnetization perpendicular to the slice 
selection and read-out directions (e.g., along the y-axis). A schematic 
depiction of the situation is shown in FIG. 3. A column of magnetization 
300 is centered at location x and z (z can be taken to be zero). Imagine 
that one is reconstructing an image of a column 300 as shown. 
The voltage induced in the loop whose inner wire is located at angle 
.theta. is proportional to the magnetic field produced by that wire if it 
were a transmitter and driven with unit current. The magnetic field 
B.sub.x +iB.sub.y at location (x,y) due to the wire at .theta. is: 
##EQU1## 
The voltage induced on the wire at .theta. can then be written as a 
superposition of the voltages induced by all magnetization: 
##EQU2## 
with .alpha.=e.sup.i.theta.. Overall constants have been ignored. 
This can easily be inverted with the contour integral 
##EQU3## 
The integration contour is the unit circle. Since the integrand has a 
simple pole at .alpha.=i(x-iy)/R with residue -ie.sup.-n.pi.(x-iy)/R /R, 
the integral is easily performed. The answer is: 
##EQU4## 
Since x is a known quantity, one can see that the result of the 
integration gives a value for the Fourier Transform of the magnetization 
density. 
A crucial observation is that a complete determination of V(.theta.) 
together with the evaluation of this integral yields all values of the 
Fourier Transform of the magnetization density. However, if the 
magnetization has experienced a phase-encoding gradient previously in the 
sequence with a strength G.sub.y and duration .tau., then the 
magnetization density along a column is 
EQU m(x,y)e.sup.i.gamma.GyY.tau.. [Equation 5] 
In this case, evaluation of the integral yields values of the Fourier 
Transform at different values in k space. 
One difficulty in evaluating the integral in the reconstruction arises from 
the exponential term in the integrand: 
EQU e.sup.in.pi.e.spsp.u.theta.. [Equation 6] 
When .theta.=-.tau./2, the exponential term is e.sup.+n.pi.. For n larger 
than 3 or 4, the size of this peak makes an accurate evaluation of the 
integral difficult. 
One way to circumvent the difficulties in the numerical integration is to 
presume in the idealized NMR receiver that one is able to measure the 
Fourier Transform of V(.theta.). That is, what is measured are the 
coefficients .alpha..sub.k from the Fourier expansion of the voltage: 
##EQU5## 
Substituting this expression into the reconstruction integral: 
##EQU6## 
The integral over .alpha. vanishes unless k is negative. This result gives 
the answer: 
##EQU7## 
In other words, by measuring the negative Fourier coefficients of the 
voltage induced in the wires and performing a sum one may calculate values 
of the Fourier Transform of the magnetization density. 
Now it is time to discuss a more realistic implementation. In an actual 
embodiment, it is likely that multiple receiver coils would be used to 
gather sufficient data to reconstruct two (or possibly three or more) 
values of the Fourier Transform of the magnetization density. Standard 
phase-encoding pulses would still be needed in order to gather all 
projections. Consider the relatively simple coil of four wires. The first 
negative Fourier coefficient of the voltages is given by: 
##EQU8## 
The expression has been rewritten to make explicit the following fact: the 
term V(O)-V(.pi.) is nothing but the voltage induced in a loop that has 
one wire along the cylinder at .theta.=0 and a return path along the 
bottom of the cylinder at .theta.=.pi.. So also, the other two terms in 
the voltage Fourier coefficient are the same as the voltage induced in the 
horizontal loop. 
This observation yields an actual practical implementation. The basic 
"building block" coil is a two loop arrangement of FIG. 4. From this, the 
voltage Fourier coefficient .alpha..sub.-1 is given by the voltage induced 
in the vertical saddle coil loop 1 combined with the voltage in the 
horizontal saddle coil loop 2 shifted by 90 degrees. This can be viewed as 
a simple quadrature receiver. In fact, it can be implemented as a four 
legged birdcage coil receiving in quadrature. 
The next question is whether one may measure additional Fourier 
coefficients from this four wire situation. The answer is no. Given only 
four wires, the next negative Fourier coefficient, .alpha..sub.-2, is 
indistinguishable from the Fourier coefficient .alpha..sub.2. In order to 
measure higher Fourier coefficients one must have additional loops. 
A straightforward way to do this is to use an eight wire configuration. One 
may construct the voltage Fourier coefficients .alpha..sub.-1 and 
.alpha..sub.-2 from the signals induced in each wire on the cylinder. That 
is, 
##EQU9## 
This can be recognized as the signal in a building block coil combined 
with the 45 degree phase shift of the signal on the second building block 
coil. Again, one implementation can use a birdcage coil receiving in 
quadrature. This time the receiver is an eight legged cage. 
The voltage Fourier coefficient .alpha..sub.-2 is written in a similar 
form: 
##EQU10## 
This is not a simple superposition of signals from building block coils. 
Instead, it is the signal of two opposed saddle coils receiving in 
quadrature. One way to realize this coil is to construct a quadrature 
eight legged birdcage coil tuned to its second harmonic resonant 
frequency. Of course, the coil must be distinct from the first in order 
for its second resonant frequency to coincide with the first resonant 
frequency of the first. 
Higher order situations are similarly constructed. 
Two major questions remain concerning this technique: (1) what is the 
signal to noise cost in the image and (2) how can one construct coils 
which behave as independent receivers. Simulations of data reconstruction 
have been performed using eight wire coils to reduce the number of 
phase-encoding acquisitions by a factor of two. The response to noise 
generated by the sample--and hence correlated in the coils--presently 
appears to be identical in this reconstruction and in standard two 
dimensional imaging. A serious concern is that reconstruction is 
impossible if noise generated by the coils is sufficiently high. 
Coil coupling is another concern. Only if the coils can be substantially 
decoupled can the reconstruction proceed in the manner described 
previously. The implementation using two birdcage coils offers a 
possibility of solving the coupling problem since two birdcage coils 
operating in different modes (but the same frequency) have no intrinsic 
mutual inductance between coils. And capacitive coupling may be minimized 
(e.g., using techniques employed for realizing practical quadrature 
detection coils, per se). 
As will be appreciated by those in the art, practical coil constructions 
for RF receiving in MRI typically include tuning and impedance matching 
capacitances in conjunction with transmission lines, etc. For purposes of 
simplifying the discussion in this case, such conventional aspects of RF 
receiving coils and their associated RF transmission lines, etc., are not 
depicted in the FIGURES or otherwise described. 
Another way to understand the underlying theory, is to imagine a simplified 
imaging experiment which attempts to reconstruct the transverse 
magnetization density in a sample tube that is parallel to the y axis. The 
x and z location of the column are known. What is needed, is a 
reconstruction of the sample along the y direction. This simplified 
experiment can be viewed as merely part of a standard two-dimensional 
Fourier Transformation MRI imaging sequence. A slice/selective RF 
excitation provides a section of sample with a known value of z and the 
read-out gradient G.sub.x provides frequency encoding in the x-direction. 
Thus, after Fourier Transformation of the acquired data, the Fourier 
content of the data in a standard two-dimensional Fourier transform 
acquisition provides the sum of the transverse magnetization in the 
hypothetical column or sample now being considered. 
Standard two-dimensional FT imaging uses repeated acquisitions with 
phase-encoded echoes to generate the Fourier transform of the transverse 
magnetization along the y direction. If the field of view along the y 
direction is taken to be L, the Fourier transform is usually written as 
EQU m(n)=.intg.m(y)e.sup.2.pi.iny/NL dy [Equation 15] 
and m=m.sub.x +im.sub.y is the complex transverse magnetization. 
For the purposes of illustration, consider the idealized RF receiver coil 
(FIG. 2) for this experiment. The receiver consists of a collection of 
long wires parallel to the static field and laid on the surface of a 
cylinder. The loops are closed by return paths at infinity. In this 
idealized receiver coil one may measure the echo signal by monitoring the 
voltage induced in each wire. Denote the voltage in the wire at position 
.theta. by V(.theta.). As shown above, the Fourier transform of the 
magnetization density is expressible in terms of the Fourier transform of 
the induced voltages. Let V(n) be the Fourier coefficient of the voltage, 
then the expressions for the Fourier transform of the magnetization take 
the form: 
##EQU11## 
where R is the radius of the coil; the field of view, L, is 2R. 
Only the five lowest Fourier coefficients are shown. In principle, given 
sufficiently many voltage Fourier coefficients, one may construct all 
terms in the Fourier transform of the magnetization density. Thus, one can 
reconstruct the entire column of the sample within one spin echo response. 
There are two important practical considerations that rule out the 
possibility of a complete reconstruction from one echo, however. One 
problem is coil coupling. An actual coil of separate loops surrounding a 
cylinder would not behave exactly as described. One reason is that coils 
in receivers are tuned circuits and voltages produced by echoes induce 
currents. Since the idealized receiver coil has a collection of loops with 
large mutual inductance between loops, the signal in each loop is not that 
just produced by the echo. The crucial observation--and this is key to 
feasibility--is that even though one cannot build the idealized coil, one 
can build separate coils that directly measure the voltage Fourier 
coefficients where there is substantially no intrinsic mutual inductance 
between these coils. 
One embodiment of a multiple coil set is a pair of birdcage resonators. 
Previously, these coils have been developed as a means of producing a 
homogeneous RF field. Homogeneity is due to the current distribution on 
the legs of a driven birdcage that varies as cos .theta.. One can use the 
birdcage as a quadrature transmitter and generate a complex current 
distribution exp(-i.theta.). In this situation, a driving voltage produces 
a voltage distribution across the legs of the birdcage that varies as 
exp(-i.theta.). 
By using the standard reciprocity principle, we can see how to produce a 
coil to measure V(-1). Since the voltage distributions are the same in 
transmission and reception, a standard birdcage resonator produces a net 
output voltage proportional to the sum of voltages induced on each leg 
weighted by exp(-i.theta.). 
A coil that measures V(-2) requires a birdcage coil with a current 
distribution that varies as cos 2.theta.. By extending the previous 
results one can see that this coil measures a sum of voltages induced on 
each let with a weighting factor of exp(-2i.theta.). One method of 
producing a cos 2.theta. distribution is to construct a birdcage coil and 
tune it to its second resonant frequency. Normally, a birdcage coil has 
many resonant frequencies, each of which is approximately a multiple of 
the lowest fundamental frequency. What one here requires is one coil whose 
fundamental frequency coincides with the NMR frequency (e.g., 15 MHz) and 
a separate coil whose second harmonic is at the same frequency. 
The two coils may be placed concentrically around the sample with 
substantially no intrinsic mutual inductance. Since there is substantially 
no intrinsic coupling between the coils, each coil behaves independent of 
the other and the net signal on each output is the proper voltage Fourier 
coefficient. One still has to contend with capacitive coupling between the 
coils, as well as residual inductive coupling. However, careful adjustment 
of the relative alignment of the two coils and other now standard 
techniques for decoupling quadrature-connected receive coils should 
provide adequate isolation. 
Birdcage resonators are not the only way to construct these coils. Some 
other configurations are shown in FIGS. 5a-5d. Note that quadrature as 
well as non-quadrature coils may be constructed. Non-quadrature coils will 
be much easier to construct, but the lower signal to noise ratio of these 
coils may degrade the image substantially. 
FIG. 5a depicts a "low pass" birdcage. FIG. 5b depicts a homogeneous 
quadrature saddle coil. Arrows denote the direction of current flow. Since 
the coil has a homogeneous reception pattern, the signal is essentially 
the same (albeit with higher signal to noise ratio) as a non-quadrature 
saddle coil (FIG. 5c). Another design for a coil to measure V(-2) is shown 
in FIG. 5d. 
The second practical consideration facing complete reconstruction from one 
echo is the signal-to-noise ratio. One expects that the signal to noise 
ratio of human MRI is insufficient to allow for single echo 
reconstruction. Therefore, one may concentrate on a reduced 
implementation. For example, only two voltage Fourier coefficients will be 
measured in the present exemplary embodiments: V(-1) and V(-2). Given 
these, one can construct three Fourier coefficients of the magnetization 
by truncating the sums for the expression of m(n): 
##EQU12## 
An actual imaging sequence will be a hybrid technique of reconstruction 
using standard phase-encoding in the y direction and using the extra 
spatial information generated by the two voltage signals. That is, a 
typical data acquisition sequence may first acquire an echo with no phase 
encoding. From this, one can construct m(-1), m(0) and m(1). Next, a 
sequence will acquire an echo with a phase-encoding factor of 
exp(2i.pi.y/R). From this, one can construct the terms m(1), m(2) and 
m(3). This is repeated for the rest of the positive and all negative phase 
encodings: 
TABLE I 
__________________________________________________________________________ 
Data Gathering 
sub-cycle 
encoded magnetization values captured 
__________________________________________________________________________ 
a m.sub.a (-1) 
m.sub.a (0) 
m.sub.a (1) 
b .dwnarw. 
.dwnarw. 
m.sub.b (1) 
m.sub.b (2) 
m.sub.b (3) 
c .dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
m.sub.c (3) 
m.sub.c (4) 
m.sub.c (5) 
. .dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
. .dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
. .dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
q m.sub.q (-3) 
m.sub.q (-2) 
m.sub.q (-1) 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
r m.sub.r (-5) 
m.sub.r (-4) 
m.sub.r (-3) 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
.dwnarw. 
M(-4) 
M(-3) 
M(-2) 
M(-1) 
M(0) 
m(1) 
M(2) 
M(3) 
M(4) 
__________________________________________________________________________ 
Where: M=Fourier coefficients along y-axis dimension 
M(0)=m.sub.a (0) 
M(1)=[m.sub.a (1)+m.sub.b (1)]/2 
M(2)=m.sub.b (2) 
M(3)=[m.sub.b (3)+m.sub.c (3)]/2 
M(4)=m.sub.c (4) 
M(-1)=[m.sub.a (-1)+m.sub.q (-1)]/2 
M(-2)=m.sub.q (-2) 
M(-3)=[m.sub.q (-3)+m.sub.r (-3)]/2 
M(-4)=m.sub.r (-4) 
The net result is that one only requires one-half of the usual number of 
echoes in order to fully reconstruct the image. Notice that one acquires 
the even projections (m(0), m(2), m(4), and so on) entirely conventionally 
from the signal V(-1) from coil #1. The odd projections then are 
calculated from both V(-1) and V(-2). The odd projections are calculated 
twice and averaged in the presently preferred embodiment. This provides a 
more artifact free reconstruction. Examples of one dimensional 
reconstructions are discussed below. 
Notice that the coil to measure V(-1) is a uniform receiver coil and 
resembles standard designs in imaging and spectroscopy. For present 
purposes, this will be referred to as the "primary" channel. The coil to 
measure V(-2) is highly non-uniform. This will be referred to as the 
"secondary" channel. 
The signal-to-noise ratio of multi (e.g., two) channel reconstruction 
deserves special treatment. Since, for the case N=2, one has a system of 
two receivers, the noise in a reconstructed image depends on whether the 
noise in the two channels is correlated or uncorrelated. If the coils 
themselves generate the noise, then the noise is uncorrelated in the two 
channels. Noise generated by the sample produces a noise voltage which is 
received by both coils and is therefore correlated. (Notice that the noise 
is correlated but not necessarily in phase in both channels. The relative 
phase of the noise voltage depends on the location of the noise generating 
sample.) 
Consider a specific example. A point sample is placed at the center of the 
coil. In this simplified arrangement, the magnetization produced by the 
sample will not generate any signal in the secondary channel. So also, any 
noise generated by the sample will not be received by this channel. The 
primary channel, will receive both signal and noise generated by the 
sample. A quick calculation of the noise in an image with standard 
phase-encoded imaging and multiple receiver coil imaging shows: 
##EQU13## 
The noise at the center of the image increased by .sqroot.2. This is just a 
consequence of the multiple coil acquisition acquiring one-half the data. 
Therefore, multiple coil acquisition has the same signal-to-noise ratio 
per unit time as standard imaging in this example. 
Away from the center of the image, noise actually decreases as compared to 
standard imaging. Since the noise is correlated in the frequency domain, 
the Fourier transform of the data (i.e., the image) shows structured 
noise. 
This analysis changes if the noise is completely generated by the coils. 
Using the same example as before, the secondary channel will have a noise 
voltage even though there is no sample generated signal. Following in the 
standard noise analysis, the ratio of the noise in two imaging procedures 
is: 
##EQU14## 
The noise has again increased by a factor of .sqroot.2 at the center. And, 
unlike the previous example, noise never decreases compared to standard 
imaging. 
MRI of biological tissue in mid to high field strengths is in the regime of 
sample generated noise. There may be a loss in signal to noise ratio. This 
procedure is applicable to sequences well above the signal to noise ratio 
threshold where speed is the issue. 
The expressions for the Fourier transform of the magnetization density, 
m(n), involve infinite sums of voltage Fourier coefficients, V(n). In 
practice, as proposed above, one only measures signal from a finite number 
of coils (e.g., two coils). The effects of truncating the infinite sum at 
only two terms, for example, is considered below. 
Also, given signal from only two receiver coils, some Fourier projections 
of the magnetization density can be calculated more reliably than others. 
That is, the previous section contains the expressions for m(-1), m(0) and 
m(1) and V(-2). For the most artifact free reconstruction, calculating all 
three m(n)'s from one echo (resulting in a 67% time reduction), 
calculating two m(n)'s from one echo, or calculating three m(n)'s from one 
echo but redundantly calculating every other m(n) and averaging the 
results will provide different quality MRI images. 
Considering these effects for quadrature birdcage coil receivers, in a 
typical imaging scenario, the acquired time domain signal is Fourier 
Transformed to yield terms in the Fourier Transform along the y direction 
for a given x. The remaining problem is a one-dimensional reconstruction 
of density along the y direction. 
The profile of such a simple point sample is shown in FIG. 6. Here, signal 
only arises from a small sample located off center. A standard 128 
projection reconstruction with a single receiver coil is shown in FIG. 7. 
This displays the magnitude of the reconstructed profile; the point spread 
is the usual behavior of a finitely sampled Fourier transform. 
FIG. 8 shows the magnitude of a reconstruction using two receivers and 
calculating three Fourier projections per echo. The artifact in the 
reconstruction is quite large. A less ambitious approach of calculating 
two Fourier projections per echo (FIG. 9) with a 50% time savings 
decreases the artifact but it is still large. 
The best results so far are obtained with a redundant calculation of three 
projections per echo; every other echo is calculated twice and averaged 
(as noted above in Table I). A magnitude reconstruction with this approach 
is shown in FIG. 10. The level of artifact is significantly reduced. The 
height of the false peak is roughly 2% of the height of the sample peak. 
The 50% time savings is preserved. 
FIG. 11 shows a standard reconstruction of a point sample with sample 
generated noise. An image acquired in half the time using two receivers 
shows an increase in noise as shown in FIG. 12. As expected, the noise 
level has increased by .sqroot.2. Towards the edge of the field of view 
noise decreases. 
While only a few exemplary embodiments have been described in detail above, 
those skilled in the art will recognize that many variations and 
modifications may be made in these exemplary embodiments while yet 
retaining many of the novel features and advantages of this invention. All 
such variations and modifications are intended to be encompassed by the 
scope of the appended claims.