Effects of inversion and saturation times on relationships between ...

Radiol Phys Technol (2010) 3:120–126 DOI 10.1007/s12194-010-0087-9

Effects of inversion and saturation times on relationships between contrast agent concentrations and signal intensities of T1-weighted magnetic resonance images Mahmood Nazarpoor

Received: 30 June 2009 / Revised: 2 February 2010 / Accepted: 5 February 2010 / Published online: 27 February 2010 Ó Japanese Society of Radiological Technology and Japan Society of Medical Physics 2010

Abstract The present study was an attempt to investigate the effect of variation of inversion time (TI) and saturation time (TS) on the linear relationship between contrast agent concentration and signal intensity (SI) on Turbo Fast Low Angle Shot (TurboFLASH) T1-weighted images in MRI. For this purpose, inversion recovery (IR) and saturation recovery (SR) sequences (Center out Phase-Encoding acquisition) were used. A phantom was designed to hold 25 vials which contained either different (between 0 and 19.77 mmol/L) or constant (1.20 mmol/L) concentrations of contrast agent. The vials of constant concentration were used for the measurement of coil non-uniformity, which was normalized to give a correction factor. The vials of different concentrations were used to measure the SI by using different sequences and different TI and TS values. To calculate the corrected SI for different concentrations, we multiplied the SI of each vial by its correction factor. The relationships between the corrected SI and the concentration [were evaluated], where the threshold of (R2 = 0.95 and 0.99) was maintained. This study shows that different sequences and different TI and TS values can have an effect on the correlation between the SI and concentration. Regardless of the values of TI, TS, and the different IR and SR sequences chosen, the linear relationship between the SI and concentration was about twice that previously reported (i.e., 0.8 mmol/L, R2 = 0.95). Keywords T1-weighted image Inversion recovery Saturation recovery Inversion time Saturation time Signal intensity M. Nazarpoor (&) Department of Radiology, Faculty of Paramedicine, Tabriz University of Medical Sciences, Tabriz, Iran e-mail: [email protected]; [email protected]

1 Introduction Changes in signal intensity (SI) depend on the magnetic susceptibility of the contrast agent, the magnetic field strength, the pulse sequence parameters, the dose of the contrast agent, the injection rate and bolus volume, cardiac output and blood volume, and the topology of tissue [1]. Contrast agents such as gadopentetate dimeglumine act indirectly on the MR signal by decreasing the relaxation times of the surrounding nuclear spins [2]. MRI is not able to measure the concentration of the contrast agent directly; it is measured indirectly from the SI. Therefore, the resulting SI–time curves must be converted into concentration time curves. The concentration–time curve can be analyzed for obtaining perfusion parameters [3]. For extracting more physiologic information from dynamic images, the shape of the SI–time curves should be analyzed precisely. If the relationship between SI and concentration can be shown to be linear over a range of concentrations, then relative changes in SI can be used instead of concentration. Different reports suggested different square correlation coefficient (R2) values for the correlation between SI and concentration in the stationary state [4–6]. For this reason, the relationship between SI and concentration should be investigated more thoroughly for determination of the maximum concentration that yields a linear response. Two common acquisition strategies in MRI are Linear Phase-Encoding and Center out Phase-Encoding. After an inversion or saturation pulse is applied, as the longitudinal magnetization recovers, a series of images are acquired. Each image is formed by applying a flip angle pulse, each of which gives one K-space line. The Center out PhaseEncoding acquisition starts with the center of K space lines and moves out from there, jumping back and forth from

Relationships between contrast agent concentrations and signal intensities

positive to negative K space. The Linear Phase-Encoding acquisition starts from the top line of K space and scans through subsequent lines [7]. Because inversion time (TI) and saturation time (TS) are variable parameters in the inversion recovery (IR) snapshot and saturation recovery (SR) sequence (see Eqs. 5 and 7 below), these affect the SI. The effect of variation of TI on the maximum linear relationship between the SI and contrast agent concentration where the IR sequence is used (Linear-phase Encoding) was investigated in a previous study [8]. The aims in this study were to investigate the effect of variation of TI and TS on the correlation between contrast agent concentration and SI, where the concentrations maintain the threshold of (R2 = 0.95 and 0.99). It should also be noted that the Turbo Fast Low Angle Shot (TurboFLASH) T1-weighted images in MRI were applied with use of IR and SR sequences (Center out PhaseEncoding acquisition).

pre-pulses or contrast agent, respectively. hinv is the flip angle of the inversion pulse. If hinv = 180°, for the inversion recovery sequence, Eq. 3 becomes TI TR SðtÞ ¼ S0 1 2 exp þ exp : ð4Þ T1 T1 Equation 4 can also be combined with Eqs. 1 and 2 to yield a relationship between C(t) and SI [11]: CðtÞ 1 þ SðtÞ ¼ S0 1 2 exp TI K T1 Pre CðtÞ 1 þ þ exp TR : ð5Þ K T1Pre For saturation recovery (hinv = 90°) TurboFLASH sequences, the relationship between SI and T1 has been defined as TS SðtÞ ¼ S0 1 exp ; ð6Þ T1 where TS is the time between the saturation 90° pulse and the excitation a pulse that traverses the line of K-space. S(t) can also be written as CðtÞ 1 SðtÞ ¼ S0 1 exp TS þ : ð7Þ K T1Pre

2 Materials and methods 2.1 Signal intensity in the IR and SR sequences For T1-weighted monitoring of the contrast agent, a number of T1-weighted sequences are available [9]. It has been suggested based on theory and confirmed for physiologic concentrations in vitro that the paramagnetic enhancement caused by contrast agents such as Gd leads to a change in the longitudinal relaxation rate.

agents [12, 13].

CðtÞ ¼ K DR1 ðtÞ;

2.2 Phantom

where DR1 ðtÞ ¼ D

1 T1 ðtÞ

ð1Þ

¼

1 1 : T1 ðtÞ T1Pre

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ð2Þ

T1(t) and T1Pre are the longitudinal relaxation times at time t after and before contrast application, respectively. C(t) is the concentration of the contrast agent at time t. K is a constant that depends on the contrast medium [9]. The relationship between signal intensity and T1, which is dependent on the concentration, will change depending on the actual MR sequence used [10]. The standard inversion recovery sequence, which is dependent on TI and the repetition time (TR), is described by the following equation: TI TR SðtÞ ¼ S0 1 ð1 cos hinv Þ exp þ exp ; ð3Þ T1 T1 where S(t) and S0 are the signal intensity after administration of contrast agent and the observed signal intensity in the absence of any magnetization preparation

Equations 5 and 7 are assumed to be linear at low concentrations and nonlinear at high concentrations. It is necessary to mention that Eqs. 5 and 7 should be multiplied by exp TTE2 at higher concentration of contrast

For assessment of the relationship between SI and the concentration in stationary vials, a phantom was designed that holds vials, which contain either a variety of or constant concentrations of contrast agent (see Fig. 1). We used vials of different concentrations to measure the maximum linear relationship between SI and concentration. The phantom of different concentrations consisted of 25 vials [glass tubes, inner diameter approximately 15 mm, filled with different concentrations of Gd-DTPA (Magnevist, Schering Health Care Ltd., West Sussex, UK)]. The concentration of Gd-DTPA varied between 0 and 19.77 mmol/L (0.00, 0.30, 0.45, 0.60, 0.75, 0.90, 1.20, 1.50, 1.80, 2.10, 2.39, 2.69, 2.99, 3.28, 3.58, 3.98, 4.96, 5.95, 7.93, 9.90, 13.85, and 19.77 mmol/L). A clinical head-and-neck coil was used with the phantom. The vials were set vertically, and the axes of the vials were perpendicular to the image plane (coronal image). The vials in the phantom with constant concentration (1.20 mmol/L) were placed in exactly the same positions of the vials with different concentrations for measurement of

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M. Nazarpoor

We used T1-weighted TurboFLASH images to measure the SI in the vials with varying and constant concentration. 2.3.1 IR image The TurboFLASH imaging parameters were as follows: Matrix size = 128 9 128, time for one FLASH line = 8.5 ms, echo time [TE] = 4 ms. TI was varied between 400 and 800 ms, pixel size = 2 9 2 mm, repetition time [TR] = 2 s, slice thickness = 10 mm, and flip angle = 15°. Each image was repeated 10 times in the MR scanner. 2.3.2 SR images

Fig. 1 Phantom with vials of various concentrations of contrast agent which was placed inside the head-and-neck coil

The images for SR were also performed with a T1-weighted TurboFLASH (TR = 2 s, TE = 4 ms. The saturation time [TS] was varied between 300 and 800 ms, pixel size = 2 9 2 mm, slice thickness = 10 mm, flip angle = 15°). Each image was repeated 10 times in the MR scanner. 2.4 Image analysis The image data were transferred from the MR scanner to a personal computer. The image processing software Interactive Data Language (IDL, Research Systems, Inc., NY, USA; http://www.rsinc.com) was used for processing. Special programs were written with the intention of automatically finding the following: –

Fig. 2 Coronal image of the phantom. The position of vials with different concentrations can be seen in this figure

coil non-uniformity. The uniformity of the SI across an MR image gives an indication of how well the MRI system represents an object. One of the major sources of image non-uniformity in an MR scanner is the RF-coil inhomogeneity [14]. Therefore, for measuring an accurate SI of an image, the response of the RF coil should be uniform. The non-uniformity of the coil was calculated from the SI of each vial with constant concentration, and it was normalized to give a correction factor. For calculating the corrected SI for different concentrations, the SI of each vial was multiplied by its correction factor. Figure 2 shows a coronal image of the phantom. 2.3 Image acquisition The phantom was positioned within the head-and-neck coil. All studies were carried out on a 1.5-T clinical MR scanner (Vision, Siemens Medical, Erhlangen, Germany).

–

–

The mean image of 10 acquisitions primarily used to improve the signal-to-noise ratio. The 9 innermost pixels out of the total number of 44 pixels, to avoid partial volume effects in measuring the mean SI. The correction factors of the non-uniformity of the coils from the SI of the vials with constant concentration. Then the SI of the vials with different concentrations was multiplied by these factors. Meanwhile, the program also drew the best-fit curve of concentration versus the SI curve on the basis of Eq. 5 or 7.

A test-fit curve computer program was performed with an initial S0 for validation of the equations. The S(t) calculated from the best-fit curve was compared with the S(t) obtained for each vial by use of the same TI or TS from the image for finding the best value for S0. Finally, the designed program also specified the maximum concentration where the R2 between the corrected SI and the concentration was calculated to be equal to 0.95 or 0.99 from the best-fit curve. When R2 is 0.95, this indicates that 95% of the variation in SI is explained by the variation in the concentration [15]. A computer program calculated R2 from the first n points in the fitted data of SI versus concentration. As n


was increased, including more points in the fitted data, the value of R2 decreased. The value of n, and hence the concentration, that gave an R2 of 0.95 or 0.99 was also found. This concentration is known as the maximum value that gives a linear relationship with SI. These programs could be run from either a UNIX workstation or a personal computer.

3 Results 3.1 Correlation between SI and contrast agent concentration by use of IR sequence

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Figure 4 shows the maximum concentrations that give R2 values of 0.95 and 0.99 versus TI values from the best-fit curves. The correlation between SI and concentration extended up to 5.34 and 2.46 mmol/L for the short TI (400 ms) and long TI (800 ms), respectively, where R2 = 0.95. These values are reduced to 2.63 and 1.57 mmol/L for these inversion times where R2 = 0.99. As can be seen from the figure, an increase in TI is associated with a decrease in the maximum concentration. In addition, the figure shows that the linear relationship depends on the level of R2 chosen. It decreases when R2 increases from 0.95 to 0.99. 3.3 Correlation between SI and contrast agent concentration with use of SR sequence

A typical result from the corrected SI (for the non-uniformity of the coil) versus concentration with curve fit (based on Eq. 5) at TI = 600 ms, which was obtained from the IR sequence, can be seen in Fig. 3. The figure shows that the T1-shortening effect is dominant at low concentrations of Gd-DTPA based on Eq. 5, and the T2-shortening effect is dominant at high concentrations and leads to a decrease in the SI. The linearity between SI and concentration gradually disappeared for increasing concentrations, as shown in Fig. 3.

A typical result from the corrected (for the non-uniformity of the coil) SI versus concentration with curve fit (based on Eq. 7), which was obtained from the SR sequence, can be seen in Fig. 5. The ST was 600 ms. As can be seen from the figure, the T1-shortening effect is dominant at low concentrations of Gd-DTPA, based on Eq. 7, and leads to an increase in the SI. At high concentrations, the T2-shortening effect is dominant and leads to a decrease in the SI, as shown in Fig. 5.

3.2 Effect of variation of TI on SI in the IR sequence

3.4 Effect of variation of TS on SI in the SR sequence

The effect of TI on the correlation between the corrected SI and the concentration of the contrast agent was also investigated with five different TI values.

The effect of variation of TS on the maximum linear relationship between the corrected SI and the concentration can

Fig. 3 Mean corrected SI versus concentration of contrast agent for the IR sequence. The linear relationship between concentrations and corrected SI that gave R2 equal to 0.95 and 0.99 was at 3.29 and 2.06 mmol/L, respectively at TI = 600 ms. The dashed lines show the curve fitted to the data. The error bars show the standard deviation of the SI from the nine innermost pixels in each vial

Fig. 4 The maximum concentration that gives R2 = 0.95 and 0.99 versus TI. The linear relationship between SI and concentration extends up to 5.34 and 2.46 mmol/L for the short TI (400 ms) and long TI (800 ms), respectively, where R2 = 0.95. These values are reduced to 2.63 and 1.57 mmol/L for these inversion times, where R2 = 0.99

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Fig. 5 Mean corrected SI versus concentration of contrast agent for the SR sequence. The linear relationship between concentrations and corrected SI that gave R2 values of 0.95 and 0.99 was at 1.98 and 0.85 mmol/L, respectively, at TS = 600 ms. The dashed line shows the curve fitted to the data. The error bars show the standard deviation of the SI from the nine innermost pixels in each vial

be seen from Fig. 6. The figure shows the maximum concentrations that give R2 values of 0.95 and 0.99 versus TS of the SR sequence. The figure illustrates that the linear relationship between SI and concentration is up to 3.37 and 1.46 mmol/L for the short TS (300 ms) and long TS (800 ms), respectively (R2 = 0.95). These values are reduced to 1.54 and 0.66 mmol/L for the two saturation times, respectively, where R2 = 0.99.

4 Discussion The MRI is unable to measure the concentration of the contrast agent within the region of interest of an image. The concentration can be measured indirectly from the SI. The T1-shortening effect is dominant at low concentrations. Therefore, the relationship between the SI and concentration is linear. At high concentrations, both T1 and T2 can be affected as the SI response becomes nonlinear with the concentration. Therefore, for calculation of the concentration from the SI, the maximum concentration for this linearity should be measured. The correlation between the MR signal intensity and the concentration of Gd-DTPA on T1-weighted images was reported by Takeda et al. [4]. They demonstrated that, with use of low-magnetic-field apparatus (0.1 T), the SI was linearly correlated with the concentration of Gd-DTPA up to 2.0 mmol/L (R2 = 0.76, TS = 100 ms, flip angle = 60°

M. Nazarpoor

Fig. 6 The maximum concentration that gives R2 = 0.95 and 0.99 versus TS with the SR sequence. The figure illustrates that the linear relationship between SI and concentration extends up to 3.37 and 1.46 mmol/L for the short TS (300 ms) and long TS (800 ms), respectively (R2 = 0.95). These values are reduced to 1.54 and 0.66 mmol/L for the two saturation times where R2 = 0.99

or 90°) when gradient echo SR sequences were used. At a higher magnetic field (1.5 T), the linearity extended up to 2.0 (R2 = 0.94, TS = 500 ms) or 3.0 mmol/L (R2 = 0.81, TS = 34 ms, flip angle = 45°) when spin-echo or gradientecho sequences were used. One of Takeda’s results is in closer agreement with this study, with TS = 500 ms linearity extended up to 2.56, R2 = 0.95; see Fig. 6). In addition, our finding for the SR sequence indicates that the linearity is not only dependent on the concentration and the R2 value chosen, but is also strongly dependent on the TS of the sequence. The difference in results between this study and that of Takeda et al. [4] may be due to differences in the TS, TR [11], flip angle, and possibly the method of measuring the maximum linearity. The contrast agents other than Gd-DTPA have different relaxation rates. Canet et al. [5] found a linear relationship of up to 0.8 mmol/L by using the Gd-DOTA contrast agent, which has roughly the same relaxation times as that of Gd-DTPA [16] at TI = 300 ms (effective TI = 716 ms) for the Linear Phase-Encoding acquisition. In addition, Fritz-Hansen et al. [17] found linearity between signal changes and tracer concentrations up to 1.0 mmol/L at an effective TI of 720 ms and with use of the IR TurboFLASH sequence (Linear Phase-Encoding). Because the phase acquisition in our study was Center out Phase-Encoding, it is impossible to compare Canet and Fritz-Hansen’s results


with ours; the two acquisitions use different methods of sampling K space. Dean et al. [18] and Unger et al. [16] reported that the linear relationship between the SI and the concentration of contrast agent extends up to 1 mmol/L; however, they did not mention the image parameters and R2 value in detail for comparing with the results of this study. Valle0 e et al. [19] reported that the relationship between signal intensity and 1/T1 (in s-1) up to 11 s-1 was linear in the FAST sequence. The 1/T1 ratio was linearly related to the Gd concentration. However, they did not mention the exact Gd concentration for comparison with this study. In addition, our findings (see Figs. 4, 6) show that the maximum linearity of the SR sequence was lower than the IR sequence for the same acquisition parameters. The difference is due to differences in the two Eqs. (5 and 7) for the IR and SR sequences. As mentioned above, different reports have given different values for the linear relationship between the SI and the concentration of the contrast agent in T1-weighted imaging. These values varied between 0.8 (IR sequence, Linear Phase-Encoding) [5] and 3 mmol/L of concentration (SR sequence, Center out Phase-Encoding) [6]. The value of R2 which gives the linear relationship between SI and concentration is important. The R2 value is different in different reports. Takeda et al. [4] accept the value of 0.76 for the linearity, and Bourke et al. [20] that R2 = 0.74 shows a reasonably strong association between the two variables. In this study, the linearity was calculated for both R2 = 0.95 and 0.99, which indicates a far higher degree of linearity. This study shows that, in the measurement of SI, TI and TS are the important parameters (see Eqs. 5 or 7). They can have an effect on the value of the relationship between SI and concentration. An increase in TI or TS leads to a decrease in the range of the linearity. In summary, the linear relationship between SI and concentration extends up to at least 2.46 mmol/L (up to TI = 800 ms, R2 = 0.95) for the IR sequence, regardless of the value of TI chosen. In addition, the concentration will not be less than 1.54 mmol/L (up to TS = 800 ms, R2 = 0.95) for the SR sequence. A TI of 800 ms is normally used for in vivo perfusion, because at this time the blood has a null signal at 1.5 T [21]. It is necessary to mention that the injected dose needs for creating a known concentration of contrast agent for the region of interest is reported by Moody et al. [21].

5 Conclusion For measuring in vivo perfusion from a T1-weighted image, it is imperative to select image parameters and the amount of contrast agent injected very carefully to avoid

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nonlinearity between SI and concentration. Different reports suggested different values for the linearity with different image acquisition parameters. In this study, we evaluated the effect of TI and TS on relationships between contrast agent concentrations and signal intensities of T1-weighted magnetic resonance images. The results show that, regardless of the values of TI and TS chosen, the dose of contrast agent that can be used while maintaining linearity is about twice that previously reported (i.e., 0.8 mmol/L, R2 = 0.95). The higher dose will improve the signal-to-noise ratio in perfusion images. The results of this study will be used for further research to measure in vivo perfusion.

References 1. Sura0 nyi P, Kiss P, Ruzsics B, Brott BC. Equilibrium signal intensity mapping, an MRI method for fast mapping of longitudinal relaxation rates and for image enhancement. Magn Reson Imaging. 2007;25:641–51. 2. Bellin MF, Van Der Molen AJ. Extracellular gadolinium-based contrast media: an overview. EJR. 2008;66:160–7. 3. L¨udemann L, Warmuth C, Plotkin M, F¨orschler A. Brain tumor perfusion: comparison of dynamic contrast enhanced magnetic resonance imaging using T1, T2, and T2 contrast, pulsed arterial spin labeling, and H215O positron emission tomography. EJR 2008; in press. 4. Takeda M, Katayama Y, Tsutsui T, Komeyama T, Mizusawa T. Dose gadolinium-diethylene triamine pentaacetic acid enhanced MRI of kidney represent tissue concentration of contrast media in the kindey? In vivo and in vitro study. Magn Reson Imaging. 1994;12:421–7. 5. Canet E, Douek P, Janier M, Bendid K, Amaya J, Millet P, et al. Influence of bolus volume and dose of gadolinium chelate for first-pass myocardial perfusion MR imaging studies. J Magn Reson Imaging. 1995;4:411–5. 6. Mørkenborg J, Pedersen M, Jensen FT, Stødkilde-Jørgensen H, Djurhuus JC, Frøkiær J. Quantitative assessment of Gd-DTPA contrast agent from signal enhancement: an in vitro study. Magn Reson Imaging. 2003;21:637–43. 7. NessAiver M, editor. All you really need to know about MRI physics, Chapters 6 and 7, 1 ed. University of Maryland Medical Center, USA; 1997. 8. Nazarpoor M, Moody AR, Martel AL, Morgan PS. The relationship between contrast agent concentration and signal intensity on T1 weighted images for measuring perfusion with MRI. 20th Annual Scientific Meeting, ESMRMB Rotterdam 2003; p. S243–4. 9. Roberts TPL. Physiological measurement by contrast-enhanced MR imaging: expectations and limitations. J Magn Reson Imaging. 1997;7:82–90. 10. Bernstein MA, King KF, Zhou XJ. Handbook of MRI pulse sequences. London: Academic Press; 2004. 11. Nazarpoor M. The effect of repetition time on the relationship between contrast agent concentration and signal intensity on T1-weighted images using inversion recovery (IR) sequence. European Society for Magnetic Resonance in Medicine and Biology (ESMRMB), Copenhagen, Denmark 2004; p. S310–1. 12. Rohrer M, Bauer H, Mintorovitch J, Requardt M, Weinmann HJ. Comparison of magnetic properties of MRI contrast media solution at different magnetic field strengths. Invest Radiol. 2005;40:715–24.

126 13. McRobbie DW, Moore EA, Graves MJ, Prince MR. MRI from protons to pictures. Cambridge: Cambridge University Press; 2006. p. 69. 14. Simmons A, Tofts PS, Barker GJ, Arridge SA. Sources of intensity non-uniformity in spin echo images at 1.5 T. Magn Reson Med. 1994;32:121–8. 15. Kleinbaum DG, Kupper LL, Muller KE. Applied regression analysis and other multivariable methods, chapter 6. Duxbury Press, Wadsworth publishing company, Inc edition; 1998. 16. Unger EC, Ugurbil K, Latchaw RE. Contrast agent for cerebral perfusion MR imaging. J Magn Reson Imaging. 1994;4:235–42. 17. Fritz-Hansen T, Rostrup E, Ring PB, Larsson HBW. Quantification of gadolinium-DTPA concentrations for different inversion times using an IR-Turbo FLASH pulse sequence: a study on optimizing multislice perfusion imaging. Magn Reson Imaging. 1998;8:893–9.

M. Nazarpoor 18. Dean BL, Lee C, Kirshch JE, Runge VM, Dempsey RM, Pettigrew LC. Cerebral hemodynamics and cerebral blood volume: MR assessment using gadolinium contrast agents and T1-weighted Turbo-FLASH imaging. Am J Neuroradiol. 1992;13:39–48. 19. Valle0 e JP, Lazeyras F, Kasuboski L, Chatelain P, Howarth N, Righetti A, et al. Quantification of myocardial perfusion with FAST sequence and Gd bolus in patients with normal cardiac function. J Magn Reson Imaging. 1999;19:197–203. 20. Bourke GJ, Daly LE, Gilvray JM, editors. Interpretation and uses of medical statistics, 3rd ed. Oxford: Blackwell Scientific Publications; 1985. 21. Moody AR, Martel A, Kenton A, Allder S, Horsfield MA, Delay G, et al. Contrast-reduced imaging of tissue concentration and arterial level (CRITICAL) for assessment of cerebral hemodynamics in acute stroke by magnetic resonance. Invest Radiol. 2000;35:401–11.