MAGNETICRESONANCE IN MEDICINE 27, 1 18-

I34 ( 1992)

Multiexponential Proton Relaxation Processes of Compartmentalized Water in Gels TOKUKO WATANABE, * NORIOMURASE,?MARTINSTAEMMLER,~ AND KLAUS GERSONDE~

* Luhorutory of Chemistry, Tokyo University of Marine Science, Konan, Minuto-ku, Tokyo 108; ?Tokyo Denki University, Hutoyuma, Saiturna 350-03, Japan; and $ Huupcabteilung Medizintechnik, FruunhoferInstitut ,fiir zrrstorungsfveie Prufverfuhren, 0-6670 St. Ingbert and Fuchrichtung Medizintechnik, Universitat des Suurlandes, 0-6650 Hornburg/Suur, Germany Received May 3 1, 199 I ; revised November 4, I99 1; accepted December 2, I99 I The proton relaxation times, T I and T 2 ,of water in Sephadex gels, exhibiting pores of varying size (i.e., with exclusion limits of molecular weight between lo3 and 10’) and water contents in the range 30 to 70% (w/w, weight ofwater to total weight), were measured at 20 MHz in the temperature range 5 to 50°C. Multiexponential analysis ofthe relaxation curves revealed the existence of two relaxation components in all gel systems. A component , ~ a2,] with long T , and T z ( T I , ]and T2,1)is associated with a large water fraction C I ~ and and a component with short T I and T z ( and T2,2)with a small water fraction and An analysis of the temperature behavior of the relaxation components gives insight into the relaxation mechanisms. The relaxation process in water, compartmentalized in the gel matrix, is mainly controlled by dipole-dipole interactions. In addition, proton exchange processes between hydration water and hydroxyl groups of the matrix chain contribute under specific conditions and lead to a dramatic enhancement of the relaxation rate. In particular, for gels with small pores and with low water content proton exchange is observed. Compartments of water in gels could be models for compartments of water in biological tissues. 0 1992 Academic Press, Inc. INTRODUCTION

The relaxation times ( T , and T 2 )of water protons in tissues are key parameters for magnetic resonance imaging (MRI ). They are most important for the contrast behavior of soft tissues in images ( I , 2). In addition, relaxation time measurements have contributed to tissue characterization and differentiation in vitro (3-10) and in vivo ( 1I - 15 ) . Water proton relaxation times reflect the specific environment of the water molecules in the tissues, due to dipolar interactions, chemical exchange processes between water molecules and the surrounding biological macromolecules, and the particular physicochemical state of the water in cellular compartments. Water in tissues is compartmentalized and therefore one expects a typical water phase for a particular compartment. The relaxation process, observed in a volume element (voxel), reflects the inhomogeneity due to the specific environments of the compartmental water and therefore often can be described as the sum of monoexponential terms ( 7, 8, 10-12). Although differences in TI and/or T 2relaxation times of tissue water are the basis of excellent anatomical images, routine MRI does not allow the determination of T I 0740-3194192 $5.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved

I I8

PROTON RELAXATION PROCESSES

119

and T 2 values which are accurate enough to specify water proton classes or water proton environments. More accurate measurements and a better analysis of relaxation processes ( i n vitro and in vivo) should be based on a large number of data points of a relaxation curve allowing the decomposition of multiexponential processes into monoexponential components. These monoexponential components may be more useful for the improved determination of TI and T 2 and allow the estimation of fractions of the relaxation components in each voxel, which correlate with the proton density of a particular water fraction ( 7-10). However, it should not be withheld that it is difficult to obtain well-digitized relaxation curves employing routine imaging procedures and that one needs special techniques ( 12). Gels with differing pore sizes can be considered models for specific water compartments, which exhibit characteristic proton relaxation behavior ( 16). Therefore, gels could also serve as simple models for compartmentalized water in tissues. In this paper, we present T I and T 2 relaxation data of compartmentalized water in crosslinked polymer gels with varying pore sizes. By multiexponential analysis of the relaxation processes at least two relaxation components can be detected in these gels. The variation of the water content in these gels provides information about the distribution of water between compartments. Furthermore, the measurement and interpretation of the temperature behavior of the water proton relaxation in each compartment (in the range +5 to +50"C) shed some light on the relaxation mechanisms of water protons in gels. By employing the diffusion equation and the bulk diffusivity of water Brownstein and T a n have demonstrated that the relaxation processes of water in pores with increasing diameters of 1 to 30 pm change from mono- to multiexponential behavior ( I 7). In pores with such large diameters the surfaces act as relaxation sinks. Sephadex gels, however, avoid this problem and therefore seem to be more suitable model systems for studies of compartmentalized water. The diameter of pores in Sephadex gels is by far smaller than 1 pm. Thus surface-like or volume-like sinks can be neglected. It seems to be quite reasonable to assign the two relaxation components to two types of compartmentalized water in Sephadex gels. EXPERIMENTAL

Sample Preparation Sephadex gels G-10, G-15, G-25, G-50, G-75, and G-100 are products ofPharmacia (Stockholm, Sweden). The pore sizes of Sephadex G-25 and G-50 were determined by gel filtration on the basis of exclusion limits of globular molecules with a known molecular weight. The water content varied between 30 and 70% (w/w, weight of water/total weight). The preparation of gels was performed as described previously ( 1 6 ) .

T I and T2 Relaxation Time Measurements T Iand T 2relaxation times were measured in a pulse spectrometer (Minispec PC20, Bruker Medizintechnik, Karlsruhe, Germany) at 20 MHz and in the temperature range 5 to 50°C. The accuracy of the temperature control was within +0.5"C. The relaxation curves were obtained by employing inversion recovery for T I and CPMG

120

WATANABE ET AL.

pulse sequences for T 2 as described elsewhere ( 7 ) . The number of sampling points for T , and T 2relaxation curves was 40 and 169, respectively. The analysis of relaxation curves was performed as described elsewhere on the basis of monoexponential and multiexponential analysis, respectively (7, 18, 19). For the analysis of the inversion recovery curves ( TI) a three-point smoothing procedure was used and for the analysis of the magnetization decay curves ( T 2 )a three-point averaging procedure was first employed. The magnetization decay and recovery in a voxel can be described by the two formulas n

W t )=

c I=

~0,1(-t/~2,,)

I

n

M(t)=

c MO,I(1 - 2 exP(-t/Tl,,))* I=

The relative distribution

LY

1

of water within the compartments is defined as n

C

a, = M o , ~ / M o , ~ .

131

I-1

M0,( represents the magnetization at time 1 = 0, To,tthe transverse relaxation time, and T ,,I the longitudinal relaxation time. The index i corresponds the compartment of water which contributes independently to the multiexponential relaxation process. The multiexponential functions were decomposed by employing the “peeling-off” method after semilogarithmic linearization ( 11 ) combined with the eigenfunction expansion analysis ( 18-20). We used two different types of CPMG pulse experiments: a “slow” method which reads out only every tenth echo with varying 7r pulse intervals of 200 to 1000 p s as described i n ( 7 ) and a “fast” method which allows the read-out of all echoes with varying 7r pulse intervals of 200 to 1000 p s (M. Staemmler and K. Gersonde, unpublished results). A more accurate determination of the fastest relaxation component T2, could be performed if the fast method was employed. With the fast method we checked T2,2determined with the slow CPMG pulse sequence. The T2.2value (fast component) and the cy2,2 value (small fraction) were found to be identical within experimental error, employing both CPMG pulse experiments (slow and fast method). Data for T2.2and a2.2presented in this paper are based on both the slow and fast CPMG pulse sequences. The variation of the T pulse interval in the spin-echo experiments did not influence the T 2values. The standard deviation of the calculated relaxation times and of the fractions cy was within 5% for the slow components and less than 30%,mostly 10 to 2070,for the fast relaxation components. The standard deviations are indicated by error bars in the figures. The accuracy of the relaxation time measurements and of the amplitude determinations in the multiexponential analysis depends on the relation between maximum and minimum relaxation rates of each relaxation component (21). The existence of at least two relaxation components in Sephadex gels is reasonable within experimental errors.

PROTON RELAXATION PROCESSES

12 1

RESULTS

Relation between Water Content and Water Proton Relaxation in Sephadex Gels On the basis of the monoexponential analysis of water relaxation processes, the gels, characterized by differing pore sizes, were attributed to two groups (see Figs. 1 and 2 in Ref. ( 1 6 ) ) .Sephadex G-10, G-15, and G-25 constitute one group, whereas Sephadex G-50, G-75, and G-100 belong to the other group. Here we present and compare as examples only the data of Sephadex G-25 and G-50. In Fig. 1 the variation of water proton relaxation times in Sephadex G-25 with increasing amounts of water (in the range 30 to 70%,w/w) is demonstrated at 37°C. The multiexponential analysis of the relaxation processes results in two components for TI and T 2,respectively. The slow relaxation components and T2,1are associated with the larger water fractions ( Y ~ and , ~ ( Y ~ , ~respectively, , reflecting the larger compartment. The fast relaxation components and T2,2are attributed to the smaller , reflecting the smaller compartment. With water fractions ct 1,2 and ( Y ~ , ~ respectively, increasing water content in Sephadex G-25 both the fast and the slow relaxation components exhibit a nonlinear increase in relaxation time (see Figs. 1A and 1B). In addition, we observe characteristic changes of the fractions (Y of the TI and T2 com-

~~

@

WATER CONTENT I % w / w l

@

WATER CONTENT l'/.w/Wl

FIG. 1. Influence of water content on T I ( A ) and T2 (B) relaxation components and on fractions a (C and Tz,lare the slow relaxation components ( 0 )attributed to the and D) in Sephadex (3-25 at 37°C. large fractions , respectively. and a2,, and T2,2are the fast relaxation components ( A ) attributed to the small fractions and a2,2,respectively. The T2,2values were determined by employing the "fast" CPMG pulse sequence with T = 100 ps. At a water content of 30% (w/w) only monoexponential behavior is observed for T , (0). Symbols without error bars mean that the standard deviation is within the mark. FIG. 2. Influence of water content on T , ( A ) and T, (B) relaxation components and on fractions a ( C and T2,1are the slow relaxation components ( 0 )attributed to the and D) in Sephadex (3-50 at 40°C. large fractions ( Y ~ and . ~ a2,1 respectively. and Tz,zare the fast relaxation components ( A ) attributed to the small fractions and a2,2,respectively. The T2,2values were determined by employing the "fast" CPMG pulse sequence with 7 = 100 ps. At a water content of 30% (w/w) only monoexponential behavior is observed for T , (8).For standard deviations see legend of Fig. 1.

122

WATANABE ET AL.

ponents, respectively (see Figs. 1C and ID). The small fraction associated with , ~ with T2,2clearly decrease with increasing and the small fraction ( Y ~ associated water content. As expected the larger fractions ( Y ~ and , ~ a2,]show inverse behavior. Note that in Sephadex G-25 with a water content of 30% the two T I relaxation components cannot be differentiated and therefore apparently and immerge into one relaxation time (see Figs. 1A and 1C). Contrarily, T2 is biexponential even in the gel with 30% water content (see Figs. I B and 1D). As is shown for Sephadex G-25, Sephadex G-50 also exhibits biexponential relaxation behavior under comparable conditions (see Fig. 2). If we compare the fast relaxation and T2,2)in Sephadex G-50 and G-25, very similar relaxation times components ( for all water contents, investigated so far, can be observed. The slow relaxation components ( and T 2 , , of ) Sephadex G-50 exhibit a dramatic increase with increasing water content (see Figs. 2A and 2B). The T I , ,and Tz,,values determined in Sephadex G-50 increase to a much larger extent with increasing amounts of water than those , exhibits a determined in Sephadex G-25 (compare Figs. 1 and 2). T 2 , 1however, much larger increase with increasing water content than the corresponding TI,Ivalue. Hence, the pore size additionally influences the slow relaxation component T2,1.The fractions a of the T I and T 2 components in Sephadex G-50 are very similar to those observed in Sephadex G-25 at varying water contents. As described for Sephadex G25, monoexponential T I relaxation behavior is also observed in Sephadex G-50 with a water content of 30%.

Influence qf Pore Size on the Relaxation Times of Water Protons in Sephadex Gels The effect of pore size on the relaxation behavior of water in Sephadex gels is demonstrated in Fig. 3. For this purpose the relaxation times ( T I and T 2 )were dePORE SIZE (EXCLUSION LIMIT IN M.W.) 103 I

t

10

15

104 I

25 5 0

to5

7 5 100

10

10'

10.

I

I

15

25 5 0

lo5

7 5 100

TYPES OF SEPHADEX G

FIG. 3. T , (A) and T2(B) water relaxation times (based on monoexponential analysis) in Sephadex gels with different pore sizes (see abscissa) and at various water contents (0,30%;A, 40%;0, 50%; m, 60%; A, 65%; m, 70%).Temperature: 40°C.

PROTON RELAXATION PROCESSES

123

termined on the basis of monoexponential analysis. The influence of pore size is shown for varying water contents (between 30 and 70%, w/w). It has already been demonstrated in Figs. 1 and 2 that the influence of water content in Sephadex G-25 and G-50 is strongly reflected by the slow relaxation components TI,1and T2,,and much less by the fast relaxation components and T2,2.Hence, it is reasonable that the monoexponential relaxation times preferentially reflect the behavior of the slow relaxation components T I , ,and T2,1. Gels containing only 30% water do not exhibit a significant change of TI and T2 with increasing pore size (see Figs. 3A and 3B). Note that the monoexponential TI (-88 ms) and T2 ( 12 ms) values of all gels with a water content of 30%, which reflect the slow relaxation component, are similar to the values of the fast relaxation components and T2,2exhibited in Figs. 1 and 2 for Sephadex G-25 and G-50, respectively, with water contents between 30 and 70%. This means that the water in gels with less than 30% water content and the water belonging to the small fraction (faster relaxation component) in gels with higher water contents are in similar environments. Hence, we must conclude that in all gels with a water content of 30% or less the water molecules first occupy positions in close contact to the gel matrix. We then further assume that in gels with higher water content the molecules reflecting , ~ ) most closely fast relaxation belong to the small water compartments ( ( Y ~ , ~(, Y ~located to gel matrix positions. The relaxation times are much less influenced by the increasing water content in the group of gels with smaller pore size (Sephadex G-10, G-15, G-25) than in the other group of gels with larger pore size (G-50, G-75, G- 100).Replacement of Sephadex G-25 (smaller pore size) by G-50 (larger pore size) results in a dramatic change of the relaxation properties at water contents higher than 40%. In the gels with larger pore size a progressive uptake of water molecules leads at first to an occupation of matrix sites and then to a filling up of the pores, which may fold up with the increasing uptake of water. Hence, the dramatic increase of the relaxation times ( T I and T 2 ) with increasing amounts of water in the group of gels with larger pores reflects the presence of larger amounts of free water in the pores. In the gels with smaller pore size the space for the uptake of free water is limited. If the water content is larger than 50% in gels with smaller pore size, a remarkable increase of TI and T2 reflects the occurrence of free water which is located outside the pores (data are not shown in Fig. 3).

-

Effect of Temperature on the Relaxation Times of Water in Gels In Fig. 4 the temperature dependence of T I (A) and T 2 ( B ) (based on monoexponential analysis) is shown for Sephadex G-25 and G-50 in the presence of 30, 50, and 70% water and in the temperature range 5 to 50°C. At a low water content (30%) the TI values of Sephadex G-25 and G-50 are essentially identical at all temperatures (see Fig. 4A ) . At higher water contents ( 50 and 70%) the TI of water in Sephadex G25 and G-50 is only identical at +5"C. Above +5"C the increase of T Iwith increasing temperature is larger for Sephadex G-50 than for Sephadex G-25 (see Fig. 4). The course of the temperature dependence of T2in the above-mentioned gels containing 30% water is very different from that of T I(compare Figs. 4A and 4B). The

124

WATANABE ET AL.

FIG.4. Temperature dependenceof T I( A ) and T2(B) water relaxationtimes (based on monoexponential analysis) in Sephadex (3-25 (a0, A ) and G-50 ( 0 ,0, A) with 30%(A, A), 50%( 0 . 0 )and 70%(W, 0 ) water content.

T2vs. temperature plots for the two gels containing 30%water are biphasic. In Sephadex G-25 with 50 and 70% water, T2decreases monotonically with increasing temperature, whereas in Sephadex G-50, T2increases monotonically. At 5°C both gels show identical T2 values as is already shown for T I . The nonlinear and biphasic behavior of both the T I and the T 2 vs. temperature plots is a further indication for the existence of multiexponential relaxation processes in these gels. Therefore, we also investigated the temperature dependence of the relaxation components. In Fig. 5 the temperature dependence of the fast and the slow T I relaxation component is shown for Sephadex G-50 ( 5 A ) and Sephadex G-25 (5B) in the temperature range from 5 to 50°C. It is obvious that the two T I relaxation components ( show a nearly linear increase and with increasing temperature (see Fig. 5 ) . Above 30°C and for the highest water increases in a nonlinear fashion, probably due to the larger content (70%) radius of diffusion and hence larger amounts of free water outside the pores of the gel. In Fig. 6 the temperature dependence of the T 2 relaxation components ( T2,,and T2,2)of water in Sephadex G-50 (6A and 6C) and G-25 (6B and 6D) is presented. Most T2 components show a nonlinear and biphasic temperature behavior in the temperature range investigated here. The complex nature of the relaxation processes, which cause this typical temperature behavior, is discussed in detail.

125

PROTON RELAXATION PROCESSES TEMPERATURE 50 40

30 20

10

1°C1

50 40

0

30 20

10

0

1000

B 500

------+

E

-100

r

I-

-

-

5c

I-'

IC

II

I:..!: 3.0

3.3

3.6

3.0

1000/T

3.3

3.6

lK-'l

(B, 0 )water relaxation components in Sephadex (0,O) and FIG.5. Temperature dependence of (3-50 ( A ) and G-25 (B) at 50% ( 0 ,0) and 70% (B, 0)water content. For standard deviations see legend of Fig. 1.

DISCUSSION

Assignment ofthe Two Fractions of Relaxation Components to Two Compartments of the Gel All gels investigated so far exhibit two fractions of water proton relaxation components, a large fraction ( ( Y ~and , ~ ( Y ~ and , ~ ) a small fraction ( C Y ~ and , ~ (Y~,~ On ) . the basis of experimental results we propose that these two fractions represent two separate water compartments in the gel, a larger compartment of water formed by the pores and a smaller compartment formed by the water trapped in the junction zones or tangling part of the matrix chains. If only slow or no water exchange between the pores and the loop junction zones exists, we observe two relaxation processes in the gel that sum up and exhibit the biexponential relaxation behavior of the water in gels. Indeed, the multiexponential analysis provided the evidence for a fast and a slow relaxation component that are assigned to a small and a large a fraction, respectively. The relaxation behaviors of both components and hence in both compartments differ remarkably, indicating different environments of the water molecules. Each compartment contains water in three phases: free water, water in the hydration shell, and matrix-bound water. Despite the existence of three water phases, one observes only one monoexponential relaxation process in each compartment. Therefore, in each type of compartmentalized water fast exchange among the three water phases must occur.

126

WATANABE ET AL. TEMPERATURE 50 4 0 30 500

20 10

0

I"CI

50 4 0 30 2 0

.

10

0

B

1000/T

[K-'1

FIG. 6. Temperature dependence of TZ,,(0, 0, A ) and T2,*(m, 0 , A) water relaxation components in Sephadex G-50 ( A and C) and (3-25 ( B and D) at 30%(A,A ) , 50% ( 0 , O ) and 70% (m, 0)water content. For standard deviations see legend of Fig. I .

The ratio of the amount of water in junctions to that in pores in a gel should change with increasing water content because of swelling of the gel and blowing up of the pores, if our assignment is correct. This becomes evident due to the decrease of a2,2 with increasing water content in the gel. Despite the changes of the size of the gel matrix, the relaxation behaviors of water protons in the junctions (smaller compartment) should be very similar in all gels. This is confirmed by the following results, as shown in Figs. 1 and 2. ( i ) The relaxation components T1,2and T2,2, assigned to the small water fractions al,2or a2,2,are practically independent of the pore size of the gel. (ii) T,,2and T2,2show relatively small variations with increasing water contents. The larger compartment ( -80% of water), assigned to the pores, exhibits relaxation properties of TI,, and T 2 , , ,which remarkably change with water content and pore size. This reflects again the swelling of the gel and the blowing up of the pores. The pores can take up more free water under these conditions. Due to the fast exchange among water phases in the pores one observes an increase in T1,land T2,1.This

PROTON RELAXATION PROCESSES

127

increase of water relaxation with increasing amounts of water in the gel and the characteristic 01 distribution of the relaxation components are strong indications for the validity of the compartment model of the gel.

Efective Relaxation Mechanisms in Gels Proton relaxation times of compartmentalized water have been determined in tissues (3-15), gels (22-25), food materials ( 2 6 ) , and plants (27). In general, a monoex-

ponential relaxation process of water in a closed compartment indicates fast exchange between free water and hydration water according to (l/Ti),,,=Xf/~i:,,+X,/~ih

( i = 1,2)WithXf+Xh= 1,

[41

where x indicates the population of water molecules in each phase and the suffixes f and h relate to free and hydration water. For simplicity, in the case of gel matrix the term for hydration water may also include another term for bound water. As no experimental relaxation data for bound water are available, we speak in the following about “hydration” and “free” water. The most important and predominant relaxation mechanism is based on intra- and intermolecular dipole-dipole interactions. If this relaxation mechanism is the only one that contributes to the relaxation process, the relaxation time must linearly increase with increasing temperature. On the other hand, if proton exchange processes via chemical exchange play the major role, the relaxation time should decrease with increasing temperature (28-30). Following the temperature dependence of the T 2relaxation components ( T2,1and T2,2)in Sephadex gels (see Fig. 6 ) it becomes obvious that both mechanisms are involved. As a typical example we discuss here the temperature behavior of the T2,2 component, measured in Sephadex G-50 containing 30% water (see Fig. 6C). The increase of T2,2with increasing temperature in the low-temperaturerange clearly reflects the dipole-dipole interaction mechanism. The “dip” range around 30°C, however, is a strong indicator for an additional contribution of proton exchange processes. In the high-temperature range, again, the dipole-dipole interaction is predominant. The typical example given above can be qualitatively explained in a more generalized form (see Fig. 7). In Fig. 7 the temperature dependence of the relaxation times is schematically demonstrated for a wide range of temperatures. The schematic T 2 vs 1 / T(emperature) plot exhibits three characteristic ranges: Two linear ranges at low and high temperature indicating a pure dipole-dipole interaction mechanism and a dip range at intermediate temperatures, where slow proton exchange processes become important overlapping with the dipole-dipole interactions. If we compare this scheme with the plots presented in Fig. 6 and based on experimental results, we find all characteristic features of the schematic curve in the experimental curves. This comparison further indicates that the particular contributions of each of the two relaxation mechanisms are different for each relaxation component. Figure 6 also shows that the occurrence of the dip range at particular temperatures depends on the type of gel and on the water content. The variation of the dip range on the temperature scale, as indicated in Fig. 6 by an arrow, reflects the strength of the interaction between water molecules and gel matrix and the differences in the structure and flexibility or rigidity

128

WATANABE ET AL.

Free water

/I

rriofional excharige

Hydration water

11

proton excttarge

hydroxyl proton (mat r i x )

1 /T

IK-'I

FIG. 7. Schematic T I vs 1 /temperature plot demonstrating the effects of dipole-dipole interaction and proton exchange in Sephadex gels. The arrow indicates the starting point of proton exchange. The dotted line demonstrates the expected course in no proton exchange.

FIG.8. Scheme indicating the state of water and matrix protons in Sephadex gels with free water ( T , f. TIf), hydration water (T,,, T2,J,and matrix protons ( TlbrTZb).Motional exchange of water occurs between free and hydration water. Proton exchange is possible between hydration water and hydroxyl protons of the gel matrix.

of the gels. The dip range indicates dramatic changes of the interaction between the hydration water and the gel matrix.

influcwce ofthe Proton Exchange on the T2 Relaxation Times in Sephadex G-25 A proton exchange within the gel is possible between the hydroxyl groups of the gel matrix (and/or tightly bound water molecules in the aggregated helices) and the hydration water. In addition, a motional exchange occurs between hydration and free water (see Fig. 8). The temperature dependence of the T 2value, which is attributed to the hydration water in the nearest environment of the hydroxyl groups, should reflect the chemical exchange processes. If a slow proton exchange occurs between a site A (hydration water), which binds protons characterized by slow relaxation, and a site B (hydroxyl groups), which binds protons characterized by fast relaxation, the observed relaxation time T i Afor site A is given by

where T2A, p2/\, T2B,and P 2 B are the intrinsic relaxation times and the fractions of the relaxation components at the sites A and B, respectively (29, 30). c 2 B and c 2 A are the probabilities per second or the rate constants for a given proton which leaves sites B and A, respectively. The number of protons changing from site A to site B and from site B to site A is equal, i.e., C2A-p2A= C ~ B - P ~ B . On the basis of the temperature dependence of T2,1the rate of proton exchanges between hydroxyl groups of the matrix and the hydration water is estimated for Sephadex G-25 with 30% water content. At about 15°C the T2,,vs 1 / T plot (see arrow in Fig. 6B) exhibits a dramatic change of the temperature behavior (dip range), indicating

129

PROTON RELAXATION PROCESSES

a remarkable contribution of chemical exchange processes. We state that the protons of the hydration water of each compartment constitute site A and the protons of the hydroxyl groups of the gel matrix of the same compartment constitute site B. The T, relaxation time of the hydroxyl protons (TZB) is very short, i.e., nearly 100 ps, and cannot be measured under the present experimental conditions (23). The intrinsic relaxation time of the hydration water (T,A), i.e., in the absence of an influence of the exchange processes, can be estimated as follows. The experimental T2,1value corresponds to T;A (see Eq. [ 5 ] ) . In the low-temperature range ( 5 to 10°C) T;A equals T2+,.By linear extrapolation of the T;A value from the low-temperature into the high-temperature range we obtain T2Avalues for 20,40, and 50°C (see Table 1 ). The amounts of water and of hydroxyl protons in Sephadex G-25 with 30%water content are determined on the basis of the weights of dry and wet gel and of the molecular mass. The calculation of the fractions of water and of hydroxyl groups leads to p A = 0.72 and pB = 0.28, respectively. Hence, the term ( T2B+ 1 / c 2 B ) can be calculated from Eq. [ 51. Assuming TZB= 0.1 ms, CAcan be calculated to be 20 to 89 s-’ and CBto be 50 to 230 s-l in the temperature range 20 to 50°C. The calculated data are compiled in Table 1. It should be emphasized that the rate of proton exchange is very slow in comparison with the thermal motion. Then the water protons experience the very short relaxation time of hydroxyl protons. If the proton exchange becomes fast, the proton leaves site B before it experiences the short relaxation time at site B. This is the reason why a contribution of proton exchange decreases in the high-temperature range and in “soft” gels with higher water contents. The good agreement between the expression ( 1 / TZA CA)and the observed 1/ T ; A , which is expected from the theory ( 3 0 ) ,provides reasonable evidence that the assumed values for pA, pB,T2A,and T,, are realistic. The activation energy ( E A )for the proton exchange in G-25 with 30% water content was calculated from the temperature dependence of CAand was found to be 4.8 kcal/ mol. This value was very similar to that determined from the slope of the 1 / T2,1vs T(emperature) plot (above 15”C), resulting in 4.6 kcal/mol. The slopes of the 1 / Tz,lvs T(emperature) plots in Sephadex G-25 with 50 and 70% water content led to

+

TABLE 1 Relaxation and Chemical Exchange Rates of Protons in the System “Hydration” Water/Hydroxyl Groups of Sephadex G-25 with 30% Water Content Temperature (“C)

l/TZA,(s-’)

20 40 50

43.5 71.4 90.9

I/T,

(s-I)

24.1 7.2 4.2

C:, (s-’)

C, ( s - ’ )

T:,

(ms)

T~

(ms)

20

50 168

51 15

20

65

89

230

11

4

6

Nole. 1/TIA,corresponds to the experimental Tz,,value. The T,, values related to temperatures above 20°C (the range where chemical exchange processes occur) were obtained by extrapolation from the lowtemperature into the high-temperature range. C, refers to the rate of proton donation from hydration water to the hydroxyl groups; C, indicates the rate of proton backdonation from hydroxyl groups to hydration water. r Ais the lifetime of protons in hydration water; T~ is the lifetime of protons in hydroxyl groups.

130

WATANABE ET AL.

activation energies of 4.8 and 5.1 kcal/mol, respectively. These values for the activation energy are similar to hydrogen bonding energies. Therefore, it may be reasonable that the breaking of hydrogen bonds is involved in these proton exchange processes.

Intrinsic TIRelaxation Times of Hydration Water In the previous section we discussed the evidence of proton exchange processes that occur between the hydroxyl protons of the gel matrix and the hydration water in Sephadex G-25. In the case of T Irelaxation phenomena chemical exchange processes do not play a role ( 2 9 ) . For Sephadex G-25 and G-50 we estimate the intrinsic TI relaxation times of the hydration water on the basis of T l h values employing Eq. [4]. The fractions of the hydration water ( x h )in gels containing 30, 50, and 70% water are 0.77, 0.33, and 0.14, respectively. This estimation of the fraction of hydration water is based on the assumption that at least 2590 of the water in the gels are hydration water (31, 32). This assumption seems to be quite reasonable because in all gels containing 30% water only one T I relaxation component was observed. The experimental values for the and T1,2relaxation components correspond to ( 1 / T,)obs in Eq. [ 41. The T I value of free water, corresponding to T I in Eq. [ 41 was measured for distilled water. In Fig. 9 the calculated T l h values are plotted versus temperature. The temperature dependence is shown for both the slow (TI,,) and the fast ( relaxation components and for 50 and 70% water content in the gels. are identical in both gels in the range 50 to 70% T l h of the fast component water content. Although the measured values (see Fig. 5 ) showed distinct differences for gels with differing pore sizes and water contents, the calculated Tlhvalues are identical in all cases. This finding supports the suggestion that the states and the

o * 0

10

-

-

20

S ‘ 1

30

TEMPER AT UR E

40

50

[‘C I

FIG.9. Temperature dependence of the intrinsic relaxation time Tlhof the “hydration” water. (a) Fast relaxation components (small compartment) in Sephadex G-25 and G-50. ( b ) Slow relaxation component (large compartment) in Sephadex G-25. (c) Slow relaxation components (large compartment) in Sephadex G-50. Fast relaxation components of Sephadex G-25 with 50% ( 0 )and 70% water content (m) and of Sephadex G-50 with 50% (0)and 70% water content (0).Slow relaxation components of Sephadex G-25 with 50% ( 0 )and 70% water content (m) and of Sephadex (3-50 with 50% (0)and 70% water (0).

131

PROTON RELAXATION PROCESSES

mobilities of the hydration water in the small compartments (junction zones) are identical in all gels. By taking up more than 30% water the gel swells. Then the larger compartment is also filled up with water molecules. Tlh,calculated from the slow relaxation component T1,l,shows a distinct pore size dependence (see Fig. 9). Note also that the water content (between 50 and 70%) does not influence the Tlh of the slow relaxation component. Furthermore, the Tlhvalues of the water in the large compartment (pores of the gel) are more than 50 times greater than those of the small compartment (junction zones). It can be readily assumed that in the pores of the gel the mobility of hydration water is larger than that in the loop junction zones. It may be also true that the mobility of the gel matrix itself increases with increasing water content. Hence, the temperature behavior of Tlhdetermined on the basis of the slow relaxation component indicates that the motional properties and the structure of the hydration water are mostly influenced by the nature of the gel matrix. values It is shown in Fig. 5 for Sephadex G-50 and G-25 that the observed apparently increase with increasing temperature; however, this is true for Sephadex G-25 to a much lesser extent than for Sephadex G-50. This temperature dependence of TI,I indicates that spin-lattice relaxation effects including magnetic dipole-dipole interactions are dominant. The isotropic tumbling of a proton pair is described by 1

-= G[ Tl,l

7,

1

+ o;r;

+

1

+47c4w;r:

1

and ~

1 = 'G T2,1 2

[

37,

+ 1 +5w ; r ; 7,

+

1

+ 2rc 46);r;

3.

[71

The constant G is determined by the nuclear gyromagnetic ratio and the internuclear distance. o, and 7, are the angular resonance frequency and the nuclear correlation time, respectively ( 2 9 ) . If the tumbling motion of this proton pair is isotropic, the relaxation times are determined by only one correlation time. In this case T1,lreaches should be about 1.5, if r, = 4.8 X s and the minimum and the ratio T1,1/T2,1 w, = 20 MHz. According to the temperature dependence of T I , ]the , correlation time is much less than 4.8 X lop9 s and therefore the ratio of T1,1/T2,1 should then be close to 1.0, in particular at higher temperatures. However, the observed ratios of T1,1/T2,1 are about 2.3 and 2.5 for Sephadex G-50 with 50 and 70% water content, respectively. Therefore, the tumbling motion of the water in Sephadex G-50 is anisotropic and different correlation times influence the TI,Iand T2,1relaxation times. It should also be mentioned that the ratio T I , /] T2,1is slightly but significantly smaller in Sephadex G-50 with 70% water content than that with 50% water content. The swelling of the gel by the uptake of larger amounts of water results in a blowup of the pores and hence a faster tumbling motion of the water molecules. In the case of Sephadex G-25 the observed ratio of TI,I/ T2,I increases with increasing temperature because of the decrease of T2,1with temperature due to the proton exchange processes described above. The activation energy of the tumbling motion is about 4 kcal/mol for Sephadex G-50 with 50 and 70% water content, while it is about 1 kcal/mol for Sephadex G-

132

WATANABE ET AL.

25 with 50 and 70% water content. It should also be mentioned that the apparent activation energy of the tumbling motion becomes smaller in the presence of proton exchange processes. This finding is supported by spin probe ESR measurements (Watanabe et al., unpublished results). CONCLUSIONS

1. The multiexponential analysis of the T I and T2 proton relaxation processes in Sephadex gels revealed the existence of two relaxation components indicating two nonexchangeable water compartments, i.e., water in the pores (this is the large compartment comprising about 80%of the total water) and water associated to the junction zones (this is the small compartment comprising about 20% of the total water). 2. The relaxation times of water protons in both compartments and in all gels are predominantly controlled by dipole-dipole interactions and under special conditions additionally by proton exchange processes between hydration water and the hydroxyl groups of the gel matrix. 3. In particular, the temperature dependence of the T2,,relaxation component observed in a gel with small pores, such as Sephadex G-25 (with a pore diameter of G-25 (50% water) > G25 (70% water) > G-50 ( 50% water) > G-50 (70%water). G-25 ( 50% water) and G25 (70% water) exhibit the adequate rigidity. 4. The TI,, and T2,,relaxation times assigned to the larger water compartment (pores of the gel) depend on the pore size and the water content in gels. Water in gels can be considered a simple model for water in biological tissues. In contrast to gels, tissues exhibit water compartments which vary largely in size. The water clusters in the pores of Sephadex G-25 and G-50 exhibit diameters of about 15 and 22 A,respectively. Hence, in tissues with water clusters (or pores) exhibiting a smaller diameter and smaller water content the T2relaxation time should be more dramatically reduced than the T Irelaxation time. The identification of two water compartments in gels by multiexponential analysis of the relaxation processes and the observation of the characteristic temperature behavior, which reflects the effect of two different relaxation mechanisms, lead to the conclusion that tissue characterization could be improved by analysis of the multiexponential relaxation processes and by determination of the temperature behavior of these processes. Hence, the size of water compartments, the amount of water, and the interaction of hydration water with biological macromolecules (via proton exchange processes) in the tissue are the basis for tissue characterization. It has been suggested that the cross-relaxation and /or the chemical exchange between protons of free or highly mobile water and protons of macromolecules or immobile

PROTON RELAXATION PROCESSES

133

water are predominant mechanisms in biological tissues (31-33). In this paper we show that in Sephadex gels the proton exchange affects the water proton relaxation rate only under specific and limited conditions. 5. In Sephadex gels the “inverse” temperature dependence of T , water relaxation times was observed in the temperature range 10 to 40°C for specific conditions, i.e., for gels with a small pore size and with small water contents. In these gels the compartmental water showed an abnormal thermal behavior in the freezing and thawing process, which means that a fraction of water does not freeze out, when the temperature decreases below O’C, and crystallizes at about - 12”C,when the temperature increases starting from 77K (34, 35). The relaxation data of water in gels suggest that the properties of the compartmentalized water in tissues also depend on the size of water clusters, on the mobility of water molecules in the pores, and on the flexibility of the surrounding matrix. All these properties seem to be important for freeze-preserving biological tissues and food materials. ACKNOWLEDGMENTS This work was supported by the Fonds der Chemischen Industrie (K.G.) and the Medizinische Biophysik e.V. (K.G.) and by a Grant-in-Aid for Scientific Research (No. 6247004) from the Ministry of Education, Science and Culture (T.W., N.M.). REFERENCES 1. “Magnetic Resonance Imaging” (D. D. Stork and W. G. Bradley, Eds.), C. T. Mosby Corp., St. Louis, 1988.

2. S. H. KOENIG,R. D. BROWN 111, M. SPILLER,AND N. LUNDBOM, Magn. Reson. Med. 14,482 ( 1990). 3. P. S. BELTON,R. R. JACKSON,AND K. J. PACKER,Biochim. B i o p h j ~Actu 3,286 ( 1972). 4. K. R. FOSTERAND H. A. RESING,Science 194,324 (1976). 5. W. C. SMALL,M. B. MCSWEENEY, J. H. GOLDSTEIN, C. W. SEWELL,A N D R. W. POWELL,Biochirn. Biophys. Acta 112, 991 (1983). 6. M. B. MCSWEENEY, W. C. SMALL,V. CERNY,W. SEWELL,R. W. POWELL,AND J. H. GOLDSTEIN, Rudiology 153, 741 (1984). 7. R. BARTHWAL, M. HOEHN-BERLAGE, AND K. GERSONDE, Magn. Reson. Med. 3,863 (1986). 8. 2. KOVALIKOVA, M. HOEHN-BERLAGE, K. GERSONDE, R. PORSCHEN, C. MITTERMAYER, AND R.-P. FRANKE,Radiology 164,543 ( 1987). 9. M. KVEDER,I. ZUPANCIC, G. LAHAJNAR, R. BLINC,D. SUPUT, D. c . AILON,K. GANESAN, AND C. GOODRICH, Magn. Reson. Med. 7, 432 (1988). 10. R. L. KAMMAN, K. G. Go, W. BROUWER, AND H. J. C. BERENDSEN, Magn. Reson. Med. 6,265 ( 1988). 11. K. GERSONDE, L. FELSBERG, T. TOLXDORFF, D. RATZEL,AND B. STROBEL,Magn. Reson. Med. 1, 463 (1984). 12. K. GERSONDE, T. TOLXDORFF, AND L. FELSBERG, Magn. Reson. Med. 2, 390 ( 1985). 13. P. R. LUYTEN,C. M. ANDERSON, AND J. A. DEN HOLLANDER, Mugn. Reson. Med. 4,431 ( 1987). 14. H. B. W. LARSSON, J. FREDERIKSON, L. KJAER,0. HENRIKSON, AND J. OLESEN, Mugn. Resan. Med. 7,43 (1988). 15. P. A. NARAYANA, W. W. BREY, M. V. KULKARNI, AND L. L. MISRA,Magn. Reson. Med. 4, 153 (1987). 16. N. MURASEAND T. WATANABE, Mugn. Reson. Med. 9, 1 ( 1989). 17. K. R. BROWNSTEIN AND C. E. TARR,Phys. Rev.A 19,2446 ( 1979). 18. R. REPGES,T. TOLXDORFF,L. FELSBERG, G. BROSZIO,A N D K. GERSONDE, in “Proceedings of the International Symposium CAR 85,” pp. 25-29, Springer-Verlag, Berlin, 1985. 19. L. FELSBERG, B. MECKING, T. TOLXDORFF,R. REPGES,AND K. GERSONDE, in “Proceedings of the International Symposium CAR 85,” pp. 9-14, Springer-Verlag, Berlin, 1985. 20. S. W. PROVENCHER, Makromol. Chem. 64,2772 (1978).

134 21. 22. 23. 24. 25.

26.

27. 28. 29. 30. 31. 32. 33. 34. 35.

WATANABE ET AL.

R. J. S. BROWN,J. Magn. Reson. 82, 539 (1989). D. E. WOESSNER AND B. S. SNOWDEN,JR., J. Colloid Interface Sci. 34,290 ( 1970). T. F. CHILD AND N. G. PRYCE,Chem. Commun., 1214 ( 1970). F. DE LUCA,B. MARAVIGLIA, AND A. MERCURIO, Magn. Reson. Med. 4, 189 ( 1987). M. AIZAWA,S. SUZUKI,T. SUZUKI, AND H. TOYAMA, Bull. Chem. SOC.Japan 46, 116 ( 1973). P. J. LILLFORD,A. H. CLARK,AND D. V. JONES,in “Water in Polymers” (S. P. Rowland, Ed.), ACS Symposium Series, Vol. 127, p. 177, Arner. Chem. SOC.,1980. L. WITHERS,In[. Rev. Cyzol. Suppl. IIB. 101 (1986). D. E. WOESSNER,J. Chem. Phys. 3 5 4 1 ( 1961). D. E. WOESSNER,J. Chem. Phys. 39,2783 (1963). D. E. WOESSNERAND J. R. ZIMMERMANN, J. Phys. Chem. 67, 1590 (1963). H. T. EDGESANDR. T. SAMULSKI,J. M a p . Reson. 31,207 (1978). S. H . KOENICAND R. BROWN,in “NMR Spectroscopy of Cells and Organisms” (R. K. Gupta, Ed.), Vol. 2, p. 115, CRC Press, Boca Raton, FL, 1987. S. D. WOLFFAAND R.S. BALABAN, Magn. Reson. Med. 10, 135 (1989). N. MURASE,K . GONDA, AND T. WATANABE, in “Fundamentals and Applications of Freeze-Drying to Biological Materials, Drugs and Foodstuffs,” pp. 5 1-57, Inter. Inst. Refrigeration, 1985. N. MURASE,K. GONDA,AND T. WATANABE, J. Phys. Chem. 90,5420 ( 1986).