Biexponential apparent diffusion coefficient parametrization in adult vs newborn brain

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1 Magnetic Resonance Imaging 19 (2001) Biexponential apparent diffusion coefficient parametrization in adult vs newborn brain Robert V. Mulkern a,c, *, Sridhar Vajapeyam a, Richard L. Robertson a, Paul A. Caruso a, Michael J. Rivkin a,b, Stephan E. Maier c a Department of Radiology, Children s Hospital, Harvard Medical School, Boston, MA USA b Department of Neurology, Children s Hospital, Harvard Medical School, Boston, MA USA c Department of Radiology, Brigham and Women s Hospital, Harvard Medical School, Boston, MA USA Received 1 March 2001; accepted 8 April 2001 Abstract The decay of brain water signal with b-factor in adult and newborn brains has been measured over an extended b-factor range. Measurements of the apparent diffusion coefficient (ADC) decay curves were made at 16 b-factors from 100 to 5000 s/mm 2 along three orthogonal directions using a line scan diffusion imaging (LSDI) sequence to acquire data from 0.09 ml voxels in a mid-brain axial slice. Regions-of-interest (ROIs) in cortical gray (CG) and white matter in the internal capsule (IC) were selected for ADC decay curve analyses using a biexponential fitting model over this extended b-factor range. Measures of the fast and slow ADC component amplitudes and the traces of the fast and slow diffusion coefficients were obtained from CG and IC ROIs in both adults and newborns. The ADC decay curves from the newborn brain regions were found to have a significantly higher fraction of the fast diffusion ADC component than corresponding regions in the adult brain. The results demonstrate that post-natal brain development has a profound affect on the biexponential parameters which characterize the decay of water signal over an extended b-factor range in both gray and white matter Elsevier Science Inc. All rights reserved. Keywords: Brain water diffusion; Biexponential decay; Water compartmentation; Newborn brain 1. Introduction Recent experimental studies have demonstrated that there is a fast and a slow apparent diffusion coefficient (ADC) associated with the decay of in vivo water signal in human brain when sampled over an extended b-factor range [1 5]. The observation of multiple ADC components modeled with bi- or multi-exponential decay functions has also been made in several animal studies [6 8]. Of course, a biexponential model allows for interpretations based on extra- and intracellular brain water compartmentation [8]. Alternatively, the non-exponential behavior may be a manifestation of restricted diffusion processes and/or water compartmentation within as well as between cells [9 14]. Indeed, non-exponential behavior has been reported in single compartment systems such as water within packed * Corresponding author. Tel.: ; fax: address: mulkern@bwh.harvard.edu (R.V. Mulkern). polystrene beads [13] and within the pores of salt water ice [15]. Given the lack of any unequivocal interpretation of multi-component ADC behavior for either biological or materials science applications, it is of interest to gather further empirical information regarding this phenomenon. Here we report profound differences in the biexponential parametrization of water signal decay curves with b-factor from cortical gray (CG) matter and internal capsule (IC) white matter in the adult vs the newborn human brain in vivo. 2. Materials and methods Imaging was performed with a 1.5 T Signa scanner operating at the 5.7 or 5.8 hardware/software configuration (General Electric Medical Systems, Milwaukee, WI) with 2.3 Gauss/cm maximum gradient strengths. A line scan diffusion imaging (LSDI) sequence [3,16 20] was used to image an axial mid-brain slice at 16 equally spaced b X/01/$ see front matter 2001 Elsevier Science Inc. All rights reserved. PII: S X(01)

2 660 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) Table 1 Clinical data Case Age at exam Indication for exam MRI findings Follow-up interval/status 1 1 day Posterior fossa arachnoid cyst Normal 1 yr./developmentally normal on prenatal ultrasound 2 1 day Lt. body seizures Rt. frontoparietal infarction 5 mo./mild lt. hemiparesis 3 3 days Stridor Normal 1 mo./developmentally normal 4 5 days Perinatal seizures Normal 2 mo./developmentally normal, no further seizures on phenobarbital 5 7 days Perinatal apneic episodes Normal 1 mo./developmentally normal 6 7 days Myoclonis during sleep Normal 5 mo./developmentally normal 7 21 days Eye deviation Normal 3 mo./developmentally normal 8 22 days Hypoglycemia Normal 1 yr./developmentally normal Abbreviations: Lt., left; Rt., right; mo., month; yr., year. factors from 100 to 5,000 s/mm 2 using three separate diffusion gradient directions of (1, 1, 1/2), (1/2,1, 1) and (1,1/2,1). The effective repetition time (TR) and echo time (TE) were 2,500 and 118 ms, respectively. The diffusion gradient pulse pair had a leading edge separation, of56 ms. The diffusion gradient pulse widths, were fixed at 50 ms. The diffusion gradient amplitude G along each axis was incremented to vary the b-factor. The scan time for 48 total images of the selected slice, including the 16 b-factors, 3 gradient sensitization directions, and 48 LSDI columns per setting, was 6.2 minutes with individual voxel dimensions of mm 3. Four healthy adult males (mean age 40 5 years) and eight newborns were examined. The newborns received MR scans for the clinical indications listed in Table 1. In all but one (patient 2), normal imaging findings were encountered and follow-up demonstrated normal developmental progress. Patient 2 presented with focal left sided seizures and was found to have areas of decreased diffusion in the right precentral gyrus and left superior parietal lobule, as indicated with clinical LSDI scans at two b-factors of 5 and 750 s/mm 2 [20]. Otherwise, the brain appeared normal with any areas of decreased diffusion being well-removed from the ROI s sampled with the single slice multi-b-factor LSDI sequence. Furthermore, at 15 month follow up, the patient was found to be developmentally and neurologically normal. Since the biexponential parameters obtained from this patient within the ROI s sampled were within 5% of the means obtained from the other newborns, patient 2 has been retained in the normal category. The ages of the newborns at the imaging sessions ranged from 1 to 22 days with a mean age of 8 days and a mean gestational age of 39 1 weeks. Regions-of-interest (ROI) of approximately 0.25 ml within the cortical gray (CG) matter and within the left internal capsule (IC) white matter were selected for analysis. For each ROI, four decay curves representing signal intensity vs b-factor were generated; one for each of the three diffusion gradient directions and one generated from the cubed root of the product of these three decay curves. The latter decay curve is referred to as the composite decay curve. Each decay curve was fit to a biexponential function of the form S A exp( D a b) B exp( D b b) (1) following removal of data points in which the signal intensity fell within one standard deviation of mean baseline noise value as measured from an ROI outside of the head. The decay curves were fit to Eq. (1) using a Marquardt- Levenberg algorithm as implemented within the commercial software package C-PLOT (Certified Scientific Software, Cambridge, MA). In addition to the ROI analyses, the image software processing package IDL (Research Systems Inc., Boulder, Colorado) was used to perform pixel-by-pixel biexponential analyses so that images of the biexponential parameters A, D a, B, and D b could be viewed. Fitting decay curves to multi-exponential functions is a notoriously difficult but well-studied problem [21]. Our use of a biexponential fit to the brain water signal decay over the extended b-factor range from 100 to 5000 s/mm 2 has been validated from an empirical perspective by comparison with the nonnegative least squares algorithm, as presented in an earlier report [2]. From the separate fits along each of the three diffusion gradient directions, the means and standard deviations (SD) of the biexponential parameters D a,d b, and A/(A B) were obtained for each ROI. These means were used to evaluate inter-individual parameter means and SD s for the adult and the newborn populations for both the CG and IC data. Statistically significant differences between the interindividual mean biexponential parameters for the adult and newborn CG and IC data were sought using Student s paired t-test with p 0.05 considered significant. The biexponential parameters extracted from the composite ADC decay curves were compared with the averages obtained from individual fits along the three separate diffusion gradient directions to assess differences between the two alternate methods of analysis. Phantom studies of ethanol and isopropanol were performed in order to assess the potential for any instrumentation artifact as a source of non-monoexponential decay curves observed in the human brains.

3 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) Fig. 1. ADC decay curves from phantoms containing ethanol (open diamonds) and isopropanol (filled squares) using the same sequence parameters applied for the study of human brains. There is no curvature displayed by these decay curves over the full b-factor range studied, no significant variation with diffusion sensitization gradient and, due to the small diffusion coefficients for these substances, signal remains above baseline noise values (open triangles). 3. Results Fig. 1 provides the decay curves from the ethanol and isopropanol phantoms. The curves appear as straight lines on these semi-log plots of signal intensity vs b-factor, indicating pure monoexponential decay with no dependence on the diffusion gradient direction. The top four panels of Figs. 2a and b (left and right) show images of an adult and a newborn brain which are based on pixel-by-pixel biexponential decompositions of the composite multi-b-factor data set. The images are labeled according to the parameters of Eq. (1). Several differences between the adult and newborn cases meet the eye. First, there is significantly more signal intensity observed for the A image, representing the amplitude of the fast diffusion coefficient, in the newborn brain than in the adult brain. This is accompanied by a noisy B image in the newborn brain, representing low amplitudes for the slow diffusion ADC component, compared to the adult brain. Additionally, the D b image in the adult brain shows considerably more structure than that seen for the newborn brain with areas of gray matter having higher signal intensities than areas of white matter. The lower two panels of Figs. 2a and b are diffusion weighted images of the adult and newborn brains, respectively, taken from the composite multi-b-factor data set at a b factor of 1,200 s/mm 2. The lower left panels show all the anatomy while the lower right panels depict typical ROI s used for sampling cortical gray matter and internal capsule to provide data for statistical evaluation of the biexponential fit parameters. Experimental decay curves from adult and newborn brains for the CG and IC ROI s are provided in Figs. 3 and 4, respectively. All decay curves display curvature on these semi-log plots indicative of non-monoexponential behavior. They are well-characterized by biexponential functions shown as solid lines through each curve. In general, signal intensities from the adult brain at the highest b-factors remain well-above baseline noise values while those from the newborn brain approach the baseline noise values plotted at the bottom of each figure. The CG decay curves in both adult and newborn brains show very little dependence on the direction of the diffusion sensitization gradient (Figs. 3a and b) whereas a considerable dependence of the IC decay curves on the diffusion gradient direction is observed (Figs. 4a and b). In particular, when the superior-to-inferior (z-axis) gradient is 1/2 vs 1, as it is only for the (1, 1, 1/2) direction, a slower rate of signal decay with b-factor occurs within the IC, consistent with fibres running in the superiorto-inferior direction. There is also a smaller fast fraction (A/(A B)) obtained from decay curves acquired along the (1, 1, 1/2) direction compared to the other two directions. For example, from the adult IC data the inter-individual mean SD of A/(A B) was for the (1, 1, 1/2) direction vs and for the (1/2,1, 1) and (1,1/2,1) directions, respectively. In the

4 662 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) Fig. 2. Parametric images of the biexponential parameters obtained from pixel-by-pixel fits to Eq. (1) for an adult brain and a newborn brain using the composite data set. The high b-factor images in the lower panels show the anatomy (left) and the locations of the ROI s in cortical gray (CG) matter and internal capsule (IC) selected for inter-individual statistical analyses. newborns with less well-developed fibre tracks, the interindividual A/(A B) fractions in the IC for the same three respective directions were , and , again demonstrating an attenuated fast A/(A B) fraction with the reduction of diffusion gradient strength along the superior-to-inferior direction. Table 2 provides the inter-individual means and SD s of the biexponential parameters which best characterized the ADC decay curves extracted from CG and IC ROIs. Both the directionally averaged values and values extracted from the composite decay curves, shown in parentheses, are provided in the Table. With the exception of the adult A/(A B) ratio in the IC, there is very little difference between the parameters found by directional averaging of individual fits and those obtained from the composite decay curves. Adult and newborn brain fast diffusion coefficients D a, were sim-

5 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) Fig. 3. (a) Typical decay curves from adult cortical gray matter for all three diffusion sensitization gradients as well as for the composite data set. The curves are clearly non-monoexponential and well-characterized by the biexponential fits shown as solid lines through the data. The signal remains above baseline noise values indicated by the solid line at the bottom of the plot. (b) Typical decay curves from newborn cortical gray matter for all three diffusion sensitization gradients as well as for the composite data set. The curves are clearly non-monoexponential and well-characterized by the biexponential fits shown as solid lines through the data. The signal approaches baseline noise values plotted at the bottom of the figure (solid line) at the highest b-factors sampled.

6 664 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) Fig. 4. (a) Typical decay curves from adult white matter in the internal capsule (IC) for all three diffusion sensitization gradients as well as for the composite data set. The curves are clearly non-monoexponential and well-characterized by the biexponential fits shown as solid lines through the data. The signal remains above baseline noise values indicated by the solid line at the bottom of the plot and, unlike the CG data, show a marked dependence on the diffusion gradient direction. (b) Typical decay curves from newborn white matter in the internal capsule (IC) for all three diffusion sensitization gradients as well as for the composite data set. The curves are clearly non-monoexponential and well-characterized by the biexponential fits shown as solid lines through the data. The signal remains above baseline noise values indicated by the solid line at the bottom of the plot and, unlike the CG data, shows a marked dependence on the diffusion gradient direction.

7 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) Table 2 Inter-individual means SD (N 4 for adults and N 8 for newborns) for the biexponential parameters in the CG and the IC for adult and newborn populations as averaged from fits along all three diffusion gradient directions ilar in the IC ROI s while for CG ROI s adult D a values were larger than the newborns by some 15 to 20% (P 0.05). Slow diffusion coefficients D b were similar for both adult and newborn brains in CG ROI s while adult D b values were approximately half those found for the newborns (P 0.05) in IC ROI s. For both CG and IC ROI s, a very significant difference (p 0.001) was found for the fraction of the fast ADC component, A/(A B), between adult and newborn brains. Specifically, adult ADC decay curves displayed fast ADC fractions in the 0.55 to 0.75 range compared to newborn fast ADC fractions in the 0.79 to 0.90 range (Table 2). 4. Discussion D a um 2 /ms D b um 2 /ms A/(A B) CG (Adult) ( ) ( ) ( ) CG (Newborn) ( ) ( ) ( ) IC (Adult) ( ) ( ) ( ) IC (Newborn) ( ) ( ) ( ) Values in parentheses are inter-individual means and SD s taken from the composite decay curves which, with the exception of the adult IC A/(A B) ratio, agree very well with the directionally averaged values. There have been several studies reporting the effects of brain maturation on the apparent diffusion coefficients in newborns. Huppi et al. [22] and Neil et al. [23] have shown that the ADC in human newborns, as measured in the 5 to 1000 s/mm 2 b-factor range, decreases over the first few months of life while the anisotropy in white matter regions like the internal capsule increases. In an animal model of kitten brain maturation, Baratti et al. [24] measured regional brain relaxation times and the trace of the diffusion tensor over the first two months of life. Using 5 b-factors below 1,100 s/mm 2, they found the trace of the ADC to decrease from values in the 1.1 to 1.3 um 2 /ms range in the newborn to an average of 0.7 um 2 /ms in the adult kitten, or cat, brain at 2 months of age. Several studies have now concluded, however, that at least two ADC components are required to describe ADC decay behavior over wide b-factor ranges in adult human brains with the fraction of the fast ADC component (A/(A B)) reported to be on the order of 0.7 [1 5]. It is unclear how this finding affects interpretations made in previous studies of maturation on water diffusion [22 27]. The use of a monoexponential decay model in the presence of biexponential behavior can lead to erroneous conclusions [5]. For instance, apparent decreases of ADC with age, made on the basis of monoexponential decay assumptions and measurements, may in fact be due to a growth in amplitude of the slower diffusing second component with age. Regarding the nature of biexponential ADC behavior, it is tempting to identify the fast diffusion component with the extracellular volume in brain and the slow diffusion component with the intracellular volume. The relative sizes of these components, however, is inconsistent with known extracellular volume fractions in either the adult or very young brain whose extracellular volumes have been estimated to be on the order of 0.2 [28 32]. It is possible that some combination of water exchange and/or T2 weighting can account for this discrepancy [1,4,5,33]. If so, and the extracellular space is in fact associated with the fast ADC component, then it is reasonable to hypothesize that the fast ADC component fraction would be larger in the newborn brain than in the adult brain since cellular development and myelination are both much less advanced [28 32]. This is precisely what we have found in this comparative study of adult vs newborn brain. The fraction of the fast diffusion component is substantially larger in the newborn vs the adult brain in both gray and white matter (Table 2). Though this result is generally consistent with an extra- and intracellular interpretation for the two observed ADC components in brain, the interpretation is hardly proven from this observation alone. Indeed, Duong et al. [34] have questioned the very validity of the assumption that intra- and extracellular water molecules have substantially different intrinsic diffusion coefficients. Using 19 F NMR signals from an exogenous molecule selectively distributed within either the intra- or the extracellular space of rat brains in vivo, they found no statistically significant difference in the diffusion coefficient of the fluorinated molecule in either environment. The authors inferred from this observation that water may also have the same diffusion coefficient in either environment and that the commonly accepted notion of a small intracellular diffusion coefficient to explain decreased ADC values in stroke is untenable [34]. If this logic is accepted, then the biexponential ADC decay curves we observe cannot be attributed to intra- and extracellular water compartmentation. In this case, the non-monoexponential behavior must be attributed to something else. Indeed it is possible that though the ADC decay curves appear wellsuited to biexponential modeling, the underlying physical model and mathematical description may prove considerably more complicated. For instance, Peled et al. [12] have shown how experimental ADC decay curves from in vitro frog sciatic nerve preparations, which appeared to be biexponential, could also be modeled using restricted diffusion effects within parallel solid cylinders with a distribution of axonal radii similar to that measured independently with x-ray diffraction methods. Thus the argument may be made that, for white matter at least, restricted diffusion and the

8 666 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) underlying microtopology of the cellular architecture lead to non-exponential ADC decay curves which mimic biexponential decays over the b-factor range examined. Presumably such effects could also be explained within gray matter regions using distributions of spheres or some other appropriate model for the shape and size distributions of the cells [35 40]. Thus it is clear that competing theories exist for explaining the non-monoexponential behavior of brain water ADC decay curves over an extended but clinically accessible range. Further experimental and theoretical studies will be needed to clarify the true nature of the non-exponential ADC decays observed in brain. What emerges from this study, however, is that in both gray matter and white matter regions, developmental processes in the brain dramatically affect the shapes of the brain water signal decay curves. Of clinical relevance in the setting of the newborn brain is that the fast ADC component signal dominates in healthy tissue. Recent studies in humans [20] and animals [41] have indicated that standard diffusion imaging methods, which have relied on b-factor settings around 1,000 s/mm 2 or below and which are therefore sensitized primarily to the fast ADC component, may be less sensitive to stroke in the newborn than in the adult brain. Perhaps altering the diffusion imaging protocol to sample higher b-factors with greater sensitivity to the slow ADC component in the newborn may improve the ability to detect and assess hypoxic ischemic injury in this population, a hypothesis that remains to be tested. Using the multi-directional, multi b-factor approach allows for relative quantitation of the fast and slow ADC component fractions. Whether the additional scan time required to make such measurements proves valuable in the clinical setting as quantitative indicators for therapeutic intervention in either the adult or the newborn remains to be seen. In this regard it is of practical interest to consider how multi-b-factor data acquired along different directions should be analyzed. For instance, if one samples along three separate diffusion gradient directions, a single high signalto-noise data set can be derived using the composite, cubed root product data and then analyzed with a single biexponential fit. This is computationally more convenient than performing three biexponential fits to the lower signal-tonoise decays along the individual directions sampled. The good agreement of the two approaches for the biexponential parameters, as exemplified by the results in Table 2, indicate that there is not a very large difference between the two approaches, with the exception of the internal capsule data. It is of interest to consider why such differences may be anticipated, particularly for regions of anisotropic diffusion. The biexponential decay along the separate directions will be of the form S 1, 1, 1/2 S a exp( D 1, 1, 1/2 b) S b exp( D 1, 1, 1/2 b) (2a) where S 1/2,1, 1 S a exp( D 1/2,1, 1 b) S b exp( D 1/2,1, 1 b) S 1,1/2,1 S a exp( D 1,1/2,1 b) S b exp( D 1,1/2,1 b) D 1, 1, 1/2 D xx D yy D zz /4 2D xy D xz D yz D 1/2,1, 1 D xx /4 D yy D zz D xy D xz 2D yz D 1,1/2,1 D xx D yy /4 D zz D xy (2b) (2c) (3a) (3b) 2D xz D yz (3c) and with a similar set of relations for the D i,j,k. One can see that when Eqs. (2a c) are multiplied together as for the composite decay approach, a number of cross-terms will appear and the tensor elements of the fast and slow ADC components then become entangled, rendering efforts to extract the trace of either component from biexponential fits of composite decays problematic. Only in the case of no anisotropy for either component will the signals from Eqs. (2a c) be identical and the two methods for obtaining the traces of both components agree. A further complication is that Eqs. (2a c) assume that the amplitudes S a and S b have no dependence on the direction of the diffusion sensitization gradients. As we have shown above and as also reported by Clark and Le Bihan [5], this is not the case. Despite these considerations, there appears to be a fair agreement between the biexponential parameters obtained from individual directional fits, followed by calculation of the means, and those obtained directly from the composite data sets with the largest difference found for the amplitude of the second ADC component in the adult IC (Table 2). A complete study of the anisotropies associated with the fast and slow ADC components will require six-directional measurements [42 44] and considerable theoretical analysis which lies beyond the scope of this work. We do reiterate a final but important empirical observation regarding the diffusional anisotropy in the IC decay curves. Namely, anisotropic affects, as probed with different diffusion sensitization directions, are not restricted to the diffusion coefficients D ijk and D ijk alone but also affect the relative amplitudes of the fast and slow components. From the adult brain IC data, the fraction A/(A B) measured with the (1, 1,1/2) was approximately half the values obtained along either of the other two directions with full strength of the diffusion gradient roughly oriented with the fiber tract direction. Similarly in the newborns the inter-individual A/(A B) fractions in the IC, higher altogether than the adult values, showed a decrease to values around 0.70 for the (1, 1, 1/2) direction compared to values around 0.90

9 R.V. Mulkern et al. / Magnetic Resonance Imaging 19 (2001) for the along fiber diffusion sensitization directions. Any model which purports to explain the biexponential ADC phenomenon must account for the diffusion gradient directional dependencies of not only the diffusion coefficients but also of the relative amplitudes obtained from biexponential fits of ADC decay curves in the brain. Clark and Le Bihan have conjectured that varying water exchange rates along different directions between the compartments may account for the anisotropic behavior of the fractional amplitudes [5], though this remains to be proven. 5. Conclusions We summarize the primary findings on the multi-component ADC phenomena as observed to date. Human brain water signal decay curves over an extended b-factor range up to 4000 to 6000 s/mm 2 are well-characterized by biexponential functions in both gray and white matter [1 5]. The present study demonstrates that there is a definitive age dependence of the biexponential parametrization with newborn brains showing a much larger fast diffusing fraction than found in adults. In adults, Mulkern et al. have shown that the T1 values of the fast and slow ADC components are strikingly similar [4]. Also in adults, Clark and Le Bihan have presented evidence which suggest that the T2 values of the two ADC components are similar by demonstrating a lack of dependence on echo time of the fast ADC fraction over the 80 to 180 ms echo time range [5]. These investigators also noted that the fast diffusing fraction showed anisotropic behavior, being larger when diffusion sensitization gradients were aligned along the fiber tracts within the internal capsule, as we have also found in this study. Further studies are needed to elucidate the degree to which water compartmentation, exchange, and/or cellular and subcellular geometrical restrictions [14] to water diffusion determine the non-monoexponential shape of the human brain water signal decay curves in the clinical setting where such information may prove quite valuable. Acknowledgment This work was supported in part by NIH 1RO1 NS A1 (SEM). References [1] Mulkern RV, Gudbjartsson H, Westin C-F, Zengingonul HP, Gartner W, Guttmann CRG, Robertson R, Kyriakos W, Schwartz R, Holtzman D, Jolesz FA, Maier SE. Multi-component apparent diffusion coefficients in human brain. NMR in Biomed 1999;12: [2] Zengingonul HP, Mulkern RV. Measurement and analysis of nonexponential signal decay curves in brain diffusion and muscle relaxation magnetic resonance studies in humans. Int J Imaging Syst Technol 1999;10: [3] Maier SE, Bogner P, Bajzik G, Mamata H, Mamata Y, Repa I, Jolesz FA, Mulkern RV. 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