Regional 'H Transverse Magnetization Studies in Perfused Rabbit Kidney. Received March

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1 MAGNETIC RESONANCE IN MEDICINE 20,78-88 ( I99 I ) Regional 'H Transverse Magnetization Studies in Perfused Rabbit Kidney R. V. MULKERN,' M. E. STROMSKI, H. R. BRADY, S. R. GULLANS, T. SANDOR, AND F. A. JOLESZ Department of Radiology and the Renal Division. Brigham and Women j. Hospital, Harvard Medical School, Boston, Massachuserts Received March A Carr-Purcell-Meiboom-Gill imaging sequence consisting of 128 echoes is used to extract transverse magnetization decay curves (TDCs) at I.9 T from 1.7 X 1.7 X 5-mm3 voxels within the cortex, outer medulla, and inner medulla of perfused rabbit kidneys. The spatially localized TDCs within each tissue type are found to be better approximated by biexponential. as opposed to monoexponential, functions. The biexponential parameters characterizing the TDCs demonstrate an improved degree of tissue specificity over that available from monoexponential analyses. The fraction of the quickly relaxing TDC component and the relaxation rate of this component are observed to decrease from cortex to inner medulla. A two-site exchange analysis is used to convert biexponential TDC parameters into water volume fractions and exchange rates. The exchange rates between the fast and slowly relaxing pools increased from cortex to inner medulla. All exchange rates were less than 1.5 Hz, indicating a relatively slow water exchange process. The imaging methods and subsequent analyses ofl'er the potential to generate unconventional MR images with tissue contrast dependent upon water compartmentation and exchange. Q 1991 Academic Press. Inc. INTRODUCTION Methods for obtaining spatially resolved in vivo 'H transverse relaxation decay curves are now available (1-7) and offer the potential for increasing tissue specificity with MRI. The degree to which the methods will actually improve tissue specificity depends, to a large extent, on determining appropriate models for interpreting the observed relaxation behavior. Both recent in vivo results and numerous in vitro reports (8-16) have indicated that the decay of the 'H transverse magnetization in a variety of tissues is better characterized by a multiexponential fitting function as opposed to a single exponential function. One of the potential factors responsible for multiexponential transverse magnetization decay curve (TDC) behavior is the biophysical compartmentation of tissue water. Several questions arise within this context, including: (a) To what extent does compartmentation of water between intra- and extracellular spaces influence transverse relaxation? (b) To what extent does the partitioning of water between so- ' Present address: Department of Radiology, Childrens Hospital, 300 Longwood Avenue, Boston, MA /9 I $ Copynght by Academlc Press Inc. All nghts of reproduction in any form reserved

2 H TRANSVERSE MAGNETIZATION STUDIES 79 called free and macromolecular bound states influence the relaxation? (c) Can multiexponential TDC decompositions from image data sets be used to measure various water volume fractions and intercompartmental water exchange rates? (d ) Can these parameters be used as new image contrast parameters that will be useful for diagnosis? Incorporating the effect of water exchange between magnetically inequivalent environments into the Bloch equations predicts that TDCs will be described by multiexponential functions ( I 7). The relative sizes of the volume fractions and relaxation rates which best characterize a TDC are often called apparent in that they do not directly reflect the real sizes of the different proton pools and intrinsic relaxation rates within each pool. Only after the exchange of protons between compartments is taken into account can the apparent and real parameters be linked. In theory, the linkage is direct, though nonlinear. In practice, even with the simplest two-site exchange model, the number of parameters obtained from a biexponential TDC decomposition is not sufficient to yield all of the model parameters, though several methods for overcoming this obstacle have been proposed ( ). In this work, we experimentally determine tissue TDCs from image data sets of perfused rabbit kidneys. We demonstrate that TDCs from the inner medulla, outer medulla, and cortex are better characterized by biexponential functions than monoexponential functions. We demonstrate an increase in the ability of biexponential analyses to discriminate between tissues in the kidney over that available from monoexponential analyses. The apparent biexponential parameters are used in conjunction with a two-site exchange analysis to evaluate a set of real model parameters. These include water volume fractions, exchange rates between fractions, and intrinsic relaxation rates within the two compartments of the model. MATERIALS AND METHODS Kidneys from anesthetized adult New Zealand White rabbits ( n = 6) were removed surgically and perfused via the renal artery with a modified Krebs-Henseleit solution. The perfusate contained 1 15 mm sodium chloride, 25 m M sodium bicarbonate, 5 mmpotassium chloride, 1 m A4 magnesium sulfate, 0.4 mmmonosodium phosphate, 1.6 mmdisodium phosphate, 1.2 mm calcium chloride, 4 mm sodium lactate, 5 mm D-glucose, 1 mm L-alanine, and 0.2 wt% bovine serum albumin (Cohn Fraction V). The perfusate was bubbled with a 95% 0 2/5% C02 mixture throughout the experiments. The perfusate temperature was maintained at 37 C and the flow rate was maintained at 20 ml/min. Perfused kidneys were placed within the imaging volume of a 30-cm, 1.9-T IBM /MIT imaging system. Imaging experiments were completed within 35 min of kidney removal and perfusion. A Carr-Purcell-Meiboom-Gill (CPMG ) imaging sequence, previously tested for its ability to measure spectroscopically reliable transverse relaxation rates ( 7), was used to obtain image data sets from which regional transverse magnetization decay curves were extracted and analyzed. The sequence consisted of 128 echoes with 9.6- ms echo spacings. The selective 90 and 180 pulses used in the sequence were 2 ms in duration and consisted of three lobe sinc functions multiplied by a cosine Hamming window. Phase encoding was performed prior to the collection of each echo. The phase twist was removed following each echo collection with a compensating phase-encode gradient.

3 80 MULKERN ET AL. Two signal averages for each of the 128 phase-encoding steps were employed. The 90 pulses were phase cycled 180 between signal averages to minimize systematic error due to pulse imperfections (22). Images were magnitude calculated on 128 X 128 matrices with standard 2D FT methods. A total delay of4 s between excitations was used to minimize spin-lattice relaxation effects. The field of view (FOV) was 72 mm and slice thickness was 5 mm for all studies. Flip angles were accurately set with the stimulated echo method described by Perman el a/. (23), considerably reducing any errors introduced in transverse relaxation rate measurements due to imperfect 180 pulses (24-26). A variation of the CPMG imaging sequence, known as the rapid acquisition relaxation enhanced (RARE) sequence, was used to produce snapshot images in 8 s (27). This permitted rapid and precise slice localization prior to performing each 17-min CPMG study. The vertical position of each kidney within the horizontal bore of the magnet was adjusted until coronal RARE kidney images produced a maximum filling of the 72-mm FOV. The CPMG imaging sequence was then used to acquire a 128 echo image data set of the selected slice. The image data sets were transferred to a MicroVax-I1 computer (Digital, Inc., Maynard, MA) equipped with an ITEX board (Imaging Technology, Inc., Woburn, MA). Regions of interest ( ROIs) were identified and TDCs, represented by the signal intensity decay vs echo time, were extracted. Images reconstructed from the 16th or 22nd echo were employed for the purpose of defining ROIs due to the high contrast between tissue types in these images. The TDCs extracted from the data sets were best fit to the following normalized biexponential function using a maximum likelihood method described previously (12): MT( t)/mo = a exp( -Rd) + ( 1 - a)exp( - R2ht). [I1 In this expression, MT( t)/m, is the transverse magnetization as represented by the normalized signal intensity, and RZa and R2h are the observed relaxation rates of the quickly and slowly relaxing components, respectively, with a representing the fraction of the quickly relaxing component. The TDC parameters of [I] are linked to a twosite exchange model using the analysis described below. METHOD OF TWO-SITE EXCHANGE ANALYSIS The simplest two-site exchange model is one in which the nuclei under observation are confined to two volume fractions fand g. The intrinsic transverse relaxation rates in fand g are those which would be measured in each compartment in the absence of exchange and are defined as R2j and R2y, respectively. The Larmor frequencies are assumed to be the same in both volume fractions. Bodily spin transport of nuclei (chemical exchange) between the two proton pools is characterized by exchange rates kfg and k,,, whose inverses represent average lifetimes of exchanging nuclei within fractions f and g, respectively. Volume normalization and detailed balance dictate that, under steady state conditions, the volume fractions and exchange rates obey the following two relations: f+g= 1 [21 fkfg - gk,,.= 0. [31

4 H TRANSVERSE MAGNETIZATION STUDIES 81 The apparent biexponential TDC components in 111 are related to the real parameters of the model with relations developed by Zimmerman and Britton ( 17). However, since there are a total of four independent model parameters and only three independent experimental parameters, an inversion between apparent and real parameters cannot be performed without an independent measurement of one intrinsic relaxation rate (19). Therefore, the assumption is made that the relaxation rate of protons within the perfusate is representative of the intrinsic relaxation rate of the water protons within the slowly relaxing fraction. This proton pool is taken, by convention, to be the fpool. Some useful combinations of the experimental quantities (R2n, R2b, a, and R2f) are now defined in order to simplify the equations used for the calculation of exchange parameters. These are In terms of the experimentally determined quantities defined in [ , the real model parameters may be directly expressed. A derivation of the inversion is provided in the Appendix. The real model parameters are given by [g( 1 - g)(2g - 1)*(4C: - LY~)] ~ kgy= a( 1-8) * 2g [lo1 R2g = R2f+ [a - kgf/( 1 - g)l/( 1-2g) The remaining exchange parameters are calculated with [ 21 and [ 31. Note that there is a sign ambiguity in the expression for the exchange rate krf. This is a consequence of the nonlinearity of the original equations (17). In the analyses of data reported below, only the + sign in Eq. [lo] yielded nonnegative values for kgf, an obvious physical constraint. RESULTS Figure 1 depicts the 22nd echo image (TE = ms) taken from one of the six complete 128 echo image data sets collected for this study. The 3 X 3-pixel boxes seen in Fig. 1 represent 1.7 X 1.7 X 5-mm3 voxels from which TDCs were extracted. Sampling regions were chosen to lie within the cortex, outer medulla, or inner medulla, as differentiated in the 16th or 22nd echo images. The renal papilla was avoided when analyzing the images because anatomically it can be less than 5 mm thick. Figure 2 presents typical semilog plots of echo amplitude vs echo time (TDCs) obtained in the cortex, outer medulla, inner medulla, and a vial of the perfusate used

5 82 MULKERN ET AL. FIG. 1. The 22nd echo image (TE = 2 1 I ms) of a 128-echo CPMG image data set. Two 1.7 X 1.7 X 5- mm3 voxels ( ROIs) are depicted in the cortex, outer medulla, and inner medulla. in the study. Each of the tissue TDCs in Fig. 2 was fit with both a monoexponential function and a biexponential function [I]. The sums of squared deviations were calculated for both types of fit. Biexponential functions generally provided between 15 (inner medulla) and 40 times (cortex) smaller sums of squared deviations than mono x -cj.- ffl - c A Perfusate i.~ 0 A Inner Medulla m 10 0 Outer Medulla Echo Time (ms) FIG. 2. Typical semilog plots of the signal intensity vs echo time (TDCs) extracted from 1.7 X 1.7 X 5- mm3 voxels in the cortex, outer medulla, inner medulla, and the perfusate.

6 H TRANSVERSE MAGNETIZATION STUDIES 83 TABLE 1 Apparent Biexponential TDC Relaxation Parameters in Various Regions of the Kidney a R2o (Hz) Rib (Hz) R2 c (24) 0.84 f ?z f k 0.15 OM(24) 0.71 k k 0.8 I 2.18 k f 0.26 IM (19) 0.49 f k f f 0.14 Note. Mean values and standard deviations of the biexponential fitting parameters obtained from fits of the 66 TDCs extracted from the cortex (C), outer medulla (OM), and inner medulla (IM). exponential fits. The perfusate TDC in Fig. 2 was clearly monoexponential and the single relaxation rate calculated from the slope of this curve was found to be 0.8 Hz. A total of 66 TDCs were extracted from 9-pixel ROIs in the image data sets of the six different kidney studies. At least four and up to six nonoverlapping ROIs were sampled within each of the three tissues identified in the kidney. This resulted in a total of 24 TDCs from the cortex, 23 from the outer medulla, and 19 from the inner medulla. The means and standard deviations of the biexponential TDC fitting parameters are reported in Table 1. Included in Table 1 are the means and standard deviations of the relaxation rates R2, found from fitting curves to a single exponential function. Table 2 contains the results of a paired t test (two-tailed) as applied to the mean values of TDC fitting parameters obtained from the six kidney data sets. This table serves to test the discriminatory power of each of the four tissue characterization parameters of Table 1. The ability to differentiate between cortex and outer medulla (C-OM), cortex and inner medulla (C-IM), and outer medulla and inner medulla (OM-IM) are reported as very significant, P < 0.001; significant, P < 0.05; or not significant (NS), P > A direct conversion of the data in Table 1 into two-site exchange parameters using the relations presented above was performed. The intrinsic relaxation rate, R, of the slowly relaxing pool was taken to be equal to the perfusate relaxation rate (0.8 Hz). Mean values of the exchange parameters were calculated using the mean values of the TABLE 2 Results of Paired t Test for Determining Specificity Characteristics of Bi- and Monoexoonential Fitting Parameters in Kidney C-OM 0.00 I NS NS C-IM NS OM-IM Norc Results of paired t tests as applied to data obtained from the six kidney studies (C, cortex; OM, outer medulla; IM, inner medulla). P values are less than those indicated in the table or are >0.05 and not significant (NS).

7 84 MULKERN ET AL. TABLE 3 Real Two-site Exchange Model Parameters in Three Regions of the Kidney C 0.88 f t f ko.1 OM 0.83 f f f IM f f k 0.2 Nofe. Fraction of protons g, exchange rates kdand krg, and the larger of the two intrinsic relaxation rates RZgr in the cortex (C), outer medulla (OM), and inner medulla (IM). TDC components listed in Table 1. The results of the analysis appear in Table 3. In order to estimate limits in the accuracy of the calculated exchange parameters, the R, value used in the analysis was varied from to 2 that found in the perfusate. The t values appearing in Table 3 indicate the resultant uncertainties in the average exchange parameters associated with this range of R2f values. DISCUSSION Detailed CPMG imaging studies of perfused rabbit kidneys reveal that the transverse magnetization in the cortex, outer medulla, and inner medulla relaxes in a nonexponential manner. We have chosen to fit the tissue TDCs with biexponential functions and so reduced the sum of squared deviations by factors of 15 to 40 compared to those calculated from monoexponential fits. The choice of optimal echo times and repetition rates in clinical spin-echo imaging is often based on maximizing expressions for contrast-to-noise (CNR) ratios that inherently assume monoexponential transverse relaxation (28). These observations suggest that biexponential transverse relaxation functions may be more useful for optimizing imaging parameters designed to bring out the diagnostically useful cortexmedulla contrast (29). In addition, the improved tissue TDC characterization obtained with biexponential over monoexponential fits suggests that single R2 measurements are prone to serious error, reducing their diagnostic specificity. This is apparent from Table 2 which demonstrates that the biexponential parameters a and RZa may be used to differentiate between any two of the three tissue types with a much higher level of confidence than the single R2 values which fail to yield significant differentiation between the outer medulla and the inner medulla. The ability to resolve at least two components in kidney tissue TDCs with CPMG imaging techniques provides an opportunity to make pixel-by-pixel maps of apparent biexponential parameters ( 1-4). Table 3 demonstrates that apparent TDC parameters may be converted to real two-site exchange model parameters. These may also be mapped on a pixel-by-pixel basis. Thus, maps of either apparent or real parameters obtained from biexponential TDC studies may be generated and tested for their use as diagnostic imaging tools. However, in order to calculate the real parameters, an independent measurement of one intrinsic relaxation rate appears necessary. We assumed that the perfusate R2 represented a meaningful measure of R, of the model. This assumption is justifiable if the fluid within the f compartment of the model

8 H TRANSVERSE MAGNETIZATION STUDIES 85 resides within an environment in which water molecules have relatively unrestricted translational and rotational degrees of freedom, as in the extracellular space. The existence of at least two TDC components in kidney have been observed previously by Francois ef al. (8). These workers performed nonimaging, in vitro CPMG analyses of whole mice kidneys using much smaller echo spacings ( 10 fis) than available from CPMG imaging experiments. They suggested that intra- and extracellular water compartmentation was responsible for the two most slowly relaxing components in four component TDC decompositions. These are the two components which are primarily detected with imaging pulse sequences in which the first echo is, by necessity, collected some 10 ms after the initial excitation. The delay is long enough to minimize contributions from solid-like proton pools associated with macromolecules and membranes. An alternative explanation for the two observed TDC components is so-called free and macromolecular bound water (13). In this case, the perfusate R2 may not be an appropriate measure of Ryof the model. Still, there are limits on the values which can be associated with free water transverse relaxation rates. In obtaining the results presented in Table 3, R2, spanned a range from 0.4 to 1.2 Hz. This corresponds to a range of transverse relaxation times ( T2) of 2500 to 830 ms, certainly encompassing T2 values expected for free water. Within the limits imposed by this spread of R, values, it is of interest to compare the real exchange parameters with apparent relaxation parameters. The average apparent volume fraction, a, is that associated with the quickly relaxing proton pool. It is seen to decrease from values around 0.84 in the cortex to much smaller values around 0.49 in the inner medulla. The two-site exchange calculation reveals that the real size of the fast relaxing pool (g) spans a substantially smaller range between the different tissue types than the apparent fraction. This is reflected in g values which range from 0.88 in the cortex to 0.72 in the inner medulla (Table 3). It is possible that these g values represent real intracellular water volume fractions. However, in the alternate interpretation, the g fraction would be associated with protons experiencing an environment in which translational and rotational degrees of freedom are restricted, e.g., the bound water. Since bound water fractions acting as relaxation sinks in tissue or protein solutions are generally accepted to be no larger than 10% (9, 30), it appears unlikely that an interpretation based on free and bound water volume compartmentation is viable. The largest exchange rates, kg,f, are observed in the inner medulla, leading to the largest disparity between the apparent and the real volume fractions in this tissue. All of the mean exchange rates calculated are less than 1.5 Hz, indicating relatively long lifetimes (greater than 500 ms) of water molecules within the compartments of the model. The true nature of the two most obvious components contributing to the perfused rabbit kidney tissue TDCs as obtained with clinically applicable CPMG imaging techniques has not been revealed in this study. Furthermore, it is possible that a continuous distribution of exponentially decaying terms (31) may provide an equally good or even better fit to the TDCs. The demands on the quality and quantity of experimental data, however, can become quite high if the data alone are to be used to differentiate between continuous distributions and discrete exponential analyses ( 32). Therefore,

9 86 MULKERN ET AL. fitting the TDCs to biexponential models and analyzing them in terms of a two-site exchange model provides a means to test the relative merits of the model itself with well-designed experiments. These experiments should include direct manipulations of the biological compartments with osmotic agents (8) and with paramagnetic agents (20) in the perfusate to study their effects on the TDC components. It would also be of interest to perform regional longitudinal magnetization decay curve ( LDC) studies. The combination of TDC and LDC biexponential decompositions can alleviate the use of a measurement of R2f to close the exchange equations and extract model parameters (21). The motivation for pursuing such studies lies in the fact that new and unique contrast options in MRI, based on water compartmentation and exchange, appear feasible using the methods proposed above. The ability to interpret images based on these contrast parameters will depend on choosing the most appropriate biophysical models responsible for the underlying relaxation behavior. CONCLUSIONS Clinically applicable CPMG imaging techniques have been used to generate spatially localized tissue TDCs in perfused rabbit kidneys. The TDCs were found to be much better characterized with biexponential functions than with monoexponential functions. The biexponential parameters a and Rza provide better differentiation between inner medulla, outer medulla, and cortex than do R2 values calculated from monoexponential analyses. A two-site exchange model was used to link apparent relaxation parameters with real water volume fractions and exchange rates. Both the apparent volume fractions and the real volume fractions of the quickly relaxing pool were found to decrease from cortex to inner medulla. The largest exchange rates between the quickly relaxing pool and the slowly relaxing pool were found in the inner medulla. All the exchange rates were relatively small (kjg, k,, < 1.5 Hz), suggesting a slow exchange regime for tissues in the perfused rabbit kidney. The CPMG imaging sequence, coupled with biexponential TDC fits and two-site exchange analyses, appears to offer the potential to generate unconventional MR images in which the contrast between tissue types is based on water compartmentation and exchange rates. APPENDIX The two-site exchange equations derived by Zimmerman and Britton ( 17) may be written in the form a=(l- The left hand sides of [ A 1 ] - [ A3 ] have been defined above ( [ 4 ] - [ 61 ) as combinations of the experimentally determined apparent quantities. They represent the knowns in

10 H TRANSVERSE MAGNETIZATION STUDIES 87 this system of equations. The quantities kfg andf, which appear in the original reference ( 17) have been eliminated with the use of [ 21 and [ 31. The convention that RZa > R2b has been adopted in this analysis. The equations represent a system with three knowns and four unknowns. Once it is assumed that a measurement of R, may be made, [A 11 - [ A3 ] may be inverted to yield R2g, kgf, and g in terms of the known quantities. There is no special reason for choosing R2fover R, as known. The alternate solution in which R2g is chosen leads to an equally acceptable but redundant solution. Proceeding then, one solves for RZg from [ A3 ] to obtain Upon substituting [ A41 into [A 11 and rearranging one may obtain where P has been defined in terms of the known parameters above [ 7 1. In a previous publication (20), the basic relationship for kg, expressed by [ 101 was derived. Substituting [ 101 into [ A5 1, subtracting a from both sides, squaring the result, and canceling terms leads to Minor rearrangement of this expression leads to [ 91, in which g is elegantly expressed in terms of the known quantities R2f, a, Rzar and R2b, as condensed into the variable l- defined in [8]. REFERENCES 1. K. GERSONDE, L. FELSBERG, T. TOLXDORFF, D. RATZEL, AND B. STROBEL, Magn. Reson. Med. 1, 463 (1984). 2. K. GERSONDE, T. TOLXDORFF, AND L. FELSBERG, Mugn. Reson. Med. 2, 390 (1985). 3. L. R. SCHAD, G. BRIX, W. SEMMLER, F. GUCKEL, AND W. LORENZ, Magn. Reson. Imaging 7, 357 (1989). 4. H. B. W. LARSSON, J. FREDERIKSEN, J. PETERSEN, A. NORDENBO, I. ZEEBERG, 0. HENRIKSEN, AND J. OLESEN, Mugn. Reson. A4c.d. 11, 337 ( 1989). 5. R. L. KAMMAN, C. J. G. BAKKER, P. VAN DUK, G. P. STOMP, A. P. HEINER, AND H. J. C. BERENDSEN, Mugn. Reson. Imaging 5,381 (1987). 6. J. D. HAZLE, P. A. NARAYANA, AND W. A. KUDRLE. J. Magn. Reson. 83, 595 (1988). 7. R. V. MULKERN. S. T. S. WONG, P. JAKAB, A. R. BLEIER, T. SANDOR, AND F. A. JOLESZ, Mugn. Reson. hfed. 16,61 (1990). 8. A. FRANCOIS, L. VAN GERVEN, G. ATASSI, H. EISENDRATH, M. GIELEN, AND R. WILLEM, Magn. Reson. Med. I, 449 (1988). 9. W. T. SOBOL, L. G. CAMERON, W. R. INCH, AND M. M. PINTAR, Biophys. J. 50, 181 ( 1986). 10. W. T. SOBOL AND M. M. PINTAR, Magn. Reson. Med. 4, 537 ( 1987). 11. Y. MAUSS, D. GRUCKER, D. FORNASIERO, AND J. CHAMBRON, Magn. Reson. Med. 2, 187 (1985). 12. T. SANDOR, A. R. BLEIER, P. RUENZEL, D. F. ADAMS, AND F. A. JOLESZ, Mugn. Reson. lmaging 6, 27 (1988). 13. B. M. FUNG AND P. S. PUON, Biophys. J. 33,27 ( 198 I ). 14. S. BRADAMANTE, E. BARCHIESI, S. PILOTTI, AND G. BORASI, Mugn. Reson. Med. 8,440 ( 1988).

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