Optimization of 13C-{1H} double coplanar surface-coil design for the WALTZ-16 decoupling sequence

JOURNAL

OF MAGNETIC

RESONANCE

82,622-628

( 1989)

Optimization of 13C-(I‘H > Double Coplanar Surface-Coil Design for the WALTZ-16 Decoupling Sequence J. MISPELTER, B. TIFFON, E. QLJINIOU, AND J. M. LHOSTE Institut Curie, Section de Biologie, INSERM U-219, Centre Universitaire, Bit. 112, F 91405 Orsay Cedex, France Received June 24,1988; revised September 20,1988

A crucial problem for in viva carbon- 13 NMR is the need of efficient proton decoupling while avoiding excessive heating of the conductive biological tissues under observation. The difficulty comes mainly from the inherent radiofrequency field inhomogeneity of surface coils. First, this severely penalizes the yield of RF power actually used for decoupling. For example, maximum sensitivity of a surface coil is obtained at a depth about 0.5 to 0.6 times the coil radius, when using an excitation 180” pulse at coil center ( I ). In contrast, the decoupling field is maximum close to the coil and decreases by a factor of about 0.6 in the ‘3C-sensitive volume, assuming a doubletuned single-coil probe. Thus, only 36% of the energy deposited in the sample is actually used for decoupling. Second, efficient cyclic sequences (2) for decoupling tend to be no more efficient than modulation techniques in the heterogeneous RF field of a single coil. They require indeed an accurate setting of pulse angles for the elements of the sequence. Nevertheless, it has been demonstrated (3) that the configuration with two coaxial coplanar coils allows actual use of such sequences due to a rather homogeneous decoupling field in the 13C-sensitive volume (3, 4). As a result, WALTZ- 16 decoupling (5) was found to be four-fold more efficient in power than conventional noise modulation for a particular probe design (3). A property sometimes considered a major drawback of the configuration with two coplanar coils is that the inner 13C coil is nearly short circuited at the proton frequency. Induced currents in that coil create a RF field which opposes the decoupling field of the proton outer coil. In some instances, this may result in an inefficient probe for decoupling. In fact, the parasitic field decreases more rapidly with depth than the primary field of the outer coil. One expects, and indeed observes, that in some sample space the magnitude of decoupling field presents a flat maximum with depth, i.e., a null RF gradient. Such a configuration resembles closely a “flux concentrator” (6). It was also proposed for localization purposes ( 7) and as a surface probe for production of homogeneous excitation BI fields (8). The latter consisted of a large transmitter coil and a smaller receiver coil tuned to the same frequency. Appropriate circuitry allowed a control of the current induced in the inner coil during the excitation pulse in order to obtain the desired spatial distribution of RF field. A 13C- { ‘H ] probe based on this design could work as well but with several drawbacks. The irradiated volume is unnecessarily large (the authors (8) advocate a transmitter coil three times 0022-2364/89 $3.00 Copyright Q 1989 by Academic F’rss, Inc. All rights of rqmduction in any form reserved.

622

623

NOTES

larger than the receiver coil) and the power requirement for the decoupler rapidly increases with the coil diameter. Furthermore, the induced current must be controlled during reception of the 13C signal. This implies double tuning of the receiver coil with inherent difficulties of construction and of preserving carbon sensitivity. The purpose of this Note is to show that an optimum 13C- { ‘H > probe may be obtained by properly choosing its physical dimensions. For optimum, we mean setting the maximum homogeneous decoupling field region as close as possible to the volume of maximum “C sensitivity. Without lack ofgenerality, we choose this region at a depth around 0.6 times the carbon coil radius, assuming a 180“ excitation pulse at coil center ( 1). For simplicity, computation was limited to an on-axis magnetic field and circular coils of thin wire. This latter approximation is valid for non-thinwire coils such those of the experimental model described below. As a result. the following formula for mutual inductance between two coaxial coils of mean (or equivalent) radius a and b works as well, M=pc$&

1

K(k)-;E(k)

,

with k = 2&b/( d* + (a + 6)2). E(k) and K(k) are complete elliptic integrals easily evaluated by a direct numerical calculation (9). Here, the distance d between coil centers is zero (coplanar coils). Due to coil coupling a current i is induced in the inner coil tuned at the carbon frequency wc. It is proportional to the current i,, circulating in the outer coil driven at the proton frequency WH, i =

-iOM/Lc[(uH/wc)2/((WH/oC)’

-

1)1,

I’1

where Lc is the carbon coil inductance. The frequency-dependent factor is equal to 1.067 for the 13C/ ‘H couple. This means that the 13C coil is actually short circuited at the proton frequency by its tuning capacitor. In contrast, the tuning capacitor of the outer proton coil presents a high impedance at the carbon frequency. Thus, the decoupling coil does not perturb significantly the carbon RF field distribution. The total decoupling field for a unit current flowing in a proton outer coil of radius b and at a distance y from the plane of the coil is given by a2 2(a2 + y*p*

E f(oeloc) Lc.

1 [Jl 9

where a one-turn carbon coil of radius a is assumed. In fact, this expression is independent of the number of turns of the coils unless they look like a long solenoid. This can be readily proved from the fact that Lc and Mare proportional to n$ and n(:& , respectively, and the respective contributions to B2 are proportional to nc and nH . It follows that adjustment of B2( y) can be made only through the coil radii a and b and by the wire diameter of the inner coil. The latter allows one to modify Lc but not M. At high frequency, Lc is expressed as Lc = yoa[ln( 16a/d) - 21,

l41 where d is the wire diameter of the carbon coil. To prove the validity of this approach, an experimental model was built. It is schematically illustrated in Fig. 1. The proton outer coil was machined from copper foil

624

NOTES

0 0

50

100

mm

FIG. 1. On-axis RF field magnitude for (a) the proton outer coil alone; (b) to (e) the coplanar coaxial two-coil configuration with the inner coil short circuited (see Table 1 for their physical characteristics), Field values are normalized to the on-center field magnitude of the outer coil alone. Full lines are computed field distributions. The dashed curve represents on-axis sensitivity for the inner coil, assuming a 180” pulse at coil center ( 1) .

( 1 mm thick) as a flat foil coil with bl and b2, respectively, of 79 and 120 mm. It was tuned to about 40 MHz, matched to 50 D, and driven at a constant power of -10 dBm with an RF generator. On-axis field distribution was mapped using an electrically shielded (IO) small one-turn coil (diameter 0.9 mm) fed to an oscilloscope. The observed peak-to-peak induced voltage (7.2 mV at coil center) was directly proportional to the magnitude of I&(y). Curve a of Fig. 1 shows that the RF field of this coil is identical to that predicted for a thin-wire coil of equivalent radius b equal to 2( 1/ bI + 1/ bZ)-‘. Short-circuited coils of varying inductances but similar mean diameters (Table 1) were inserted in a coplanar coaxial configuration and the field was mapped as described above. Figure 1 confirms prediction of Eq. [ 31 and that a two-turn coil (case d) behaves much like a similar one-turn coil (case c) . Mutual inductances M were estimated from the resonance frequency shift observed when inserting the shortcircuited coils. Table 1 indicates a remarkable constancy of M independent of inner coil design and as predicted by Eq. [ 11. A point which has been perhaps neglected in previous designs is that the wire diameter of the inner coil affects the decoupling field distribution (Fig. 1). As a result, the optimum design for this particular probe model is for coils c or d. A higher decoupling field is still obtained with a thinner wire (coil e) but its homogeneous region is displaced toward the coil plane where 13C sensitivity generally tends to zero (except for the undesired “high-flux” regions). Furthermore, a coil made of thin wire would result in a degradation of r3C S/N due to a poor coil Q, to a decreased filling factor (II), and to increased sample dielectric losses. The latter could be partly alleviated

52s

NOTES TABLE 1 Characteristics of Coils for the Experimental Model (See Fig. 1 for illustration) Mutual Equivalent radius”

Wire diameter

(mm)

(mm)

Inductance WI

Proton coil Ia)

95.3

Flat foil coil, 41 mm w.. 1 mm thick

304

Carbon coils (b)

52.5

On edge foil coil, 15 mm w., 0.25 mm thick

192

(c)

51.2

(d)

51.5

W

52.5

2.5 2.0 (2

244 969

turns) 0.17

429

Measured (nW

-Calculated (n1-l)

-

71

65 136 (2 X68) 69

65.2

61.: 124.8 (2x 62.4) 65.2

’ The equivalent radius is the radius of a thin-wire coil which produces the same field distribution far from coil wire. For a circular coil of circular cross section it is close to the mean radius. For a flat foil coil (Fig. 1) it is given by l/h = l/2( l/b, + I/h,), where b, and /I* are the inner and outer radius of the ring.

in a symmetrical series-tuned configuration (12, 13). In contrast, a smaller inductance (coil b) has several advantages with respect to S/N but the decoupling field is reduced and the homogeneous region is displaced far away from the coil plane where 13CS/N decreases. In practice, a compromise must be made and after a reasonable choice of the 13C coil design is made, the question of optimum proton coil radius alone remains. To illustrate this, Fig. 2 shows the computed on-axis field magnitude for varying outer to inner coil radius ratios (b/a), assuming a typical 13C coil of 10 mm mean diameter and 0.5 mm wire diameter. It is evident that as b/a increases the region of homogeneous maximum field moves away from the coil plane. But the maximum field strength first increases and then decreases significantly when b/a increases. As a result, the optimum b/a ratio ranges from 1.6 to 2.0 for this particular 13Ccoil design. More generally, Eqs. [ 1 ] to [ 41 can be rewritten such that the decoupling field & per unit current flowing in the proton outer coil is expressed as BJn&

= F(yla,

b/a, dl2a)

f51 which must be optimized for b/a and d/2a such that it is at a maximum for a desired y/a where 13C S/N is maximum. Figure 3 shows the computed solution for aB2/ a( y/ a) = 0 as a function of b/ a for several values of wire diameters d/2a. They correspond to the positions where Bz is homogeneous and at a maximum, i.e., where decoupling is optimum when using WALTZ- 16. The limiting curves for d/2a = 0.2 and 0.02 are given for completeness but correspond generally to unrealistic coil designs. Then, for a chosen d/2a (remembering that B,,,, increases as d decreases but

626

NOTES

0

5

10

mm

15

FIG. 2. Computed on-axis RF field magnitude for several proton outer coil radii (b) and a carbon inner coil with a radius (a) of 5 mm and a wire diameter of 0.5 mm.

at the expense of 13C sensitivity) and y/a (for example, 0.6)) one could graphically obtain two solutions for b/a. The solution closest to 1.O must be rejected because it corresponds to a much smaller B2maxthan for the other solution and to a very sensitive maximum field position with respect to coil dimensions. It is probable also that Eq. [ 1 ] fails in that range for non-thin-wire coils. This calculation shows that the requirement for optimum decoupling at y/a = 0.6 appears too restrictive. There is no corresponding solution ford/2a > 0.06, a condition which probably gives a too thin wire, especially for small coils (2a x 10 mm). In fact, a shift of optimum decoupling space to about 0.8-0.9 a could be tolerated provided one increases slightly the center-coil pulse-length setting. Then, optimum design becomes less critical with respect to d/2a. Nevertheless, b/a must be smaller than about 2. It is interesting to note that most designs of the literature (3, 4, 14-19) fulfill this requirement. Figure 4 summarizes computation results in the form of a diagram where d/2a is plotted as a function of b/a for a desired optimum decoupling position in a tolerable range from 0.6 to 0.8 times the carbon coil radius. Dashed lines limit an acceptable region of coil design. On the left side of this area, there is no solution. Below d/2a = 0.05, this corresponds to unreasonably thin wire at least for small coils. On the right side, the optimum decoupling space is too far from the carbon coil plane, where sensitivity decreases significantly. Thus coil designs are rather limited. We propose the limits d/2a < 0.1 and 1.4 < b/a < 2.0. In conclusion, the coplanar coaxial coil configuration for a 13C- { ‘H } probe creates a homogeneous proton RF field region which coincides with the greatest decoupling field obtainable in sample space. This allows use of the efficient WALTZ-16 decou-

62-l

NOTES

d/Za

ru

= 0

Y/a 1 .o

0.5

0 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

FIG. 3. Coordinate (y) of the maximum homogeneous axial field position as a function of proton outer coil radius (b) for varying wire diameters (d) of the carbon inner coil. All dimensions are normalized with respect to the inner coil radius (a).

d/2a

\ I

0.10 I\

I \ \ \

0.05

0 1.0

2.5

3.0 b/a

FIG. 4. Location of optimum ‘%- { ‘H } probe design in the (d/2a, b/a) plane when using cyclic sequences for decoupling. Full lines correspond to the indicated normalized coordinate y/a where decoupling is optimum. Dashed lines limit an acceptable plane portion for an optimum design. a is the carbon coil radius, d is the diameter of its wire, and b is the proton coil radius.

628

NOTES

pling sequence which compensates the unavoidable decrease of RF field strength when inserting the carbon coil. In addition, due to a large decrease of RF field near the coil plane (at least on-axis) an unused energy deposition in that sample space is partly avoided. In contrast, the carbon RF field distribution remains fortunately undisturbed. For optimum results, the homogeneous RF field space must fit the maximum 13CS/N space. This Note gives the necessary guidelines for obtaining optimum decoupling in the volume of interest. The rather strong requirements are solely on the ratio of wire to coil diameter of the carbon coil and on the proton to carbon coil radius ratio. The former results in a compromise between 13C sensitivity and maximum decoupling field strength while the latter is easy to fulfill. Other coil parameters, such as the number of turns or the proton coil shape, can be freely chosen for best performance at the working frequency. ACKNOWLEDGMENT This work was initiated after fruitful discussions with Dr. M. Decorps, which we gratefully acknowledge. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. IO. II. 12. 13. 14. 15. 16. 17. IS. 19.

M. DECORPS, M. LAVAL, S. CONFORT, AND J. J. CHAILLOUT, .I Magn. Reson. 61,418 ( 1985). A. J. SHAKA, J. KEELER, AND R. FREEMAN, .I. Mugn. Reson. 53,313 ( 1983). B. TIF’FON, J. MISPELTER, AND J. M. LHOSTE, J. Magn. Reson. 63,544 ( 1986). R. C. LYON, R. G. TSCHUDIN, P. F. DALY, AND J. S. COHEN, Magn. Reson. Med. 6, 1 ( 1988). A. J. SHAKA, J. KEELER, T. FRENKIEL, AND R. FREEMAN, J. Magn. Reson. 52,335 ( 1983). K. M. BRINDLE, M. B. SMITH, B. RAJAGOPALAN, AND G. K. RADDA, J. Magn. Reson. 61,559 ( 1985). M. R. BENDALL, D. FOXALL, B. G. NICHOLS, AND J. R. SCHMIDT, J. Magn. Reson. 70,181( 1986). P. STYLES, M. B. SMITH, R. W. BRIGGS, AND G. K. RADDA, J. Magn. Reson. 62,397 ( 1985). M. FAN, P. G~NORD, S. KAN, AND J. TAQUIN, Magn. Reson. Med. 4,59 1 ( 1987). C. N. CHEN, V. J. SANK, S. M. COHEN, AND D. I. HOULT, Magn. Reson. Med. 3,722 ( 1986). D. I. HOULT, Prog. NMRSpectrosc. 12,41 ( 1978). J. MURPHY-B• ESH AND A. P. KORETSKY, J. Magn. Reson. 54,526 ( 1983). M. DECORPS, P. BLONDET, H. REUTENAUER, AND J. P. ALBRAND, J. Mugn. Reson. 65,100 ( 1985). A. N. STEVENS, R. A. ISLES, P. G. MORRIS, AND J. R. GRIFFITHS, FEBS Lett. 150,489 ( 1982). P. C. CANIONI, J. R. ALGER, AND R. G. SHULMAN, Biochemistry 22,4974 ( 1983). N. V. REO, B. A. SIEGFRIED, AND J. J. H. ACKERMAN, J. Biol. Chem. 259, 13,664 ( 1984). J. R. ALGER, K. L. BEHAR, D. L. ROTHMAN, AND R. G. SHULMAN, J. Magn. Reson. 56,334 ( 1984). N. V. REO, C. S. EWY, B. A. SIEGFRIED, AND J. J. H. ACKERMAN, J. Mugn. Resort. 58,76 ( 1984). B. A. SIEGFRIED, N. V. REO, C. S. EWY, R. A. SHALWITZ, J. J. H. ACKERMAN, AND J. M. MCDONALD,

J. Biol. Chem. 260, 16,137 (1985).