Ni-DTPA doped agarose gel—A phantom material for Gd-DTPA enhancement measurements

Magneric Resonance Printed in the USA.

Imugging, All rights

Vol. 1 I, pp. reserved.

125-133,

1993 Copyright

0

0730-725X/93 $6.00 + .oO 1992 Pergamon Press Ltd.

l Original Contribution

Ni-DTPA DOPED AGAROSE GEL -A FOR Gd-DTPA ENHANCEMENT

PHANTOM MATERIAL MEASUREMENTS

P.S. TOFTS,* B. SHUTER,~~ AND J.M.

POPE?

*Institute of Neurology, Queen Square, London WClN 3BG, United Kingdom tSchoo1 of Physics, University of New South Wales, Kensington, NSW 2033, and Royal North Shore Hospital, St. Leonards, NSW 2065, Australia In order to study the relationship between the concentration of Gd-DTPA in tissue, and the resulting changes in relaxation times and signal intensity, a phantom material that has similar relaxation times to tissue and that can be doped with Gd-DTPA is required. The “tissue-equivalent” material should not contain Gd; nor should it alter the relaxivities of Gd-DTPA from their values in aqueous solution (R, = 4.5 set-’ mM-‘; R, = 5.5 set-’ mM-’ at 1.5 T). Conventional materials, based on CuSO,-, MnC12-, or GdCI,/LaCI,-agarose mixtures, are not suitable, since Gd is displaced from the GCDTPA chelate. The new material, consisting of Ni-DTPA dissolved in agarose, is easy to prepare and does not interact with Gd-DTPA. Its relaxation times are stable; relaxivity RI was within 4% of its aqueous value over 109 days. Tts have low dependence on temperature (0.2-1.0%/°C at 21°C) and on field strength, allowing the material to be used as a relaxation time standard for quality assurance. Equations giving the concentration of Ni-DTPA and agarose to produce a required ?‘t and T2 are provided. Keywords:

Phantom

material; Agarose; Gel; Relaxation

Ni-DTPA.

clear, and appropriate designs may be impossible to construct. To characterise the instrument, the aqueous values of relaxivity are the most appropriate, since these are well defined and easily measured. The ideal tissue equivalent material should therefore have the following properties:

INTRODUCTION

The concentration of Gd-DTPA in tissue can, in principle, be measured from the signal enhancement, or from the change in relaxation times, resulting from the presence of Gd-DTPA in the tissue.’ In vitro simulation of relevant tissue properties is a valuable technique for studying the properties of Gd-DTPA under controlled conditions, the major properties affecting signal enhancement being tissue Ti and Gd-DTPA relaxivities. This allows our model of the performance of the magnetic resonance imaging instrument (i.e., predictions of the signal enhancement, and change in measured relaxation times, produced by particular concentrations of Gd-DTPA) to be confirmed. Only when the instrument has been characterised in this way, using objects of known Gd-DTPA concentration, can it be used to measure concentrations of Gd-DTPA in vivo. In vivo values of relaxivity may be slightly altered from the in vitro (aqueous solution) values; however this is hard to simulate in a phantom material since the causes and amount of alteration (if any) are still unRECEIVED5/12/92;

times; Gd-DTPA;

1. It should not contain Gd, since we wish to establish an unambiguous relationship between signal enhancement [or the change in measured relaxation time(s)] and the concentration of Gd-DTPA in the material. 2. The relaxivity of Gd-DTPA in the material should be the same as it is in aqueous solution. That is, the change in l/T, or l/T2 caused by adding a particular concentration of Gd-DTPA to the tissue should be the same as the change caused by adding the same concentration of Gd-DTPA to water. Provided that Gd-DTPA does not bind, or interact, with any constituent of the tissue equivalent material, we expect this latter condition to be met. 3. It should be possible to produce any required value STo whom correspondence should be addressed.

ACCEPTED7/15/92. 125

126

Magnetic

Resonance

Imaging

of Tr and T2 (within the clinical range) by appropriate choice of the concentrations of the constituent materials. 4. It should have stable T, and T2 values that are, as far as possible, independent of temperature, and of field strength. Early work on tissue equivalent materials used solutions of paramagnetic salts, usually CuS04 or MnCl*, to reduce the relaxation times of water. Unfortunately Tl and T2 could not be chosen independently, and two-component mixtures were developed. These consisted of agar doped with MnC12,* agarose doped with CUSO~,~ and agarose doped with a GdC13/LaC13 mixture. 4,5 By measuring the relaxivities of each component, a material can be designed to give any required relaxation times between those of the constituent components.6 Howe’ investigated Niz+-doped agarose mixtures at 0.08 T, and demonstrated their reduced T, temperature coefficients. These ionic mixtures may be adequate if other ionic compounds are to be added, provided that they do not react with those already in the mixture (for example by precipitation). They are used routinely for quality control standards, and for intercomparisons between MRI machines at different sites. They cannot be used as a tissue-equivalent material to which Gd-DTPA, or any other Gd chelate, is to be added, since interaction and a subsequent change in relaxivities occurs. We have therefore investigated metals chelated with DTPA as dopants for agarose. While the T, s of Cu*+, Mn*+, and Gd3+ are strongly dependent on temperature and field, that of Ni*+ is relatively independent of temperature and field.’ This is because the correlation time for Ni*+ is dominated by electron spin relaxation, which gives a correlation time fast enough for complete motional narrowing at all practical fields, regardless of temperature.’ We have therefore used Ni*+, in preference to Cu*+, Mn*+, or Gd3+, to dope agarose; this gives the advantage of reduced T, temperature dependence compared to conventional mixtures. We show explicitly the effect of interaction between and between Ni*+ and Gdcu*+ and Gd-DTPA, DTPA. The evidence for interaction is the observation that the relaxation rate of the mixture is more than the sum of the relaxation rates produced by each individual component measured in isolation. The interaction of metallic salts CuSO, and NiC12 with Gd-DTPA was studied in aqueous solution. A new material is described, consisting of Ni-DTPA in agarose, which does not react with Gd-DTPA, and has the required low dependence on temperature and field. A summary of this work has been presented previously.9

0 Volume

11, Number

1, 1993

METHODS All measurements were made on the General Electric Signa 1.5 T whole body clinical imager at the Royal North Shore Hospital, Sydney, using the head coil (bird-cage resonator) for transmit and receive. Images (256 x 128) were collected from a 16-cm field of view. Slice thickness was 3 mm. A hexagonal array of 13 25mm diameter bottles, supported in an expanded polystyrene block, was scanned with an axial slice. All measurements were made at room temperature (21 “C) except those on the temperature dependence of the relaxation times of the tissue-equivalent material. Tl measurements were made using a set of spinecho images with a range of TR values (4000, 2000, 1000, 500, 240, 120, 60 msec), and TE = 25 msec. The manufacturer’s pulse sequence CSMEMP (contiguous slice multi-echo multi-planar) was used to provide a good slice profile (by means of a numerically optimised RF pulse and a gradient that varies during slice selection). A region of interest approximately 1.5 cm* in area placed on the TR = 4000 msec image and the manufacturer’s least squares fitting program were used to calculate a Tl value from all the images. The accuracy of the T, values could not be confirmed directly, but good agreement with T,s obtained spectroscopically on the same machine has previously been reported. lo The linearity of the (l/T, vs. concentration) graph for Gd-DTPA in aqueous solution (see below) suggests that there are no gross errors in the T, values. An intercomparison of measured T, values for a set of gels with Tl values in the range 60-2800 msec was made with an identical imager and procedure at another site (NMR research group, Institute of Neurology, Queen Square, London) that had access to calibrated gels. The mean difference between the two sites was 6 msec (not significant), and the maximum 49 msec (3% of T,). Linear regression yielded T, (QSL) = 1.02 T, (RNSH) - 5 msec, where QSL denotes Queen Square London, and RNSH is Royal North Shore Hospital, Sydney. The accuracy of measurements made at Queen Square on the calibrated gels (covering 2001600 msec) was always within 16070, and over the more restricted range of 200-1000 msec, corresponding to the clinical range, it was always within 7% (mean 3%). We expect some inaccuracy in Tls below about 60 msec (the shortest TR used), and above about 4 set (the longest TR used). These correspond to T;’ > 17 set-’ and T[’ < 0.25 set-r . Nonuniformity of T, values was investigated using a 16-cm polythene container filled with MnC12 solution. Tl values were measured in 26 regions evenly distributed within a central circle 12 cm in diameter. The values were all within 3% of the mean value (915 msec).

Ni-DTPA

doped

agarose

An error AT, in a T, measurement propagates to an error in l/T, of A(l/T,) = AT,/T:. Hence errors in measurements of lightly doped gels (long T,) are less important, and these samples were placed near the periphery of the field of view, where the uniformity is worst, keeping the central (uniform) regions for the heavily doped (short TI) gels. T, measurements were made using a set of single echo images SE2000125, SE2000/50, SE2000/100, SE2000/200, SE2000/400 and the CSMEMP sequence. The manufacturer’s least squares fitting program calculated T2 from all images in a region of interest approximately 1.5 cm2 in area placed on the SE2000/25 image. These gave longer T2 values than the manufacturer’s multi-echo sequence (SE2000/20,40,60,80), and smoother decay curves. Measured T2 in distilled water (not deoxygenated) was about 1000 msec for the single echo set, and 200 msec for the multi-echo set. Measurements on a Bruker 4.7 T spectrometer gave 2.1 set using a multi-echo technique. Published values measured on spectrometers are in the range 1.8-2.6 set (three groups). l1 The longer (and more accurate) value obtained using the single echo sequence led us to use this in preference to the multi-echo sequence. We expect that the most likely instrumental errors would reduce measured values of T2 (rather than increase them), by adding extra sources of decay of the transverse magnetisation. We expect that the relaxation rate l/T, would be increased by a given amount, independent of the true T2. This error is about 0.5 see-’ (using the measured value for water [l set], and assuming the true T2 of water is 2 set). This is smaller than all the measured relaxation rates (see below). Any such errors will be present in both undoped and doped gels, and therefore will not affect the measurement of relaxivity R2, which only depends on differences in l/T, values (i.e., relaxation rates), not on absolute values of T2. We therefore expect the measured values of R2 to be accurate. An intercomparison of measured T2 values over the range 45-330 msec was made with the imager at Queen Square, London. The mean difference between the two sites was 0.7 msec (not significant), and maximum difference 4 msec. Linear regression gave T,(QSL) = 1 .OO T,(RNSH) + 0.9 msec. The accuracy of measurements made at Queen Square on the calibrated gels (covering 50-370 msec) was within 11%. Uniformity was measured using an array of gels made up identically. Over a 14 cm diameter area, the range was ?2% (mean value 201 msec). For Cd-DTPA in aqueous solution, additional echoes were collected at 75 and 800 msec. For Cd-DTPA in 2% agarose gel (no Ni-DTPA) echo times 20-200 msec were used. Ni-DTPA was made up by addition of excess

gel 0 P.S. TOFTS ET AL.

127

DTPA (Aldrich 98%) (2:l) to NiC12. The solution was neutralised with NaOH or KOH (agarose will not gel at low pH). Agarose gels were prepared as follows. Agarose powder (Sigma type 1) was weighed and then added to 50 ml of doped water. A number of bottles containing the mixtures were gently warmed in a microwave oven at low power for 8-10 min, with frequent pauses for swirling and taking care not to scald the gel. Once the mixture was completely clear, with no signs of translucent strands, it was boiled for 3060 set to ensure complete mixing, adjusted for water loss, shaken, and boiled again briefly. The solution was then poured into the bottles; these were topped up as the gel cooled and contracted. The lids were screwed up tightly, expelling excess gel and leaving very little air in the bottle. Gels invariably had a uniform appearance in the image. The temperature dependence of the relaxation times of some gels was studied using a commercially available expanded polystyrene vessel (designed for transporting cooled food and drink). The temperature was measured with a laboratory mercury-in-glass thermometer. Gels were allowed to equilibrate in the vessel in water at the appropriate temperature. The lid of the vessel was then fixed in place and the apparatus examined on the Signa in the usual way. On completion of data collection the temperature was again measured; it was always within 1“C of the temperature just before fixing the lid.

RESULTS Aqueous Solutions of Gd-DTPA The T,s and T2s of aqueous solutions of GdDTPA in concentrations up to 4 mM were measured. Linear regression of the data gave l/T, = (0.2 f 0.2) set-’ + (4.50 f O.O4)[Gd] set-’ mM-‘, and l/T2 = (0.8 f 0.2) set-’ + (5.49 +- O.O6)[Gd] set-’ mM-‘. We have given (result f standard error); [Gd] is the concentration of Gd in mM. The TI data are shown in Fig. 1, labeled “Gd-DTPA only.” Gd-DTPA in 2% Agarose Gel The TIs and T2s of 2% agarose gels containing Gd-DTPA in concentrations up to 8 mM were measured. 1/T, versus [Gd-DTPA] was linear up to 4 mM (i.e., T, 2 56 msec), fitting l/T, = (0.2 f 0.2) see-’ + (4.37 f 0.04) [Gd] sect’ mM-‘. l/T, versus [GdDTPA] was linear over the range l-8 mM, fitting l/T2 = (16.8 f 0.3) set-’ + (5.44 f O.O5)[Gd] see-’ mM-‘. At lower [Gd-DTPA] T2 appeared independent of concentration. Interaction Between Cu2+ and Gd-DTPA The TI s of aqueous solutions of Gd-DTPA and 1.6 mM CuSO4 were measured (Fig. 1). This concentration

Magnetic Resonance Imaging 0 Volume 11, Number 1, 1993

128

[Gd-DTPA]

+ +

Gd-DTPA

only

-X-

Gd-DTPA

+1.6mMCuSO4

---

Gd3+

Fig. 1. Interaction between Cu2+ and Gd-DTPA in aqueous solution at 1.5 T and 21°C. For Gd-DTPA only, the data fit l/T, = 0.2 set-r + 4.50[Gd] set-’ mM_r. For GdDTPA + 1.6 mM CuS04, there is clear evidence of interaction. At low [Gd] the slope of the curve approaches the Rr measured for Gd3+ (13.2 set-’ mM-r; dotted line).

of CuS04 has a T’ (752 msec), in the absence of GdDTPA, appropriate for a tissue substitute. The solutions were measured 24 hr after production. The plot of l/T’ versus [Gd] was nonlinear. As the concentration of Gd-DTPA increased, the relaxation rate increased dramatically, to much more than the sum of the rates produced by the individual components (CuS04 and Gd-DTPA) in solution. The initial slope of the plot, over the range [Gd] = O-O.5 mM, is 10.66 set-’ mM-‘, approaching the relaxivity measured for free Gd3+ ions (13.2 set-’ mM-‘). We interpret this to inGd from Gd-DTPA, dicate that Cu2+ is displacing forming free Gd3+ ions.

Gd-DTPA X

1

only

Gd-DTPA+Ni2+

(32dJ

- - -

(mM)

Gd-DTPA+NQ+

(1 d)

Gd-DTPA+N12+H

+

Gd-DTPA+N12+

(6d)

16d)

Fig. 2. Interaction between Ni2+ and Cd-DTPA in aqueous solution at 1.5 T and 21°C. For Gd-DTPA only, the fit of Fig. 1 is shown. For Gd-DTPA + 2 mM NiC12, the gels were measured at times 1, 6, 32, and 116 days after manufacture. Data at 116 days are shown as a broken line to avoid confusion with the nearby 32 day data. There is clear evidence of interaction, increasing with time. This is probably the result of displacement of Gd from the DTPA.

these added ions were themselves chelated with DTPA before addition to Gd-DTPA, then little or no interaction should take place. To ensure that there were no free ions remaining, the approach to chelation was studied (Fig. 3). We observed changes in Tl in aqueous solutions of the metals Cu2+, Ni2+, and Gd3+ as DTPA (pH 7-8, measured with universal indicator paper, and adjusted with NaOH) was added and gauged complete chelation by the leveling off of the l/T’ curve at higher DTPA:metaI ratios. On this criterion, for Gd3+ and Ni2+ ions, DTPA:metal ratios > 1.6 ap-

Interaction Between NiZt and Gd-DTPA The Tls of aqueous solutions of Gd-DTPA

and 2 mM of NiC12 were measured (Fig. 2). This concentration of NiCl* has a T, (695 msec), in the absence of Cd-DTPA, appropriate for a tissue substitute. The solutions were measured at a range of times (1,6,32, and 116 days) after production. The plots of l/T, versus [Gd] were nonlinear at all times. The relaxation rates again increased dramatically, to much more than the sum of the rates produced by the individual components (NiC& and Gd-DTPA) in solution, and these rates increased with time. ~--I-

GdCD0.5mM

x

CuSO45mM

-

NiCl2 5mM

1

Interaction Between Metals and DTPA The increased relaxivity observed when Cu’+ and Ni2+ ions are added to Gd-DTPA supports the view that Gd3+ is displaced from Gd-DTPA (Figs. 1, 2). If

Fig. 3. Interaction between metal ions and DTPA at 1.5 T and 21°C. Metal concentrations were CuSO,: 5 mM; NiCl,: 5 mM; GdCI,: 0.5 mM.

Ni-DTPA doped agarose gel 0 P.S. TOFTSET AL.

129

peared sufficient to ensure chelation. For Cu2+ ions it seemed that a DTPA:CuSO, ratio of 0.5 was sufficient to ensure chelation, the slower l/T, reduction at higher ratios probably indicating the formation of more complex Cu-DTPA chelates. ‘* Interaction Between Ni-DTPA and Gd-DTPA in Tissue Equivalent Material From the results of the interaction studies (Figs. l3), it was expected that Ni-DTPA would be a more suitable dopant than Cu*+ or Ni*+. A concentration of 4 mM Ni-DTPA in 2% agarose has suitable relaxation times for a tissue equivalent material (T1 = 1434 msec, T2 = 54 msec). These concentrations were chosen to test the hypothesis that varying amounts of GdDTPA (l/16 to 4 mM) could be added to such a tissue substitute without any interaction. The gels were scanned 1 day after production and then again at 9, 16, 23, and 109 days after production to assess the stability of their relaxation times. Figure 4 shows the data for freshly prepared gels (day 1). Data for older gels are almost identical. There was no visible non-linearity in the plot of Ti’ versus [Cd-DTPA], and the slope of the plot was very close to that for aqueous solution. Linear regressions of T, and T2 data versus Gd-DTPA concentration are shown in Table 1. The values of R, relaxivity in Ni-DTPA doped gel (R, = 4.44-4.69 set-’ mM-‘) are very close to the values measured in aqueous solution (4.50 f 0.04) and in gel alone (no Ni-DTPA) (4.37 f 0.04). Similarly the values of R2 relaxivity in Ni-DTPA doped gel (R2 = 5.14-5.27 set-’ mM_‘) are close to the values measured in aqueous solution (5.49 f 0.06) and in gel alone (no Ni-DTPA) (5.44 + 0.05). This indicates that there is no significant interaction between Gd-DTPA and the tissue equivalent material. The changes in relaxivities over the time were small and random. The changes in fitted values of T;’ and TF’ in undoped gel, the first term in each regression, were also small and ran-

oi.

of Gd-DTPA

with 4 mM Ni-DTPA

T,-‘, T;’ in set- ‘; [Cd] is millimolar (mM).

(0.7 (0.6 (0.6 (0.8 (0.7 (0.2 (0.2

f f + k + f f

0.1) 0.2) 0.4) 0.2) 0.1) 0.2) 0.2)

+ + + + + + +

+

3

3.5

GdDTPA + Ni-DTPA -

fitted

14 1

Relaxation Properties of Tissue Equivalent Material Having established that Ni-DTPA in agarose is a suitable tissue equivalent material, its relaxation properties were measured in more detail, for a range of agarose concentrations (0, 0.5%, 1’70, 2%, 4%) and Ni-DTPA concentrations (0, 4 mM, 8 mM, 16 mM) at pH 7-8 (adjusted with NaOH). At each concentra-

tion of agarose, the relaxivities R1 and R2 of Ni-DTPA were measured by linear regression of the relaxation rates l/T,, l/T2 against concentration of Ni-DTPA. Tables 2 and 3 show the slope (i.e., relaxivity R1 or R2), and the estimated error in the slope, from the regression analysis. Similarly the relaxivities of agarose were measured at each concentration of Ni-DTPA. R, of Ni-DTPA was almost constant (0.105-0.114 set-’ mM_‘) over the range of agarose concentrations,

in 2% agarose

(4.44 (4.56 (4.69 (4.44 (4.59 (4.37 (4.50

1.5 [Gd-DTLI](T$

Fig. 4. Interaction of Cd-DTPA with 4 mM Ni-DTPA in 2% agarose (tissue equivalent material), 1 day after preparation, at 1.5 T and 21 “C. For Gd-DTPA in aqueous solution, the fit of Fig. 1 is shown (RI = 4.50 + 0.03 see-’ mM-I). For the tissue equivalent material, R, = 4.44 f 0.02 set-’ mM-‘. The gels were stable over a period of 109 days (see Table 1).

k f f + + f f

(tissue equivalent

material),

at 1.5 T and 21°C T;’

T,-’ regression 1 day 9 days 16 days 23 days 109 days pure gel (no Ni-DTPA) aqueous solution

1

1--....Gd-DTPA aaueous

dom with time.

Table 1. Stability

0.5

0.02) 0.06) 0.11) 0.05) 0.03) 0.04) 0.04)

[Cd] [Gd] [Gd] [Gd] [Gd] [Gd] [Gd]

regression

(19.0 f 0.2) + (5.20 f (19.0 +- 0.3) + (5.24 k (19.0 + 0.3) + (5.27 + not measured (19.1 f 0.2) + (5.14 + (16.8 + 0.3) + (5.44 + (0.8 + 0.2) + (5.49 +

0.05) [Cd] 0.08) [Gd] 0.07) [Gd] 0.06) [Gd] 0.05) [Gd] 0.06) [Gd]

Magnetic

130

Table 2. l/T, (set-‘)

Resonance

Imaging

0 Volume

11,

Number 1, 1993

values measured in tissue equivalent material (Ni-DTPA in agarose) at 1.5 T and 21°C [Ni-DTPA]

[agarose] 0% 0.5% 1% 2% 4% RI agarose (set-’

Vo-‘)

OmM

4mM

8mM

16 mM

0.30 0.29 0.27 0.30 0.30 0.00 f 0.01

0.70 0.67 0.68 0.70 0.75 0.02 * 0.01

1.12 1.15 1.10 1.15 1.16 0.01 f 0.01

2.12 2.07 1.96 1.97 2.01 -0.02 f 0.02

R, Ni-DTPA (set-’ mM-‘) 0.114 0.112 0.106 0.105 0.106

f -t k + f

0.005 0.003 0.001 0.001 0.001

Table 3. l/T, (set-‘) values measured in tissue equivalent material (Ni-DTPA in agarose) at 1.5 T and 21°C [Ni-DTPA] [agarose] 0% 0.5% 1% 2% 4% R2 agarose (set-’

Vo-I)

OmM

4mM

8mM

16 mM

1.0 5.3 10.5 20.7 39.7 9.75 f 0.12

1.4 5.5 9.6 18.6 34.0 8.20 k 0.14

1.7 5.8 10.1 18.5 35.3 8.42 1- 0.01

2.6 7.1 11.2 20.2 36.5 8.48 f 0.09

Table 4. l/T, (set-‘)

R2 Ni-DTPA (set-’ mM_‘) 0.10 0.11 0.06 -0.01 -0.11

rt k + + k

0.01 0.02 0.06 0.12 0.24

values measured in mixtures of DTPA and agarose at 1.5 T and 21°C [DTPA]

[agarose] 0% 0.5% 1% 2% 4% Rz agarose (set-’

VoO-‘)

OmM

8mM

16 mM

32 mM

1.0 5.3 10.3 20.4 39.1 9.59 * 0.10

1.1 5.4 9.7 18.5 34.7 8.42 + 0.09

1.1 5.1 9.2 17.7 34.1 8.29 t 0.03

1.1 5.3 9.7 18.0 34.5 8.34 + 0.04

with a suggestion of lower RI values at the higher concentrations of agarose. R2 of Ni-DTPA was significantly positive (about 0.1 set-’ mM-‘) at low values of agarose concentration, declining to zero at the high agarose concentrations. RI of agarose was not significantly different from zero. R2 of agarose declined significantly with increasing Ni-DTPA concentration, from 9.75 f 0.12 set-’ %-’ at 0 mM Ni-DTPA to 8.48 -t 0.09 set-’ %-’ at 16 mM Ni-DTPA. From these measurements of relaxivity it is clear that T, behaviour is dominated by Ni-DTPA (since RINi_DTPA[Niand TZ is dominated by DTPA] > RI .,,,,,,[agarose]) agarose (since R 2agarosebgarosel B R2wmPA[NiDTPA]), as expected. The decline in agarose R2 with increasing [Ni-DTPA], and the decline in Ni-DTPA

R2 DTPA (set-’ mM-‘) 0.00 0.00 -0.02 -0.07 -0.12

f 0.01 f 0.01 ? 0.02 Ik 0.04 * 0.09

R, with increasing

[agarose], both suggest significant interaction between the agarose and the Ni-DTPA. As a consequence, in designing the tissue equivalent material to have a particular T, and T2, relaxivities measured close to the required T, and T2 must be used.

Interaction Between Agarose and DTPA Since Ni-DTPA appeared to reduce the R2 relaxivity of agarose (Table 3), the interaction between DTPA and agarose was investigated in the absence of Ni2+ (Table 4). T2s were measured for a variety of concentrations of agarose (0, 0.5’70, 1’70, 2%, 4%) and neutralised DTPA (0 mM, 8 mM, 16 mM, and 32 mM). Linear regressions were performed. R2 values for agarose were similar to those obtained in the presence of

Ni-DTPA doped agarose gel 0 P.S. TOFTSET AL.

131

Ni-DTPA (9.59 + 0.10 set-‘%-’ at 0 mM DTPA declining to 8.29 + 0.03 set-‘Vo-’ at 16 mM DTPA). There was a suggestion that Rz values for DTPA were negative at high agarose concentrations. These reduced relaxivities at high concentrations confirm that DTPA binds to agarose. Temperature Dependence of Tissue-Equivalent Material

The temperature dependence of the relaxation times of several gels having T’ and T2 in the clinical range was measured from 3-39°C (Figs. 5 and 6). Concentrations of 4, 8, and 16 mM Ni-DTPA in 2% agarose were used, giving T’ = 400-1400 msec, Tz = 40-90 msec. The temperature coefficient at 21°C was estimated by fitting a straight line through the data at 16, 22, and 30°C. T’ was relatively independent of temperature for the two more heavily doped gels. These altered by 3-4% over the range 16-39°C with temperature coefficients of -0.2%/“C (16 mM Ni-DTPA; T’ = 500 msec) and +0.2%/“C (8 mM Ni-DTPA; T, = 800 msec). The lightly doped gel (4 mM Ni-DTPA; TI = 1300 msec) altered by 21% over the same range, with a temperature coefficient of +l.O%/“C. T2 altered by 22-25% over this range for all three gels, with temperature coefficients of - 1.3 to - 1.5%/“C. DESIGNER

MATERIAL

Using the measured relaxation times, a “designer material” with any required T’ and T2 value (within a range determined by the relaxation times of the constituent materials) can be produced.6 The relaxation times of the Ni-DTPA tissue equivalent material are:

1500

1500,

1000

/

1000

g

+

F

i

-20

2om

+

+

+

1 L

+

070

5

10

15

20

temperature +

4mM Ni-DTPA

+

25

30

35

40’

(deg C)

8mM Ni-DTPA

-**m

dependence of T2 in tissue equivalent material (Ni-DTPA in 2% agarose). T2 is dominated by relaxation by the gel, which shows high temperature dependence.

Fig. 6. Temperature

T;’ =

T;,’ + R,,C,

+ RINCN

TF’ = TG’ + RzaCa + RzNCN

(la) ,

(lb)

where T’,, Tzw refer to water; R’,, Rza, RIN, RzN are the relaxivities of agarose and Ni-DTPA respectively; and C,, C, are the concentrations of agarose (Vo) and Ni-DTPA (mM) respectively. Solving Eq. (1) for C,, C,, we obtain: c

=

T;’ - T,-,’- (&N/RIN)(T;’ - Z-2)

(24

a R2a

c

N

=

-

(Rxv/Rt~)R,a

K’ - C-id- (R,a/&a)U-F’- G,‘) RIN

- (RI~/Rz~)RzN

. (2b)

At typical tissue values (T’ = 1000 msec, T2 = 100 msec) we can use the values measured for 1% agarose and 8 mM Ni-DTPA in Tables 2 and 3. Using R,, = 0.01 set-’ %-‘; RZa = 8.42 set-’ %-‘; R’N = 0.106 set-’ mM-‘; RZN = 0.06 set-’ mM-’ in Eq. (1) we obtain T,-,’ = 0.242 set-‘; Tg’ = 1.20 set-’ and C, = 0.119 TF’ - 0.067 T;’ - 0.13% agarose CN = 9.440 T;’ - 0.011 Tc’ - 2.27 mM Ni-DTPA

1 Oo

t

t 5

10

4mM Ni-DTPA

15 20 temperature

+

25 (deg C)

8mM Ni-DTPA

30

35

4o”

-*mm 16mM Ni-DTPA

Fig. 5. Temperature dependence of rr in tissue equivalent material (Ni-DTPA in 2% agarose) rr is dominated by relaxation from Ni-DTPA (particularly at the higher concentrations) and therefore has little dependence on temperature.

(3a) . (3b)

Equation 3 can be used to find the concentration of agarose and Ni-DTPA needed to give a required T, and T2 (in units of seconds). For example, a material with T’ = 1000 msec, T2 = 80 msec at 21°C would consist of 1.29Vo agarose and 7.03 mM Ni-DTPA. The accuracy of relaxation times of materials made using

Magnetic

132

Resonance

Imaging

Eq. 3 will be similar to the accuracy of the relaxation time measurements made in characterising the material, i.e., errors will be of the order of 10% or less, using the intercomparison study reported in the Methods section above. DISCUSSION ‘Transition elements Cu, Mn, Ni, used as paramagnetic relaxation agents, will always displace Gd from Gd-DTPA (and probably from other Gd chelates), and therefore they must be chelated themselves if they are to be used in the presence of a nontoxic (and therefore chelated) Gd compound. The stability constants for the chelates we have studied13*14 are Cu-DTPA 1027.9; Gd-DTPA, 1022.5; Ni-DTPA, 1020.2. The fact’that Cu has a higher stability constant than Gd supports the view that Cu displaces Gd from Gd-DTPA, as suggested by Fig. 1. The slow interaction between NiC12 and Gd-DTPA (Fig. 2) is consistent with the stability constant for Ni being lower than for Gd. The values of relaxivity we have measured for GdDTPA in aqueous solution at 1.5 T and 21’C (R, = 4.50 f 0.04 set-’ mM-‘, R2 = 5.49 +- 0.06 set-’ mM_‘) are in good agreement with previous work although most of it is at lower fields. Koenig” reports RI = 4.34.5 set-’ mM-’ at 25”C, with little dependence on field strength above 0.5 T. At 0.5 T Weinmann et al.16 found RI = 4.52 set-’ mM-‘, R2 = 5.66 set-’ mM-‘; Unger et al.” found R, = 4.68 set-’ mM-‘, R2 = 5.17 set-’ mM-‘. The Tl temperature coefficient of the tissue-equivalent material is dominated by the relaxation behaviour of the Ni-DTPA, particularly at the higher concentrations of Ni-DTPA. Our low values of Tr temperature coefficient (-0.2 to + 1.0 Yo/“C) are consistent with those found by Kraft et a1.8 for Ni2+ in 1% agarose at 22°C. For 1 mM Ni2+ (T, = 1000 msec), the temperature dependence of T,was about +l%/“C; for 2 mM Ni2+ (T,= 550 msec) it was