MAGNETIC RESONANCE IN MEDICINE
28, 97-104 ( 1992)
Direct Observation of the Magnetization Exchange Dynamics Responsible for Magnetization Transfer Contrast in Human Cartilage in Yitro G. A. MORRIS*AND A. J. FREEMONT~ * Department of Chemistry and Department of Rheumatology, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom Received November 5, 1991; revised January 29, 1992; accepted February 12, 1992 Saturating irradiation far off-resonance can lead to diminution in the water signal seen in MRI, giving rise to magnetization transfer contrast. This results from transfer of magnetization between “solid” protons with restricted motion, which give rise to a band some tens of kilohertz wide, and the narrow signal from mobile protons. In the work reported here a high-power pulse spectrometer, which can detect signals from both mobile and immobile protons, was used to investigatethe dynamics of magnetization transfer in cartilage in vitro. Magnetization transfer in modified Hoffman-Fodn inversion transfer experiments was well-described by a single rate constant model; full analytical solutions are offered for the resultant biexponential magnetization recovery curves. The use of pulsed methods to generate magnetization contrast may in some circumstances offer advantages over the steady-state saturation methods used hitherto. 0 1992 Academic Press, Inc. INTRODUCTION
Magnetization transfer contrast ( MTC) in magnetic resonance imaging arises when the application of saturating preirradiation far from resonance causes differential perturbation of the intensities of signals from different regions of a subject ( 1 - 4 ) . In a T ) is applied 5typical experiment, irradiation at a level of about 400 Hz (ca. 10 kHz from resonance. Although this irradiation is too far from resonance for appreciable direct saturation of the protons of bulk water, substantial reductions in water signals are seen in many tissues. The origin of the effect lies in the transfer of longitudinal magnetization between solid-like protons with restricted motion ‘H,, which have very short transverse relaxation times T2 and hence give rise to a band tens of kilohertz wide, and the narrow (long T 2 )signal from “free” (e.g., bulk water) protons ‘ H f . To date, all investigations of magnetization transfer contrast and its origins have used the saturation transfer method, originally introduced by Forskn and Hoffman ( 5 ) , in equipment designed for the detection only of free protons, i.e., those with T2’s longer than a few milliseconds. In the experiments described below, a solid-state spectrometer capable of exciting and detecting very broad signals was used for direct observation of both exchange partners, ‘ H f and ‘HI, using the method of inversion transfer rather than that of saturation transfer ( 5 ) . This allows the direct quantitation of the exchange partners ‘Hfand ] H I , and the determination of exchange rate constants without the need for the measurement of the apparent free water spin-lattice relaxation 91
0740-3 194192 $5.00 Copynghl 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
98
MORRIS AND FREEMONT
time during saturation T , sat ( I , 2). By selectively inverting the broad component 'H, of the proton bandshape and monitoring the spectrum as a function of time following inversion, it is possible to follow the rapid recovery of the inverted 'H, signal and diminution of the sharp 'H signal, followed by their recovery through spin-lattice relaxation. THEORY
For exchange of longitudinal magnetization M , between two unequally populated sites A and B, the rates of change of M t and M: are given by
where the rate constant kA is for transfer of magnetization from A to B and kB from B to A, the spin-lattice relaxation times are Tf and T?, and the equilibrium magnetizations are M t and M t . In general these equations lead to a biexponential recovery toward equilibrium following a disturbance. Although it is common practice to assume perfect selectivity of perturbation when analyzing saturation or inversion transfer data (see, e.g., ref. ( 6 ) ) , neither saturation recovery nor selective inversion-recovery experiments will in general succeed in leaving one site completely unperturbed. This is particularly important in the case under scrutiny here, where it is not possible to perturb the free proton signal 'Hf without affecting the very broad "restricted" signal IH,. It is therefore desirable to find a general solution for the biexponential time evolution of M e and M! from arbitrary starting conditions. The analysis is most easily followed using the reduced deviations from equilibrium LY and 6:
Let the initial conditions (e.g., following attempted selective inversion of one site) be a- and p- ;thus for perfect inversion of B, leaving A unperturbed, a- would be 0 and B- would be 2. The eigenvalues for the time evolution are
El
=
1 [(RA RB) - 61 2
- -
+
+
+
and
E2 =
1 [(RA R s ) 2
--
+
+
+ 61,
[3]
where RA = kA l / T f , RB = kB 1 IT?, and 6 = fiRA - R B ) ~4kAkB.Given the boundary conditions a( 0) = a _ ,p(0) = p-, and &(a) = p ( m ) = 0, the solutions are then
MAGNETIZATION EXCHANGE DYNAMICS IN CARTILAGE
99
and
These solutions may be applied to any experiment in which the exchanging magnetizations evolve in the absence of radiofrequency irradiation. MATERIALS AND METHODS
Experiments were camed out in vitro on a sample of cartilage, approximately 17 mm long X 3 mm wide X 1.5 mm deep, from the surface of the tibia1 plateau of a 40-year-old male with no joint disease. A 7.05-T Varian Unity 300WB spectrometer was used, with the sample stationary in a Doty Instruments 'H/19F CRAMPS probe. Steady-state saturation transfer experiments were camed out by measuring the proton peak height as a function of resonance offset for a saturating field yB2/2x of 500 Hz. In order to perturb the restricted and free proton signals differentially, the pulse sequence of Fig. 1 was used to invert the broad proton signal 'H, while leaving the narrow component ' H f largely unaffected; after a variable delay T a 90" pulse was used to measure the spectrum following magnetization exchange. Nonselective pulses used 1 kW to generate a radiofrequency field strength yB1/2a of 125 kHz, while the rectangular selective 180" pulse used ca. 0.25 W to give 2.1 kHz. Following NMR examination the sample was dehydrated by soaking in two changes of acetone, heated to constant mass at 80"C, and then subjected to elemental analysis for C, H, and N. RESULTS
The steady-state transfer of saturation by magnetization transfer in cartilage is illustrated by Fig. 2, which shows the amplitude of the narrow proton signal component as a function of the resonance offset of a saturating radiofrequency field. The sharp central feature derives from direct saturation of the free protons 'H f , but the broad main feature of Fig. 2 reflects saturation of the broad signal of relatively immobile
90"
180"
z FIG.1. Pulse sequence for selective inversion of the broad component of the proton spectrum of cartilage. Nonselective 180" and 90" pulses were of 4 and 2 ps, respectively, while the selective 180" pulse had a duration of 235 ps. The delays T used were of 0, 1, 2.5, 5 , 10, 20, 40, 50, 100, 150, 300, 300, 600, 1200, 6000, 10,000, and 10,000 ms.
100
MORRIS AND FREEMONT
-80
-60
-40
-20
0
20
40
60
80
Offset / kHz
FIG.2. Signal amplitude as a function of steady-state saturation resonance offset for the cartilage sample described in the text; a saturating field strength yBZ/2x of 500 Hz was used.
restricted protons 'H,, which then exchange magnetization with the sharp signal, causing its height to decrease. Figure 3 shows the spectra recorded using the pulse sequence of Fig. 1 as a function of the delay, 7, in order to follow directly the exchange between the two pools of magnetization. The narrow signal component 'H following the two 180" pulses is initially about 92% of its unperturbed amplitude, as a result of slightly imperfect cancellation of the effects of the two 180" pulses, but then falls until 7 100 ms, as magnetization is exchanged with the inverted restricted protons IH,. The effects on the broad component are more rapid; the equilibrium between solid and mobile magnetization favors the latter, so the rate constant k,, for transfer of signal from 'H, to 'H is larger than that kfo, for the reverse process. Integrals of the narrow and broad components ' H f and 'HI were estimated by determining the integral of a baseline-corrected region of 7.5 kHz either side of the signal maximum, and then subtracting this from the total integral. Although a crude procedure, this gives results that are relatively insensitive to the choice of integration region, and achieves the desired partitioning of the signal between the restricted motion pool 'H, responsible for MTC effects and a population of protons 'H with a range of relaxation properties but sharing sufficient motional averaging to raise T2well above the 10 ps or so expected for "solid" protons. Nonlinear least-squares fitting was used to fit the measured integrals to Eqs. [4] and [ 5 ] in order to extract the exchange parameters. Because magnetization exchange in this system is much faster than the spin-lattice relaxation of either the broad or the narrow signal component, it was not possible to distinguish between the two T I values, and a single spin-lattice relaxation rate was assumed in the fitting. The disparity between the exchange and relaxation timescales also favors the accurate determination of exchange parameters by reducing correlation between the fitted exchange and relaxation rates.
-
101
MAGNETIZATION EXCHANGE DYNAMICS IN CARTILAGE
1
H,
1
Hr
X I
xloojl 0
.01
_I
1.2
10
seconds
FIG. 3. Spectra obtained as a function of exchange interval T using the pulse sequence of Fig. 1 (top), with (bottom) vertical scale expanded 100-fold to show the broad component 'H,.
Figure 4 shows a comparison between the experimental measurements and the results of fitting these to Eqs. [4] and [ 51, with rate constants kf,, of 5.2 s-I and k,,, of 59 s-' and a T I of 1.3 s. Although the numerical values of these parameters can be obtained with quite high confidence from the experimental data, the simple form of the recovery curves obtained almost certainly conceals a multiplicity of rate processes. It is perhaps salutary to note that despite the heterogeneity of cartilage and the known complexity of its transverse relaxation processes ( 7), the simple model of a single firstorder magnetization exchange process provides an unexceptionable fit to the observed data, with an rms deviation of less than 0.4%. The rate constant kf,, of 5.2 s - I obtained is significantly greater than those found for kidney and skeletal muscle ( I ) , which is perhaps a reflection of the high density of exchangeable OH protons and H 2 0binding sites in the cartilage matrix. This interpretation is supported by recent evidence for the importance of the hydroxyl site of cholesterol in determining magnetization exchange rates in model bilayer systems ( 3 , 4 ) . In cartilage, the data of Fig. 3 demonstrate that essentially the whole of the restricted motion pool IH, is in contact with 'H (via combined spin diffusion within IH, and exchange). However, in more heterogeneous systems the analysis of exchange data is be more problematic, since it is necessary to take into account contributions to IH, and ' H f from regions of the sample with very different, or even zero, exchange rate constants. A first approximation would be to allow for the presence of nonexchanging signals. In principle both IH, and 'Hf can contain such components, so it would be necessary to introduce four additional parameters (for the initial and final values of the two nonexchanging signals) into the fitting procedure outlined above.
102
MORRIS AND FREEMONT 1.05
0.95
0.85
0.75
0.00
0.10
0.1s
0.0
2.0
4.0
6.0
FIG. 4. Experimental integrals derived from the data of Fig. 3 (circles) compared with the theoretical expressions [4] and [ 51 (continuous lines) obtained using nonlinear least-squares fitting to give the parameters listed in the text. (Top) Integral of the narrow signal component ' H f and (bottom) integral of the broad signal 'H,, with (left) expansion of the early phase of magnetization exchange from 0 to 150 ms, and (right) the full time dependence of the two signals, showing the initial rapid exchange of magnetization followed by slow recovery of the averaged magnetization by spin-lattice relaxation.
Dehydration of the cartilage sample used indicated a water content of 78%;elemental analysis of the dehydrated cartilage matrix gave proportions by mass of 42.5% C, 6.9% H, and 13.2% N. Comparing these figures with the relative integrals of the signals 'H f and 'H, ( 'H f / IH, = kev/kfor1 1.3) shows that a significant proportion (approximately 7%) of the mobile proton pool ' H f as measured in the experiments of Fig. 3 must arise from the cartilage matrix; or conversely, nearly half of the matrix hydrogen is sufficiently mobile to form part of IHf. These figures are only approximate, since arbitrary choices of radiofrequency field strength B1 for the selective 180" pulse and of integration limits determine which signals form part of 'H, and which of IH f . The stronger the selective B1 field, and the wider the integration limits, the lower is the upper limit of T2 for signals to be included in the inverted signal 'H,. The choices made here deliberately place a low ceiling on the T2 of 'Hr, since it is the broad components of IH, which determine the efficiency of MTC. The fact that only about half of the cartilage matrix protons belong to the restricted motion pool 'H, is perhaps not too surprising; cartilage components such as proteoglycan contain large numbers of pendent groups such as N-acetyl and -OH which would be expected to show motional averaging. Although such signals make a signif-
-
MAGNETIZATION EXCHANGE DYNAMICS IN CARTILAGE
103
icant contribution to the integral of 'H f, they probably represent a far less important part of the peak signal amplitude, since their T2 values are likely to be substantially less than that of the mobile water. They will also be chemically shifted, although with the limited resolution of the apparatus used here it would not be possible to disentangle such signals from the skirts of the main water line. The effects of the presence of a distribution of kfo, and T2 values may be seen on close examination of the data of Fig. 3, where the shape of the base of the IH line changes significantly as a function of 7.Similar changes are visible in the results of a Carr-Purcell method A experiment, although analysis of the signal peak heights gives a T 2value of 10 ms with no evidence of nonexponential behavior. DISCUSSION
The modified Hoffman-Forskn inversion transfer experiment described above allows the direct determination of the rate of exchange between 'Hf and 'H,, without the need for measurements of apparent spin-lattice relaxation rates in the presence of saturation, and without the need for assumptions about the transverse relaxation of 'H and 'H,. The high radiofrequency field strengths used here would clearly be very difficult to produce in vivo, but direct observations of magnetization transfer in vitro such as those reported here should allow some of the uncertainties behind steady-state saturation transfer measurements to be investigated, by providing reliable figures for exchange rate constants. The observation that a small but significant contribution to the "free water" signal is made by protons of the cartilage matrix has some implications for attempts to use MR imaging for determining the degree of hydration of cartilage in vivo. The need to avoid susceptibility artifacts and the loss of signal due to rapid T2 relaxation in certain zones of cartilage mean that very short TEexperiments are necessary if all the water signals are to contribute to the image of a joint ( 7). The data presented above suggest that the distribution of water T2's and cartilage matrix T;s may overlap, making it difficult to determine by NMR an unambiguous degree of hydration. It is interesting to speculate on the possibility of performing pulsed rather than steady-state experiments in vivo. It should be possible to produce differential perturbation of 'H and 'H, with field strengths of 10 kHz or less; one such experiment has been proposed (8).This would have the significant advantage of avoiding the radiofrequency power deposition problems associated with magnetization transfer contrast imaging at high fields. The effects observed in the experiments are significantly smaller than those in steady-state experiments (compare for example the changes in signal amplitude in Figs. 2 and 3 ) , making the basic pulsed experiment less attractive than the steady-state. However, where k,,,
28, 97-104 ( 1992)
Direct Observation of the Magnetization Exchange Dynamics Responsible for Magnetization Transfer Contrast in Human Cartilage in Yitro G. A. MORRIS*AND A. J. FREEMONT~ * Department of Chemistry and Department of Rheumatology, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom Received November 5, 1991; revised January 29, 1992; accepted February 12, 1992 Saturating irradiation far off-resonance can lead to diminution in the water signal seen in MRI, giving rise to magnetization transfer contrast. This results from transfer of magnetization between “solid” protons with restricted motion, which give rise to a band some tens of kilohertz wide, and the narrow signal from mobile protons. In the work reported here a high-power pulse spectrometer, which can detect signals from both mobile and immobile protons, was used to investigatethe dynamics of magnetization transfer in cartilage in vitro. Magnetization transfer in modified Hoffman-Fodn inversion transfer experiments was well-described by a single rate constant model; full analytical solutions are offered for the resultant biexponential magnetization recovery curves. The use of pulsed methods to generate magnetization contrast may in some circumstances offer advantages over the steady-state saturation methods used hitherto. 0 1992 Academic Press, Inc. INTRODUCTION
Magnetization transfer contrast ( MTC) in magnetic resonance imaging arises when the application of saturating preirradiation far from resonance causes differential perturbation of the intensities of signals from different regions of a subject ( 1 - 4 ) . In a T ) is applied 5typical experiment, irradiation at a level of about 400 Hz (ca. 10 kHz from resonance. Although this irradiation is too far from resonance for appreciable direct saturation of the protons of bulk water, substantial reductions in water signals are seen in many tissues. The origin of the effect lies in the transfer of longitudinal magnetization between solid-like protons with restricted motion ‘H,, which have very short transverse relaxation times T2 and hence give rise to a band tens of kilohertz wide, and the narrow (long T 2 )signal from “free” (e.g., bulk water) protons ‘ H f . To date, all investigations of magnetization transfer contrast and its origins have used the saturation transfer method, originally introduced by Forskn and Hoffman ( 5 ) , in equipment designed for the detection only of free protons, i.e., those with T2’s longer than a few milliseconds. In the experiments described below, a solid-state spectrometer capable of exciting and detecting very broad signals was used for direct observation of both exchange partners, ‘ H f and ‘HI, using the method of inversion transfer rather than that of saturation transfer ( 5 ) . This allows the direct quantitation of the exchange partners ‘Hfand ] H I , and the determination of exchange rate constants without the need for the measurement of the apparent free water spin-lattice relaxation 91
0740-3 194192 $5.00 Copynghl 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
98
MORRIS AND FREEMONT
time during saturation T , sat ( I , 2). By selectively inverting the broad component 'H, of the proton bandshape and monitoring the spectrum as a function of time following inversion, it is possible to follow the rapid recovery of the inverted 'H, signal and diminution of the sharp 'H signal, followed by their recovery through spin-lattice relaxation. THEORY
For exchange of longitudinal magnetization M , between two unequally populated sites A and B, the rates of change of M t and M: are given by
where the rate constant kA is for transfer of magnetization from A to B and kB from B to A, the spin-lattice relaxation times are Tf and T?, and the equilibrium magnetizations are M t and M t . In general these equations lead to a biexponential recovery toward equilibrium following a disturbance. Although it is common practice to assume perfect selectivity of perturbation when analyzing saturation or inversion transfer data (see, e.g., ref. ( 6 ) ) , neither saturation recovery nor selective inversion-recovery experiments will in general succeed in leaving one site completely unperturbed. This is particularly important in the case under scrutiny here, where it is not possible to perturb the free proton signal 'Hf without affecting the very broad "restricted" signal IH,. It is therefore desirable to find a general solution for the biexponential time evolution of M e and M! from arbitrary starting conditions. The analysis is most easily followed using the reduced deviations from equilibrium LY and 6:
Let the initial conditions (e.g., following attempted selective inversion of one site) be a- and p- ;thus for perfect inversion of B, leaving A unperturbed, a- would be 0 and B- would be 2. The eigenvalues for the time evolution are
El
=
1 [(RA RB) - 61 2
- -
+
+
+
and
E2 =
1 [(RA R s ) 2
--
+
+
+ 61,
[3]
where RA = kA l / T f , RB = kB 1 IT?, and 6 = fiRA - R B ) ~4kAkB.Given the boundary conditions a( 0) = a _ ,p(0) = p-, and &(a) = p ( m ) = 0, the solutions are then
MAGNETIZATION EXCHANGE DYNAMICS IN CARTILAGE
99
and
These solutions may be applied to any experiment in which the exchanging magnetizations evolve in the absence of radiofrequency irradiation. MATERIALS AND METHODS
Experiments were camed out in vitro on a sample of cartilage, approximately 17 mm long X 3 mm wide X 1.5 mm deep, from the surface of the tibia1 plateau of a 40-year-old male with no joint disease. A 7.05-T Varian Unity 300WB spectrometer was used, with the sample stationary in a Doty Instruments 'H/19F CRAMPS probe. Steady-state saturation transfer experiments were camed out by measuring the proton peak height as a function of resonance offset for a saturating field yB2/2x of 500 Hz. In order to perturb the restricted and free proton signals differentially, the pulse sequence of Fig. 1 was used to invert the broad proton signal 'H, while leaving the narrow component ' H f largely unaffected; after a variable delay T a 90" pulse was used to measure the spectrum following magnetization exchange. Nonselective pulses used 1 kW to generate a radiofrequency field strength yB1/2a of 125 kHz, while the rectangular selective 180" pulse used ca. 0.25 W to give 2.1 kHz. Following NMR examination the sample was dehydrated by soaking in two changes of acetone, heated to constant mass at 80"C, and then subjected to elemental analysis for C, H, and N. RESULTS
The steady-state transfer of saturation by magnetization transfer in cartilage is illustrated by Fig. 2, which shows the amplitude of the narrow proton signal component as a function of the resonance offset of a saturating radiofrequency field. The sharp central feature derives from direct saturation of the free protons 'H f , but the broad main feature of Fig. 2 reflects saturation of the broad signal of relatively immobile
90"
180"
z FIG.1. Pulse sequence for selective inversion of the broad component of the proton spectrum of cartilage. Nonselective 180" and 90" pulses were of 4 and 2 ps, respectively, while the selective 180" pulse had a duration of 235 ps. The delays T used were of 0, 1, 2.5, 5 , 10, 20, 40, 50, 100, 150, 300, 300, 600, 1200, 6000, 10,000, and 10,000 ms.
100
MORRIS AND FREEMONT
-80
-60
-40
-20
0
20
40
60
80
Offset / kHz
FIG.2. Signal amplitude as a function of steady-state saturation resonance offset for the cartilage sample described in the text; a saturating field strength yBZ/2x of 500 Hz was used.
restricted protons 'H,, which then exchange magnetization with the sharp signal, causing its height to decrease. Figure 3 shows the spectra recorded using the pulse sequence of Fig. 1 as a function of the delay, 7, in order to follow directly the exchange between the two pools of magnetization. The narrow signal component 'H following the two 180" pulses is initially about 92% of its unperturbed amplitude, as a result of slightly imperfect cancellation of the effects of the two 180" pulses, but then falls until 7 100 ms, as magnetization is exchanged with the inverted restricted protons IH,. The effects on the broad component are more rapid; the equilibrium between solid and mobile magnetization favors the latter, so the rate constant k,, for transfer of signal from 'H, to 'H is larger than that kfo, for the reverse process. Integrals of the narrow and broad components ' H f and 'HI were estimated by determining the integral of a baseline-corrected region of 7.5 kHz either side of the signal maximum, and then subtracting this from the total integral. Although a crude procedure, this gives results that are relatively insensitive to the choice of integration region, and achieves the desired partitioning of the signal between the restricted motion pool 'H, responsible for MTC effects and a population of protons 'H with a range of relaxation properties but sharing sufficient motional averaging to raise T2well above the 10 ps or so expected for "solid" protons. Nonlinear least-squares fitting was used to fit the measured integrals to Eqs. [4] and [ 5 ] in order to extract the exchange parameters. Because magnetization exchange in this system is much faster than the spin-lattice relaxation of either the broad or the narrow signal component, it was not possible to distinguish between the two T I values, and a single spin-lattice relaxation rate was assumed in the fitting. The disparity between the exchange and relaxation timescales also favors the accurate determination of exchange parameters by reducing correlation between the fitted exchange and relaxation rates.
-
101
MAGNETIZATION EXCHANGE DYNAMICS IN CARTILAGE
1
H,
1
Hr
X I
xloojl 0
.01
_I
1.2
10
seconds
FIG. 3. Spectra obtained as a function of exchange interval T using the pulse sequence of Fig. 1 (top), with (bottom) vertical scale expanded 100-fold to show the broad component 'H,.
Figure 4 shows a comparison between the experimental measurements and the results of fitting these to Eqs. [4] and [ 51, with rate constants kf,, of 5.2 s-I and k,,, of 59 s-' and a T I of 1.3 s. Although the numerical values of these parameters can be obtained with quite high confidence from the experimental data, the simple form of the recovery curves obtained almost certainly conceals a multiplicity of rate processes. It is perhaps salutary to note that despite the heterogeneity of cartilage and the known complexity of its transverse relaxation processes ( 7), the simple model of a single firstorder magnetization exchange process provides an unexceptionable fit to the observed data, with an rms deviation of less than 0.4%. The rate constant kf,, of 5.2 s - I obtained is significantly greater than those found for kidney and skeletal muscle ( I ) , which is perhaps a reflection of the high density of exchangeable OH protons and H 2 0binding sites in the cartilage matrix. This interpretation is supported by recent evidence for the importance of the hydroxyl site of cholesterol in determining magnetization exchange rates in model bilayer systems ( 3 , 4 ) . In cartilage, the data of Fig. 3 demonstrate that essentially the whole of the restricted motion pool IH, is in contact with 'H (via combined spin diffusion within IH, and exchange). However, in more heterogeneous systems the analysis of exchange data is be more problematic, since it is necessary to take into account contributions to IH, and ' H f from regions of the sample with very different, or even zero, exchange rate constants. A first approximation would be to allow for the presence of nonexchanging signals. In principle both IH, and 'Hf can contain such components, so it would be necessary to introduce four additional parameters (for the initial and final values of the two nonexchanging signals) into the fitting procedure outlined above.
102
MORRIS AND FREEMONT 1.05
0.95
0.85
0.75
0.00
0.10
0.1s
0.0
2.0
4.0
6.0
FIG. 4. Experimental integrals derived from the data of Fig. 3 (circles) compared with the theoretical expressions [4] and [ 51 (continuous lines) obtained using nonlinear least-squares fitting to give the parameters listed in the text. (Top) Integral of the narrow signal component ' H f and (bottom) integral of the broad signal 'H,, with (left) expansion of the early phase of magnetization exchange from 0 to 150 ms, and (right) the full time dependence of the two signals, showing the initial rapid exchange of magnetization followed by slow recovery of the averaged magnetization by spin-lattice relaxation.
Dehydration of the cartilage sample used indicated a water content of 78%;elemental analysis of the dehydrated cartilage matrix gave proportions by mass of 42.5% C, 6.9% H, and 13.2% N. Comparing these figures with the relative integrals of the signals 'H f and 'H, ( 'H f / IH, = kev/kfor1 1.3) shows that a significant proportion (approximately 7%) of the mobile proton pool ' H f as measured in the experiments of Fig. 3 must arise from the cartilage matrix; or conversely, nearly half of the matrix hydrogen is sufficiently mobile to form part of IHf. These figures are only approximate, since arbitrary choices of radiofrequency field strength B1 for the selective 180" pulse and of integration limits determine which signals form part of 'H, and which of IH f . The stronger the selective B1 field, and the wider the integration limits, the lower is the upper limit of T2 for signals to be included in the inverted signal 'H,. The choices made here deliberately place a low ceiling on the T2 of 'Hr, since it is the broad components of IH, which determine the efficiency of MTC. The fact that only about half of the cartilage matrix protons belong to the restricted motion pool 'H, is perhaps not too surprising; cartilage components such as proteoglycan contain large numbers of pendent groups such as N-acetyl and -OH which would be expected to show motional averaging. Although such signals make a signif-
-
MAGNETIZATION EXCHANGE DYNAMICS IN CARTILAGE
103
icant contribution to the integral of 'H f, they probably represent a far less important part of the peak signal amplitude, since their T2 values are likely to be substantially less than that of the mobile water. They will also be chemically shifted, although with the limited resolution of the apparatus used here it would not be possible to disentangle such signals from the skirts of the main water line. The effects of the presence of a distribution of kfo, and T2 values may be seen on close examination of the data of Fig. 3, where the shape of the base of the IH line changes significantly as a function of 7.Similar changes are visible in the results of a Carr-Purcell method A experiment, although analysis of the signal peak heights gives a T 2value of 10 ms with no evidence of nonexponential behavior. DISCUSSION
The modified Hoffman-Forskn inversion transfer experiment described above allows the direct determination of the rate of exchange between 'Hf and 'H,, without the need for measurements of apparent spin-lattice relaxation rates in the presence of saturation, and without the need for assumptions about the transverse relaxation of 'H and 'H,. The high radiofrequency field strengths used here would clearly be very difficult to produce in vivo, but direct observations of magnetization transfer in vitro such as those reported here should allow some of the uncertainties behind steady-state saturation transfer measurements to be investigated, by providing reliable figures for exchange rate constants. The observation that a small but significant contribution to the "free water" signal is made by protons of the cartilage matrix has some implications for attempts to use MR imaging for determining the degree of hydration of cartilage in vivo. The need to avoid susceptibility artifacts and the loss of signal due to rapid T2 relaxation in certain zones of cartilage mean that very short TEexperiments are necessary if all the water signals are to contribute to the image of a joint ( 7). The data presented above suggest that the distribution of water T2's and cartilage matrix T;s may overlap, making it difficult to determine by NMR an unambiguous degree of hydration. It is interesting to speculate on the possibility of performing pulsed rather than steady-state experiments in vivo. It should be possible to produce differential perturbation of 'H and 'H, with field strengths of 10 kHz or less; one such experiment has been proposed (8).This would have the significant advantage of avoiding the radiofrequency power deposition problems associated with magnetization transfer contrast imaging at high fields. The effects observed in the experiments are significantly smaller than those in steady-state experiments (compare for example the changes in signal amplitude in Figs. 2 and 3 ) , making the basic pulsed experiment less attractive than the steady-state. However, where k,,,
