Nuclear magnetic relaxation studies of water in frozen biological tissues. Cross-relaxation effects between protein and bound water protons

JOURNAL

OF MAGNETIC

RESONANCE

58,

11%

13 1 ( 1984)

Nuclear Magnetic Relaxation Studies of Water in Frozen Biological Tissues. Cross-Relaxation Effects between Protein and Bound Water Protons J. M. EscANY~,*~-~

D. CANET,?

AND J. ROBERT*

*Laboratoire de Biophysique et Service de Midecine Nuclkaire, 18 rue Lionnois, F-54000 Nancy, and TLaboratoire de Methodologie RMN, Equipe de Recherche Associk au CNRS no 22, Universitt? de Nancy-l, B.P. 239, F-54506 Vandoeuvre les Nancy Cedex, France Received April

11, 1983; revised

November

3, 1983

Water proton longitudinal relaxation has been investigated in frozen mouse tissues including tumors. The nonfreezable water which gives rise to a relatively sharp NMR signal at this temperature (263 K) is identified as water bound to macromolecules. Measurements have been carried out by the nonselective inversion-recovery method at 90 and 6 MHz. Partially selective inversion has been achieved at 90 MHz by the DANTE sequence. The experimental data are analyzed by means of Solomon-type equations. This analysis provides the cross-relaxation term from which the dipolar contribution to water relaxation rate, arising from interactions with macromolecular protons, is calculated. This contribution seems to be dominant. The number of water protons interacting with a given macromolecular proton is found to be of the order of 10. The data at both frequencies can be consistently interpreted in terms of water diffusion, with a characteristic time of about 10m9 sec. These conclusions are valid for all the tissues investigated here, their relaxation parameters exhibiting only slight differences. INTRODUCTION

It has been recognized for some time that the fast-exchange two-state (FETS) model can be successfully applied to NMR data concerning water in biological tissues (1-3). According to this model, water molecules exchange rapidly between a “free” state, similar to that of pure water, and a “bound” state highly affected by the presence of proteins and other macromolecules. However, there is a lack of understanding of the motional mechanisms of water molecules in the bound state, and thus of the relaxation sinks for protons (4). We have already presented (5) frequency dispersion studies of water proton longitudinal relaxation time in tissues at temperatures around the freezing temperature. The comparison of properties at temperatures a little higher and a little lower than freezing has yielded the proportion of nonfreezable water (identified to a good approximation with bound water), its relaxation time, and its Larmor frequency dependence. This latter property was shown to be compatible with a translational diffusion model introduced previously (6). No unanimity exists, however, for such a mechanism, and the older model of a distribution of rotational correlation times (7-9) has been widely used. On the other hand, recent work (10-14) has given evidence for the particular 0022-2364184

$3.00

Copyright 0 1984 by Academic Press, Inc. All rights of reproduction in any form reserved.

118

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importance of cross-relaxation mechanisms between bound water protons and protein protons, either in protein solutions or in tissues. We present in this paper a study of water proton longitudinal relaxation in frozen mouse tissues at a temperature where only the nonfreezable water is observed. These experiments have been performed at two Larmor frequencies (90 and 6 MHz) by using a standard inversion-recovery experimental method. Also, selective inversion by means of the DANTE sequence of Morris and Freeman (15) has been attempted. These experiments are analyzed through the Solomon equations, with the aim of determining the cross-relaxation term and of gaining a better insight into the mechanisms of dipolar interactions between bound water protons and macromolecular protons. We shall assume that protons of unfrozen water interact with macromolecular protons rather than with protons of frozen water. The preponderant contribution to intermolecular dipolar interactions arises very likely from macromolecular protons because of their strong dependence with respect to the distance between protons. EXPERIMENTAL

Proton T, relaxation times have been measured with a highly modified HX 90 Bruker spectrometer operating in the FT mode at 263 K. This temperature is lower than the freezing transition for all tissues investigated (269 to 264 K (5)). Thus, the recorded NMR signal using a delay time between the rf pulse and the beginning of acquisition of 400 psec is that of “unfreezable” water (i.e., water that remains sufficiently mobile to give a proton NMR signal with a linewidth of the order of 200 Hz). We shall assume, in this paper, that this fraction corresponds to bound water. This assumption rests on arguments developed previously (5). Recovery curves were measured by the 180”-7-90’ method, the inversion selectivity being adjusted by the number of pulses of an appropriate DANTE sequence. The spectral width is 2500 Hz, and for selective experiments the frequency difference between the carrier and Larmor frequencies is about 1000 Hz, thus giving a pulse spacing T’ of about 1 msec in the inverting pulse train. As shown by Morris and Freeman (15), the effective selectivity (i.e., the frequency window, centered on l/7’, which is excited by this sequence of rf pulses) expressed in hertz can be estimated as 0.64/(NP~‘) where NP is the number of pulses of the train. Because of the linewidth of the signal to be inverted (-200 Hz), the DANTE sequence may comprise up to eight pulses. In this study, we have used standard one-pulse inversion, and with NP equal to 2,4, 6, and 8, as shown in Fig. 1, in order to gain a variable selectivity effect for bound water versus macromolecular protons. These experiments have been performed at the normal proton frequency of 90 MHz, and by using the variable field property of the magnet, at 6 MHz. However, since no lock was available at the latter frequency, the field stability was not sufficient enough to perform selective inversion. Recovery could be bi- or multiexponential, and cross-relaxation effects are expected to manifest themselves in the initial part. This necessitates an accurate definition of the recovery curves, and 7 values are started at 1 msec and incremented in millisecond steps. Also, since linewidth in the series of partially relaxed spectra is constant, it is

120

ESCANYG,

CANET,

AND

ROBERT

CqLb

“N”a.“; 4.450

\

Dante

/ 6.30’

NP=4

\ /

Dante NP=6

Dante NP:E

B inverting n

after

90’

trains proton

for T, measurements. signal (hatched area).

pulse T

JIL inverting

spectrum

pulse

sequence

FIG. 1. (A) Definition of the standard and selective pulse representation of selective inversion occurring only for water

(B) Schematic

equivalent to monitor peak areas or peak heights. For practical reasons, we have chosen the latter. Tissues from 3 to 6 month old inbred C3H mice have been examined. Two grafted tumors of the rhabdomyosarcoma type (named hereafter tumor 1 on females, and tumor 2 on males) as well as hind limb muscle, kidney, liver, and spleen, have been studied. Tissues were dissected immediately after death, gently blotted free of blood, and placed in stoppered NMR tubes. Measurements were made in the 10 hours following death; in the mean time tissues were kept at 277 K. For each determination, measurements were performed on three samples of each type of tissue. RESULTS

A biexponential behavior is observed in every case (Fig. 2). The following notation will be used throughout: XI and X2are the time constants defining the two exponent&;

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121

WATER

A

9 (lin)

lY (log)’

I.

’

0.8 I.

\

0.1I.

\ 0.4 1.

4 0.04

\ c 0

4

6

16

12

16 32

w 64

128

2 (w

FIG. 2. Example (NP = 2), 3-(NP

266

't 0-w

of magnetization decay shown with linear = 4), 4-(NP = 8); muscle at 90 MHz.

and logarithmic

d scales:

l-standard,

2-

X, corresponds to the last and longest part of the recovery which is easily isolated by a semilogarithmic plot, due to the large difference between A, and X2.’ The magnetization of the bound water protons will be denoted by Z(T) and its normalized value by 44

=

10 - 47) 2z 0

where IO is its equilibrium

value with d(7) = ale”’

+ u2eX2r.

’ In our previous study (5), the very first part of the recovery corresponds therefore to the inverse of /X,1.

had not ken

considered.

The quoted

( T,)0ba

122

ESCANYI?,

CANET,

AND

ROBERT

We define the ratio of the amplitude of the slower decay to the amplitude by +-AL

at T = 0

131

a1 + a2 .

The initial slope of the magnetization will be denoted by b(0). The same conventions hold for protein protons, with the notations S, 7 and T(O). These observables are extracted from the experimental data in the following way: a semilogarithmic plot of the recovery curves yields directly h, ; the intercept of the extrapolated line with the d axis provides al. From the extrapolation of a(~) at T = 0 we obtain aI + a2 as well as b(O), and finally X2 is deduced from the first part of the recovery curves from which arex’7 is subtracted. All experimental data are gathered in Table 1 (90 MHz experiments) and Table 2 (6 MHz experiments). TABLE 90 MHZ

Value

mblb (msec)

R’

Tissue 1 2

12 11 10 11 9 9

Tumor Tumor Muscle Spleen Kidney Liver

1 2

155 150 150 150 137 135

Tumor Tumor Muscle Spleen Kidney Liver

1 2

wJ)d

Mean f SD

l.mle (msec-‘)

Tumor Tumor Muscle Spleen Kidney Liver

INVERSION-RECOVERY

Standard

Tumor Tumor Muscle Spleen Kidney Liver

1 2

1 DATA

DANTE NP = 2

DANTE NP = 4

DANTE NP = 6

DANTE NP = 8

12 12 11 11 9 9

13 9 9 10 8 7

11 7 7

16 9 10 11 10 7

Same as for standard

0.77 0.71 0.73 0.70 0.70 0.73

0.76 0.74 0.80 0.77 0.76 0.80

0.80 0.80 0.80 0.78 0.77 0.80

experiment

0.80 0.83

0.83 0.80 0.80 0.79 0.77 0.81

0.929 t 0.021

0.731 + 0.034

0.596 f 0.043

0.466 + 0.040

0.40 1 f 0.032

0.045 0.041 0.047 0.033 0.039 0.033

0.025 0.026 0.026 0.022 0.025 0.022

0.018 0.015 0.022 0.018 0.023 0.015

0.015 0.012 0.016 0.013

0.010 0.009 0.010 0.009 0.014 0.01 I

Notes. -, not measured; uncertainties: 0.01 and 0.03; d between 0.02 and 0.04;

’ between e between

0.7 and 1.5 msec; b between 0.001 and 0.004 mscc-‘.

1 .O and 3.0 msec; ‘between

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TABLE 6 MHz

l/IU” (mW

Tissue Tumor Muscle Liver

STANDARD

1

4 5 3.5

WATER

123

2

INVERSION-RECOVERY

DATA

l/W (msec)

Ylc

.‘7(0)d

30 30 24

0.80 0.81 0.81

0.92 0.95 0.84

l.m)l’ (msec-‘) 0.06 I 0.064 0.056

Notes. Uncertainties: a between 1.O and 2.0 msec; b between 1.0 and 2.0 msec; ’ between 0.02 and 0.03; d between 0.03 and 0.04; e between 0.009 and 0.0 18 msec-‘.

ANALYSIS

Since biexponentiality is observed for water magnetization recovery, it seems pertinent to analyze our data within the approximation of Solomon equations (16). According to the notations defined in the previous section, Z will represent water proton magnetization whereas S will stand for the magnetization of a given macromolecular (protein) proton interacting by dipolar coupling with water. RI and Rs will be the relaxation rates of the water and macromolecular protons, respectively, u is the cross-relaxation term, and f is the ratio of the number of macromolecular protons and water protons mutually interacting (f is of course positive but can be smaller than unity). In the following equations, further assumptions have been made: all macromolecular protons share the same relaxation rate (this hypothesis can be justified by spin diffusion (I 7)) and u represents an average cross-relaxation term associated with the dipolar coupling between macromolecular and water protons. All these approximations are akin to previous approaches (10-14). One has

- S,,)

WI

$7) = -~(Z(T) - IO) - R.@(T) - So)

[4bl

fin) = -R,(Z(T) - Z,,) -fa(S(~)

and with the normalized

magnetizations,

as defined in [l]

b = -Rid

- fu‘t

PaI

?- = -ud

- R,T.

[W

These equations are solved by computing vectors of the relaxation matrix:

the eigenvalues Xi and A2, and the eigen-

[61 It appears convenient

to define the following

relaxation parameters, instead of RI,

Rs, and CT: R,=R,+-R,

and

x=- 2uVf

R- .

171

124

ESCANYB,

CANET,

AND

ROBERT

This yields

[81 and b-1

1+ X\Tf.$$))

R-lG-3?

[91

where 2(O) and a(O) are the initial values of the normalized magnetizations I and d; these will depend on whether a standard nonselective single pulse, or a pulse train is used for inversion. It is immediately seen that two possible values of u could be deduced from R if f was known. Once (r is determined, R+ and R_ are obtained from Xi and Xz. The only means for obtaining f is to vary the ratio I(O)/&(O). This is, in principle, accomplished by substituting for the single nonselective inverting pulse a DANTE train of NP small pulses, each of them corresponding to a flip angle CY,so that NPa = a. The time 7’ elapsed between two consecutive pulses allows the proton magnetization vector to precess by an angle of exactly 27r. However, in our case, full selectivity (a(O) = 1, I(0) = 0) cannot be achieved because of the relaxation processes which take place between pulses. We give below expressions allowing us to calculate the actual ratio “r(O)/&(O), with the single assumption that all transverse S magnetization has totally vanished after a time 7’. This seems perfectly justified by the experimental value 7’ = 1 msec, which certainly is much greater than Tzs, since the signal due to macromolecular protons would otherwise be observable. We shall need two further quantities: d r = ZY/2Z0 (assuming that the X axis of the rotating frame coincides with the rf field), and T1; which is equal to l/(?rAv), where Au is the experimental water linewidth. Prior to the application of the pulse train, an equilibrium state is assumed, and ‘Z- = d = ~+r = 0. To calculate magnetizations at the end of the pulse sequence, we first consider the effect of a pulse of flip angle CC d - d cos a + d y sin (Y- (1 - cos a)/2 ~~~coscy+(1

-cosa)/2

dy+ -73 sin ff + dYcos ff + sin (~12. We then express the evolution during the time 7’ between two pulses:

PW [lob1 [1Ocl

d - a, exp(X,r’) + a2 exp(X27’)

1114

7 -

[l lb1

aIll

exp(X,T’) + az”;T, exp(X27’)

11ICI

6, - by exp(-r’/T%;) where

P-I a17a2=7+2R-,,37j72

(a - xti7)

[lldl

and

11lel

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125

This procedure yields the required T(O)/&(O) value, provided that all relaxation parameters and fare known. Since these parameters must be determined, we have devised a fitting procedure which is described below. For each tissue investigated, 40 possible values for the set (R,, Rs and a) corresponding to 20 fixed values off in the range 0.001 to 5, are derived by calculating X, R- and R, from the experimental data (X, , XZ, and 3) pertaining to the standard inversion recovery experiment. Figures 3A and B exemplify the variations of RI, Rs and u, determined in this way as a function off; in the case of muscle; the two possible solutions for X in [9] correspond to the two possible signs of u. For each set (R,, R- , X, f), the effect of the selective inversions for NP = 1 to 8 are calculated through formulae [lo] and [ 1 l] and compared to experimental results; only the 2 values have to be considered since XI and X2 are necessarily identical to those of the standard experiment. This should lead to an optimum value off and is exemplified in Fig. 4 and Table 3. It is clear that negative u can be rejected. A positive u is consistent with experimental results but, unfortunately, fcannot be determined with great accuracy; it should lie in a range 0.01 to 1.0, (this is observed for muscle as well as for other tissues). Having selected a possible range for J it is possible to go back to formulae [7] and [8], or to Fig. 3, to get the final result: RI, Rs, and u. In this way, the uncertainties in these parameters due to the poor definition offare obtained. These results are reported in Table 4. Some further comments are needed for explaining the somewhat wide range found forJ: It can be seen from Fig. 4 that the X parameter is not very sensitive tof: Another experimental parameter, b(O), which could have been used in determiningfis, likewise, little dependant on its choice and would be more prone to experimental errors. Therefore, for obtaining/accurately, it would be necessary to determine Jr! very precisely; this would require a perfect adjustment of pulse widths, which is not achieved here as seen, for instance, in the experimental a(O) values. The phenomenon of cross-relaxation is demonstrated in spite of the fact that the S signal is not visible, and this prevents experiments like cross-saturation (18). Furthermore, although u is poorly determined, a range of u values can be provided and the productfa is seen to be less sensitive to the choice off: Finally, standard inversionrecovery experiments at 6 MHz have been interpreted assuming the same range of fvalues. The relevant results for RI, Rs, u, andfu are given in Table 5 for three tissue species: tumor 1, muscle, and liver. DISCUSSION

The prominent feature of the results given in Tables 4 and 5 is the similarity of the relaxation parameters which can be determined with a reasonable accuracy, i.e., RI, Rs, and fu, for the different tissues investigated here. This is not surprising since, according to our previous conclusions (5, 6), the differences of r, at temperatures above the freezing point are essentially attributed to the bound water proportion. Nevertheless, the small differences which remain here, for nonfreezable water, obey the same hierarchy as for higher temperatures. This is true for RI, Rs, as well asfa. Concerning the frequency dependence, it is observed that, as expected, RI, Rs, and fu increase when going to lower frequencies. It must be remembered that we Previously (5) measured an effective relaxation rate ( 1/T&,b, which must be identified

126

ESCANYI?,

CANET,

AND

ROBERT

ICJI (Ins-’

RIRs (m-1)

B

0.1

0.05

0

3. Representation of RI, Rs, and g as a function 0 positive; (B) solution with c negative.

FIG.

with

offfor

the muscle

data at 90 MHz:

(A)

solutjon

with /A,/ of this paper. The variation of (l/T,),, with frequency has been found to be (1/TI),b, = A/G + B. [I21

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WATER

127

Os3L,=, a51

'2

‘4

‘6

‘8

'2

‘4

‘6

‘6

I O8 '1

NP

I NP

FIG. 4. Calculated values of the parameter R as a function of the number of pulses of the DANTE train, for muscle at 90 MHz, with the solutions corresponding to 0 > 0 and Q < 0. The parameterfis obtained from the best fit to experimental data (stars).

We are here interested in the nonfreezable water and we shall focus on the behavior of RI and $7 with respect to frequency. For that purpose, let us write ( 1/T1)Obsas

[I31 where kI depends on the cross-relaxation term u and can be evaluated by means of formula [8] using the numerical values given in Tables 4 and 5. We find for k,, 1.2 1 + 0.03 and 1.30 k 0.0 1 at 90 and 6 MHz, respectively (the quoted uncertainties refer only to the tissue nature). Inserting numerical values in [ 131, we can conclude that the frequency variation of RI is responsible for roughly 70% of the frequency variation of the observed relaxation times. We therefore shall not consider Rs and limit ourselves to the study of the mechanisms leading to the frequency dependence of RI and u. The relaxation rate involves different bipolar contributions, including the intramolecular interaction RF, the intermolecular water-water interaction R$:&,, the intermolecular water-protein interaction R%!$, and finally a term arising from other than dipolar mechanisms, Rother. Our aim is to determine the importance of R$.?i, in R,, since it reveals most of the properties associated with the water-protein interactions. On the other hand, jk solely depends on these dipolar interactions. These two quantities can be expressed as a function of the spectral densities J’(w) as (16)

R&‘:$ =f;y4h2

$7 =fi where w/27r is the Larmor

+i"(-

+‘(O)+

$P(o)+

;J’(w)+;

J2(2w)

t P(24)

frequency, y is the gyromagnetic

ratio of proton, and h

128

ESCANYE,

CANET,

AND

TABLE CALCULATED EXTREMUM

VALUES

OF fl,

VALUES~“=

9(O),

and

0.01

3

l.?(O)1 FOR THE MEAN

Standard

DANTE DANTE DANTE DANTE

NP NP NP NP

= = = =

2 4 6 8

VALUE

f = 0.1, AND FOR THE

AND f = 1.0, IN THE CASE OF MUSCLE

f = 0.01 Experiment

ROBERT

f=

R

J(O)

IJiOl

0.73 0.74 0.76 0.78 0.80

1.0

0.77 0.62 0.52 0.44

0.032 0.023

TISSUE

0.1

(U > 0) f=

1.0

33

9(O)

I%l)l

.n

J(O)

Ij(O)l

0.018

0.73 0.77 0.79 0.81

0.83

0.73 0.80 0.83 0.86 0.87

1.0 0.77 0.62 0.52 0.45

0.032 0.019 0.014

0.014

0.032 0.022 0.016 0.012

0.011

1.0 0.77 0.62 0.52 0.45

is the Planck constant divided by 2~. In the common diffusion, the J”s can be expressed as

P(0) = 6J’(O),

0.010

0.011

0.008

model (6, 26) of translational

[16bl

J’(w) = 4J’(w)

where K is a constant which can be determined in very simple models such as hard spheres (16) and will be treated here as unknown, 7 is the average time between successive diffusion steps, ~3s,~is the Bessel function of order 3/2. We shall now introduce for clarity, the reduced expressions j’:

i y4/$,2J’= z 5

y4h2Kji

=

TABLE J; (r, f~, RI,

AND Rs VALUES OBTAINED FROM 90 MHz DATA PROCEDURE DESCRIBED IN THE TEXT”

f

f range

(msec-‘)

Tumor

1

0.1

Tumor

2

0.1

0.210.0 1 0.5/0.05

Muscle Spleen

0.1 0.1

0.2/0.0

1

Kidney Liver

0.1 0.1

0.5/0.01 1.o/o.o 1

0.12 0.13

a The

quoted

1.0/0.01

uncertainties

fg

RI (msec-‘)

+ 0.10

0.007

f 0.003

0.11

f

0.05

0.011

+ 0.004

0.11

f

0.16

0.10

+ 0.13

0.011 0.010

f 0.007 -c 0.004

f 0.18 f 0.20

0.012 0.013

+ 0.007 f 0.009

to variations

ACCORDING

(msec-‘)

0.07

correspond

1,2,3

4

0

Tissue

i=

kji,

off

within

0.015 0.023 0.021 0.022 0.026 0.026 the given

-+ + rt f + +

TO THE

RS (msec-‘)

0.003 0.004 0.007 0.004 0.007 0.008

range.

0.068 0.084 0.085 0.076 0.092 0.107

f + 2 f k

0.003 0.004 0.007 0.004 0.007

f

0.008

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TABLE

Tissue Tumor Muscle Liver

f 1

0.1 0.1 0.1

transforming

f

5

RI, AND Rs AT 6 MHZ,FORTHE f RANGE (SAME REPRESENTATION AS FOR TABLE 4)

CALCULATEDVALUESOFW,~~,

range

0.2/0.01 1 .O/O.Ol 1.o/o.o I

0 (msec-‘) 0.20 0.16 0.23

fu (msec-‘)

+ 0.29 + 0.25 + 0.36

129

WATER

0.020 0.016 0.023

f 0.007 + 0.009 31 0.013

DETERMINEDAT~~

RI (msec-‘) 0.054 0.051 0.065

+ 0.007 f 0.009 + 0.013

MHz

RS (msec-‘) 0.229 0.183 0.262

f 0.007 f 0.009 f 0.013

[15a] and [ 15b] into the following: R$A$ = kfr,

fu = I& with j’(w) =

r = 2j1(2w) + j’(w) +j’(O)/3

[17al

s = 2j1(2w) - j’(O)/3

117’4

s*4,204 0

udu u4 + cd=?=.

Figures 5A and B represent s and r for different 7 values. These curves allow one to determine ? from the experimental ratio of fu at 6 and 90 MHz. We find ? N l-2. lo-’ sec. In a second step, from the JC value itself, the scaling factor @ can be calculated, and consequently R$T$ (formula [17a] and curves 5B). This yields R’$‘?$ (90 MHz) = 0.040 +- 0.028 msec-’ and Ri$!Y$(6 MHz) = 0.060 f 0.043 msec-‘, to be compared with RI (90 MHz) = 0.022 f 0.004 msec-’ and RI (6 MHz) 0.057 + 0.006 msec-‘. This means that, within this model and within experimental errors, the bound water relaxation rate seems dominated by the dipolar interaction with the macromolecular protons. The last point to be discussed is the frequency behavior of R$?$ as shown in figure 5b. We postulated that RI, which can be assimilated in R$&, is essentially responsible for the linear variation of l/T, with respect to l/h in the frequency range considered. Figure 5B, for the selected r, exhibits some curvature that is not experimentally observed (5, 6). This can be explained by (i) an oversimplified diffusion model, and (ii) the presence in the (l/T& expression (formula [ 151) of the term involving Rs whose frequency dependence could counterbalance the considered curvature. Finally, it was tempting to directly determine T by looking at the linear part (continuous line in the series of curves 5B). The above considerations indicate, however, that this would have introduced a serious bias. CONCLUSION

The main conclusion reached in this paper concerns the importance of dipolar interactions between protons of bound water and macromolecular protons in biological tissues. This contribution, recalculated from the cross-relaxation term, seems to constitute the major part of the water relaxation rate. Although the cross-relaxation rate

130

ESCANYl?,

CANET,

AND ROBERT

FIG. 5. Representation of the frequency dependence of the relaxation parameters calculated in the diffusion model for different values of the parameter ? (given in psec): (A) s rate: circles correspond to the values fitting the experimental ratio s(9O)/s(6); (B) r rate: the dashed line represents the variations deduced from s as compared to a linear variation (- - -), the continuous line results from the direct evaluation of i by r, data (see Ref. (6)).

u is determined with poor accuracy, the quantityfa which is involved in the water proton relaxation rate can be obtained with more reliability. The quantity 1/‘represents the number of water protons interacting with a macromolecular proton and is found to be of the order of 10. The whole data set can be consistently explained in terms of water diffusion, with a characteristic time around 10m9 sec. Finally, the relaxation parameters in the various tissues investigated here show little difference at this temperature. This further confirms that the discrimination observed at higher temperatures is essentially due to the proportion of free water. However, the slight variations noticed here affect the three relaxation parameters (water and protein relaxation rates RI and Rs, and cross-relaxation ratefa) in the same way. This trend parallels that for water T, in the various tissues at normal temperature (6).

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WATER

REFERENCES

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