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A study of the proton exchange in tissue water by spin relaxation in the rotating frame
Volume
22, number
2
CHEMICAL
PHYSICS
A STUDY OF THE PROTON BY SPIN RELAXATION
1 October
LETTERS
EXCHANGE
1973
IN TISSUE WATER
IN THE ROTATING
FRAME*
R.T. THOMPSON, R.R. KNISPEL and M.M. PINTAR Departments of Physics and Statistics, University of Waterloo, Waterloo, Ontario, Canada Received 24 June 1973 Revised manuscript received 5 July 1973
The exchange rate of the water protons in mouse tissues was determined for the first time. The process was studied by proton spin relaxation in the rotating frame. The exchange correlation time was found to be =5 X 10e6 sec. The actual residence rime of a water proton on one water molecule in tissue was estimated to be =lO-’ It is shown that because of the fast exchange the estimate (210%) of the amount of ordered water is too low.
It is well known that the exchange of protons between non-equivalent sites in one molecule, or among different molecules, modulates the spin energy. The exchange can be studied by nuclear magnetic resonance methods [l] . If the proton exchange is slow, so that the proton spends enough time at each non-equivalent site, several absorption lines, one for each site, are observed. Such a situation is best studied by the NMR absorption experiment. If the exchange rate becomes larger, an averaging over all different sites takes place. The absorption spectrum becomes a single narrow line. This is referred to as exchange narrowing. It occurs if the exchange rate is such that 807, < 1, where 60/2n is the difference between the Larmor frequencies at non-equivalent sites and r, is the exchange correlation time. In such a situation the exchange process is best studied by relaxation methods. If the exchange rate is less than IO4 set-l , a spinspin relaxati’on experiment is employed. For faster exchange the relaxation in the rotating frame can be used to study the process. The proton magnetic resonance absorption line of tissue [2] consists of a broad line of ~10 kHz which is due to protons on molecules other than water, and * This investigation
was supported by Public Health Service Research Grant No. lRO1 CA-14384-01 from the National Cancer Institute.
set
of two narrower components from water protons. The less narrow (1000 Hz) water component was assigned to the protons of the bound water and the more narrow (10 Hz) water component to the protons of the majority or “free” water. The intensity of the majority water line is about ten times stronger than the intensity of the bound water line. It is not understood whether the 10 Hz proton absorption line represents the absorption of protons on water molecules with a large degree of orientational and positional disorder characteristic of an almost isotropic liquid, or if this line is narrow because of the fast exchange of protons between different water molecules which are partially ordered. It is possible that the two effects are combined, that is, the line may be a super-position of an almost isotropic liquid component and an exchange-narrowed ordered liquid component. To check the origin of this narrow line we measured directly the exchange of water protons by spin-locking the proton spins in the rotating frame and measuring the proton spin-lattice relaxation time (Tl,) in this frame. The effect of the fast exchange (&are < 1) on relaxation in the rotating frame has been explained by Meiboom [3] . His relaxation rate, modified for the present experimental situation, is given by
T-’ =R 1P
+A7
e
/(1+4w2r2). 1 e
(1) 335
Volume
22, number
I
CHEMICAL
2
C3H/
He J
MOUSE
TISSUES
PHYSICS
01 17 MHz
-:l;______
Fig. 1. The proton spin-lattice relaxation rate in the rotating frame versus the rotating field strength in set-' , HI y = WI. The experiment was made at 17 MHz at room temperature. In this formula R is the proton relaxation rate in the absence of exchange. It can be related to the relaxation studied in the laboratory frame. The constant A measures the interaction which is being modulated by the exchange and o1 is the product of the gyromagnetic ratio y and the rotating field H, . The experiment on protons of tissue water was performed at room temperature using a commercial 17 MHz Spin-Lock Electronics spectrometer. The 90” pulse-field pulse spin-locking sequence was employed. Typical results are shown in fig. 1. Using eq. (1) and data in fig. 1 the following r, are obtained for the C3H/HeJ mice tissues: muscle r, = 5 X 1O-6 set, and spleen 7, = 8 X lo@ sec. These values are accurate to +SO%. The values of A are 3 X IO6 and 3.2 X lo6 sece2 for muscle and spleen, respectively. Having obtained r, and A it became clear that the spin-spin relaxation rate, TF’, which is equal to T
LETTERS
1 October
1973
ly, 43 msec and 50 + 10 msec, is within the limits of error. Furthermore, it can be shown why no dependency of Tcl on the 180” pulse separation in a T, experiment was observed [5] . The effect of the spin exchange on the TT’ rate was studied in the fast exchange limit (6~7, Q 1) by Luz and Meiboom [6]. Their result is, TT1 = R + [l - (re/tp)
tanh(tp/re)]
Are .
(2)
In this formula R is the spin-spin relaxation rate in the absence of the exchange, it is observed in the limit tp + 0, and 2t, is the 180” pulse separation. The smallest pulse separation used in the study of the spin-spin rate was 100 psec. Since the experimental T2 was not observed to increase [S] as 2t, was reduced from 10 msec to 100 psec it must be that the product (re/tp) tanh(tp/re) is much smaller than 1 even at 2t, of 100 psec. In fact, with r, = 5 psec and tp = 50 psec the product is 0.1. This, therefore, represents only a 1% reduction of the exchange rate ATE, which is difficult to notice. If the pulse separation were 20 psec then the effect of the exchange on T2 would be reduced by a factor of two. A check on the fast exchange condition, which was used in both eqs. (1) and (2), shows that for the two tissues studied 6~7, is ~10-~ which is, as required, much less than one. A few words should be said about the interaction which is modulated by proton exchange. Meiboom [33 studied the effect of proton exchange between 160 and 170 water molecules. However, his experimental rates at comparable pH for the natural concentration of 170 are too small to explain the relaxation observed in tissue water. We propose that the relaxation is due to the proton exchange between ordered and disordered water molecules. To explain the results obtained for tissue water the average interacting field should be ~100 mG. This is a very plausible value. Since r, is 5 X lo@ set this means that every 5.X 1O- 6 set a proton originally residing on a water molecule in a truly isotropic liquid environment finds itself in a local field of 100 mG. It must be remembered of course that in tissues there is a distribution of the correlation times and that 7, is merely representative of this distribution. How many actual exchanges the proton must have made before it reached a local field of this magnitude - an ordered water molecule - is open
Vohrme
22, number
2
CHEMICAL
PHYSICS
to debate. It would seem that there must be between five to ten exchanges. The actual residence time of a water proton in tissue is thus only in the neighbourhood of 106 sec. This means that during a relaxation period in the laboratory frame, which is about a second, a proton visits as many as lo6 water molecules. The presented results have implications for the amount of ordered water in tissue. Since the exchange correlation time of water protons in tissues is =:5 X 1O-6 set, the absorption line of at least a portion of the ordered liquid is exchange narrowed. Consequently, the observed narrow majority water proton absorption component, must have a considerable admixture of the exchange narrowed ordered water signal. As a result, the percentage of free water which was evaluated by using this narrow line intensity is overestimated. That is, the percentage of the ordered
LETTERS
water in tissuesfwhich estimated.
1 October
1973
was put at clO%, is under-
The authors are grateful to Dr. W.R. Inch from the Ontario Cancer Treatment and Research Foundation, London Clinic for providing the tissue samples.
References [l]
[2] ]3] (41 [S] [6]
C.S. Johnson Jr., in: Advances in magnetic resonance, Vol. 1, ed. J.S. Waugh (Academic Press, New York, 1965) p. 33. C.F. Hazlewood, B.L. Nichols and C.F. Chamberlain, Nature 222 (1969) 747. S. Meiboom, J. Chem. Phys. 34 (1961) 375. J.P. Carver, private communication. CF. Hazlewood, private communication. Z. Luz and S. Meiboom, J. Chem. Phys. 39 (1963) 366.
337
22, number
2
CHEMICAL
PHYSICS
A STUDY OF THE PROTON BY SPIN RELAXATION
1 October
LETTERS
EXCHANGE
1973
IN TISSUE WATER
IN THE ROTATING
FRAME*
R.T. THOMPSON, R.R. KNISPEL and M.M. PINTAR Departments of Physics and Statistics, University of Waterloo, Waterloo, Ontario, Canada Received 24 June 1973 Revised manuscript received 5 July 1973
The exchange rate of the water protons in mouse tissues was determined for the first time. The process was studied by proton spin relaxation in the rotating frame. The exchange correlation time was found to be =5 X 10e6 sec. The actual residence rime of a water proton on one water molecule in tissue was estimated to be =lO-’ It is shown that because of the fast exchange the estimate (210%) of the amount of ordered water is too low.
It is well known that the exchange of protons between non-equivalent sites in one molecule, or among different molecules, modulates the spin energy. The exchange can be studied by nuclear magnetic resonance methods [l] . If the proton exchange is slow, so that the proton spends enough time at each non-equivalent site, several absorption lines, one for each site, are observed. Such a situation is best studied by the NMR absorption experiment. If the exchange rate becomes larger, an averaging over all different sites takes place. The absorption spectrum becomes a single narrow line. This is referred to as exchange narrowing. It occurs if the exchange rate is such that 807, < 1, where 60/2n is the difference between the Larmor frequencies at non-equivalent sites and r, is the exchange correlation time. In such a situation the exchange process is best studied by relaxation methods. If the exchange rate is less than IO4 set-l , a spinspin relaxati’on experiment is employed. For faster exchange the relaxation in the rotating frame can be used to study the process. The proton magnetic resonance absorption line of tissue [2] consists of a broad line of ~10 kHz which is due to protons on molecules other than water, and * This investigation
was supported by Public Health Service Research Grant No. lRO1 CA-14384-01 from the National Cancer Institute.
set
of two narrower components from water protons. The less narrow (1000 Hz) water component was assigned to the protons of the bound water and the more narrow (10 Hz) water component to the protons of the majority or “free” water. The intensity of the majority water line is about ten times stronger than the intensity of the bound water line. It is not understood whether the 10 Hz proton absorption line represents the absorption of protons on water molecules with a large degree of orientational and positional disorder characteristic of an almost isotropic liquid, or if this line is narrow because of the fast exchange of protons between different water molecules which are partially ordered. It is possible that the two effects are combined, that is, the line may be a super-position of an almost isotropic liquid component and an exchange-narrowed ordered liquid component. To check the origin of this narrow line we measured directly the exchange of water protons by spin-locking the proton spins in the rotating frame and measuring the proton spin-lattice relaxation time (Tl,) in this frame. The effect of the fast exchange (&are < 1) on relaxation in the rotating frame has been explained by Meiboom [3] . His relaxation rate, modified for the present experimental situation, is given by
T-’ =R 1P
+A7
e
/(1+4w2r2). 1 e
(1) 335
Volume
22, number
I
CHEMICAL
2
C3H/
He J
MOUSE
TISSUES
PHYSICS
01 17 MHz
-:l;______
Fig. 1. The proton spin-lattice relaxation rate in the rotating frame versus the rotating field strength in set-' , HI y = WI. The experiment was made at 17 MHz at room temperature. In this formula R is the proton relaxation rate in the absence of exchange. It can be related to the relaxation studied in the laboratory frame. The constant A measures the interaction which is being modulated by the exchange and o1 is the product of the gyromagnetic ratio y and the rotating field H, . The experiment on protons of tissue water was performed at room temperature using a commercial 17 MHz Spin-Lock Electronics spectrometer. The 90” pulse-field pulse spin-locking sequence was employed. Typical results are shown in fig. 1. Using eq. (1) and data in fig. 1 the following r, are obtained for the C3H/HeJ mice tissues: muscle r, = 5 X 1O-6 set, and spleen 7, = 8 X lo@ sec. These values are accurate to +SO%. The values of A are 3 X IO6 and 3.2 X lo6 sece2 for muscle and spleen, respectively. Having obtained r, and A it became clear that the spin-spin relaxation rate, TF’, which is equal to T
LETTERS
1 October
1973
ly, 43 msec and 50 + 10 msec, is within the limits of error. Furthermore, it can be shown why no dependency of Tcl on the 180” pulse separation in a T, experiment was observed [5] . The effect of the spin exchange on the TT’ rate was studied in the fast exchange limit (6~7, Q 1) by Luz and Meiboom [6]. Their result is, TT1 = R + [l - (re/tp)
tanh(tp/re)]
Are .
(2)
In this formula R is the spin-spin relaxation rate in the absence of the exchange, it is observed in the limit tp + 0, and 2t, is the 180” pulse separation. The smallest pulse separation used in the study of the spin-spin rate was 100 psec. Since the experimental T2 was not observed to increase [S] as 2t, was reduced from 10 msec to 100 psec it must be that the product (re/tp) tanh(tp/re) is much smaller than 1 even at 2t, of 100 psec. In fact, with r, = 5 psec and tp = 50 psec the product is 0.1. This, therefore, represents only a 1% reduction of the exchange rate ATE, which is difficult to notice. If the pulse separation were 20 psec then the effect of the exchange on T2 would be reduced by a factor of two. A check on the fast exchange condition, which was used in both eqs. (1) and (2), shows that for the two tissues studied 6~7, is ~10-~ which is, as required, much less than one. A few words should be said about the interaction which is modulated by proton exchange. Meiboom [33 studied the effect of proton exchange between 160 and 170 water molecules. However, his experimental rates at comparable pH for the natural concentration of 170 are too small to explain the relaxation observed in tissue water. We propose that the relaxation is due to the proton exchange between ordered and disordered water molecules. To explain the results obtained for tissue water the average interacting field should be ~100 mG. This is a very plausible value. Since r, is 5 X lo@ set this means that every 5.X 1O- 6 set a proton originally residing on a water molecule in a truly isotropic liquid environment finds itself in a local field of 100 mG. It must be remembered of course that in tissues there is a distribution of the correlation times and that 7, is merely representative of this distribution. How many actual exchanges the proton must have made before it reached a local field of this magnitude - an ordered water molecule - is open
Vohrme
22, number
2
CHEMICAL
PHYSICS
to debate. It would seem that there must be between five to ten exchanges. The actual residence time of a water proton in tissue is thus only in the neighbourhood of 106 sec. This means that during a relaxation period in the laboratory frame, which is about a second, a proton visits as many as lo6 water molecules. The presented results have implications for the amount of ordered water in tissue. Since the exchange correlation time of water protons in tissues is =:5 X 1O-6 set, the absorption line of at least a portion of the ordered liquid is exchange narrowed. Consequently, the observed narrow majority water proton absorption component, must have a considerable admixture of the exchange narrowed ordered water signal. As a result, the percentage of free water which was evaluated by using this narrow line intensity is overestimated. That is, the percentage of the ordered
LETTERS
water in tissuesfwhich estimated.
1 October
1973
was put at clO%, is under-
The authors are grateful to Dr. W.R. Inch from the Ontario Cancer Treatment and Research Foundation, London Clinic for providing the tissue samples.
References [l]
[2] ]3] (41 [S] [6]
C.S. Johnson Jr., in: Advances in magnetic resonance, Vol. 1, ed. J.S. Waugh (Academic Press, New York, 1965) p. 33. C.F. Hazlewood, B.L. Nichols and C.F. Chamberlain, Nature 222 (1969) 747. S. Meiboom, J. Chem. Phys. 34 (1961) 375. J.P. Carver, private communication. CF. Hazlewood, private communication. Z. Luz and S. Meiboom, J. Chem. Phys. 39 (1963) 366.
337