MAGNETIC RESONANCE IN MEDICINE 5, 555-562 (1987)

An MRI Phantom Material for Quantitative Relaxometry

K. A. KRAFT, P. P. FATOUROS, G. D. CLARKE, AND P. R. s. KISHORE

Department of Radiology, Medical College of Virginia/Virginia Commonwealth University, Richmond, Virginia 23298

Received April 20, 1987; revised July 17, 1987

Most phantom media in current use exhibit T, relaxation times that are significantly dependent on both temperature and operating frequency. This can introduce undesirable variability into relaxation measurements due to temperature fluctuations, and complicates direct comparison of imagers operating at different magnetic field strengths. Our investi- gations of a nickel-doped agarose gel system have demonstrated near independence of the proton relaxation rates to a wide range of temperatures and frequencies. We therefore propose the adoption of Nit+ as a relaxation modifier for phantom materials used as relaxometry standards. 0 1987 Academic Press, Inc.

INTRODUCTION

MRI phantoms have become indispensable tools for evaluating imager performance, for sequence development, and in quantitative work, such as determining the reliability of TI and T2 measurements. One characteristic of an ideal phantom material is in- dependently variable T I and T2 relaxation times, in order to reproduce the full range found in tissues and physiologic fluids. Other desirable qualities include long-term stability of relaxation parameters and ease of preparation. In addition, for quantitative comparison of imagers operating at different magnetic field strengths and having somewhat variable ambient temperatures, a phantom material having minimal fre- quency and temperature dependence of its relaxation parameters would be highly beneficial.

Most media proposed for use in phantoms suffer deficiencies which render them nonideal. Aqueous paramagnetic solutions ( I ) generally exhibit nonphysiologically long Tz relaxation times relative to T I . Pure gels (e.g., gelatin (2), agar (3), polyvinyl alcohol ( 4 ) , silicone (3, polyacrylamide (6), and agarose (7)) are usually inadequate because of the difficulty of changing TI over a large range independently of Tz. The incorporation of nonaqueous components (e.g., glycerol (2)) into gels as a TI modifier may lead to chemical-shift artifacts in images. A possible concern with the use of graphite (2, 4 ) as a Tz modifier is an inadvertent nonuniform dispersal throughout the gel due to sedimentation.

Perhaps the simplest and most versatile formulations for tissue-mimicking phantom media are paramagnetically doped gels. In these systems, the proton T I rates are con- veniently modulated by varying the paramagnetic ion concentration, whereas the T2 rates are primarily a function of the concentration of gelling agent. Agar and agarose gels incorporating copper, manganese, and nickel ions have been studied (3, 7). One

555 0740-3194/87 $3.00 Copyright 0 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.

556 KRAFT ET AL.

apparently neglected factor in the choice of paramagnetic solutes is the temperature and magnetic field dependence of the proton relaxation rates. Aqueous solutions of both Cu2+ and Mn", among others, exhibit relaxation rates that are strongly dependent on both temperature and frequency. In addition, Mn2+ is an efficient T2 relaxer and therefore is not desirable as an independent modulator of TI. Solutions of Ni2+, how- ever, as well as several other paramagnetic aquoions, exhibit proton relaxation times that are much less sensitive to temperature and magnetic field fluctuations. We report here experiments demonstrating the superiority of nickel in these respects, and offer a qualitative explanation based on the accepted theory of paramagnetic relaxation. Using paramagnetically doped agarose gels as a model system, we conclude that nickel is in general a better choice for a TI modulator in phantom materials, especially for use in quantitative relaxometry.

MATERIALS AND METHODS

Agarose gels doped with copper sulfate or nickel chloride were prepared as previously described (7). No pH adjustment of the paramagnetic stock solutions was carried out. Most spectroscopic relaxation time measurements of solutions and gels were performed on a Bruker Biospec imager/spectrometer interfaced to a 40-cm-bore 2.35-T magnet (proton Larmor frequency 100 MHz).

Samples were contained in 25-ml glass vials and placed within the central homo- geneous BI field of a 16-cm proton imaging coil used as both transmitter and receiver. TI relaxation was measured using the inversion recovery method with 12 variable delays; T2 times were evaluated via the Carr-Purcell-Meiboom-Gill sequence using 9 variable delays. Relaxation times were extracted from a computer fit of the intensity data using a three-parameter exponential function.

For temperature dependence studies, samples were heated or cooled to the approx- imate desired temperature and then simply encased in a precut block of polystyrene to afford thermal insulation. Temperatures were monitored using a copper-constantan thermocouple, and were generally found to vary by less than 1 "C during the relaxation measurement. Temperatures were varied from near 0°C to a maximum of 65"C, safely below the remelting point of the agarose gels.

The magnetic field dependence of TI for both solutions and gels was measured using a variety of MR instruments. Spectroscopic data were obtained at 0.12 T (Larmor frequency 5 MHz), 2.4 T (100 MHz, Bruker Biospec), 6.3 T (270 MHz, IBM/Bruker AF270), and, from the literature (8), 0.047 T (2 MHz). Supplemental imaging TI measurements were obtained at 1.0 T (42 MHz, Siemens Magnetom) and 1.5 T (64 MHz, General Electric Signa) using either an inversion recovery or a variable TR spin-echo sequence, with TI times determined from a multiparametric exponential fit to the data.

RESULTS

The temperature dependence of the proton relaxation times for various aqueous paramagnetic solutions has been investigated by several workers (9-1 I). We repeated TI measurements for selected paramagnetic species as a function of temperature at 100 MHz. The results (Fig. 1) indicate that Cu2+ and Mn2+ solutions exhibit TI re-

MRI PHANTOM FOR QUANTITATIVE RELAXOMETRY 557

FIG. 1. The temperature dependence of the proton T, values for several aqueous paramagnetic solutions at 100 MHz.

laxation times which increase rapidly with temperature, whereas the TI of Ni2+ and Co2' solutions are much less temperature dependent. These data suggested that gels doped with nickel and cobalt might constitute more suitable standards for relaxation measurements than corresponding copper or manganese-doped gels. Figure 2 displays the temperature dependence of both TI and T2 for 2% agarose gels doped with either 2 mMCu2+ or 5 mMNi2+. Although the temperature dependences of T, are analogous to those seen in solution, the T2 values are determined primarily by the gel concen- tration, and hence their variation with temperature is muted.

A systematic study of the temperature dependence of TI and T2 for a series of nickel- doped agarose gels was undertaken. Four agarose concentrations (0.5, 1, 2, and 4%), as well as three nickel concentrations ( I , 2, and 5 mM), were employed. Representative data from samples containing 1% agarose (Fig. 3) demonstrate that only at low nickel concentrations does the TI temperature dependence become significant.

TI and T2 data (interpolated to 20°C) were tabulated for the 12 samples and are plotted against each other in Fig. 4 to show the functional effect of varying the agarose or nickel concentrations. From the figure, it is evident that T2 is largely a function of

558

./ 0.1 - 2% AGAROSE

0.002 M CuSOa

2% AGAROSE

T' 0.OOSM NiClp

a-

/: 0.6 -

(S) . TI T2

0'4: 0.2 - -=. . /; 1 -0-. @J?._,_

10 20 30 40 50

KRAFT ET AL.

.

the gel concentration, and that T, is almost solely dependent on the metal ion con- centration. At the lower gel concentrations the nickel begins to compete effectively with the gel matrix in reducing the observed T2 relaxation time, thus washing out the independence of T2 on nickel concentration. Nevertheless, a plot such as Fig. 4 is

TI (i mM NI)

o/

20 30 40 50 60 10

T, "C

FIG. 3. The temperature dependence at 100 MHz of T , and T2 for several 1% agarose gel samples doped with varying concentrations of Ni".

MRI PHANTOM FOR QUANTITATIVE RELAXOMETRY 559

FIG. 4. Proton T I versus 7; plot for 12 Ni2+-doped agarose gels at 20°C. The numbered columns denote the percentage agarose in each sample; the rows are labeled with the Ni2+ concentration.

useful for estimating by interpolation the composition of gels necessary to mimic a wide range of physiologically relevant T,/T2 combinations.

Proton relaxation in aqueous paramagnetic solutions has also been previously studied as a function of magnetic field strength (12-14). Comparative NMR dispersion data (15 ) show that many commonly employed paramagnetic relaxation modifiers, in- cluding Mn2+ and Cu2+, exhibit a pronounced frequency dependence in aqueous so- lution over the approximate Larmor frequency range l to 100 MHz. Figure 5 shows our results of a limited TI frequency-dependent study of both 5 mM aqueous Ni2+ and a sample of 1% agarose gel doped with 2 m M Ni2+. Similar data for 2 mM Cu2+ (aq.) and a copper-doped agarose gel are also included in the figure for comparative purposes. Although the proton relaxation rates for the copper-containing samples are clearly field dependent, those of the nickel-doped analogs exhibit no apparent frequency dependence up to at least 100 MHz at room temperature. In addition, the field de- pendence of the two paramagnetically doped gels appears to approximate that of the corresponding aqueous solutions. The measurements for aqueous copper are empir- ically in agreement with the results of Koenig and Brown (15). The results for aqueous nickel are in general agreement with those of other investigators (16, 17).

DISCUSSION

The data presented demonstrate that the TI dependence of paramagnetically doped gels on temperature and magnetic field strength closely approximates solution behavior, and may therefore be expected to be amenable to analysis in terms of the Solomon- Bloembergen-Morgan theory (11, 18-20). Proton relaxation in this formalism is mod- eled as the sum of an electron-nuclear dipolar interaction and a scalar coupling, which for certain paramagnets (notably Mn2+ (aq.)) contributes significantly to proton re- laxation. The interactions are modulated according to an overall correlation time ( T ~ )

which includes contributions from molecular reorientation, ligand exchange on and

560

6 .

5 -

4 -

l /T i ,s '

3 -

2 -

1 -

KRAFT ET AL.

0

--o 0 0-0-0- -

0 -. Q-0-

I . 1 10 100 1wO

Proton Larmor Frequency , MHz

FIG. 5 . The magnetic field dependence of the proton T , for Cuz+- and Nizf-doped water and agarose gels at 22°C. Open squares, 5 mMNi2+ (aq.); closed squares, I % agarose gel doped with 2 mMNi2+; open circles, 2 mM Cuz+ (aq.); closed circles, 2% agarose gel doped with 2 mM Cuzc. The dispersion curve for Ni2+ (aq.) between 100 and 270 MHz is known to vary with temperature; the dashed segment indicates uncertainty regarding its exact shape.

off the aquoion, and electron spin relaxation of the paramagnet. It is now recognized that for many of the commonly employed paramagnetic relaxation enhancers, 7c in aqueous solution is dominated by either reorientational tumbling or electron spin relaxation, which in turn dictates the gross temperature and magnetic field dependence of the proton relaxation rates.

A group of aquoions including Cu2+, Mn2+, Gd3+, and Fe3+ all have intrinsically long electron relaxation times, and their dipolar correlation times are instead deter- mined by their tumbling rate in solution, which for all small hydrated ions is of the order 10" s-'. The strong temperature dependence of proton TI values in these so- lutions directly reflects the exponential dependence of the aquoion reorientational correlation time on temperature (cf. Fig. I). The magnetic field dispersion of TI in these solutions exhibits an inflection point at the field value where the product of the electron Larmor frequency (us) and the correlation time T~ equals unity. The similarity of the hydrodynamic properties among these aquoions results in comparable reori- entational correlation times and hence nearly superimposable dispersion curves, es- sentially differing only in terms of absolute relaxivity over the approximate proton Larmor frequency range 1 to 100 MHz (15).

Examples of aquoions having their correlation times dominated by fast electron spin relaxation (ca. s) are Ni2+, Co2+, Nd3+, and Fe2+. For this category of aquoions, the reorientational motion is masked by a faster electron relaxation rate, thereby reducing the temperature dependence of the proton TI (Fig. 1). Another con- sequence of the short T~ of these paramagnetic complexes is a shift in the expected magnetic field dispersion to considerably higher field strengths. In practical terms this means that extreme narrowing conditions ( w g C 6 1, o l ~ c 6 1, where wI is the proton Larmor frequency) remain valid throughout the magnetic field range within which

MRI PHANTOM FOR QUANTITATIVE RELAXOMETRY 56 1

most imagers operate, resulting in substantially field-independent proton relaxation times over that regime. At very high magnetic field strengths (>4 T) additional field- dependent relaxation mechanisms may come into prominence (21, 22), thereby strongly increasing the proton relaxivity of the aquoions, as seen for nickel at 6.3 T (Fig. 5 ) .

Unlike the TI relaxation time, which is primarily a function of the paramagnetic ion concentration, the T2 of doped gels is most strongly dependent on the gel con- centration. This is demonstrated by the data in Figs. 3 and 4 and also by the comparative temperature dependence of the proton relaxation times of copper- and nickel-doped agarose gels (Fig. 2). The T2 temperature dependence of aqueous copper solutions would roughly parallel that of TI (Fig. 1). (For copper solutions at 100 MHz the ratio T,/T2 = 3.5/3, whereas in the low field limit TI and T2 are identical.) Figure 2 shows that although the TI temperature dependence of copper-doped gel resembles the so- lution data, that of T2 does not, and is in fact identical to T2 data (not shown) for undoped agarose.

Because T2 relaxation in doped gels is not primarily mediated through paramagnetic interactions, it cannot be addressed using the Solomon-Bloembergen-Morgan theory. Instead, proton T2 relaxation in gels may be described using a two-state model wherein a free water component undergoes rapid exchange with a water fraction bound to macromolecules (23). In this formalism the observed relaxation rate is considered to represent a weighted average of the individual free and bound contributions. Most tissue relaxation data may be adequately described within the two-state framework (24) . Qualitatively, proton T2 relaxation in both tissues and gels is primarily due to magnetic field heterogeneity at the molecular level associated with the bound water component, and is not significantly influenced by fast motional processes. Hence T2 values in these systems are found to be virtually independent of frequency (24) .

Using NMR, the aquated Ni2+ ion has been studied via its interaction with oxygen- 17 (25), nitrogen-15 (26), and water protons (16, 17). An investigation of proton TI relaxation in nickel solutions as a function of temperature, frequency, and pH dem- onstrated a small but significant TI rate dependence on all three parameters (1 7). One observation from this work (1 7) is that at the three pH values considered, the frequency dependence of the proton TI is fortuitously minimized in the vicinity of room tem- perature, but undergoes somewhat greater fluctuation at either higher or lower tem- peratures. A similar result would be expected for nickel-doped gels.

CONCLUSION

Although paramagnetic complexes in general have been of interest recently because of their possible use as clinical imaging contrast agents, nickel and other metals have been excluded on the basis of their low proton relaxivity. Because metal toxicity man- dates that doses of contrast agents be kept to a minimum, an intrinsically low relaxivity is a problem in viva However, for use in phantoms, the proton relaxation characteristics of Ni2+ (as.) render it a nearly ideal paramagnetic relaxagent. Its incorporation into agarose gels results in a versatile phantom material whose TI and T2 times may be varied nearly independently. Stability of such gels over periods in excess of 1 year have been reported (7). We conclude that the near independence of the proton relax-

562 KRAFT ET AL.

ation times of nickel-doped agarose gels to a wide range of temperatures and frequencies well justifies their use in quantitative imaging relaxometry.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the cooperation of Dr. David Hoult and his colleagues, Drs. C.-N. Chen and L. K. Hedges, in providing relaxation data at 5 MHz.

REFERENCES

I . N. J. SCHNEIDERS, R. N. BRYAN, J. FORD, A N D M. R. WILLCOTT, “Annual Meeting of the Society of

2. E. L. MADSEN AND G. D. FULLERTON, Magn. Reson. Imaging 1, I35 (1982).

4 . 1. MANO, H. GOSHIMA, M. NAMBU, AND M. 110, Mugn. Reson. Med. 3,921 (1986).

Magnetic Resonance in Medicine, 1982,” pp. 137-1 38. [Abstracts]

3. R. MATHUR-DE VRE, R. GRIMEE, F. PARMENTIER, A N D J. BINET, Mugn. &?Son. Med. 2, 176 (1985).

5. D. c. GOLDSTEIN, H. L. KUNDEL, M, E. DAUBE-WITHERSPOON. L. E. THIBAULT, A N D E. J. GOLDSTEIN, lnvrsl. Radio!. 22, 153 (1987).

6. F. DELUCA, B. MARAVIGLIA, AND A. MERCURIO, Ma@. Reson. Med. 4, I89 (1987). 7. M. D. MITCHELL, H. L. KUNDEL, L. AXEL, A N D P. M. JOSEPH, Mugn. Reson. Imugmg 4,263 (1986). 8 M. NITTA el at., “Annwai Meeting of Jupunese Suciery of Radiological Technology, 1984.” 9. R. HAUSSER ANDG. LAUKIEN, Z. Php. 153, 394 (1959).

10. R. A. BERNHEIM, T. H. BROWN, H. S. GUTOWSKY, A N D D. E. WOESSNER, J. Chem. Phy.~. 30,950

11. N. BLOEMBERGEN AND L. 0. MORGAN, J. Chem. Phys. 34,842 (1961). 12. A. W. NOLLE A N D L. 0. MORGAN, J. Chem. Phys. 26, 642 (1957). 13. L. 0. MORGAN A N D A. W. NOLLE, J. Chern. P h j ~ 31, 365 (1959). 14. R. HAUSSER AND F. NOACK, 2 Phys. 182,93 (1964). 15. s. H. KOENIG AND R. D. BROWN, Mugn. Reson. Med. 1,478 (1984). 16. H. L. FRIEDMAN, M. HOLZ, AND H. G. HERTZ, J. Chem. Phys. 70. 3369 (1979). i7 . H. G. HERTZ AND M. HOLZ, J. Mugn. Reson. 63, 64 ( I 985). 18. I. SOLOMON, Phys. Rev. 99, 559 (1955). 19. 1. SOLOMON AND N. BLOEMBERGEN, J . Chem. Phys. 25,261 (1956). 20. N. BLOEMBERGEN, J . Chem. Phvs. 27, 572 (1957). 21 M. GUERON, J. Mugn. Reson 19, 58 (1975). 22. A. J. VEGA A N D D. FIAT, Mol. P h y ~ . 31, 347 ( 1976). 23. R. COOKE AND R. WIEN, Bioyhy.s. J. 11, 1002 ( I97 1). 24. P. A. BOTTOMLEY, T. H. FOSTER, R. E. ARGERSINGER, AND L. M. PFEIFER, Med. Phys. 11,425 (1984). 25. J. W. NEELY AND R. E. CONNICK, J. Amrr. Chem. Soc. 94, 3419 (1972). 26. N. BENETIS, J. KOWALEWSKI, AND L. NORDENSKIOLD, J . M a p . Reson. 58,282 (1984).

( 1959).