Mri measurements of T1, T2 and D for gels undergoing volume phase transition

Magnetic Resonance Imaging 21 (2003) 135–144

MRI measurements of T1, T2 and D for gels undergoing volume phase transition Kaung-Ti Yung* Department of Physics, Geneva College, 3200 College Avenue, Beaver Falls, Pennsylvania 15010, USA Received 12 June 2002; received in revised form 20 October 2002; accepted 20 October 2002

Abstract Gels consist of crosslinked polymer network swollen in solvent. The network of flexible long-chain molecules traps the liquid medium they are immersed in. Some gels undergo abrupt volume change, a phase transition process, by swelling-shrinking in response to external stimuli changes in solvent composition, temperature, pH, electric field, etc. We report that during volume phase transition changes of NMR longitudinal relaxation time T1, NMR transverse relaxation time T2, and diffusion coefficient D of the PMMA gel, and D of the NIPA gel. We describe how the gels were synthesized and the reason of using the snapshot FLASH imaging sequence to measure T1, T2, and D. Since T1, T2 and D maps have identical field of view and data are extracted from identical areas from their respective maps, these values can be correlated quantitatively on a pixel-by-pixel basis. Thus a complete set of NMR parameters is measured in-situ: the gels are in their natural state, immersed in the liquid, during the phase transition. The results of spectroscopic method agree with that of snapshot FLASH imaging method. For the PMMA gel T1, T2 and D decrease when gels undergo volume phase transition between deuterated acetone concentration of 30% and 40%. At its contracted state, T1 is reduced to a little less than one order of magnitude, T2 over two orders of magnitude, and D over one order of magnitude, smaller from values of PMMA gel at the swollen state. At an elevated temperature of 54°C the thermosensitive NIPA gel is at a contracted state, with its D reduced to almost one order of magnitude smaller from that of the swollen NIPA at room temperature. © 2003 Elsevier Science Inc. All rights reserved. Keywords: PMMA and NIPA gels; Volume phase transition; Longitudinal relaxation time; Transverse relaxation time; Diffusion coefficient

1. Introduction Polymer gels consist of crosslinked polymer network swollen in solvent. The network of flexible long-chain molecules traps the liquid medium they are immersed in. Some gels undergo abrupt volume changes [1], up to three orders of magnitude, by swelling-shrinking in response to external stimuli changes in solvent composition, temperature, pH, electric field, etc. This interesting volume change is reproducible and is a phenomenon of first order phase transition. Because of these properties gels have been explored for possible applications in biologic separation, including gel permeation chromatography and gel electrophoresis, and in biomedical drug delivery processes that use hydrogel as carriers. In addition, hydrogels have the potential as experimental models of biologic tissue and to perform functions * Tel.: ⫹1-724-847-6128; fax: ⫹1-724-847-6714. E-mail address: [email protected] (K.-T. Yung).

such as artificial muscles and organs, chemical valves, and actuators. When ferromagnetic “seed” material is embedded in gels they are sensitive to induction heating by a magnetic field, as well as their volume changes are coupled to the NMR relaxation times of the surrounding liquid [2,3]. They attracted more attention lately because of the syntheses of shape memory gels [4] and self-oscillating gels [5], making them good candidates as intelligent materials in biomedical and industrial applications. Hydrogel structures have been analyzed by a number of methods, but despite the wide range and number of these studies, there remains some very important unresolved issues concerning the structure and relationships between gel structure and diffusive transport within the gel matrix. The two most extensively studied gels in the literature are polyacrylamide (PMMA) and N-isopropylacrylamide (NIPA or PNIPAM). We measure, by both spectroscopic and imaging methods, changes of the NMR longitudinal relaxation time T1, the NMR transverse relaxation time T2, and the diffusion coefficient D of the PMMA

0730-725X/03/$ – see front matter © 2003 Elsevier Science Inc. All rights reserved. PII: S 0 7 3 0 - 7 2 5 X ( 0 2 ) 0 0 6 3 9 - 2

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gel, and D for the NIPA gel, during volume phase transition. We describe first how the gels were synthesized and the pulse sequences used to measure T1, T2, and D before presenting the results of spectroscopic and imaging measurements.

2. Sample preparation and pulse sequences Both PMMA and NIPA gels are synthesized by free radical polymerization. For the PMMA gel 3.982 g acrylamide (AAM, CH2¢CHCONH2, Polysciences, Warrington, PA) as monomer, 32 mg of N,N'-methylene-bis-acrylamide (bis, CH2¢CHCONHCH2NHCOCH¢CH2, Sigma Chemical Co., St. Louis, MO) as crosslinker, 94 mg of Sodium Acrylate (NaAc, CH2O¢COONa, Polysciences) as ionizer, and 8 mg of Ammonium Persulfate GR (APS, (NH4)2S2O8, EM Science, Gobbstown, NJ) as free radical initiator are dissolved in 20 mL of distilled, dionized water (18.1 M⍀-cm resistivity). The solution is then flushed with nitrogen gas for 15 min to remove dissolved oxygen which might otherwise scavenge free radicals and inhibit polymerization. To catalyze the polymerization 48 ␮l of N,N,N'N'-Tetramethylethylene-diamine (TEMED, (CH3)2N CH2CH2 N (CH3)2, Aldrich Chemical Company) as an accelerator was then added to the pregel solution. As a last step, heparinized glass capillary tubes (Chase Instruments Corp, Lindenhurst, NY) of 2⬙ long and 1.1 mm I.D. were inserted into the solution. Gelation is completed within 20 min. The formed gel cylinders were left inside the tubes under the ventilation hood overnight. The gel cylinders were then taken out of the tubes and immersed in a water bath to wash away unreacted monomers and other residual chemicals. During the three to four days while gels absorb water and swell, water was repeatedly changed until the gel swells to an equilibrium value of about 4.3 mm, almost twice its original diameter. It may be safe at this point to assume that all the sodium cations, originated from the sodium acrylate groups, are replaced by protons. The fully swollen gel ‘worms’ were then taken out of the beaker, cut to appropriate length of 2 to 2.5 cm, and dried for three days. The dried PMMA gel worms were then inserted into 9 standard NMR 5 mm O.D. tubes that contain solution of deuterated-acetone (CD3COCD3) and water, with the acetone volume concentration cd ranges from 0% (pure water), 10%, . . . , to 80%. In pure water the swollen gels are transparent and invisible, while the contracted gels in the cd 80% solution are opaque in color and smaller, with about 20 fold volume reduction. According to literature the standard PMMA gels as synthesized above have a critical concentration of cd around 32% [6] to 34% [4] where phase transition takes place. We first tried to acquire MR image of gels in the mixture of regular acetone (CH3COCH3) and water. Because water protons and acetone protons have different but close resonance frequencies due to different shieldings of the nuclei,

signals of acetone protons showed up as chemical shift misregistration artifacts in the frequency encoding direction (this chemical shift appears in the NMR spectrum as well). Therefore the deuterated acetone was used instead. Before inserting the dry gels into the deuterated acetone-water solution tube, spectroscopic measurements of T1 (inversion recovery sequence), T2 (CPMG sequence), and D (pulse field gradient sequence) were performed on each tube to obtain these values of the solution, in the absence of gel worms. As expected, throughout the entire range of acetone concentration, T1, T2, and D of water stay within the range of their perspective accepted values. T1, T2, and D values of the acetone mixture obtained later from the imaging method are expected to agree with values from the spectroscopic method obtained here. To synthesize the NIPA gels we used the above PMMA recipe but the acrylamide was replaced by the N-isopropylacrylamide (CH2¢CHCONHC3H7, Polysciences)—monomer: 689.4 mg, NaAc: 85.58 mg, APS: 8.2 mg, bis: 13.2 mg and TEMED: 25 ␮l in 10 mL water. Then heparinized glass capillary tubes are inserted to the pregel solution as before. The amount of NaAc (the ionizer) controls the degree of ionization of the NIPA gels, thus the degree of volume reduction, as well as the critical temperature: the higher the NaAc concentration, the higher the transition temperature and the smaller the size of contracted gels. In this preparation the swollen gel is about 1.9 mm in diameter and its ionization is 13% (for 609 mM NIPA and 91 mM NaAc, total monomer concentration is 700 mM), the phase transition temperature is expected to be around 43°C according to Li and Tanaka [7]. Other NIPA gels [4,8] with different degree of ionization change phase when warmed above between 32°C to 37°C [4]. We observed under an optical dissecting microscope the above synthesized NIPA gel shrank to its contracted state at 43°C (the temperature used in the hyperthermia treatment), agreed with the expected temperature in the literature, and the diameter of the shrunken gel at this elevated temperature was about 0.61 mm, a volume reduction of 30 fold from the swollen state, assuming the gel is homogeneous and isotropic. We acquire magnetization prepared MR microimages with the Doty imaging probe (Doty Scientific, Columbia, South Carolina) on the Varian VXR 500S (Varian Medical Systems) spectrometer with a resonance frequency of 500 MHz. The main reason for using the 500S is that the Doty imaging probe, powered by the Highland digital current amplifier (Highland Technology, San Francisco, CA), is capable of achieving the desired strength of gradient field that is needed to produce strong enough diffusion weighting. At the same time, the high gradient also enables us to achieve higher image resolution. However, this high resolution causes a problem for measuring T2 using the conventional spin echo imaging sequence, described as follows. In general a T2 map is calculated from a series of T2 weighted images with increasing echo time. We first used a multiple spin echo pulse sequence on a water sample, but the calcu-

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lated T2 map showed a T2 value of 400 ms, almost one order of magnitude smaller than its expected 2–3 s. We thus realized that the mean-free diffusion pathway water molecules travel between the spin echo excitation and acquisition (about 20 –30 ms) is about 15–20 ␮m. This distance is comparable to the image pixel size of MR microscopy (40 ␮m or less), causing the image to be influenced greatly by diffusion effects: the diffusion of molecules within the imaging gradients causes a strong relaxation of the transverse magnetization. The reason for this is that the apparent T2app (a diffusion enhanced relaxation) is shorter than the intrinsic spin-spin relaxation T2 by the following relation, as derived by Brandl and Hasse [9], for a conventional spin echo imaging sequence: 1 T 2app

⫽

1 D␲2 D␲2 2 ⫹ C , 2 C1 ⫹ P T 2 ⌬x ⌬s 2 2

(1)

with D the diffusion coefficient. The constants P, C1 and C2 contain information of the slice profile and the timing of the gradient pulses, ⌬x is the in plane resolution and ⌬s is the slice thickness. The relaxation dependence on D is not seen in the whole-body medical MRI because of the larger ⌬x (in the mm range) and the larger ⌬s (in the cm range). However, lower values of ⌬x (in the ␮m range) and ⌬s (1 mm) in our case give a more profound decay of T2, this effect has significant consequences. It is concluded by Brandl and Hasse [9] that quantitative spin-spin interaction T2 values can not be calculated from a series of spin echo images obtained with increasing echo times. Hesse et al. [11] and others [10,11] thus developed the snapshot FLASH (Fast Low Angle SHot, a gradient echo, instead of a spin echo imaging sequence) method to measure T2 correctly, as well as to measure T1 [10,12]. The snapshot FLASH has a spectroscopic part DEFT (Driven Equilibrium Fourier Transform) placed in front of the imaging part FLASH. In other words, the snapshot FLASH is basically a magnetization prepared MR microscopy [13]—the magnetization used in the imaging stage FLASH is prepared by the spectroscopic stage DEFT as follows: DEFT sequence

Crusher gradients

FLASH sequence

Magnetization preparation stage

Spoiling period

Imaging stage

Note that crusher gradients are applied in all three axes during the spoiling period of 5 ms between two stages. Similar to the above method for T1 and T2 we place a spectroscopic pulse field gradient (PFG) as the DEFT part in front of the imaging part to measure D. To give different weighting, the DEFT part may be any desired spectroscopic sequence, as shown in the following table:

137

DEFT

Weighting

Spectroscopic PFG Spectroscopic CPMG Spectroscopic SR

D T2 T1

The DEFT is a PFG sequence for measuring D or is a CPMG sequence for measuring T2. For these two measurements, a 90° RF pulse at the beginning of DEFT rotates the longitudinal magnetization Mz onto the transverse plane and it becomes the transverse magnetization Mxy. Mxy then evolves on the transverse plane according to the chosen spectroscopic sequence within DEFT, and eventually refocuses and forms an echo. At the peak of the echo a ⫺90° RF pulse rotates Mxy back to the z axis to become Mz again. Therefore this Mz is attenuated by the applied DEFT relaxation during the echo time TE between the two 90° pulses. After a short spoiling period this prepared Mz is then used in the FLASH imaging. For T1 we use the saturation recovery (SR) spectroscopic sequence as the DEFT part: a 90° RF pulse rotates Mz to the transverse plane, after a chosen time interval (the saturation recovery time ti) and after the spoiling period the image is obtained by FLASH. The saturation recovery time ti is varied to create different T1 weighting. The crusher gradients dephase therefore eliminate residual, if any, Mxy caused by possible RF imperfections. This is crucial for the saturation recovery sequence because any residual Mxy is projected to the transverse plane as Mxy Cos␣ and is mixed with the tilted magnetization Mz Sin␣, this will severely compromise the image quality, making quantitative extraction of data from a series of differently weighted images impossible. Although the magnetization preparation part DEFT uses different spectroscopic sequences to obtain different weighting of T1, T2, and D, the imaging part FLASH is identical for all three measurements. For one particular sample all images have the identical field of view. In fact all extracted values of T1, T2, and D (in most cases the average of 100 pixels) are obtained from identical areas in their respective T1, T2, and D maps. It is thus possible to correlate T1, T2, and D data on a pixel-by-pixel basis to determine how each relates to the others in a quantitative way. Another advantage of the snapshot FLASH imaging is that the complete set of NMR parameters T1, T2, and D is measured in-situ: the gels are in their natural state, i.e., immersed in the liquid, during the volume phase transition. The small Mz, grows on the z axis due to longitudinal relaxation, is tilted by a sinc RF pulse of 300 ␮s toward the xy plane. The flip angle ␣ (typically between 3° to 4°) is controlled by the strength of the RF wave (the length of it is kept constant). The image is taken perpendicular to the gel cylinder axis (in our case the z axis), i.e., a transverse slice, with a slice thickness of 1 mm. The flip angle ␣ is very small (3.7°) so that the echo time (3.6 ms) and the repetition time (7.4 ms) can be very small as well. During the 5 ms acquisition time 128 real and 128 imaginary data points were acquired. The

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Fig. 1. Saturation recovery signal of proton in PMMA gels, and in a solution with volume concentration of 70% water and 30% deuterated acetone. A total of 12 images are acquired.

phase encoding time is 0.8 ms and 64 encoding steps are used. The total imaging time is 64 ⫻ 7.4 ms ⫽ 474 ms, this 128 ⫻ 64 image was then scaled up by linear interpretation on the second dimension by the software package Viewit [14] to an 128 ⫻ 128 one. The field of view is 5.3 mm ⫻ 5.3 mm thus the in plane resolution is 41 ␮m. After 3 s wait time the entire snapshot FLASH sequence is repeated and a total of up to 512 transients are acquired. The reason of acquiring so many transients is that gradient echo images, due to low signal to noise ratio, are noisier in general, as compared to spin echo images. And in particular in diffusion weighted images the prepared Mz is severely weakened by the application of the pulse field gradients in the DEFT part. The DEFT sequence requires phase cycling among different transients to cancel effects of RF field inhomogeneities, to which this sequence is particularly sensitive.

3. T1, T2, D decrease as gel shrinks We describe the T1 measurement of PMMA gels first. A series of T1 weighted images are obtained at various ti’s, from 0.5 sec to 15 sec, with 128 transients acquired for each image. We choose the longest ti to be 15 s, which is five times the longest T1 in the gel and water-acetone mixture, to ensure all magnetization from every part of the sample all are recovered back to the z axis. The 15 sec ti image, practically a proton density map, is used as the asymptotic limit of an ideal infinite ti and its signal strength is the reference S0 in the formula S ⫽ S0 (1 ⫺ e⫺ti/T1). Fig. 1, in

Fig. 2. The straight line fit according to equation S ⫽ S0 (1 ⫺ e⫺ti/T1) for the cd 30% case of Fig. 1. T1 is the negative inverse of the slope, the image with ti ⫽ 15 sec is used as the reference signal S0.

a series of 12 images, shows the smooth saturation recovery of Mz for the case of deuterated acetone concentration cd of 30%. Two proton signals are present in each image, one from the PMMA gel area and the other from the acetonewater mixture area, each is an average of 100 pixels. At a shorter ti the gel signal is greater than the solution signal, probably because the gel T1 is smaller than the solution T1, thus Mz recovers faster in gel, resulting in a stronger signal. At a longer ti, however, the gel signal is lower than that of solution, indicating that within the same number of pixels more protons are present in the solution than in the gel, possibly because the gel has shrunk and water protons have been expelled out of the polymer network. Fig. 2 shows for the case cd ⫽ 30%, using eleven S images, a straight line fit gives T1 as the negative inverse of the slope, down to 6 orders of magnitude of signal attenuation. Fig. 3 shows that the phase transition occurs around 30% to 40% cd, and T1 of the contracted state is about 0.6 s. We plot also the previously determined spectroscopic T1 form the water-acetone solution at the absence of gel worm. As can be seen the two solution T1’s are approximately the same and they stay within a bound of 2 to 3 s throughout the entire range of acetone concentration. To verify the gel T1 of the imaging method we carefully removed the acetone-water solution from the NMR tube by a long needle syringe, until no fluid was visible on the gel surface. Then we measure T1 again on the stand-alone gel using the identical inversion recovery spectroscopic sequence used for the solution T1 before, for each case of cd. The results are plotted in Fig. 3 and, as can be seen, the spectroscopic values of gel are in excellent

K.-T. Yung / Magnetic Resonance Imaging 21 (2003) 135–144

Fig. 3. T1 decreases with increasing acetone concentration cd. Values from spectroscopic method and from snapshot FLASH imaging method are plotted for both protons of gel and protons of solution, phase transition occurs at cd 30%, in agreement with the critical acetone concentration reported in the literature.

agreement with the imaging values of gel. The phase transition seems not very sharp and occurs between 30% cd and 40% cd with a contracted state T1 of about 0.4 s. The average of the spectroscopic and the imaging T1 is 0.5 s, a little less than one order of magnitude smaller than that of the gel in aqueous solution. For the transverse relaxation time measurement we take a series of 8 T2 weighted images with a spectroscopic CPMG sequence as the DEFT part. The acquisition parameters of this CPMG are identical with those used in the spectroscopic measurement for both the solution mixture, and later for the stand-alone gel worm. The interval between ␲ pulses 2␶ is 1 ms and 256 transients are acquired for each image. The different T2 weighting is achieved by varying the total echo time te in CPMG from 0.4 sec to 1.1 sec. Fig. 4 shows that at cd 30% T2 is the inverse of the negative slope of the straight line fitting of signals from the S images, with S0 ⫽ S(te ⫽ 0.4 sec) in the formula ln (S/S0) ⫽ ⫺ te/T2. The fitted gel T2 is 1.179 sec. However, at higher cd as gel contracted more toward completing the phase transition, the apparent fitted gel T2 is much greater (14.4 sec at cd 50%) than the solution T2, an obviously erroneous result. This can be explained [15] if the apparent relaxation is diffusion dominated: 1 2 te ⬍⬍ ␥ DG 2t 3e , T2 12

(2)

139

Fig. 4. Up to 30% cd the fitted T2’s seem reasonable. But at higher cd’s fitted gel T2’s are greater than the solution T2’s. This apparently false result might be due to the fact that diffusion effects in the FLASH part dominate the image contrast, making the te weighting in the DEFT part irrelevant, thus the imaging method can not be used to quantitatively calculate T2 for this range of cd’s.

with ␥ the gyromagnetic ratio. Therefore the total relaxation of signal may be writtten as: S ⫽ S 0e ⫺te/T2e ⫺bD,

(3)

with b the attenuation factor. The first exponential factor is the desired T2 weighting, accomplished by varying te in the DEFT part. Since T2 is small at high cd, this exponential is very small, making the overall signal S very weak. The second exponential factor is an additional relaxation caused by diffusion effect within the imaging gradients in the FLASH part—this is an undesired effect. Yet, because the first exponential is so small this undesired effect dominates the total relaxation, making the T2 weighting of the DEFT part practically irrelevant. Hence this apparent T2 is due to the fact that the total relaxation is dominated by diffusion within the FLASH part, instead of by the desired te weighting in the CPMG part. In fact, at high cd the resulting contrast of any te image is not too different from each other, since the apparent diffusion relaxation is identical in the imaging stage for all values of te. Therefore although the snapshot FLASH is capable of measuring T2 of the swollen gel with 1 or 2 s T2’s, it apparently may not be suitable for contracted gels with T2’s in the millisecond range. Fig. 5 shows how T2 decreases as gel shrinks along the collapse curve at higher values of cd, and only the spectroscopic T2’s of the stand-alone gels are shown, not the T2 extracted from images. The spectroscopic curve shows that the phase transition of gel begins around 30% cd, and the collapsed gel at

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distances [16]. The measured D directly reflects the molecular mobility of translational molecular motion. On the other hand molecular mobility affects T1 and T2 values as well, but they may also be affected by experimental conditions such as the strength of magnetic field. Note that although we use NMR means to measure D here, diffusion does not depend on NMR environment and can be defined outside NMR context. The most widely used NMR spectroscopic method for measuring D is the pulsed-gradient field spin echo (PGSE) sequence introduced by Stejskal and Tanner [17]. It is a spectroscopic spin echo sequence with a pair of pulsedgradient applied before and after the refocusing ␲ pulse. The attenuation of signal due to diffusion is described by the general expression S ⫽ S0 e⫺bD, with b the attenuation factor, S the signal amplitude from a nonzero gradient, and S0 the signal amplitude from a zero gradient. For the spectroscopic Stejskal-Tanner PGSE experiment the b factor is well known: b ⫽ ␥ 2G2␦ 2共⌬ ⫺ ␦ /3兲, Fig. 5. T2 decreases with increasing acetone concentration cd. Values from spectroscopic method and from snapshot FLAS imaging method are plotted for both protons in gel and protons in solution, except for the imaging method those with cd’s greater than 30%.

cd ⫽ 80% has a T2 of 10.2 ms, more than two orders of magnitude smaller than that of the swollen gel. Lastly we determine D. The translational diffusion is the most fundamental form of transport in physical, chemical, and biologic systems. In nonuniform systems a macroscopic flux of different molecular species can be observed and the diffusion coefficient D is determined by measuring the concentration of the species at different times by either physical or chemical means based on the first Fick’s Law. Unfortunately, under equilibrium conditions when the concentration of the species is uniform and stable one can not monitor macroscopic evolution, other approaches such as chemical or radioactive tracer techniques must be used. However, these techniques are highly invasive and may severely perturb the media under study. An alternative in studying diffusion is to monitor the random walks, either on an individual molecular basis, as with neutron scattering, or on a macroscopic, statistical scale, as with PFG diffusion NMR. Within a homogeneous region and for a space scale considerably exceeding the intermolecular distances, the molecular mean square displacement satisfies the Einstein relation 具(r ⫺ r0)2典 ⫽ 6 D t. This relation may be considered as an alternative definition of the self-diffusion coefficient equivalent to that by Fick’s laws. It is required that these displacements must be much larger than the molecular dimensions or, more strictly, than the mean lengths of the elementary jumps of diffusion. NMR field gradient technique is the only method available today that allows a measurement of molecular displacements over such long

(4)

with G the gradient strength, ␦ the duration of each of the two gradient pulses and ⌬ the time interval separating their leading edges. The imaging version of PGSE is to include a pair of pulsed-gradient in the regular spin echo imaging sequence, i.e., the diffusion weighting gradients are interspersed among the imaging gradients of phase encoding, slice selection, and read-out. Thus the b factor calculation is sometimes complicated. To be consistent with the above T1 and T2 measurements we used instead the snapshot FLASH with a spectroscopic PGSE as the DEFT part, with b factor calculated from the simple Eq. (4). To allow for maximum possible diffusion, the first diffusion gradient is applied immediately after the excitation RF pulse (90°), and the second immediately before the third RF pulse (⫺90°), which is at the echo time 2␶ and which rotates Mxy to the z axis. The acquisition parameters used in the PFG of the DEFT part of snapshot FLASH are identical to the above spectroscopic PGSE used on the acetone-water mixture and on the stand-alone gels. To achieve different diffusion weighting a series values of G are used, other parameters are kept the same: ␦ ⫽ 1.7 ms, ⌬ ⫽ 5.387 ms, and 2␶ ⫽ 10 ms. For the FLASH part gradients are applied along the read-out direction and their strength varies from 0 to 56 Gauss/cm, corresponding to a b factor range of 0 to about 800 s/mm2. For a water sample gradients along the phase-encoding direction (y axis in our experimental setup) and along the slice-selection direction (z axis) have been applied, the resultant D’s are very close to D obtained from G applied along the read-out direction (x axis). Values of b factor greater than 800 s/mm2 were tried as well on the water sample to test the upper limit of b that renders an accurate diffusion coefficient. It is found that a good straight line fit up to b ⫽ 1050 s/mm2 (Fig. 6). Beyond this the low signal to noise ratio prevents further attenuation by the diffusion

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Fig. 6. Two straight line fits for determining water diffusion coefficient D. Valid range of b factor for a good D value is from 0 to 1050 sec/mm2.

gradient so that if all points in the plot are used in fitting, the resulting D is smaller than the accepted value. The extracted diffusion coefficient D is the negative slope of the straight line in the ln(S/S0) vs b plot. Due to the weak signal a total of 512 transients are acquired for each image. Fig. 7 shows five straight line fits of D for gels in 0%, 20%, 40%, 60%, and 80% acetone-water solution. Fig. 8 summarizes the results of imaging method and the spectroscopic method,

Fig. 7. Straight line fittings of gel’s D in 0%, 20%, 40%, 60%, and 80% acetone-water solution, 10 images are acquired for each.

141

Fig. 8. D decreases with increasing acetone concentration cd. Results of imaging method and spectroscopic method agree very well.

we see that these two results agree with each other very well. The diffusion coefficients of the solution as determined by imaging and by spectroscopy stay in a range between 1.5 to 2.5 ⫻ 10⫺3 mm2/s while those in the gel network drop drastically. As before the transition is not very sharp, it occurs between 30% to 40% cd and reaches a value of 0.143 ⫻ 10⫺3 mm2/s at 80% cd, over one order of magnitude smaller than that of the swollen gels. For the diffusion coefficient of the NIPA gel we inserted the swollen gel worm into a 5 mm NMR tube filled with dionized water and used the snapshot FLASH to obtain D. Attempts were made to measure D’s in 5 degree increment, for the entire temperature range between 23°C and 54°C. This way, with phase transition occurs at 43°C we may observe the entire process of gel collapse. However, due to the heating setup inside the Doty probe, convective flow of water [18] was detected and imaged (not shown), the partially contracted gel worm moved physically from time to time during image acquisition, even after microcapillary tubes were inserted inside the NMR tube to inhibit such motion. This prevents us from obtaining data for the entire temperature range. However, with much difficulty and some luck, we obtained one good set of images at 54°C: before phase transition (5 images used in straight line fitting) D(H2O, 25°C) ⫽ 2.24 ⫻ 10⫺3 mm2/s and D(gel, 25°C) ⫽ 1.39 ⫻ 10⫺3 mm2/s, and after phase transition (4 images used) D(H2O, 54°C) ⫽ 4.34 ⫻ 10⫺3 mm2/s and D(gel, 54°C) ⫽ 0.366 ⫻ 10⫺3 mm2/s. These results of D, each is an average of 100 pixels, show that before volume change, D of gel is about 62% of D of water, but after volume change, D of the shrunken gel is more than one order of

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magnitude smaller than D of the surrounding water. It is known [19] that for free water D ⫽ D0 exp(⫺Ea/kB T), where D0 is the diffusion coefficient at some reference temperature, Ea is the activation energy required to break two hydrogen bonds simultaneously (0.18 eV) and kB is the Boltzmann constant. When the range of temperature variation is not too large, the high temperature approximation of the above relation gives that D varies with T linearly [20 – 22]. Our water diffusion coefficient D(H2O, 54°C) agrees with the literature value at this elevated temperature, indicating that the measured D of the shrunken gel at 54°C is valid. Given the sensitivity of diffusion to temperature is about 7.2% per degree Kelvin (greater than the sensitivity quoted in the literature [19]), proton D in gel at 54°C is expected to be 3.48 ⫻ 10⫺3 mm2/s were it not subjected to the contracted polymer network. Therefore, due solely to the effect of gel contraction, D is reduced to almost one order of magnitude smaller.

4. Discussion For PMMA gels it is observed that the overall signal amplitudes are lower for the higher cd images, because of smaller number water protons are present in gel and in solution. As the gel reduces in size with increasing acetone concentration the distance between crosslinks within the gel network becomes shorter. This reduces the effective pore volume between crosslinks within which water molecules move about, therefore restricting the random migration of protons and resulting in a smaller D. For T1 and T2, when gels shrink drastically the mass density of the gel network increases, making water molecules trapped within the network behave more like those in a solid, thus effects of motion averaging greatly reduced, resulting in decreased relaxation times. The behaviors of the measured T1, T2 and D agree with this physical picture. At the contracted state at a volume reduction of about 20 fold, T1 reduces to a little less than one order of magnitude, D reduces to about one order of magnitude, and T2 reduces to over two orders of magnitude smaller. We also observed that T2 seems to correlate more strongly with D than T1 with D, this may be explained as follows. From a pure signal acquisition point of view, signals of the T1 weighted images are from the recovered Mz that grows back along the z axis, so the Mz used by the imaging FLASH sequence was never on the transverse plane. Thus it was not affected by the enhanced relaxation caused by diffusion effects, suffered only by Mxy which is on the xy plane. On the contrary, for both cases of D and T2 experiments, the FLASH Mz was on the xy plane, therefore experienced similar diffusion relaxation within DEFT. We do not find in the literature similar T1 and T2 reductions when gels undergo volume change. Tabak et al. [23] measured spectroscopic T1 of polyacrylamide gel immersed in solutions of different deuterated acetone concentration as

we did, their results showed no T1 variation at higher cd’s for protons in the fluid trapped inside gel network. Moreover, their measured T1 is relatively long (8.4 sec) and remains at this value through higher acetone concentrations up to cd 60%, well passed the phase transition concentration of cd 30%. Corti et al. [24] measured T2 for CD and CD2 groups of D3-acrylamide (CD2-CD-CONH2) gel by spectroscopic method. They reported the measured T1 of CD is two orders of magnitude smaller and the measured T2 three orders of magnitude smaller, after gel completed the volume change at cd 50%. However, these T2’s are the ones correspond to local segmental motion of these two side chains, not the T2 of the trapped fluid within gel network under consideration here. For water trapped among the PA chains the measured relaxation rates T1⫺1 and T2⫺1 of D2O does not show large variations up to cd 60%. Thus for both T1 and T2 the microscopic motions of the fluid inside gel are largely independent by the dynamics and the progressive shrinking of the polymer chains, in consistent with the earlier conclusions about T1 of Tabak et al. [23]. The investigators thus concluded that the large part of the water trapped among the PA chains in gels is practically the same as the free liquid, in contrary to relaxation times reduction reported here. It seems puzzling that their T1 and T2 of liquid molecules inside the gel network are completely insensitive to increasing acetone concentration, and that this does not reflect fundamental variations of the physical environment, inside which they diffuse, undergoing a volume change as drastic as that of a phase transition. As far as the author is aware of there seems to be no report in the literature on diffusion coefficient measurement for NIPA gels at an elevated temperature, however, D decreases with increasing acetone concentration for PMMA gels was observed by Pavesi and Rigamonti [25]. They used stimulated echo spectroscopic sequence to study polyacrylamide gels in up to about cd 50% and to plot the dependence of D upon cd along the collapse curve. The D value at 50% cd is about 0.8 ⫻ 10⫺3 mm2/s while ours is 0.19 ⫻ 10⫺3 mm2/s at the same cd. A possible explanation of this discrepancy is due to the fact that the degree of ionization determines where phase transition takes place. In their sample no ionizer was added thus only a spontaneous ionization of limited degree occur due to preparation and thermal effects. On the contrary we added 50 mM NaAc as the ionizer, this drives the phase transition to occur earlier at a smaller cd (similar to the NIPA case higher ionization drives the transition temperature higher). In fact, our D at 40% cd equals roughly to their D at 50% cd, suggesting that, if the possible cross relaxation in their case is ignored, our higher degree of ionization brings about the phase transition at a cd of 10% less. Moreover, their D decreases with increasing ⌬, the time interval between the onset of the two pulsed gradients, this is reported by Pavesi and Balzarini [26] as well. Although we did not investigate this dependence, some findings in the literature about this are interesting. PMMA gels synthesized by Penke et al. [27] were not washed or

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soaked in water prior to their measurements, in contrast to the procedure we adopted, thus their gels are considered to be incompletely swollen gels. They used the stimulated echo sequence as well to measure D but, unlike the research group mentioned above, found no time dependence of the diffusion coefficients within the examined range of ⌬. Their data also showed no effect of the crosslinker concentration C on the diffusion of water molecules up to 10% C. However, this result may or may not hold under the situation of NIPA volume phase transition where the effective crosslinker concentration could increase as great as 30 fold when gel volume decreased by 30 fold. Both groups used stimulated echo method but it is puzzling that the ⌬ dependence of D is at odds with each other. Aside from differences in material preparation and experimental errors, one possible explanations for this discrepancy is that the cross relaxation between protons of water and protons on the polymer chains might be a factor, as pointed out by Peschier et al. [28]. They compared the stimulated echo method with the spin echo method and found that only stimulated echo experiments have the apparent dependence of the diffusion coefficient on the diffusion time. This time dependence of D is usually interpreted as a consequence of restricted diffusion, however, this should affect both methods equally. This effect is shown to be caused by cross relaxation between water protons and gel matrix protons. It is concluded by them that macromolecular systems should be checked for cross relaxation when using the stimulated echo method for self-diffusion measurements.

5. Conclusions NMR parameters T1, T2 and D of gels undergoing volume phase transition are measured in-situ from the identical area within a sample, thus can be correlated quantitatively on a pixel-by-pixel basis. The results of spectroscopic method agree with that of snapshot FLASH imaging method. For the PMMA gel T1, T2 and D decrease when gels undergo volume phase transition between acetone concentration cd 30% and cd 40%. At its contracted state, T1 is reduced to a little less than one order of magnitude, T2 over two orders of magnitude, and D over one order of magnitude, smaller from values of PMMA gel at the swollen state. At an elevated temperature of 54°C the thermosensitive NIPA gel is at a contracted state, with its D reduced to almost one order of magnitude smaller from that of the swollen NIPA gel at room temperature.

Acknowledgments The author thanks the guidance of Professor Paul C. Lauterbur and the use of instruments at The Biomedical Magnetic Resonance Laboratory, University of Illinois at Urbana-Champaign. This research is funded in part by Na-

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tional Institutes of Health, Biomedical Research Technology Grant, PHS 5 P42 PR05964 (1990-1995), PHS 2P41 PR05964 (1996), the Servants United Foundation, PHS Grant number 5 T32 CA 09067, awarded by the National Cancer Institute, DHHS, and Illinois Department of Commerce and Community Affairs Grant No. 91-82128.

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