A cylindrical-window NMR probe with extended tuning range for studies of the developing heart

JOURNAL

OF MAGNETIC

RESONANCE

82,238-252

(1989)

A Cylindrical-Window NMR Probe with Extended Tuning Rangefor Studies of the Developing Heart GERALD

J. KOST,

STEVEN E. ANDERSON, GERALD B. MATSON, AND CLAIRE B. CONBOY

Biomedical Engineering, Departments ofMedical Pathology and Human Physiology, and the Nuclear Magnetic Resonance Facility, University of California, Davis, California 95616 Received May 19, 1988; revised August 8, 1988 Three matched cylindrical-window NMR probes were designed and constructed in graduated sizes (16, 25, and 30 mm) for neonatal, immature, and adult heart spectroscopy. The cylindrical probes were made of copper foil and had two symmetrical cylintical conductive blades separated by openings subtending 90” arcs. The tuning range included both sodium-23 (52.9 MHz) and phosphorus-3 1 (8 1.OMHz). The ability to tune to sodium-23 expedited shimming for phosphorus-3 1 experimental measurements. Standardization of phosphorus-3 1 spectra was achieved with an MDPA-filled capillary tube placed outside the cylindrical window. The finite element method was used to derive the electrical potential, magnetic field, and current densities. B, field mappings showed uniformity throughout the usable areas, an attribute facilitating comparisons of spectra from hearts of different sizes. We summarize the current designs for low-inductance NMR probes of this type. a 1989 Academic press, hc.

The cylindrical-window design is based on a low-inductance resonant structure concept (Z-6). A matched set of three NMR probes was inexpensive to construct, demonstrated excellent signal-to-noise characteristics, and facilitated experiments using hearts with a broad range of sizes. These probes were used to study changes in intracellular pH and high-energy phosphate metabolites during hypoxia and ischemia, to investigate protective measures such as hypothermic potassium cardioplegia and catalase-superoxide dismutase ( 7, 8)) and to describe myocardial sodium/ hydrogen exchange (9). Here, we present the probe design, an example of a phosphorus-3 1 spectrum from the neonatal heart, and the theoretical analysis, including the electrical potential, magnetic field, and current density mappings. We conclude with a summary of the design criteria for related cylindrical NMR probe structures. METHODS

Rationale for probe construction. The probe usable volumes accommodated hearts from rabbits of different ages. Neonatal (45- 150 g, 2-7 days old), immature (300700 g, 3-4 weeks old), and adult (2-3 kg) rabbit hearts weighed 0.25-0.70,0.75-2.5, and 4.5-8.0 g and required three different probes sized for 16, 25, and 30 mm o.d. NMR sample tubes ( Wilmad, Buena, New Jersey), respectively. For the heart studies, a modified Langendorff rabbit heart preparation was perfused at 35-37°C with phosphate-free Krebs-Henseleit buffer adjusted to pH 7.35-7.45. Left intraventricu0022-2364189 $3.00 Copyrkht 8 1989 byAcademic Press, Inc. AU rights of reproduction

in any form reserved.

238

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239

lar balloon pressure was measured to monitor function. The perfused heart was positioned inside the appropriate 16 mm (neonatal), 25 mm (immature), or 30 mm (adult), 8 in. (20.32 cm) high glass sample tube, which was then lowered into the corresponding NMR probe positioned vertically in the 4.7 T Oxford superconducting magnet of a Nicolet Magnetics NT-200 spectrometer operated in the pulsed Fourier transform mode with a Nicolet 1280 computer system. A semiautomated, computerized data reduction system ( 10) was used to quantify changes in pH and high-energy phosphate metabolites observed during the experimental protocols. Probe design. The design was based on a low-inductance resonant structure ( 1-6). Figure 1 is an isometric (axonometric) drawing of the probe, which accommodated a 16 mm o.d. sample tube used for neonatal hearts. With the probe oriented vertically, the B, excitation field was horizontal and perpendicular to the B0 field of the superconducting magnet. The stippled area is the conductive element. In order to minimize the resistive losses in the probes, the conductive element was fabricated with 0.002 in. thick reagent-grade copper foil (J. T. Baker, Phillipburg, New Jersey) mounted on a 19.16 mm o.d. (16.50 mm i.d.) supporting glass cylinder held with spacers inside an aluminum cylindrical housing with an internal diameter of 69.60 mm. The window height ( W) is 16 mm. The windows subtend angles of 90”. Thicker copper foil (up to 0.005 in.) was used to construct the larger probe. The heart was centered between the windows in the sample tube. A sealed capillary tube (C) was attached over the window outside the copper foil for standardization of phosphorus-3 1 spectra. This standard was made by filling 16 mm of a 1.5 mm i.d. ( 1.8 mm o.d.) capillary tube (Kimble No. 34505, Allied Scientific, Pittsburgh, Pennsylvania) with 0.22 A4 methylene diphosphonic acid (MDPA) (Sigma No. M9508, St. Louis, Missouri) in D20 and fusing the open end closed. Placement of the standard outside the supporting glass, rather than inside the sample tube next to the heart, avoided damaging the fragile neonatal and immature epicardium. ATC porcelain capacitors (American Technical Ceramics, Huntington Station, New York), attached to the copper foil as shown in Fig. 1, were used to tune with the inductance of the structure. Circuitry for fine tuning was connected to the copper foil at the top of the probe (Fig. 2). These elements were close to the structure to minimize extraneous magnetic energy storage and energy dissipation in the capacitor leads which were copper foil. The probe was tunable to 8 1.O MHz (phosphorus-3 1) and to 52.9 MHz (sodium-23) through use of additional capacitance ( Cext) connected to the circuit with an RF connector at the end of a rod which could be positioned externally. Two 42 mm high cylindrical copper foil (0.002 in. thick) shields (s, and s2) were attached inside the supporting glass cylinder above and below the windows. The vertical distance between the bottom of the lower shield and the top of the upper shield was 100 mm. These shields minimized dielectric and inductive losses from the physiological solution, which filled the sample tube to a minimum depth of 90-95 mm. The cylindrical conducting bands (dr and d2) were 16 mm high. Table 1 gives the dimensions and details of the other probes constructed. Theoretical analysis. The theoretical analysis followed accepted principles of electromagnetics ( 6, 11) and NMR probe analysis ( 12- 18). A two-conductor transmission line model was assumed to approximate the probe performance. The approach

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Sl ? 4 1t

FIG. 1. This isometric (axonometric) drawing shows the probe designed for neonatal hearts. The heart is perfused within a 16 mm o.d. glass NMR tube and is centered between the cylindrical windows ( W) formed by copper foil (stippled area). Two copper foil shields, one above (s,) and one below (sz) the cylindrical window, reduce dielectric and inductive losses and exclude unwanted signal from above and below the heart. The MDPA capillary standard (C) is attached outside the copper foil at a consistent angle relative to the center of the cylindrical window. The small boxes represent fixed capacitors, which were distributed evenly across the break in the wide conductor.

resembled that used by Leroy-Willig (15) and Carlson (27), in that it provided a complete solution to Maxwell’s equations for the specialized cylindrical geometry. On the plane cutting horizontally through the center of the cylindrical windows (see Fig. l), each quadrant is symmetrical due to the equal 90” angles subtended by the two opposing copper foil conductors. The theoretical solution on this transverse plane is accurate for the case of infinitely long conductors. We discuss below how the

CYLINDRICAL-WINDOW

241

NMR PROBE

TABLE 1 Cylindrical-Window

NMR Probe Design Outside diameter of NMR sample tube (probe size)

Heart Age group: Typical weight(g): Diameter (D) of copper foil (mm) Ratio of diameter (D) to diameter of grounded shield” Window dimensions (mm) Height Chord width Circumference Copper foil dimensions* 4,4 (mm) s17~2 (mm) Physically usable dimensions i.d. of sample tube (mm) Area (mm2) Usable area (%I) Volume (V,) (cm4 Ratio of volumes Shimmed linewidth (Hz) Without heart With heart 3’P 90’ pulse’ (ps) Value of 0 Unloaded (U) Loaded (L)d Ratio QU/QL ( vp/Q~)“~ Tuned frequency (MHz) Unloaded Change when loadedd

16mm

25 mm

30 mm

Neonatal 0.25-0.70

Immature 0.75-2.5

Adult 4.5-8.0

19.16

29.88

34.88

0.28

0.43

0.50

16 13.55 15.05

25 21.13 23.47

30 24.66 27.39

16 42

25 37.5

25 35

15 176.7 61 2.83 1.00

24 452.4 65 11.31 4.00

29 660.5 69 19.82 7.00

7.0-8.0 8.0-10.0 20.5

8.5-10.0 9.5-11.0 30

8.5-10.0 9.5-l 1.0 56

131 97 1.4 0.17

194 85 2.3 0.36

185 62 3.0 0.57

81.00 80.92

81.00 80.80

81.00 80.68

a The internal diameter, 69.60 mm, of the grounded shield was the maximum allowed by the cylindrical stack housing of the superconducting magnet. * See Fig. 1. ’ P2 optimized for hearts. d Loaded with Krebs-Hensleit buffer.

finite length of the cylindrical windows and the placement of the shields above and below them may have influenced the theoretical results. The electrical potential distribution in the transverse plane was obtained by solving Laplace’s equation, V29 = 0, where $ is the electrical potential (6, 11, IS, 17). The

242

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ET

AL.

boundary conditions were + 1 and - 1 V on the back and front copper foil arcs, respectively, where the copper foil intersects the transverse plane at a radius of 9.58 mm, and 0 V along the grounded metal housing, which formed the probe shield at a radius of 34.80 mm. The electrical field, E, was derived from the gradient of the electrical potential E = -V9. The B, field was orthogonal to the E field. The isocontour map of lines of equal Bi magnitude was derived from the magnetic field after norrnalization with respect to the magnitude at the center (0,O) of the probe. Isocontours were expressed as a percentage of change relative to the center. Current density in the copper foil conductors was determined using the methods described by Lowther and Silvester ( 19) and Silvester and Ferrari (20). The finite element method was used to obtain the numerical solutions (19, 20). Software written locally and used in the UCD School of Engineering was modified for this research. Programming and computations were performed on a VAX 1 1 / 785 computer. In the half plane, the finite element grid included 889 nodes and 864 elements arranged in I mm radial increments and 5” angular increments in cylindrical coordinates. The resolution was 0.1 mm2 at the center of the probe and 0.93 mm2 at the edge of the copper foil. The other probe sizes (25 and 30 mm) were analyzed with a slightly coarser grid. The theoretical analysis was confirmed, and current densities were calculated (19, 20) using commercially available computer-aided design electromagnetics software called MagNet (Compunetics Technologies, Claremont, California). RESULTS

The extended tuning range expedited shimming of the B0 field. While the heart was being prepared, the probe was first tuned to 52.9 MHz and shimmed on the strong sodium-23 signal from Krebs-Henseleit perfusate placed in a glass sample tube in the probe. At this stage, linewidth at half-height typically measured 7.0-8.0 Hz with the 16 mm probe. Shim settings from prior experiments usually required little modification. Then, the perfused heart in another sample tube was placed in the probe, and the 23Na linewidth was rechecked and minimized with additional shimming as necessary. Acceptable values were 8.0-10.0 Hz for the 16 mm probe. Table 1 gives shimmed linewidths for 23Na for the 25 and 30 mm probes. The external capacitance (see Fig. 2) was then disconnected, and the probe was tuned to 8 1.O MHz for 3’P measurements. The 3LP spectral linewidth was checked briefly. Additional shimming was required only rarely. Overall, the total time for shimming was only 15-20 min, an advantage for experiments with fragile neonatal and immature hearts. Since shimming was performed in parallel with preparation of the heart, less time was consumed prior to data acquisition. The extended tuning range also allowed measurement of myocardial intracellular 23Na with the aid of paramagnetic chemical-shift reagents in other experiments, as reported in abbreviated form elsewhere(9). There was no satisfactory method for placing an MDPA capillary standard inside the glass sample tube with the fragile neonatal and immature hearts. A vertical orientation along the inside wall resulted in abrasion of the epicardium and movement, which produced artifact& changes in peak intensity. A small MDPA-filled sphere

CYLINDRICAL-WINDOW

NMR PROBE

243

MATCH

FIG. 2. This schematic shows the equivalent circuit of the I6 mm probe. The inductance, L , corresponds to the stippled copper foil in Fig. 1. In parallel were two setsof fixed capacitors, IO2 and 129 pF on either side. The variable capacitors (C,, typically 0.5-10 pF) in parallel with the fixed capacitors tune the probe to the resonance frequency of phosphorus-3 1 or sodium-23, the latter with the addition of the externally switched capacitance (c,, 105 pF). The variable capacitor in series with the RF lead (top left) is the line impedance matching capacitor. Fixed sets of capacitances ( pF) for the 25 and 30 mm probes were 60 and 72 and 55 and 58, respectively.

placed in the right ventricle interfered sporadically with both right and left ventricular function. These problems were most serious with neonatal hearts, due to small working distances following ischemic challenge when the heart typically would swell or change in configuration. Placement of the MDPA capillary standard outside the cylindrical window avoided damage to the heart. Figure 3 shows the mapping of the intensity of the standard peak as a function of circumferential position around the IOOt: 65 goz g

80-

5 E

70-

: k

60-

+ 5

50-

P L

403oL

’ -45 0 -90 DEGREES OF ARC FROM CENTER

45 90 OF WINDOW

FIG. 3. The figure shows the variation in the percentage of maximum intensity of the MDPA capillary standard peak as a function of position in degrees of arc from the center of the cylindrical window for the 16 mm probe. The line is an average of three mappings made by moving the capillary standard along the outside of the cylindrical window at approximately 5” increments. Data were obtained with perfusate in the sample tube. The maxima occurred at +20”-25’. The minima occurred at +45”, the edges of the copper foil, and at +90”, the midpoints of the copper foil.

244

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probe. The capillary tube was placed either at 20-25” from the center of the cylindrical window, to yield maximum intensity, or at the center of the window (o”), to yield minimum sensitivity to positional change. The standard peak intensity remained stable over time. A reproducible MDPA peak for intensity standardization facilitated data reduction and comparison of successive experiments ( IO). Figure 4 shows a typical 31P spectrum for a neonatal heart (100 g rabbit). The spectrum was acquired with the 16 mm probe illustrated in Fig. 1. Signal-to-noise ratios and definition of the standard peak were excellent. During ischemia the MDPA peak was occasionally used for measurement of intracellular pH from the calibrated chemicaI shift in the inorganic phosphate peak when the phosphocreatine peak, ordinarily used for pH referencing, either vanished or became too small relative to the noise. The chemical-shift position of the MDPA peak relative to the phosphocreatine peak was determined during the initial control period in an individual experiment, and then the relative position was used to avoid any uncertainty introduced by interexperimental changes in shimming. The variation (SD) due to angular position (-45” to +45”) in the cylindrical window was equivalent to 0.033 pH units. Therefore, for consistency the MDPA capillary tube was fixed in the same angular position for a given set of experiments. For the spectrum shown, intracellular pH was 7.10. This spectrum was obtained using 100 W of RF power and a 90” pulse duration of 20.5 ps. Table 1 gives the 90” pulse durations for the other probes. Pulse width was roughly proportional to (VP/ QL) ‘12, where V, is the usable volume and QL is the value of Q with the probe loaded with Krebs-Henseleit perfusate in the sample tube.

STD

PCr

FIG. 4. Phosphorus-3 1 Fourier transform spectrum obtained from a 0.39 g (wet weight) neonatal heart during a control perfusion at 3%37°C. Conditions of data acquisition were 148 FIDs, 10 s intervals, 4K data files, and +4000 Hz spectral width. EM was 25 Hz, with no other spectral processing. The signal-tonoise ratios of the peaks were excellent, despite the small heart size. STD is the peak from the MDPA capillary standard, which was placed outside the cylindrical window. Other peak identities were PCr, phosphocreatine; and r-, OI-,and @-ATP, adenosine triphosphate. The horizontal axis is chemical shift in parts per million ( ppm) .

CYLINDRICAL-WINDOW

NMR PROBE

245

The range of usable volume, the volume within the sample tube in a cylinder of the same height as the window, was large (Table 1). The ratios of the usable volumes were 1.00,4.00, and 7.00 for the 16,25, and 30 mm probes, respectively. The probe dimensions were designed for this progression, which reflects growth of the rabbit heart from neonatal to adult. Table 1 also gives mean measurements of the probe Q. Values of Q for the three probes ranged from 13 1 to 194 to 185 unloaded, and from 97 to 85 to 62 when loaded to a minimum height of 90 mm (90-100% volume capacity). The tuned frequency shifted little in any of the probes after loading. The smallest change occurred with the 16 mm probe, where loading decreased the frequency to 80.92 MHz, a shift of less than 1 part in 1000. From a practical standpoint, over 200 experiments have been performed with these probes since 1985. Occasionally, accidental spillage of physiological solution flooded the probe. Because of the cylindrical assembly of the design, we were able to dismantle and clean the probe, check the Q, reshim, and resume the experiment after as little as 30 min. Figure 5 shows the mapping of the equipotential lines of the electric field on the COPPER FOIL(A)\

HEART TUBE INTERNAL

METAL I

J DIAMETER

-

FIG. 5. This is an isocontour mapping of the electrical potential for the 16 mm probe on the transverse plane cutting through the center of the cylindrical windows and the copper foil blades (A and B). The equipotential contour lines are uniform in direction in the central region. The 10% increments give the magnitude of the electrical potential as percentages of the values at the copper foil. The location of the internal boundary ( 15 mm i.d.) of the sample tube housing the heart is indicated. The metal shield has a diameter of 69.60 mm, 3.63 times the 19.16 mm diameter ofthe copper foil.

246

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transverse plane through the middle of the cylindrical windows of the 16 mm probe. The equipotential lines are perpendicular to the direction of the electric field. Equipotential lines were uniformly distributed in the central region. The copper foil blades (at A and B) diverted the magnetic flux through the openings and effectively “compressed” the curvature into a linear outline in the center. An important determinant for the degree of curvature near the opening of the windows was the ratio of the diameter of the metal housing (grounded shield), 69.60 mm, to the diameter of the copper foil. At a radius 3.63 times the radius of the copper foil (see Table 1)) the metal housing had little influence in the 16 mm probe. In contrast, at a ratio of only 2.00 in the 30 mm probe, the grounded shield tended to “squeeze” the magnetic flux lines into more of an elongated ellipsoid shape with the linear part in the center. The 25 mm probe balanced these two field-shaping influences. Within the constraints of the fixed radius of the metal stack housing, the 90” arc of the copper foil windows achieved a good compromise of field uniformity in all three probes. Figure 6 shows the lines of equal magnitude of the B1 magnetic field. The stippled areas represent cross sections through the glass of the supporting tube bearing the

L

COPPER

FOIL

FIG. 6. The isocontours are lines of equal magnitude of the magnetic field of the 16 mm probe. The percentage change in magnitude of the magnetic field is relative to the magnitude at the center. To avoid local myocardial ischemia caused by wall contact, there was a 0.5-l .O mm clearance along the internal circumference of the glass sample tube. Therefore, a less than k2.596 change in magnitude occurred throughout the central area where the heart was positioned during an experiment.

CYLINDRICALWINDOW

247

NMR PROBE

copper foil and the sample tube holding the heart. The isocontours show there was little variation in the magnitude of the magnetic field. A 0.5 to 1.O mm clearance between the epicardium and the wall of the glass tube was used to protect the heart from mechanically induced contact &hernia. Thus, for the majority of heart tissue, the magnetic field was homogeneous to within *2.5%. The larger probes also had excellent magnetic field homogeneity. Local minima appeared toward the center of the copper foil (Fig. 6), while local maxima occurred at the edges. These local maxima were due to high current density toward the edges of the copper foil, as shown in Fig. 7. The 16 mm design had the largest increase in current density at the edges, while the broader, wider copper blades used for the larger probes had more uniform current distribution. The circumferential peak intensity, shown in the mapping of the MDPA capillary standard (Fig. 3)) was consistent with the magnetic field mappings. For example, the MDPA capillary peak intensity was low at the edges of the copper due to the local maxima there, which resulted in a tip angle much larger than the 90” selected for the central region of the probe. DISCUSSION

The cylindrical-window NMR probe finds its historical roots in designs described by Ran et al. ( I ) and Lafond (3)) and the slotted tube resonator described by Schneider and Dullenkopf (2) in 1977. From the standpoint of electromagnetic theory (6, II ), a resonant structure may be a loop, cylinder, or box-like configuration with low capacitance and low inductance which enable resonance at high frequencies. The limiting case is a completely enclosed rectangular box, or “cavity resonator,” with maximum voltage developed on opposing sides (6). The resonator dimensions determine the resonant wavelength. Energy oscillates between the electric and the magnetic fields, the homogeneity of which depends on the structural design. Efficient energy storage optimizes transmitter and receiver performance for NMR probe applications. 360. 16mm

;

260.

ii 240. z ;noo-

25mm

\ 5

160.

; P 3 0

120. 60. 40 O,.,..,,l,, 14

12

IO

6

6

CIRCUMFERENTIAL

4

2

0

2

4

DISPLACEMENT

,,,I

6

6

IO

I2

I

14

(mm)

FIG. 7. The plot shows the current density in the copper foil conductive elements along the circumference in relative units. The 16, 25, and 30 mm designations correspond to the probe sires used for the neonatal, immature, and adult rabbit hearts, where the radius of the copper foil was 9.58,14.94, and 17.44 mm, respectively. The abscissa gives the circumferential distance from the center ofthe copper foil element.

248

KOST

ET

AL.

In 198 1 Hardy and Whitehead (21) developed a split-ring resonator for spectroscopy at very high frequencies (200-2000 MHz), and Hall et al. (22) later modified the design for imaging. In 1978 Hoult (4) attributed to J. Dadok a low-inductance structure where foil necessarily replaced wire in a single-turn saddle-shaped coil for high frequencies ( 100-600 MHz). In 1979 Alderman and Grant (5) published a design for a foil structure used as a decoupler. Their objective was to minimize electric fields and the associated eddy currents in the sample by employing a low-voltage, high-current, low-inductance coil, thereby reducing heat production in conductive samples ( 14, 23-25). Their design was later adapted to imaging (26). Recently, Leroy-Willig et al. (15) described a low-inductance slotted cylinder with low dielectric losses used for magnetic resonance imaging (4-40 MHz). The design of the cylindrical-window heart spectroscopy probes was based on the historical precedent of these low-inductance resonant structures. The signal-to-noise ratio for NMR signal acquisition is directly proportional to the Larmor frequency squared, the magnitude of the B1 magnetic field, and the sample volume, and inversely proportional to the square root of the sum of the resistive losses associated with the probe and the inductive and dielectric losses associated with the sample ( 14). Therefore, the usable volumes of the cylindrical-window NMR probes were selected to match heart sizes to produce the largest filling factors (see Table 1). For example, the 16, 25, or 30 mm vertical height of the window was only slightly larger than the vertical dimension of the neonatal, immature, or adult heart, respectively. The angle subtended by the window between the edges of the copper foil was selected to achieve B1 field homogeneity on the transverse plane intersecting the usable volume, so that spectroscopic measurements from hearts of different sizes and ages could be compared rationally. Excellent homogeneity assured that sampling errors related to unequal measurements from dissimilar myocardial structures (e.g., left ventricular walls, septum) would be minimal when comparing results obtained with the three probes. An angle of 90” balanced competing design factors in the three probe sizes, including the proportionately smaller percentage of usable area in the 16 mm probe and the proportionately greater influence of the grounded shield in the 30 mm probe. Use of a 90” opening agreed with other studies (2-5, 12, 15-28, 26), as summarized in Table 2. Based on theoretical analysis of a single-turn saddle coil made of wire, Ginsberg and Melchner ( 12) found that an angle of 120” between the wires was optimal for magnetic field homogeneity. Using solid conductors rather than wires, Schneider and Dullenkopf (2) selected 100.7” as the optimum angle subtended by the slot of their slotted tube design. The angle of the opening of the Alderman and Grant (5) slotted structure and similar probes (26) was based on the Schneider and Dullenkopf (2) work. Carlson ( 17) found that the optimum angle for the slotted cylinder was 82”-90”, which was within the 60”-100” span for minimization of power loss. Also, as the circumferential arc of the cylindrical conductors increased, current density was reduced and evened out (I 7). The optimum angle for the slotted-type structures listed in Table 2 ranges from an average low of 87.2” to an average high of 94.1 O,from which a midpoint of 90.7” emerges, one very close to the 90” angle selected for the cylindrical-window design. The scientific applications of the several configurations in Table 2 group into spectroscopy and imaging. Fortunately, magnetic field spatial

Schneider, 1977 (2)

Dadok, Lafond, 1978 ($4) Alderman, 1979 (5,26)

Leroy-Willig, 1985 (IS)

Joseph, 1985 (16 18)

Carlson, 1986 (17)

Present study

2

3

5

6

7

8

4

Ginsberg, 1970 (12)

1

No.

Contributor, year, and reference(s)

Cylindrical window

Theory for estimated power loss in probe

Low-inductance heart NMR spectroscopy probes

Saddle coil (of foil) Slotted cyclinder

Theory for magnetic field uniformity

Slotted cylinder

Saddle-shaped structure Slotted structure

Slotted tube

Saddle coil

Configuration of probe(s)

Two-turn distributed saddle coil Saddle coil (of foil) Slotted cylinder

imaging

Fluorine, proton, and sodium imaging coil

Low-inductance probe

High-resolution NMR spectroscopy probe for 10 mm sample tube High-frequency copper foil structure Decoupler which minimizes electric fields in sample

Theory for single-turn wire saddle cell

Purpose of theory or probe design

90

102”-134 60”-100

96”-110 82”-90

82.8”

95”

100

(Not stated)

100.7”

120

Optimum angle(s) of opening Basis for selection of angle(s)

Magnetic field homogeneity within one-half radius of center ?20% magnetic field homogeneity to 79% of coil radius Minimization of root mean square deviation in field magnitude over 70% of radius Ratio of squared magnitude of field at origin to integrated current density Magnetic field homogeneity in three probes

Cited results of No. 2, this table

-

Theoretical solution to make second derivatives of field vanish at the origin Electrostatic method

Optimum Angle for Different NMR Probe Configurations

TABLE 2

Grounded shield at 2.00 to 3.63 X radius

Grounded at (32/l 5) X radius

Grounded at (32/ 15) X radius

-

Shield diameter not specified in original publication Shield at 3 X radius

Shield at 2 X radius

Unbounded solution for height = 4 X radius

Location of surrounding zero-field boundary condition

250

KOST ET AL.

uniformity, desirable for imaging and selected spectroscopy applications (present study), and transmitter-receiver efficiency are well combined in these cylindrical structures. Current is carried in the superficial few micrometers of the copper foil (4). The current density increases toward the edges of the copper foil (17)) a natural consequence of the need to balance the net normal component of B1 away from the center of the copper foil (see Fig. 7 ) . Concentrated alternating magnetic fields induce eddy currents which produce heat and dissipate power ( 14, 23-25). These “hot spots” in the cylindrical-window NMR probes were located just outside the confines of the circumference of the glass sample tube ( see Fig. 6 ) . Apparently they did not interact significantly with the heart or the lossy perfusate inside the sample tube, except perhaps in the 30 mm probe where the flux lines surrounding these field maxima were “pushed” into the sample by the close proximity of the grounded shield. The resulting current loops in the sample inductively couple to the copper foil, increase the system noise, and tend to detune the probe. Elsewhere in the probe usable volume, the magnetic energy density, which is proportional to the field squared, was uniformly distributed. Power loss due to an alternating electric field results in heat generation in a conductive sample ( 14, 23-25). Working with copper foil surface coils, Balaban et al. (27) showed that foil in close proximity to saline can reduce relative signal-to-noise ratios due to presumed dielectric losses (14, 24) from the distributed capacitance of the conductive solution. Placement of shields above and below the cylindrical windows improved 3’P heart spectra. Gadian and Robinson (24) showed that shielding of this type reduced the dielectric losses associated with conductive solution contained within the shield, which in the cylindrical-window probe floats in potential and reduces stray electric fields. The shielding also excludes unwanted receiver signal from the regions above and below the heart. Conductivities of living tissues are of the order of 1 ohm-’ m- ‘. From the work of Gadian and Robinson (24)) an absence of shift in resonant frequency when changing from a sample of low conductivity (e.g., air) to one of high conductivity (e.g., perfusate) implies low dielectric losses. After tuning initially to 8 1.OOMHz, the decrease in frequency with perfusate loading (see Table 1) was 0.08, 0.20, and 0.32 MHz for the 16, 25, and 30 mm cylindrical-window probes, respectively. For the 16 mm probe, the shift was less than 1 part in 1000. This suggests that dielectric losses in this design were small and, due to the partitions of the myocardium, would be still smaller during heart measurements. The diameter of the grounded shield of the probes was fixed by the geometric constraints of the stack housing of the superconducting magnet. The resulting ratios of shield diameter to probe diameter were 3.63, 2.33, and 2.00 for the 16, 25, and 30 mm probes, respectively (see Table 1). Self-inductance increases about 25% with an increase in this ratio from 2 to 4, depending on the angle of the opening ( 15). In an imaging probe configuration, which was 28 cm in diameter with 85” opening angles between two cylindrical metal blades, Leroy-Willig et al. ( 15) found a ratio of 3 optimal for magnetic field homogeneity (Table 2). Ratios much less than 2 adversely affect probe Q (26)) reduce the filling factor, and add to the resistive losses. Therefore, this ratio is an important design variable. Placement of the capacitance at one end of a probe appears to influence transverse field homogeneity (16,18). Additional three-

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251

dimensional analysis of the cylindrical-window probe design would be interesting to determine the spatial distribution of the E field in the vertical direction. It is interesting that the largest Q value, about 200, was measured for the intermediate sized 25 mm probe. Pulse width (PW), which was the shortest for the smallest probe, roughly followed the relationship PW cc K( Vp/QL) ‘I* , described by Clark (28)) where VP is the usable volume of the probe, QL is the value of Q with the probe loaded with perfusate, and Kis a constant (see Table 1). Much of the change in PW was explained using this expression by the change in the probe Q in the larger sizes. In addition to these technical features, the cylindrical-window design had several practical advantages. The probes were easy to construct, inexpensive, and quickly serviceable during experiments. The extended tuning range expedited shimming on 23Na and reduced the time interval preceding “P experimental measurements. Placement of the MDPA capillary standard outside the glass sample tube avoided unnecessary mechanical trauma to the delicate neonatal and immature hearts. The magnetic field characteristics around the circumference were suitable for this standard location. The standard peak was well-defined and consistent, thereby improving comparison of a series of experiments ( 10). If necessary and desired, the standard peak could be used as a relative shift reference in an individual experiment for measurements of intracellular pH. Availability of graduated probe sizes facilitated atraumatic maximal filling of the usable active volumes with hearts from three age groups. There was excellent B, field homogeneity in all three probes, an important feature when comparing experiments with hearts from different age groups. None of the probes produced noticeable myocardial heating, which might manifest as a change in heart rate during extended control perfusion. The signal-to-noise ratios of 31P spectral peaks were excellent, even with small hearts. In summary, the practical and technical advantages of the cylindrical-window probes, and the related designs summarized in Table 2, merit consideration by those planning to construct low-inductance structures for NMR spectroscopy or imaging. The appropriate balance of design factors, which will ultimately affect the signal-to-noise characteristics, depends on the scientific application and objectives. ACKNOWLEDGMENTS This research was supported primarily by a Grant-in-Aid from the American Heart Association, California Affiliate, and with funds contributed by the American Heart Association, Central Valley Chapter. Other support included Nuclear Magnetic Resonance Awards and Faculty Research Grants from the University of California, Davis, and NIH Grant RR02479. We are indebted to the School of Engineering, University of California, Davis, for supplying the finite element sotbvare, which was modified for this research. Theoretical solutions also were obtained using MagNet, advanced computer-aided design software for electromagnetics, supplied by Mr. William Kohnen of Compunetics Technologies, Inc. (Claremont, California). REFERENCES 1. 2. 3. 4. 5.

S.KAN,P.G~NORD,C.DURET, J. SALSET,ANDC.VIBET, Rev. Sci. Instrum.44, H.J.SCHNEIDERANDP.DLJLLENKOPF, Rev.Sci.Instrum.48,68( 1977). C. LAFOND, Third cycle thesis, Universite Paris-Sud, Orsay, France. D. I. HOULT, Bog. NMR Spectrosc. 12,4 1 (1978 ). D. W. ALDERMAN AND D. M. GRANT, J. Magn. Reson. 36,447 (1979).

1725(1973).

252 6. 7. 8. 9. 10.

Il. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

KOST J. D. G. J. G. J. S. E. J. L.

ET

AL.

KRAUS , “Electromagnetics,” 3rd ed., Chap. 13, McGraw-Hill, New York, 1984. KOST, Fed. Proc. 44,437 (1985). KOST AND S. E. ANDERSON, Fed. Proc. 45,1007 (1986). ANDERSON, P. CALA, AND E. CRAGOE, Physiologist 29, 126 (1986). CHOW, D. R. OLSON, S. E. ANDERSON, Q. M. VANDERWERF, AND G. J. KOST, Comp. Meth. Prog. Biomed. 25,39 (1987). S. RAMO, J. R. WHINNERY, AND T. VAN DUZER, “Fields and Waves in Communication Electronics,” 2nd ed., Wiley, New York, 1984. D. M. GINSBERG AND M. J. MELCHNER, Rev. Sci. Znstrum. 41,122 (1970). D. I. HOULT AND R. E. RICHARDS, J. Mugn. Reson. 24,7 l(1976). D. I. HOULT AND P. C. LAUTERBUR, J. Magn. Reson. 34,425 (1979). A. LEROY -WILLIG, L. DARRASSE, J. TAQUIN, AND M. SAUZADE, Magn. Reson. Med. 2,20 (1985). P.M. JOSEPHANDJ.E.RSHMAN,M~~. Phys. 12,679(1985). J. W. CARLSON, Magn. Reson. Med. 3,778 (1986). P. M. JOSEPH AND M. SAADI-ELMANDJRA, J. Magn. Reson. 75,199 (1987). D. A. L~WTHER AND P. P. SILVESTER, “Computer-Aided Design in Magnetics,” Springer-Verlag, New York, 1986. P. P. SILVESTER AND R. L. FERRARI , “Finite Elements for Electrical Engineers,” Cambridge Univ. Press, New York, 1986. W. N. HARDY AND L. A. WHITEHEAD, Rev. Sci. Instrum. 52,2 13 (198 1). L. D. HALL, T. MARCUS, C. NEALE, B. POWELL, J. SALLOS, AND S. L. TALAGALA, J. Magn. Reson. 62,525 (1985). J. J. LED AND S. B. PETERSEN, J. Magn. Reson. 32,1(1978). D. G. GADIAN AND F. N. H. ROBINSON, J. Magn. Reson. 34,449 (1979). D. S. MCNAIR, J. Magn. Reson. 45,490 (198 1). T. A. CROSS, S. MULLER, AND W. P. AUE, J. Magn. Reson. 62,87 (1985). R. S. BALABAN, A. P. KORETSKY, AND L. A. KATZ, J. Mugn. Reson. 68,556 (1986). W. G. CLARK, Rev. Sci. Instrum. 35,3 16 (1964).