RF coil for NMR.

The present invention relates to a radio frequency (RF) coil, for example, for nuclear magnetic resonance (NMR) apparatus. A preferred embodiment of the invention provides a radio-frequency (RF) coil of the "birdcage" form, having optimized signal-to-noise ratio (SNR) particularly when receiving RF signals in a NMR imaging or spectroscopy environment.

It is now well known to image and obtain chemical shift spectra from certain nuclei, such as ¹H, ³¹P and the like, to determine the internal distribution and chemical form of those nuclei in a specimen, using NMR. In particular, NMR imaging of a particular nuclear species in the human body has proven to be medically and scientifically significant. It is now also well known that substantial increases in SNR can be observed by increasing the static magnetic field B₀ in which the specimen-to-be-imaged is immersed. It has been found that attempts to reduce the size of a volume picture element (voxel) by trading off this SNR advantage, result in relatively little reduction of the linear voxel extent, since the voxel linear dimension is apparently proportional to the cube root of the signal-to-noise ratio. However, a SNR increase can be utilized to shorten the data acquisi­tion time, with acquisition time reductions proportional to the square of the SNR increase being realizable. Accordingly, it is highly desirable to increase, to the greatest extent possible, the signal-to-noise ratio in a RF volume coil, and particularly in the form of RF volume coil known as a "birdcage" coil, which is one having a pair of conductive loop elements spaced along a common longitudinal axis, with each of the loop elements having a plurality of series-connected capacitance elements spaced along the loop peripheries, and with a like plurality of axial conductive elements electrically interconnecting the conductive loop elements at points between adjacent ones of the serially-connected capacitive elements, such as are described in U.S. Patents 4,680,548 and 4,692,705, respectively issued July 14, 1987 and September 8, 1987, and both incorporated herein in their entireties by reference.

In accordance with one embodiment of the invention, a RF volume coil with optimized signal-to-noise ratio, for NMR and the like use, has a reduced length L_c, which is between about 0.3r_s and about 1.5r_s, where r_s is the effective radius of a sample-to-be-investigated, contained within the cylindrical volume coil, with the volume coil radius r_c being between about 1.0r_s and about 1.6r_s. Such a "short" volume coil has an improved SNR for a voxel located substantially along the axis of the coil, although the sensitivity S of the coil is non-uniform, especially for voxels removed from the coil axis, relative to the SNR of a "normal"-length volume coil with Lc≧4r_s.

In one presently preferred embodiment, an optim­ized SNR volume coil, of "birdcage" form, designed for detection of NMR response signals from ³¹P nuclei at about 26MHz., has a length L_c of about 1.0r_s and a coil radius rc of about 1.1rs., and has better than a 60 percent increase in SNR relative to a cylindrical volume coil, of the same form, having a length of about four times the sample radius. Operation of the detection coil in a true-quadrature mode, to detect only the circularly-polarized NMR field, contributes an additional SNR improvement of about 40 percent.

A better understanding of the present invention will become apparent upon reading of the following illustrative description, when considered in conjunction with the drawings, in which:- <ul id="ul0001" list-style="none"><li>Figure 1 is a perspective view of one presently preferred high-pass birdcage embodiment of the optimized volume RF coil of the present invention;</li><li>Figure 2 is a graph illustrating the relative signal-to-noise ratio of volume RF coils having fixed ratios of sample radius and coil radius, for varying coil lengths, and useful in appreciating the improvement of the present invention;</li><li>Figure 3 is a graph illustrating the relative sensitivity of the coil for voxels at various radial distances from the coil axis, for various axial positions within the coil, and also useful in appreciating the features of the present invention; and</li><li>Figure 4 is a perspective view of one presently preferred low-pass birdcage embodiment of the optimized volume RF coil of the present invention.</li></ul>

Referring initially to Figure 1, a volume RF coil assembly 10, is of cylindrical form, and is supported by a non-magnetic, non-conducting and non-dielectric tube 11, of acrylic and the like material, having a radius R and a length L, which for a coil for imaging of a human head are illustratively of about 5 inches and about 8 inches, respec­tively. The axis of the cylindrical coil form 11 is aligned with the Z axis of a Cartesian coordinate system, and with the center Z=0 of that system lying at the axial center of the coil 10. An antenna portion 12 of assembly 10 is comprised of first and second spaced-apart conductive loop elements 14a and 14b, each having a width W, here, about one-half inch, with the facing edges of conductors 14a and 14b having a spacing L_a here, about 4.5 inches, such that the edge planes of conductors 14a and 14b are each at a distance L_b, here, about 2.25 inches, from the axial center Z=0 plane; the effective length L_c of the coil is about 5 inches. Each of conductors 14a and 14b is broken at each of a plurality N of locations, typically in axial alignment, by a small gap 14c so as to form a like plurality N of substan­tially identical conductive segments 14s. Advantageously, the number N of segments is represented by a power p of base 2, i.e. N=2^p, where p=1, 2, 3,... . In the illustrated embodiment, p=4 and N=16. Each of the 16 conductor gaps 14c is bridged with a serially-connected capacitive element 16. Each of a like plurality N of axial conductive elements 14e interconnect similarly disposed segments 14s of the first and second spaced-apart loop elements 14a and 14b; each axial conductive element 14e has a width W′, here, about one-half inch. First and second conductive end rings 18a and 18b, if used, are formed in planes substantially paral­lel to the planes of loop elements 14, but axially extended therebeyond; each end ring is of thickness ΔZ (here, about one-half inch) and has at least one gap 18c therein, with each gap being bridged by an associated serially-connected capacitive element 20; the end rings tend to eliminate undesirable coil resonances.

This particular high-pass "birdcage" form of optimized-SNR volume RF coil 10 has a balanced feedpoint between first and second terminals 10a and 10b, which are connected across one of the capacitors 16, illustratively connected to adjacent conductive segments 14s-1 and 14s-2, respectively, and across capacitor 16′. Advantageously, the coil will be connected for quadrature excitation and/or reception, with a second balanced feedpoint being provided between third and fourth terminals 10c and 10d, which are connected to adjacent conductive segments 14s-5 and 14s-6, respectively, and across another capacitor 16˝, which is situated in that part of coil loop 14b having a radial reference substantially at 90° to a radial reference extend­ed from the cylinder axis to the first balanced input about capacitor 16′. The use of baluns, balanced multiple-half-­wavelength cables, hybrid quadrature elements and the like, to couple the quadrature feedpoints to a single unbalanced reception cable, and the like configurations external to coil 10, are all well known to the art.

The operation of volume detection coil 10 can be analyzed by the principle of reciprocity, so that the RE coil 10 NMR signal-to-noise ratio ψ detected from a voxel located at a point (r,ϑ,z) in the cylindrical polar coordi­nate system, with origin z=0 at the coil center and with, as here, the Z axis coincident with the coil cylindrical axis, is Ψ α B₁ (r,ϑ,z) / √R      (1) where B₁ is the transverse RF magnetic field produced by a unit current and R is the total noise resistance at the NMR angular frequency ω. In optimizing ratio ψ along the coil axis, the transverse RF magnetic field B₁ of a birdcage coil geometry with length L_c and radius r_c is, for a maximum end-ring 18 unity current, produced by sinusoidal current distributions <i><u style="single">J</u></i>, so that <u style="single">J</u>=(-zsinϑ/|z|W)<u style="single">ϑ</u>+((|z|-L_c/2)cosϑ/r_cW)<u style="single">z</u>,      (2) for (L_c/2)-W≦|Z|≦L_c/2, in each loop element 14 of width W, and <u style="single">J</u>=(-cosϑ/r_c)<u style="single">z</u>, for |z|&lt;(L_c/2)-W.      (3) The magnetic scalar potential (φ_m) inside the coil obtains from matching the separate solutions from Laplace's equation to a Fourier decomposition of the currents: φ_m(r,ϑ,z)=<img file="EP0346049A2_D0001.tif" />A(k)kr_cK<img file="EP0346049A2_D0002.tif" />(krc)I₁(kr)sinϑ cos(kz)dk      (4) with A(k)=(2 cos k(L_c/2 -W)-2 cos (L_c/2))/πk²Δz      (5) where K′₁ is a derivative of a modified Bessel function of the second kind with respect to the total argument. The RF magnetic field B₁(r, ,z) is then obtained by numerical computation of the magnetic field transverse component, in a space of permeability µ₀, so that <u style="single">B</u>(r,ϑ,z)=-µ₀ <u style="single">∇</u> φ_m.      (6)

The total effective NMR noise resistance R com­prises contributions from both the coil and the sample. We consider only the contributions to noise resistance R from sample losses, as coil losses can be rendered relatively small. Again invoking reciprocity, R=σ∫&lt;<u style="single">E</u>·<u style="single">E</u>&gt;dV=<img file="EP0346049A2_D0003.tif" />∫<u style="single">E</u>·<u style="single">E</u>dV      (7) where σ is the average conductivity of the sample (and is assumed to be uniform), <u style="single">E</u> is the electric field induced in the sample by a time-dependent magnetic field <u style="single">B</u> cos(ωt) produced by a unit coil current I₁, and the volume integral extends over the entire sample. We deduce <u style="single">E</u> from Faraday's law, <u style="single">∇</u> X <u style="single">E</u> = - δB/δt      (8) and equation (6), as <u style="single">E</u>=-<u style="single">∇</u>φ_e+(µ₀ω <img file="EP0346049A2_D0004.tif" /> (A(k)/kr)I₁(kr)cosϑsin(kz) dk)<u style="single">r</u> -(µ₀ω <img file="EP0346049A2_D0005.tif" /> A(k)I′₁(kr)sinϑsin(kz)dk)<u style="single">ϑ</u>      (9) with the time dependent sin(ωt) factors suppressed, and where φ_e=µ₀ω <img file="EP0346049A2_D0006.tif" /> (A(k)I₁(kr_s)/k²r_sI′₁ (kr_s))I₁ (kr)cosϑsin(kz)dk,      (10) assuming the boundary condition of no current flow normal to the sample surface at sample radius r_s, and also that the magnet fields associated with the induced currents do not themselves significantly alter the RF magnetic field B₁. The sample noise resistance R is obtained by substitution of equations (5), (9), and (10) in equation (7), and numerical integration.

Referring now to Figure 2, the achieved NMR signal-to-noise ratio SNRa=B₁/√R, at the center of the coil (for X=0, Y=0 and Z=0) is plotted along ordinate 22 as a function of coil length L_c, which is plotted along abscissa 24 for several values of coil radius r_c, where both the coil length and coil radius are in terms of the effective radius r_s of the sample within the coil. The SNR values are seen to depend upon the ratio of the coil radius r_c and sample radius r_s; within the desirable range from about r_c/r_s=1.0 to about 1.6, the five curves 25, 26, 27, 28 and 29 respec­tively represent ratios of 1.1, 1.2, 1.3, 1.4 and 1.5. The effective sample radius r_s will not only depend upon the size of the sample, but also the sample shape; portions of human anatomy, such as the head, may appear, within the coil, as a RF load having an effective radius r_s different from any major dimension of that anatomical portion. It will be seen that coil radius r_c is a relatively insignifi­cant factor affecting SNR ψwhen sample noise is dominant. It will also be seen that the normal coil length L_c of about 4r_s, as shown at point A, has a relative SNRa of about 0.6, which can be improved by approximately 50 percent, to a value of SNRa of about 0.9, at point B, by shortening the coil to a length of about L_c=1.4r_s. It will also be seen that a further shortening of the coil length to about L_c=1.0r_s, at point C (with a coil radius r_c of about 1.1), has a relative SNRa in excess of 1.0, and provides at least 65 percent higher SNR, relative to the SNRa value at point A, for the normal long coil. The use of quadrature opera­tion can add an additional 40%, so that SNR improvement of 100%, or better, is possible, relative to a single-fed, long birdcage RF coil.

Referring now to Figure 3, a relative signal-to-­noise ratio sensitivity S is plotted along ordinate 32 for various values of normalized radial distance (r/r_s) from the Z axis of the cylindrical coil 10, and for values, along abscissa 34, of various normalized axial distances (z/r_s) from the coil center, z=0, in either direction towards the coil ends, for a particular coil having a coil radius r_c=1.4r_s. It will be seen that the aforementioned 50 percent SNR increase, to a SNRa value of 0.9 at point B (relative to a SNR_a of 0.6 at point A), is obtained at all locations along the S=0.9 curve 36, and that even greater relative SNR values S can be obtained closer to the center of the coil and/or at radially increased distances from the coil axis. Thus, it is seen that the penalty paid in RF magnetic field B₁ inhomogeneity is relatively modest, amounting to about 33 percent in the (r, ,z=0) plane and in transaxial planes out to about z=0.75r_s. Since the NMR flip angle α produced by a RF excitation field B₁ is proportional to the magnitude of the B₁ field, and the magnetization is proportional to sinα, such inhomogeneity would result in only about a 13 percent loss in signal, at worst, at the center of the sample, if flip angle α were set at 90° at the sample surface, notwithstanding spin lattice relaxation effects. Therefore, this short volume coil design, with length L_c being less than 2r_s, for r_c/r_s between about 1.0 and about 1.6, is well suited for both NMR sample excitation and response signal reception. It will also be seen that additional reduction of the coil length, to L_c less than 1.0r_s, may provide marginally additional enhancement in SNR ψ, particularly if the coil radius r_c is also maintained at values between about 1.0r_s and about 1.6r_s. We have, however, found that additional gain in SNR cannot be real­ized in practice, as L_c approaches zero, because the orig­inally-assumed condition (that the sample noise dominates) cannot be obtained; as L_c approaches zero, the RF magnetic field B₁ decreases faster than the coil noise contributions. Also, because the coil radius r_c must be chosen to accommo­date a range of human subjects and their non-cylindrical anatomies, it may be difficult to maintain the coil radius r_c in the range of 1.0r_s to 1.6r_s.

Referring now to Figure 4, a presently preferred embodiment of a low-pass RF volume NMR coil assembly 10′ is supported by a non-magnetic, non-conducting and non-dielec­tric tube 11′, having a radius R′ and a length L′ which, for a coil devoid of end rings (which are not needed, as no interfering resonances are encountered at nearby frequencies), is slightly longer than the effective coil length L′_c. The axis of cylindrical coil form 11′ is aligned with the Z axis and the center Z=0 of that system is at the axial center of the coil. An antenna portion 12′ is comprised of first and second spaced-apart conductive loop elements 14′a and 14′b, each having the same width W as in coil 10 of Figure 1. The effective length L′_c of the coil and the radius R′ are both about 5 inches. Each of conduc­tors 14′a and 14′b is broken at each of a plurality M of locations, typically in axial alignment, by a small gap 14′c so as to form a like plurality M of substantially identical conductive segments 14′s. Advantageously, the number M of segments is represented by a power q of base 2, i.e. M=2^q, where q=1, 2, 3,... . In the illustrated embodiment, q=2 and M=4. Each of the conductor gaps 14′c is bridged with a serially-connected capacitive element 16′. Each of another plurality N (here, equal 16) of axial conductive elements 14′e are disposed perpendicular to similarly disposed segments 14′s of the first and second spaced-apart loop elements 14′a and 14′b; each axial conductive element 14e has a width W′, here, about one-half inch. The ends of each element 14′e are separated from the adjacent segments 14′s by one of gaps 14′f; each gap 14′f is bridged by a capacitive element 40.

This particular low-pass "birdcage" form of optimized-SNR volume RF coil 10′ has a feedpoint 44a at an element 14′g-1, which is separated from element 14′e-1 by a gap 14′f bridged by a capacitor 42. The unbalanced feed­point connector 44a has the shield thereof connected to segment 14′s-1 and its center conductor connected via conductor 46 to element portion 14′g-1. For quadrature excitation, a second unbalanced feedpoint 44b is located 90° from the first feedpoint 44a.

In use, a presently preferred embodiment 10′, as illustrated with 5 inch coil radius R′=r′_c and 5 inch length L′_c for a sample radius r_s of about 3.5 inches, was utilized for NNR sample excitation and response signal detection. The coil was operated in the true-quadrature mode by connec­tion of a 0° input to connector 44a and a 90° input to connector 44b, i.e. with ϑ=90° spacing, to provide an additional √2 improvement in SNR ψ and a two-fold reduction in the necessary excitation pulse power. The spectral SNR ψ of a 20ml. sample of 1M H₃PO₄, located at the coil center (z=0 and r=0), was 28, as recorded from a single free-­induction-decay (FID) in a bandwidth of 2KHz., with a 12Hz. line-broadening exponential filter and with the coil load adjusted, by connection of a resistor of the appropriate value across the coil inputs, to be equivalent to that load provided by a human head. The broadened full-width-half-­maximum H₃PO₄ line width was 54Hz. The corresponding value of SNR ψ, obtained with a ³¹P surface coil with a radius of 6.5 centimeters and distributed capacitance design, for a loaded head equivalent, was 18, with the phosphate sample located both on the surface coil axis and at a depth of 6.5 cm. from the coil (depth equal to coil diameter); a SNR ψ value of 56 was obtained at a depth of 3.8 centimeters. Loaded and unloaded coil quality factors (Q) were respectively 410 and 100 for the short birdcage coil, and were respectively 430 and 130 for the surface coil, at resonance; resonant frequency changes of the loaded coils were negligible. These values indicate that the relative contributions of sample noise to total detected noise were similar, being about 76% for the short birdcage coil and about 70% for the surface coil.

While several presently preferred embodiments of our novel short volume coil with optimized SNR, have been described herein, many variations and modifications will now become apparent to those skilled in the art. For example, while the analysis, supra, applies specifically to the high-pass and low-pass birdcage coils of Figures 1 and 4, respectively, because of the assumption of relatively good azimuthal field homogeneity (i.e. uniformity of field with respect to polar angle ϑ), the basis of this analysis is equally as well applicable to other transverse coils, such as solenoidal, saddle and sinusoidal designs, with and without distributed capacitance (i.e., most coils producing an RF field in a direction substantially perpendicular to the main static magnetic field in which the RF coil is immersed), as known to the art; these designs can all provide SNR benefit when L_c and r_c are chosen according to the invention, i.e. 0.3r_s≦L_c≦1.5r_s and 1.0r_s≦r_c≦ 1.6r_s.

Accordingly, preferred embodiments of the present invention provide a volume RF coil, for use in NMR and the like systems, having an improved signal-to-noise ratio.