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Evaluation of water content by spatially resolved transverse relaxation times of human articular cartilage
Magnetic Resonance Imaging 18 (2000) 423– 430
Evaluation of water content by spatially resolved transverse relaxation times of human articular cartilage S. Lu¨ssea,*, H. Claassenb, T. Gehrkec, J. Hassenpflugc, M. Schu¨nkeb, M. Hellera, C.-C. Glu¨era a
Department of Diagnostic Radiology, Christian–Albrechts University of Kiel, Medical Physics Working Group, Michaelisstr. 9, D-24105, Kiel, Germany b Institute of Anatomy, Christian–Albrechts University, Otto-Hahn-Platz 8, D-24118, Kiel, Germany c Department of Orthopedics, Christian–Albrechts University, Michaelisstr. 1, D-24105, Kiel, Germany Received 22 September 1999; accepted 5 December 1999
Abstract Non-invasive assessment of cartilage properties, specifically water content, could prove helpful in the diagnosis of early degenerative joint diseases. Transverse relaxation times T2 of human articular cartilage (34 cartilage slices of three donors) were measured on a pixel-by-pixel basis in a clinical whole body MR system in vitro. In vivo feasibility to measure quantitative T2 maps was shown for human patellar cartilage. The relaxation times of cartilage with collagen in the radial zone oriented perpendicular to the magnetic field increased from approximately 10 ms near the bone to approximately 60 ms near the articular surface. Cartilage water content of the tibial plateau and femoral condyles could be determined from the correlation with T2 (R2 ⫽ 0.71) with an error of approximately 2 wt.%. In vivo, directional variation would need to be considered. If confirmed in vivo, T2 measurements could potentially serve as a non-invasive tool for the evaluation of the status and distribution of water content in articular cartilage. © 2000 Elsevier Science Inc. All rights reserved. Keywords: Cartilage; Relaxation times; Water content; T2 maps
1. Introduction Articular cartilage fulfils the very important function to absorb mechanical stress and to guarantee a smooth and friction-free movement of the bones. The cartilage matrix mainly contains collagen (15–20 wt.%) and glycosaminoglycans (3– 6 wt.%). About 70 to 75 wt.% of cartilage consist of bound and unbound water [1]. The glycosaminoglycans (GAGs) are thought to be essential for maintaining a high water content [2]. On the one hand, water forms hydrogen bonds to the polar and charged groups of the GAGs (water binding). On the other hand, the repulsive forces between the negatively charged GAG chains result in an uptake of unbound water. In the electrostatic equilibrium most cartilage water is this unbound water [3]. The equilibrium between mechanical and electrostatic forces in cartilage is disturbed in the pathological state. Therefore, the water content in cartilage is changed already * Corresponding author. Tel.: ⫹49-431-5973156; fax: ⫹49-4315973127. E-mail address: [email protected] (S. Lu¨sse).
in very early stages of the disease. Hence, the determination of the water content could play an important role in the diagnosis of early degenerative cartilage changes. To date the water content can only be determined by biopsy whereas it is not possible to estimate the water content by the present non-invasive techniques. Magnetic resonance imaging (MRI) has the potential to detect small changes in water content. The transverse relaxation time T2 is the MR parameter which is most sensitive to changes in cartilage water content [3]. It has been shown that a very strong correlation between T2 and water content in cartilage exists and that a reduction of the water content from 80 to 40 wt.% decreases the measured T2 by a factor of about 20 whereas the longitudinal relaxation time T1 decreases by a factor of three and the spin density by only a factor of two [3]. However, cartilage T2 is not only influenced by the water content but also by the average orientation of the water molecules to the magnetic field. Near the subchondral bone the collagen fibrils in tibial cartilage are oriented parallel to the bone axis (radial zone) whereas at the surface the collagen fibrils are aligned perpendicular to the bone axis
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(superficial zone) [4]. In between a transitional zone with random orientation can be observed due to the bending between the two oriented structures. Hence, the net orientation of the water molecules changes throughout the cartilage layer and, therefore, these zones have also different T2 values that correlate very well with the theoretical function, the second Legendre polynomial [5]. As a result the three zones can be identified in T2-weighted MR imaging as layers of changing intensity: two hyperintense regions near the bone and near the surface and a hypointense zone corresponding to the transitional zone [4,6 –12]. In an earlier publication [3], a very good correlation between cartilage T2 and the water content was reported. However, in that study only a global T2 for the whole cartilage sample was determined. To observe locally varying water contents, T2 maps of cartilage need to be measured with high spatial resolution. A number of studies have been performed to calculate quantitative T2 images of cartilage. These T2 maps were determined by microimaging methods using high field strengths and gradients [4,5,11,13] that are not available for routine clinical use. First relaxation studies on whole-body systems that are also not in routine use have also been published [14,15] Dardzinski et al. [14] determined T2 maps in a 3 Tesla system whereas Frank et al. [15] tested their home-built local gradient system to determine cartilage T2 in a 1.5 Tesla system based on only two different echo times. In none of these publications a systematic investigation of the correlation between T2 and water content in cartilage has been studied. To our best knowledge, no method for generating spatially resolved maps of T2 distributions of cartilage on standard clinical whole-body MR systems has been developed so far. In this paper, we present first in vitro and in vivo results on T2 maps of articular cartilage obtained in a clinical scanner at a field strength of 1.5 Tesla using a monoexponential fitting procedure on eight acquired echos and we report on the association of T2 with site matched water content of articular cartilage.
2. Materials and methods 2.1. Cartilage Human cartilage/bone samples of three patients who suffered from osteoarthritis and underwent total knee-replacement surgery were used for the investigations. The patients were 44, 58, and 69 years of age. To reduce water evaporation the samples were kept in wet tissue until the MR measurements were performed. The MR images were acquired within 12 h after surgery. The menisci were removed before the measurements were performed. For all patients T2 maps were measured for the tibial plateau and in one case also for the femoral condyles. In general, the cartilage of one side of the tibial plateau was almost completely destroyed whereas the cartilage appeared largely
Fig. 1. Alignment of the specimen in the static magnetic field B0. The filled box represents one of the imaged slices. The images were measured in the lateral facette only because the cartilage of the medial facette was usually completely destroyed.
intact on the other side, usually the lateral side. Therefore, only the apparently healthy side was measured. The samples were positioned as shown in Fig. 1. In this case all collagen fibrils of the radial zone are aligned perpendicular to the static magnetic field, independent of the surface curvature. In one healthy young volunteer (31 years of age) T2 maps of patellar cartilage were measured to demonstrate in vivo feasibility of the method. 2.2. MR parameters A clinical Siemens MAGNETOM Vision scanner operating at a field strength of 1.5 Tesla was used for this study. For excitation the body coil was used whereas the signal was acquired by means of a 4 cm (in vitro) or a 8 cm (in vivo) surface coil to ensure maximum signal-to-noise ratio. The T2 measurements were performed using a multi-echo sequence (Fig. 2) with a spatial resolution of up to 156 m ⫻ 156 m ⫻ 1000 m. Multi-echo sequences are very sensitive to artifacts. The gradients between the echos were, therefore, chosen very carefully and were different for each echo to largely reduce the artifacts. Eight signals were acquired with spin-echo times between 13 and 300 msec. The repetition time was 3 sec. No fat saturation was used in the in vitro measurements. Hence, T2 maps can be calculated not only for cartilage but also for bone marrow. About seven to 13 slices were acquired to cover the whole specimen. 2.3. Calculation of T2 maps A dedicated software was written in IDL (Interactive Data Language, Research Systems, Boulder, CO, USA) to determine the T2 maps. The calculation was performed by fitting the measured data to a single exponential function on
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Fig. 2. Multi-echo sequence used to measure T2. Eight echos were collected with echo times TEi of 13, 33, 53, 75, 100, 150, 200, and 300 ms. The crusher gradients for each echo were carefully chosen to avoid artifacts.
a pixel-by-pixel basis. Three parameters, T2, the intensity, and the offset of the exponential were varied during the fitting procedure which was based on a gradient-expansion algorithm. To avoid fitting noise a global threshold was used. Those pixels which had intensities below the threshold for the shortest echo time were not considered in the fitting procedure. Their T2 was set to 0. The threshold had to be set individually for each specimen to include all cartilage and to exclude most noise for optimizing the fitting procedure. For some pixels the fitting procedure did not converge, i.e. the 2 change from one iteration to the next never fell below 1 ⫻ 10⫺3 for those pixels. The T2 of those pixels was also set to 0. 2.4. Water content After the MR measurements were carried out the water contents of the cartilage samples were determined by drying and weighing. First the cartilage was removed from the bone by means of a scalpel. The cartilage was then separated into several slices. A razor blade was used to cut each of the slices into three layers: a thin surface layer corresponding to the superficial zone, an intermediate layer (transitional zone) and a thicker deep layer (radial zone). To measure the water content of exactly the same slice that was imaged is only possible if the cartilage is cut first and then measured by MRI. Therefore, the T2 maps of the separated layers were measured additionally. To prevent surface evaporation the separated samples were kept in small air-tight plastic containers whose size were similar to the sample size. The layers were weighed, dried in an oven at 65°C for 3 days, and weighed again. The water contents were then calculated by comparing dry and wet weight. The data of the superficial zone were excluded from the analysis of the correlation between water content and T2 because T2 near the articular surface is expected to show a different behavior compared to the deep zones due to the changing collagen
orientation [4,5,10,13]. In addition, the water content near the surface might have changed during the measurement due to evaporation despite the care we had taken to prevent this effect. Also, susceptibility changes at the cartilage/air transition might have an effect on the T2 measurements.
3. Results In Fig. 3 a typical monoexponential T2 fit for one cartilage pixel is shown which describes the intensity decay of the various echos very well. The fitted relaxation time for this example is 27.2 ms with an intensity of 3660 a. u., an offset of 75 a. u., and a root mean square error of 22 a. u. Fig. 4a shows a measured image of the tibial plateau of a 44-year-old man. In this proton density weighted spinecho image (TE ⫽ 13 ms, TR ⫽ 3000 ms) the cartilage layer appears intact and has a thickness of up to 4 mm. In Fig. 4b the corresponding calculated T2 map of the tibial plateau is shown. The contours of T2 map and measured image are identical. Cartilage T2 rises from approximately 10 ms near the bone to approximately 60 ms near the articular surface. Due to the short T2 the image in Fig. 4a is slightly T2 weighted near the subchondral bone. Therefore, the signal intensity in cartilage in Fig. 4a decreases with increasing distance from the articular surface. T2 of bone marrow was also determined during the fitting procedure and ranged between approximately 50 and 65 ms. In Fig. 5 an axial spin density weighted image of a knee of a volunteer is shown. This image is overlaid by the calculated T2 map of the patellar cartilage measured in vivo. Similar to the in vitro measurements the cartilage T2 values in Fig. 5 increase from bone to surface from approximately 10 ms to approximately 50 ms. The black spots within the bone marrow in Figs. 4b and 5 represent the pixels for which the fitting procedure failed. In cartilage, the fit failed for less than 1% of the pixels.
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Fig. 3. Typical monoexponential three-parameter fit for one cartilage pixel (270 m ⫻ 270 m ⫻ 1000 m) resulting in a T2 of 27.2 ms, an intensity of 3660 a. u., an offset of 75 a. u., and a root mean square error of 22 a. u.
The water content of the cartilage samples ranged between 61.5 and 78.9 wt.% with a mean of 71.3 wt.% and a standard deviation of 3.5 wt.%. In total the water content of 34 cartilage samples (19 from tibial plateaus and 15 from femoral condyles) was determined. Based on the weighing error, the error in measuring the water content is estimated to be 1 wt.%. In the case of fast exchange of water molecules between an unbound and a bound state the relaxation rates R2 (inverse relaxation times) should be a linear function of the inverse water content assuming that changes in water content do not influence the bound water fraction [16,17]. Therefore, the correlation between the inverse water content and the transverse relaxation rates is presented in Fig. 6. As expected a linear correlation was observed. In Fig. 6 the data of the 19 tibia samples are shown together with the 15 condyle samples. Intercept and slope of the linear fit are 1.2 and 4.4 ⫻ 10⫺3 s, respectively. From Fig. 6 the water content can be determined with a mean of 70.8 wt.% and a standard error of the estimate of 1.9 wt.% (significance probability p ⬍ 0.0001, coefficient of determination R2 ⫽ 0.71). For the subgroup of tibial samples the linear fit remains virtually unchanged (Table 1). In contrast, the coefficient of determination of the femoral samples (Table 1) is considerably smaller but the standard error of the estimate decreases.
Using the correlation between water content and T2 obtained for tibial cartilage (Table 1) we estimated the water contents of the femoral samples from the T2 values and compared them with the measured water contents (by drying and weighing). To statistically compare the estimated and measured water contents correctly we used the method of Bland and Altman [18]. Therefore, the difference between estimated and measured water contents of the condyle samples are presented in Fig. 7 as a function of the measured water content. The mean of this difference is 1.4 wt.% with a standard error of 0.3 wt.%. The linear correlation between inverse water content and R2 was used to calculate the water content of the slice shown in Fig. 4a on a pixel-by-pixel basis from the T2 map (Fig. 4b). This map of cartilage water contents is shown in Fig. 8. The estimated water contents in Fig. 8 have values between 60 and 80 wt.%. As expected from the T2 map, the estimated cartilage water content increases from bone to surface considerably.
4. Discussion T2 maps of articular cartilage have been determined by several investigators [4,5,10,13–15]. Most of these measurements were performed in systems with small magnet
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Fig. 4. In vitro proton density weighted image (TE ⫽ 13 ms, TR ⫽ 3000 ms) of the tibial plateau of a 44-year-old man (a) and corresponding calculated T2 map (b) (pixel size: 270 m, slice thickness: 1 mm, matrix size: 128 ⫻ 256 pixels, total measurement time: 6:30 min). The T2 values range between 10 ms near the bone and 60 ms near the articular surface. The black spots within the cartilage layer are pixels for which the fitting procedure failed.
bores, high field strengths and high gradients [4,5,10,13]. These systems allow a high spatial resolution and accurate measurements. However, these systems cannot be used in a clinical setting. Nevertheless, the data obtained in these studies are very helpful to understand the T2 behavior in
articular cartilage. Xia [5,13] presented T2 maps of canine humeral head cartilage from dogs at a very high in-plane resolution and obtained a variation of T2 between 20 ms near the bone and 60 ms at the surface for the orientation used in the present study. He also showed that T2 depends
Fig. 5. In vivo axial proton density weighted image (TE ⫽ 13 ms, TR ⫽ 1800 ms) of the knee of a healthy young volunteer (31 years of age) and overlaid T2 map (pixel size: 470 m, slice thickness: 2 mm, matrix size: 128 ⫻ 256 pixels, total measurement time: 4 min) of the patellar cartilage. The T2 values range between 10 ms near the bone and 50 ms near the articular surface. The black spots within the cartilage layer are pixels for which the fitting procedure failed.
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Fig. 6. Correlation between inverse water content and the transverse relaxation rates R 2 of cartilage water for the tibial (Œ, 44-year-old patient; F, 58-year-old patient; ■, 69-year-old patient) and condyle samples (E, 58year-old patient). The dotted and dashed lines represent the 95% confidence intervals of the linear fit and the individual predicted value, respectively.
strongly on the angle between the static magnetic field and the cartilage layer. These data were confirmed by the relaxation studies by Gru¨nder et al. [4,19] who reported a variation of the global T2 of pig articular cartilage between 10 and 40 ms depending on the orientation of the cartilage layer. Mlynarik et al. [10] also observed a strong angular dependence of pig articular cartilage (humeral heads) but in contrast to the other investigators they obtained similar relaxation times near the bone and the articular surface. Relaxation maps of human articular cartilage in wholebody MR systems were published by Dardzinski et al. [14] and by Frank et al. [15]. Dardzinski et al. [14] measured T2 of human patellar cartilage in vivo in a 3 Tesla system and obtained cartilage T2 values between 30 ms near the bone and 60 ms near the articular surface. Frank et al. [15] calculated similar T2 maps of human patella samples in vitro in a 1.5 Tesla system using a home-built local gradient coil. However, they calculated the maps from only two images. In contrast to these investigations we measured a
Fig. 7. Bland and Altman [18] statistics for the cartilage water content of the condyle samples. The differences between the estimated water contents determined from the correlation for the tibial samples and the measured water contents determined by drying and weighing are shown as a function of the measured water contents. The mean of the difference is 1.4 wt.% with a standard error of 0.3 wt.%.
fully relaxed train of eight echos with echo times between 13 and 300 ms allowing a real fitting procedure for a more accurate determination of T2. In our measurements we used only the standard equipment of the Siemens MAGNETOM Vision. No additional components were needed. By using the pulse sequence shown in Fig. 2 we obtained T2 maps for tibial plateau cartilage in vitro (Fig. 4) of high accuracy and good spatial resolution (in-plane pixel size: 156 m—approximately 300 m, slice thickness: 1 mm). The T2 maps can also be obtained for human patellar cartilage in vivo (Fig. 5) with similar quality and a little reduced resolution (in-plane pixel size: 470 m, slice thickness: 2 mm). The tibial plateau cartilage samples (in vitro) and the patellar cartilage (in vivo) in our experiments were oriented in the same angle as the patellar cartilage in Dardzinski’s and Frank’s work [14,15]. We measured relaxation times of cartilage water between 10 ms near the bone and 60 ms near the articular surface supporting the data obtained for other types of articular cartilage. The somewhat longer relaxation times in the superficial cartilage layer in our in vitro studies
Table 1 Statistical analysis of the linear regression of the inverse cartilage water content as a function of the transverse relaxation rates R 2 for all cartilage samples, the tibial plateau samples only and the femoral samples only Measured samples
N
Slope [10⫺3]
Intercept
Mean water content [wt.%]
SEE [wt.%]
rSEE [%]
p
R2
All Tibial Femoral
34 19 15
4.4 5.0 3.0
1.2 1.1 1.3
70.7 70.5 71.2
1.9 2.2 1.1
2.7 3.1 1.5
⬍0.0001 ⬍0.0001 ⬍0.01
0.71 0.77 0.51
N, number of cartilage samples; SEE, standard error of the estimate; rSEE, standard error of the estimate relative to the mean water content, p, significance probability; R 2 , coefficient of determination.
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Fig. 8. Map of estimated cartilage water contents in one slice of the tibial plateau of the 44-year-old patient. The water contents were determined from the T2 map and the correlation between water content and T2 for all 34 cartilage samples.
(tibial plateau cartilage) compared to our in vivo measurements might result from the storage procedure of the tibial samples. These samples were covered by wet tissue prior to measurement to avoid surface water evaporation. This wet tissue might cause residual free water at the surface or even a higher water content in the superficial cartilage layer. Both of these processes would result in longer transverse relaxation times. Besides collagen orientation these difficulties in controlling the water content in the superficial cartilage layer were the reason for excluding the superficial layer from the analysis of the correlation between water content and T2. A three-component fit (T21 intensity, offset of the exponential) was used to determine the T2 maps. To fit also the offset of the exponential was necessary because of the elevated background signal in magnitude images in which noise is always positive. The obtained offset was always very small compared to the fitted intensity. In the example in Fig. 3 the offset is merely 2% of the intensity suggesting that the fit results are not very sensitive to the offset. Another way to fit would be to threshold the data and to perform a two-component fit with only T2 and the intensity as parameters. We tried this method for some fits but obtained virtually the same results as for the three-component fit. We prefered the three-component fit because otherwise manual adjustment of the threshold would be necessary. This would result in a very long time needed for the analysis and in additional individual errors. The fitting procedure is only one and probably not the largest source of error. Systematic errors arising from the measurement may occur. Especially imperfections of the pulse like long duration and inaccurate flip angle of the pulse might influence the obtained T2 values considerably. For that reason the error of determining T2 is estimated to be approximately 10%. On the other hand, errors in T2 between 1 and 5 ms would have only little influence on the very good correlation between water content and T2. The very small number of pixels for which no exponential fit is possible shows that the fitting procedure used in the present study works very well to obtain T2 maps on a pixel-by-pixel basis. The measured MR images have a
rather inhomogeneous intensity distribution due to the surface coil used. These inhomogeneities are removed in the T2 maps. To measure T2 values as accurately as possible it is necessary to acquire fully relaxed trains of spin echos. For articular cartilage that means that one has to wait about 2 to 3 sec between the excitation pulses resulting in acquisition times of about 4 to 12 min for a single scan. This is a reasonable time for future patient studies. The relaxation theory shows that a single T2 is observed for a fast exchange of spins between two fractions [17]. It also has been shown that a linear relation between inverse water content and R 2 exists assuming the fast exchange model [3,16]. As expected from theory [3,16,17] high correlations between inverse water content and transverse relaxation rates were obtained for human tibial plateau cartilage. The correlations were very similar for tibial and femoral condyle cartilage (Fig. 6). This means that cartilage water contents of tibial plateau and condyles can be estimated by the same function of the relaxation rates. The data obtained suggest that the water content in human articular knee cartilage can be determined with an error of approximately 2 wt.% and part of this error is due to the experimental procedure (measuring T2 and water content). Fig. 7 shows that the water contents of the condyle cartilage samples can be very well estimated (with an error of less than 2 wt.%) using the correlation between the water contents of the tibial samples and T2. This further our hypothesis that it is possible to predict the water content in articular cartilage from T2 for the 90° orientation. Fig. 6 shows that the relaxation times strongly depend on the water content. The T2 values decrease by a factor of four whereas the water content is reduced by 20 wt.%. Hence, T2 is a very sensitive measure of the cartilage water content as has been shown in an earlier paper [3]. From the T2 variation across the cartilage layer and the linear correlation between inverse water content and relaxation rates R 2 it can be deduced that not only T2 but also the water content in cartilage of the human tibial plateau rise with increasing distance from the subchondral bone (as confirmed in the estimated water content map in Fig. 8). This might not be
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true for the thin surface layer (superficial zone) for which we did not investigate the correlation between water content and T2 due to expected experimental difficulties. In the literature an angular dependence of the cartilage appearance in MR images has been reported [4,6 –12]. This effect is at least partly a result of T2 changes with the changing angle between static magnetic field and cartilage layer [4,5]. When determining the cartilage water content from T2 it is, therefore, very important to consider the orientation of the cartilage layer. In this study we used a perpendicular orientation of the collagen fibrils in the radial zone to the magnetic field (90° orientation). In clinical whole-body scanners this is the usual orientation of patellar cartilage but it cannot be achieved for tibial plateaus in vivo. Therefore, the data presented in the present paper cannot simply be used to determine the water content in tibial plateau and femoral condyle cartilage in vivo. For curved cartilage layers like cartilage in femoral condyles, in femoral heads, or in the central part of tibial plateaus the situation is more complex. Here one would need to measure standard curves for various orientations from which a correction factor dependent on the angle between cartilage layer and magnetic field could be determined. The in vitro work of Xia [5] showed a close relation between the angular dependence of T2 and the theoretical function for dipolar interaction as relaxation mechanism. These data give reasonable hope to find a simple function to correct the T2 values for every angle in the magnetic field. A study to obtain the T2 values at different angles is currently in progress in our laboratory.
5. Conclusions We present quantitative T2 maps of human articular cartilage obtained with the standard equipment of a clinical whole-body scanner in vitro and in vivo. The in vitro measurements showed a very close correlation between the inverse water content and the transverse relaxation rates for cartilage from the tibial plateau and the femoral condyles with collagen fibrils of the radial zone aligned perpendicular to the static magnetic field. The water content in cartilage could be estimated with an error of approximately 2 wt.%. If confirmed in vivo this method for estimating the water content in human articular cartilage could prove helpful in the diagnosis of early degenerative joint disease.
Acknowledgments The authors gratefully thank Dr. N. Karger (University Hospital Kiel, Department of Diagnostic Radiology) for many fruitful discussions.
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Evaluation of water content by spatially resolved transverse relaxation times of human articular cartilage S. Lu¨ssea,*, H. Claassenb, T. Gehrkec, J. Hassenpflugc, M. Schu¨nkeb, M. Hellera, C.-C. Glu¨era a
Department of Diagnostic Radiology, Christian–Albrechts University of Kiel, Medical Physics Working Group, Michaelisstr. 9, D-24105, Kiel, Germany b Institute of Anatomy, Christian–Albrechts University, Otto-Hahn-Platz 8, D-24118, Kiel, Germany c Department of Orthopedics, Christian–Albrechts University, Michaelisstr. 1, D-24105, Kiel, Germany Received 22 September 1999; accepted 5 December 1999
Abstract Non-invasive assessment of cartilage properties, specifically water content, could prove helpful in the diagnosis of early degenerative joint diseases. Transverse relaxation times T2 of human articular cartilage (34 cartilage slices of three donors) were measured on a pixel-by-pixel basis in a clinical whole body MR system in vitro. In vivo feasibility to measure quantitative T2 maps was shown for human patellar cartilage. The relaxation times of cartilage with collagen in the radial zone oriented perpendicular to the magnetic field increased from approximately 10 ms near the bone to approximately 60 ms near the articular surface. Cartilage water content of the tibial plateau and femoral condyles could be determined from the correlation with T2 (R2 ⫽ 0.71) with an error of approximately 2 wt.%. In vivo, directional variation would need to be considered. If confirmed in vivo, T2 measurements could potentially serve as a non-invasive tool for the evaluation of the status and distribution of water content in articular cartilage. © 2000 Elsevier Science Inc. All rights reserved. Keywords: Cartilage; Relaxation times; Water content; T2 maps
1. Introduction Articular cartilage fulfils the very important function to absorb mechanical stress and to guarantee a smooth and friction-free movement of the bones. The cartilage matrix mainly contains collagen (15–20 wt.%) and glycosaminoglycans (3– 6 wt.%). About 70 to 75 wt.% of cartilage consist of bound and unbound water [1]. The glycosaminoglycans (GAGs) are thought to be essential for maintaining a high water content [2]. On the one hand, water forms hydrogen bonds to the polar and charged groups of the GAGs (water binding). On the other hand, the repulsive forces between the negatively charged GAG chains result in an uptake of unbound water. In the electrostatic equilibrium most cartilage water is this unbound water [3]. The equilibrium between mechanical and electrostatic forces in cartilage is disturbed in the pathological state. Therefore, the water content in cartilage is changed already * Corresponding author. Tel.: ⫹49-431-5973156; fax: ⫹49-4315973127. E-mail address: [email protected] (S. Lu¨sse).
in very early stages of the disease. Hence, the determination of the water content could play an important role in the diagnosis of early degenerative cartilage changes. To date the water content can only be determined by biopsy whereas it is not possible to estimate the water content by the present non-invasive techniques. Magnetic resonance imaging (MRI) has the potential to detect small changes in water content. The transverse relaxation time T2 is the MR parameter which is most sensitive to changes in cartilage water content [3]. It has been shown that a very strong correlation between T2 and water content in cartilage exists and that a reduction of the water content from 80 to 40 wt.% decreases the measured T2 by a factor of about 20 whereas the longitudinal relaxation time T1 decreases by a factor of three and the spin density by only a factor of two [3]. However, cartilage T2 is not only influenced by the water content but also by the average orientation of the water molecules to the magnetic field. Near the subchondral bone the collagen fibrils in tibial cartilage are oriented parallel to the bone axis (radial zone) whereas at the surface the collagen fibrils are aligned perpendicular to the bone axis
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(superficial zone) [4]. In between a transitional zone with random orientation can be observed due to the bending between the two oriented structures. Hence, the net orientation of the water molecules changes throughout the cartilage layer and, therefore, these zones have also different T2 values that correlate very well with the theoretical function, the second Legendre polynomial [5]. As a result the three zones can be identified in T2-weighted MR imaging as layers of changing intensity: two hyperintense regions near the bone and near the surface and a hypointense zone corresponding to the transitional zone [4,6 –12]. In an earlier publication [3], a very good correlation between cartilage T2 and the water content was reported. However, in that study only a global T2 for the whole cartilage sample was determined. To observe locally varying water contents, T2 maps of cartilage need to be measured with high spatial resolution. A number of studies have been performed to calculate quantitative T2 images of cartilage. These T2 maps were determined by microimaging methods using high field strengths and gradients [4,5,11,13] that are not available for routine clinical use. First relaxation studies on whole-body systems that are also not in routine use have also been published [14,15] Dardzinski et al. [14] determined T2 maps in a 3 Tesla system whereas Frank et al. [15] tested their home-built local gradient system to determine cartilage T2 in a 1.5 Tesla system based on only two different echo times. In none of these publications a systematic investigation of the correlation between T2 and water content in cartilage has been studied. To our best knowledge, no method for generating spatially resolved maps of T2 distributions of cartilage on standard clinical whole-body MR systems has been developed so far. In this paper, we present first in vitro and in vivo results on T2 maps of articular cartilage obtained in a clinical scanner at a field strength of 1.5 Tesla using a monoexponential fitting procedure on eight acquired echos and we report on the association of T2 with site matched water content of articular cartilage.
2. Materials and methods 2.1. Cartilage Human cartilage/bone samples of three patients who suffered from osteoarthritis and underwent total knee-replacement surgery were used for the investigations. The patients were 44, 58, and 69 years of age. To reduce water evaporation the samples were kept in wet tissue until the MR measurements were performed. The MR images were acquired within 12 h after surgery. The menisci were removed before the measurements were performed. For all patients T2 maps were measured for the tibial plateau and in one case also for the femoral condyles. In general, the cartilage of one side of the tibial plateau was almost completely destroyed whereas the cartilage appeared largely
Fig. 1. Alignment of the specimen in the static magnetic field B0. The filled box represents one of the imaged slices. The images were measured in the lateral facette only because the cartilage of the medial facette was usually completely destroyed.
intact on the other side, usually the lateral side. Therefore, only the apparently healthy side was measured. The samples were positioned as shown in Fig. 1. In this case all collagen fibrils of the radial zone are aligned perpendicular to the static magnetic field, independent of the surface curvature. In one healthy young volunteer (31 years of age) T2 maps of patellar cartilage were measured to demonstrate in vivo feasibility of the method. 2.2. MR parameters A clinical Siemens MAGNETOM Vision scanner operating at a field strength of 1.5 Tesla was used for this study. For excitation the body coil was used whereas the signal was acquired by means of a 4 cm (in vitro) or a 8 cm (in vivo) surface coil to ensure maximum signal-to-noise ratio. The T2 measurements were performed using a multi-echo sequence (Fig. 2) with a spatial resolution of up to 156 m ⫻ 156 m ⫻ 1000 m. Multi-echo sequences are very sensitive to artifacts. The gradients between the echos were, therefore, chosen very carefully and were different for each echo to largely reduce the artifacts. Eight signals were acquired with spin-echo times between 13 and 300 msec. The repetition time was 3 sec. No fat saturation was used in the in vitro measurements. Hence, T2 maps can be calculated not only for cartilage but also for bone marrow. About seven to 13 slices were acquired to cover the whole specimen. 2.3. Calculation of T2 maps A dedicated software was written in IDL (Interactive Data Language, Research Systems, Boulder, CO, USA) to determine the T2 maps. The calculation was performed by fitting the measured data to a single exponential function on
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Fig. 2. Multi-echo sequence used to measure T2. Eight echos were collected with echo times TEi of 13, 33, 53, 75, 100, 150, 200, and 300 ms. The crusher gradients for each echo were carefully chosen to avoid artifacts.
a pixel-by-pixel basis. Three parameters, T2, the intensity, and the offset of the exponential were varied during the fitting procedure which was based on a gradient-expansion algorithm. To avoid fitting noise a global threshold was used. Those pixels which had intensities below the threshold for the shortest echo time were not considered in the fitting procedure. Their T2 was set to 0. The threshold had to be set individually for each specimen to include all cartilage and to exclude most noise for optimizing the fitting procedure. For some pixels the fitting procedure did not converge, i.e. the 2 change from one iteration to the next never fell below 1 ⫻ 10⫺3 for those pixels. The T2 of those pixels was also set to 0. 2.4. Water content After the MR measurements were carried out the water contents of the cartilage samples were determined by drying and weighing. First the cartilage was removed from the bone by means of a scalpel. The cartilage was then separated into several slices. A razor blade was used to cut each of the slices into three layers: a thin surface layer corresponding to the superficial zone, an intermediate layer (transitional zone) and a thicker deep layer (radial zone). To measure the water content of exactly the same slice that was imaged is only possible if the cartilage is cut first and then measured by MRI. Therefore, the T2 maps of the separated layers were measured additionally. To prevent surface evaporation the separated samples were kept in small air-tight plastic containers whose size were similar to the sample size. The layers were weighed, dried in an oven at 65°C for 3 days, and weighed again. The water contents were then calculated by comparing dry and wet weight. The data of the superficial zone were excluded from the analysis of the correlation between water content and T2 because T2 near the articular surface is expected to show a different behavior compared to the deep zones due to the changing collagen
orientation [4,5,10,13]. In addition, the water content near the surface might have changed during the measurement due to evaporation despite the care we had taken to prevent this effect. Also, susceptibility changes at the cartilage/air transition might have an effect on the T2 measurements.
3. Results In Fig. 3 a typical monoexponential T2 fit for one cartilage pixel is shown which describes the intensity decay of the various echos very well. The fitted relaxation time for this example is 27.2 ms with an intensity of 3660 a. u., an offset of 75 a. u., and a root mean square error of 22 a. u. Fig. 4a shows a measured image of the tibial plateau of a 44-year-old man. In this proton density weighted spinecho image (TE ⫽ 13 ms, TR ⫽ 3000 ms) the cartilage layer appears intact and has a thickness of up to 4 mm. In Fig. 4b the corresponding calculated T2 map of the tibial plateau is shown. The contours of T2 map and measured image are identical. Cartilage T2 rises from approximately 10 ms near the bone to approximately 60 ms near the articular surface. Due to the short T2 the image in Fig. 4a is slightly T2 weighted near the subchondral bone. Therefore, the signal intensity in cartilage in Fig. 4a decreases with increasing distance from the articular surface. T2 of bone marrow was also determined during the fitting procedure and ranged between approximately 50 and 65 ms. In Fig. 5 an axial spin density weighted image of a knee of a volunteer is shown. This image is overlaid by the calculated T2 map of the patellar cartilage measured in vivo. Similar to the in vitro measurements the cartilage T2 values in Fig. 5 increase from bone to surface from approximately 10 ms to approximately 50 ms. The black spots within the bone marrow in Figs. 4b and 5 represent the pixels for which the fitting procedure failed. In cartilage, the fit failed for less than 1% of the pixels.
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Fig. 3. Typical monoexponential three-parameter fit for one cartilage pixel (270 m ⫻ 270 m ⫻ 1000 m) resulting in a T2 of 27.2 ms, an intensity of 3660 a. u., an offset of 75 a. u., and a root mean square error of 22 a. u.
The water content of the cartilage samples ranged between 61.5 and 78.9 wt.% with a mean of 71.3 wt.% and a standard deviation of 3.5 wt.%. In total the water content of 34 cartilage samples (19 from tibial plateaus and 15 from femoral condyles) was determined. Based on the weighing error, the error in measuring the water content is estimated to be 1 wt.%. In the case of fast exchange of water molecules between an unbound and a bound state the relaxation rates R2 (inverse relaxation times) should be a linear function of the inverse water content assuming that changes in water content do not influence the bound water fraction [16,17]. Therefore, the correlation between the inverse water content and the transverse relaxation rates is presented in Fig. 6. As expected a linear correlation was observed. In Fig. 6 the data of the 19 tibia samples are shown together with the 15 condyle samples. Intercept and slope of the linear fit are 1.2 and 4.4 ⫻ 10⫺3 s, respectively. From Fig. 6 the water content can be determined with a mean of 70.8 wt.% and a standard error of the estimate of 1.9 wt.% (significance probability p ⬍ 0.0001, coefficient of determination R2 ⫽ 0.71). For the subgroup of tibial samples the linear fit remains virtually unchanged (Table 1). In contrast, the coefficient of determination of the femoral samples (Table 1) is considerably smaller but the standard error of the estimate decreases.
Using the correlation between water content and T2 obtained for tibial cartilage (Table 1) we estimated the water contents of the femoral samples from the T2 values and compared them with the measured water contents (by drying and weighing). To statistically compare the estimated and measured water contents correctly we used the method of Bland and Altman [18]. Therefore, the difference between estimated and measured water contents of the condyle samples are presented in Fig. 7 as a function of the measured water content. The mean of this difference is 1.4 wt.% with a standard error of 0.3 wt.%. The linear correlation between inverse water content and R2 was used to calculate the water content of the slice shown in Fig. 4a on a pixel-by-pixel basis from the T2 map (Fig. 4b). This map of cartilage water contents is shown in Fig. 8. The estimated water contents in Fig. 8 have values between 60 and 80 wt.%. As expected from the T2 map, the estimated cartilage water content increases from bone to surface considerably.
4. Discussion T2 maps of articular cartilage have been determined by several investigators [4,5,10,13–15]. Most of these measurements were performed in systems with small magnet
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Fig. 4. In vitro proton density weighted image (TE ⫽ 13 ms, TR ⫽ 3000 ms) of the tibial plateau of a 44-year-old man (a) and corresponding calculated T2 map (b) (pixel size: 270 m, slice thickness: 1 mm, matrix size: 128 ⫻ 256 pixels, total measurement time: 6:30 min). The T2 values range between 10 ms near the bone and 60 ms near the articular surface. The black spots within the cartilage layer are pixels for which the fitting procedure failed.
bores, high field strengths and high gradients [4,5,10,13]. These systems allow a high spatial resolution and accurate measurements. However, these systems cannot be used in a clinical setting. Nevertheless, the data obtained in these studies are very helpful to understand the T2 behavior in
articular cartilage. Xia [5,13] presented T2 maps of canine humeral head cartilage from dogs at a very high in-plane resolution and obtained a variation of T2 between 20 ms near the bone and 60 ms at the surface for the orientation used in the present study. He also showed that T2 depends
Fig. 5. In vivo axial proton density weighted image (TE ⫽ 13 ms, TR ⫽ 1800 ms) of the knee of a healthy young volunteer (31 years of age) and overlaid T2 map (pixel size: 470 m, slice thickness: 2 mm, matrix size: 128 ⫻ 256 pixels, total measurement time: 4 min) of the patellar cartilage. The T2 values range between 10 ms near the bone and 50 ms near the articular surface. The black spots within the cartilage layer are pixels for which the fitting procedure failed.
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Fig. 6. Correlation between inverse water content and the transverse relaxation rates R 2 of cartilage water for the tibial (Œ, 44-year-old patient; F, 58-year-old patient; ■, 69-year-old patient) and condyle samples (E, 58year-old patient). The dotted and dashed lines represent the 95% confidence intervals of the linear fit and the individual predicted value, respectively.
strongly on the angle between the static magnetic field and the cartilage layer. These data were confirmed by the relaxation studies by Gru¨nder et al. [4,19] who reported a variation of the global T2 of pig articular cartilage between 10 and 40 ms depending on the orientation of the cartilage layer. Mlynarik et al. [10] also observed a strong angular dependence of pig articular cartilage (humeral heads) but in contrast to the other investigators they obtained similar relaxation times near the bone and the articular surface. Relaxation maps of human articular cartilage in wholebody MR systems were published by Dardzinski et al. [14] and by Frank et al. [15]. Dardzinski et al. [14] measured T2 of human patellar cartilage in vivo in a 3 Tesla system and obtained cartilage T2 values between 30 ms near the bone and 60 ms near the articular surface. Frank et al. [15] calculated similar T2 maps of human patella samples in vitro in a 1.5 Tesla system using a home-built local gradient coil. However, they calculated the maps from only two images. In contrast to these investigations we measured a
Fig. 7. Bland and Altman [18] statistics for the cartilage water content of the condyle samples. The differences between the estimated water contents determined from the correlation for the tibial samples and the measured water contents determined by drying and weighing are shown as a function of the measured water contents. The mean of the difference is 1.4 wt.% with a standard error of 0.3 wt.%.
fully relaxed train of eight echos with echo times between 13 and 300 ms allowing a real fitting procedure for a more accurate determination of T2. In our measurements we used only the standard equipment of the Siemens MAGNETOM Vision. No additional components were needed. By using the pulse sequence shown in Fig. 2 we obtained T2 maps for tibial plateau cartilage in vitro (Fig. 4) of high accuracy and good spatial resolution (in-plane pixel size: 156 m—approximately 300 m, slice thickness: 1 mm). The T2 maps can also be obtained for human patellar cartilage in vivo (Fig. 5) with similar quality and a little reduced resolution (in-plane pixel size: 470 m, slice thickness: 2 mm). The tibial plateau cartilage samples (in vitro) and the patellar cartilage (in vivo) in our experiments were oriented in the same angle as the patellar cartilage in Dardzinski’s and Frank’s work [14,15]. We measured relaxation times of cartilage water between 10 ms near the bone and 60 ms near the articular surface supporting the data obtained for other types of articular cartilage. The somewhat longer relaxation times in the superficial cartilage layer in our in vitro studies
Table 1 Statistical analysis of the linear regression of the inverse cartilage water content as a function of the transverse relaxation rates R 2 for all cartilage samples, the tibial plateau samples only and the femoral samples only Measured samples
N
Slope [10⫺3]
Intercept
Mean water content [wt.%]
SEE [wt.%]
rSEE [%]
p
R2
All Tibial Femoral
34 19 15
4.4 5.0 3.0
1.2 1.1 1.3
70.7 70.5 71.2
1.9 2.2 1.1
2.7 3.1 1.5
⬍0.0001 ⬍0.0001 ⬍0.01
0.71 0.77 0.51
N, number of cartilage samples; SEE, standard error of the estimate; rSEE, standard error of the estimate relative to the mean water content, p, significance probability; R 2 , coefficient of determination.
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Fig. 8. Map of estimated cartilage water contents in one slice of the tibial plateau of the 44-year-old patient. The water contents were determined from the T2 map and the correlation between water content and T2 for all 34 cartilage samples.
(tibial plateau cartilage) compared to our in vivo measurements might result from the storage procedure of the tibial samples. These samples were covered by wet tissue prior to measurement to avoid surface water evaporation. This wet tissue might cause residual free water at the surface or even a higher water content in the superficial cartilage layer. Both of these processes would result in longer transverse relaxation times. Besides collagen orientation these difficulties in controlling the water content in the superficial cartilage layer were the reason for excluding the superficial layer from the analysis of the correlation between water content and T2. A three-component fit (T21 intensity, offset of the exponential) was used to determine the T2 maps. To fit also the offset of the exponential was necessary because of the elevated background signal in magnitude images in which noise is always positive. The obtained offset was always very small compared to the fitted intensity. In the example in Fig. 3 the offset is merely 2% of the intensity suggesting that the fit results are not very sensitive to the offset. Another way to fit would be to threshold the data and to perform a two-component fit with only T2 and the intensity as parameters. We tried this method for some fits but obtained virtually the same results as for the three-component fit. We prefered the three-component fit because otherwise manual adjustment of the threshold would be necessary. This would result in a very long time needed for the analysis and in additional individual errors. The fitting procedure is only one and probably not the largest source of error. Systematic errors arising from the measurement may occur. Especially imperfections of the pulse like long duration and inaccurate flip angle of the pulse might influence the obtained T2 values considerably. For that reason the error of determining T2 is estimated to be approximately 10%. On the other hand, errors in T2 between 1 and 5 ms would have only little influence on the very good correlation between water content and T2. The very small number of pixels for which no exponential fit is possible shows that the fitting procedure used in the present study works very well to obtain T2 maps on a pixel-by-pixel basis. The measured MR images have a
rather inhomogeneous intensity distribution due to the surface coil used. These inhomogeneities are removed in the T2 maps. To measure T2 values as accurately as possible it is necessary to acquire fully relaxed trains of spin echos. For articular cartilage that means that one has to wait about 2 to 3 sec between the excitation pulses resulting in acquisition times of about 4 to 12 min for a single scan. This is a reasonable time for future patient studies. The relaxation theory shows that a single T2 is observed for a fast exchange of spins between two fractions [17]. It also has been shown that a linear relation between inverse water content and R 2 exists assuming the fast exchange model [3,16]. As expected from theory [3,16,17] high correlations between inverse water content and transverse relaxation rates were obtained for human tibial plateau cartilage. The correlations were very similar for tibial and femoral condyle cartilage (Fig. 6). This means that cartilage water contents of tibial plateau and condyles can be estimated by the same function of the relaxation rates. The data obtained suggest that the water content in human articular knee cartilage can be determined with an error of approximately 2 wt.% and part of this error is due to the experimental procedure (measuring T2 and water content). Fig. 7 shows that the water contents of the condyle cartilage samples can be very well estimated (with an error of less than 2 wt.%) using the correlation between the water contents of the tibial samples and T2. This further our hypothesis that it is possible to predict the water content in articular cartilage from T2 for the 90° orientation. Fig. 6 shows that the relaxation times strongly depend on the water content. The T2 values decrease by a factor of four whereas the water content is reduced by 20 wt.%. Hence, T2 is a very sensitive measure of the cartilage water content as has been shown in an earlier paper [3]. From the T2 variation across the cartilage layer and the linear correlation between inverse water content and relaxation rates R 2 it can be deduced that not only T2 but also the water content in cartilage of the human tibial plateau rise with increasing distance from the subchondral bone (as confirmed in the estimated water content map in Fig. 8). This might not be
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true for the thin surface layer (superficial zone) for which we did not investigate the correlation between water content and T2 due to expected experimental difficulties. In the literature an angular dependence of the cartilage appearance in MR images has been reported [4,6 –12]. This effect is at least partly a result of T2 changes with the changing angle between static magnetic field and cartilage layer [4,5]. When determining the cartilage water content from T2 it is, therefore, very important to consider the orientation of the cartilage layer. In this study we used a perpendicular orientation of the collagen fibrils in the radial zone to the magnetic field (90° orientation). In clinical whole-body scanners this is the usual orientation of patellar cartilage but it cannot be achieved for tibial plateaus in vivo. Therefore, the data presented in the present paper cannot simply be used to determine the water content in tibial plateau and femoral condyle cartilage in vivo. For curved cartilage layers like cartilage in femoral condyles, in femoral heads, or in the central part of tibial plateaus the situation is more complex. Here one would need to measure standard curves for various orientations from which a correction factor dependent on the angle between cartilage layer and magnetic field could be determined. The in vitro work of Xia [5] showed a close relation between the angular dependence of T2 and the theoretical function for dipolar interaction as relaxation mechanism. These data give reasonable hope to find a simple function to correct the T2 values for every angle in the magnetic field. A study to obtain the T2 values at different angles is currently in progress in our laboratory.
5. Conclusions We present quantitative T2 maps of human articular cartilage obtained with the standard equipment of a clinical whole-body scanner in vitro and in vivo. The in vitro measurements showed a very close correlation between the inverse water content and the transverse relaxation rates for cartilage from the tibial plateau and the femoral condyles with collagen fibrils of the radial zone aligned perpendicular to the static magnetic field. The water content in cartilage could be estimated with an error of approximately 2 wt.%. If confirmed in vivo this method for estimating the water content in human articular cartilage could prove helpful in the diagnosis of early degenerative joint disease.
Acknowledgments The authors gratefully thank Dr. N. Karger (University Hospital Kiel, Department of Diagnostic Radiology) for many fruitful discussions.
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