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Experimental Studies |
1 Neuroimaging Branch, National Institutes of Neurological Disorders and Stroke, National Institutes of Health, Bldg 10, Rm 4N252, 10 Center Dr, Bethesda, MD 20892-2289.
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Abstract |
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 TOP Abstract IntroductionMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
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MATERIALS AND METHODS: Multisection maps of T1, T2, and the trace of the diffusion tensor (Trace[D] = 3 x Doav) were obtained in four kittens at eight time points.
RESULTS: In the adult, Doav was about 700 µm2/sec in both white and gray matter. In the newborn, Doav was 1,100–1,350 µm2/sec in white matter and 1,000 µm2/sec in gray matter. For all anatomic regions and time points, the correlation between Doav and 1/T2 was high (R2 = 0.87, P << .001). T1 showed a lower correlation with Doav and a higher sensitivity to myelinization than did T2.
CONCLUSION: Although Doav shows dramatic changes in the maturing brain, the high correlation between Doav and T2 indicates that little additional information can be obtained by measuring this diffusion parameter during normal brain development. This contrasts with previous findings in brain ischemia, where Doav and T2 appear to be uncorrelated. After including the authors' data and published iontophoretic measurements in a simple model of diffusion in tissues, the authors suggest that the underlying mechanisms of Doav reduction in brain maturation and ischemia are different. Doav changes during development are mainly affected by events occurring in the cellular compartment, while changes in extracellular volume fraction and tortuosity, which are thought to determine the reduction in Doav during ischemia, are probably of secondary importance.
Index terms: Animals • Brain, growth and development, 10.91, 10.99 • Brain, MR, 10.121411, 10.121413, 10.12146 • Magnetic resonance (MR), relaxometry, 10.12146
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Introduction |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
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Previous diffusion MR imaging studies (4–6) of brain development have demonstrated that the apparent diffusion coefficient of water molecules decreases during brain maturation. Some authors (4,5) have also suggested that diffusion-weighted MR images are more sensitive than T1-weighted images for the detection of the onset of myelinization. When investigating anisotropic tissues such as WM, however, both diffusion-weighted images and apparent-diffusion-coefficient maps not only reflect intrinsic properties of the tissue but also are affected by the subject's orientation in the magnet. For this reason, diffusion-weighted images and apparent diffusion coefficient maps are difficult to interpret and cannot be used for the quantitative characterization of water diffusion in WM (7). Scalar quantities derived from the diffusion tensor, such as the trace of the diffusion tensor (Trace[D]), do not present this problem (8). Trace(D) is equal to three times the orientationally averaged water diffusion coefficient Doav, which represents the mean value of the diffusion coefficients measured in all possible directions. Trace(D) has similar values in the WM and GM in the brains of adult cats (9), monkeys (7), and humans (10,11).
The goals of this work were (a) to measure the time course of Trace(D) in different WM and GM regions during postnatal brain development in normal cats and (b) to study the correlation between Trace(D) and T1 and T2 to establish whether Trace(D) provides information unavailable with conventional, relaxometry-based MR imaging.
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MATERIALS AND METHODS |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
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Each animal underwent eight serial MR imaging studies. The first study was performed on the 2nd or 3rd day after birth. The subsequent studies were performed weekly during the 1st month of life, biweekly during the 2nd month, and once at the ages of 3 and 4 months. Animals older than 4 months were not studied because WM myelinization, which is the latest event in brain development (13), is almost completed in 3-month-old kittens (14). Two adult cats were also imaged to obtain reference measures in a completely developed brain.
The animals were anesthetized with 1.5% isoflurane (Abbott Laboratories, North Chicago, Ill) during the MR imaging session, which lasted 1 hour 23 minutes for the diffusion-weighted acquisition, 21 minutes for T2 mapping, and 53 minutes for T1 mapping. Rectal temperature was continuously monitored with a fiberoptic thermometer and was maintained at 36.5°C–37.5°C with a water-heated pad. Kittens younger than 2 months were allowed to breathe spontaneously, and their respiratory frequency was monitored with a plethysmograph positioned around the chest. Older animals were intubated and mechanically ventilated to maintain expiratory carbon dioxide pressure at 38–40 mm Hg.
MR Imaging
We performed all MR imaging with a 2-T MR animal system (Omega; GE NMR Instruments, Fremont, Calif) equipped with self-shielded gradient coils capable of producing a maximum gradient strength of 40 mT/m. We used two home-built quadrature "birdcage" radio-frequency coils. One coil, used for kittens younger than 2 months, had an inner diameter of 39 mm. The other coil, used for kittens older than 2 months and for the adult cats, had an inner diameter of 62 mm.
Each MR imaging session consisted of three series: a set of 31 diffusion-weighted images for calculating the diffusion tensor, a four-echo Carr-Purcell-Meiboom-Gill sequence for calculating T2 maps, and five inversion-recovery spin-echo images for calculating T1 maps.
At each time point and for all techniques, we obtained eight coronal sections of the brain with the same section thickness, intersection gap, in-plane resolution, and field of view. These parameters, however, were set to different values that were dependent on the coil used and the age of the kitten. Section thickness was 1.2–2.0 mm, the intersection gap was 3.0–4.0 mm, and the field of view was 50–60 mm. The in-plane resolution was 128 x 128 at all time points. Given these parameters, the voxel size ranged from 0.18 mm3 in newborns and young kittens to 0.44 mm3 in older kittens and adult cats.
Diffusion-weighted MR imaging.—We acquired diffusion-weighted images with an interleaved echo-planar imaging sequence (15) that included a navigator echo for correction of motion artifacts. In addition to a non–diffusion-weighted image, we obtained images with five diffusion gradient strengths in six directions (11), which yielded values for the b-matrix trace that were equally spaced between 0 and 1,100 mm2/sec. The image acquisition parameters were as follows: 5,000/76 (repetition time msec/echo time msec), no cardiac gating, 16 interleaves (eight echoes per interleaf), and trapezoidal diffusion gradients with 15-msec duration, ramp time of 0.4 msec, and center-to-center separation of 36.5 msec. After image reconstruction, we computed the b matrix (16) numerically for each image. We calculated the diffusion tensor D in each voxel according to the method of Basser et al (8,17) and generated maps of Trace(D) for each section by summing the three eigenvalues of D in each voxel.
T2 mapping.—We measured T2 by using a multiecho, multisection Carr-Purcell-Meiboom-Gill sequence similar to the one described by Mulkern et al (18), with the acquisition of eight sections with four echoes per section (repetition time = 5,000 msec, echo times = 50, 100, 150, 200 msec). We were unable to acquire more than four echoes per section due to hardware limitations. T2 was computed on a pixel-by-pixel basis from best-fit values of the slope of the log of the signal intensity versus echo time. In determining the best fit, we weighted each point by the square of its magnitude (see Bevington [19]).
T1 mapping.—We measured T1 by using a series of complex inversion-recovery images (repetition time = 5,000 msec, echo time = 19 msec, inversion times = 200, 400, 800, 1600, 
msec, where the inversion time = msec corresponds to an image acquired with no inversion pulse). We removed the polar ambiguity by using the image obtained with an inversion time of msec as a reference. We then computed T1 from the slope of log([signal in the reference image] - [signal in image obtained with inversion time TI]) versus the inversion time. This method involves only a linear least-squares fit and is therefore quite robust.
Phantom Study
It is well known that the acquisition of accurate measurements of T2 with a multisection imaging sequence may be problematic (20). To verify the accuracy of the T2 values measured with our imaging sequence, we prepared eight gelatin phantoms with different concentrations of dysprosium chloride (Sigma, St Louis, Mo), adjusted to provide a T2 in the range of 25–175 msec. Accurate T2 values for the phantom were obtained with a spectroscopic 32-echo Carr-Purcell-Meiboom-Gill sequence performed with the same MR imaging unit used for the animal study. The same phantoms were then imaged with the imaging sequence used for the animal study, and the T2 values were measured in regions of interest (ROIs) drawn on the computer-generated T2 maps. We computed the percent error of the imaging-measured T2 by using the spectroscopically-measured T2 as a reference.
ROI Analysis
We drew anatomic ROIs on the T1, T2, and Trace(D) maps by using the manual tracking system provided in IDL (ITERATIVE DATA LANGUAGE; Research Systems, Boulder, Colo). Five anatomic structures were selected: cortical GM, the caudate nucleus, the internal capsule, the corpus callosum, and subcortical WM. For each anatomic structure except the corpus callosum, we measured multiple ROIs positioned on both cerebral hemispheres and on at least two sections. To avoid partial volume averaging from adjacent cerebrospinal fluid, a single ROI was drawn in the corpus callosum on the section that contained its thickest portion. The reported mean value of each parameter in each anatomic structure is the average of all measurements obtained in multiple ROIs, weighted by the number of voxels in each ROI.
Statistical Analysis
We examined the degrees of correlation between 1/T1 and 1/T2, Trace(D) and 1/T1, and Trace(D) and 1/T2. We also computed correlation coefficients for the entire data set and for each anatomic ROI. Two parameters were considered to be significantly correlated if the regression coefficient was different from zero with a P value of less than .01. Two anatomic ROIs were considered to be different if the 95% CI of the slope and/or the intercept of their respective regression lines did not overlap.
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RESULTS |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
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Maps of T1, T2, and Trace(D) at four distinctive time points during development and at approximately the same anatomic level in a representative animal are shown in Figure 1. Corresponding anatomic maps of an adult cat are also shown. The time courses of the average values and the SDs of these parameters in various anatomic ROIs are shown in Figure 2. At birth, the orientationally averaged water diffusion coefficient (Doav = Trace[D]/3) was higher than that in the adult in all brain regions (in newborns, Doav was 1,000–1,350 µm2/sec and, in adults, 600–750 µm2/sec) but was still markedly lower than that in free solution (3,000 µm2/sec at 37°C [2]).
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We first tested for correlations between parameters by using the entire data set, including data from all animals at all time points and all ROIs, in a single regression analysis (Fig 3). We found statistically significant correlations between Trace(D) and 1/T2 (R2 = 0.87), 1/T1 and 1/T2 (R2 = 0.79), and Trace(D) and 1/T1 (R2 = 0.76). We repeated the tests for each individual ROI and found significant correlations between all parameters in all ROIs. For each correlation, we also determined whether the slope and intercept of the regression lines were significantly different in different ROIs. For the regression of Trace(D) versus 1/T2, there were no significant differences between ROIs, with the exception of the ROI in subcortical WM, for which both the slope and the intercept were significantly different from those of the other ROIs. For the regressions of Trace(D) versus 1/T1 and 1/T1 versus 1/T2, all WM ROIs differed significantly from the GM ROIs.
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DISCUSSION |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
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Relaxation Measurements
To our knowledge, there have been no previous studies of the time course of changes in relaxation times during brain maturation in cats and few quantitative studies in other animal models (21) and in humans (22–25). Our results contradict most of these previous results in two important aspects.
First, we found that both T1 and T2 were significantly longer in WM than in GM in the newborn brains, whereas previous investigators (22,24) found no T1 and T2 differences between subcortical WM and GM. Second, in the aforementioned studies (22–25), large differences between WM T2 and GM T2 in the adult brain were reported, but we found T2 to be almost the same in all mature brain tissues. It is unlikely that these discrepancies are related to interspecies differences, because both the general pattern of postnatal brain maturation and the structural and chemical features of the adult brain are similar in all mammals (12), although at birth the brain may be slightly more immature in cats than in humans. We attribute these discrepancies to the fact that most quantitative studies on brain maturation were performed in the early days of MR imaging and may have been affected by technical limitations (26). In particular, they were performed at very low field strength (0.15–0.35 T), and T2 was calculated from only two echoes. The accuracy of our T2 measurements is supported by the good agreement between the imaging-measured T2 and the spectroscopically-measured T2 in the phantoms. Our finding that mature WM and GM have similar T2 values is also in agreement with accurate relaxaometry studies (27,28) of the human brain in healthy adults.
Overall, our data indicate that T1 and T2 are similarly affected by the changes occurring in the maturing brain, with the exception of a much higher sensitivity of T1 to myelinization. The different sensitivity of T1 and T2 to myelinization can be explained in terms of the different effects of myelin-associated water on T1 and T2. It has been shown (29) that T2 in WM has two distinct components: a long T2 component (about 70–90 msec at 1.5 T), which has been attributed to axonal and extracellular water, and a short T2 component (<20 msec at 1.5 T), which has been attributed to myelin water. Because our T2 relaxation curves were calculated from echoes acquired at relatively long echo times, the measured T2 corresponds to the long T2 component of axonal and extracellular water and is unaffected by myelin water. T2 in WM has two distinct components because, in the time scale of typical T2 values in brain tissues, there is no substantial exchange between myelin water and water in other compartments. In the time scale of typical T1 values, however, myelin water can diffuse across axonal and myelin membranes and interact with water molecules in other compartments. Therefore, signal decay due to T1 relaxation is monoexponential in myelinated WM, and myelin water produces T1 shortening in WM as myelinization progresses (30).
Clinical Implications of Relaxation Findings
We mentioned that, to our knowledge, there are no reliable measurements of T1 and, in particular, T2 in the developing human brain. There are, however, several advantages that would originate from knowledge of the time course of relaxation parameters in the developing brain.
First, the acquisition of "weighted" (eg, T1-weighted, T2-weighted) images instead of T1 and T2 maps for diagnostic purposes implies that one must rely on the evaluation of differences in contrast between brain regions rather than on a quantitative comparison with normative values for the population. Our data show that large changes in the relaxation properties tend to occur simultaneously in various brain regions and in different brain tissues. For this reason, if we are interested in staging brain maturation, the acquisition of weighted images is intrinsically less sensitive than the acquisition of relaxation parameters, because substantial changes in relaxation parameters may be accompanied by only minor changes in image contrast.
Second, the analysis of relaxation parameters would facilitate a more specific understanding of the biophysical determinants of the MR signal than would inspection of image contrast on weighted images. For example, we found that T1 and the long component of T2 provide similar information on brain maturation, with the exception of a clearly different sensitivity to myelinization.
Third, better knowledge of the behavior of the relaxation parameters in the developing brain could help in the design of more specific and efficient weighted imaging protocols. For example, a standard approach to monitoring myelinization in pediatric neuroradiology is to rely on T1-weighted images during the first 6 months of life and on T2-weighted images thereafter. Changes in the contrast between GM and WM on T1-weighted images have been attributed to the effect of increased myelin, whereas changes on T2-weighted images have been attributed to secondary maturation processes of myelin, such as tightening of the myelin spiral around the axon (1). Our results suggest that the WM-to-GM contrast changes observed on long repetition time and long echo time T2-weighted images obtained at the late stage of brain development are not dependent on changes in the long T2 component. As shown in Figure 4, notable changes in contrast on T2-weighted images occur when no additional changes can be appreciated on the maps of the long T2 component.
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Measurements of the Trace of the Diffusion Tensor
To our knowledge, this is the first study in which changes in orientationally averaged water diffusivity were measured in different anatomic regions during the entire course of postnatal brain development. Because previous studies of brain maturation used diffusion-weighted images (31,32) or apparent-diffusion-coefficient measurements in one (6) or two (4,5) directions, the results of those studies are not directly comparable with our results. Moreover, none of the authors of these previous studies reported data on GM, and the variability of apparent-diffusion-coefficient values in WM is generally high, probably because of differences in the relative directions of the fibers and the applied diffusion gradients, which were controlled for in our study.
Our finding that Trace(D) was significantly higher in the immature brain than in the adult brain in all anatomic regions is in agreement with and extends the results of Sakuma et al (4), Toft et al (6), and Neil et al (33). In addition, we found that Trace(D) in the newborn is statistically different in different anatomic regions, which is in agreement with previous findings (34) of reported differences in Doav between GM and subcortical WM in newborn piglets. Our data show that these regional differences are progressively less noticeable during maturation and disappear almost completely in the adult brain.
We found a high degree of correlation between Trace(D) and 1/T2 during development. Moreover, the regression lines of Trace(D) versus 1/T2 in different ROIs were virtually superimposed, with no significant differences in either slope or intercept. This result is important because it signifies that in all brain regions and at all time points Doav and T2 respond similarly to the various physicochemical and histologic changes that occur during tissue maturation.
The situation is markedly different in brain ischemia and stroke, where 1/T2 and Trace(D) are not strongly correlated. In fact, in brain ischemia, as well as in the early stage of an infarct, there is a rapid decrease in Doav (35–37), with no detectable changes on either T2-weighted images (3) or T2 maps (38). Moreover, when vasogenic edema develops at a later stage, water diffusivity in the infarcted tissue remains low, while T2-weighted signal intensity increases. Finally, during chronic infarct progression, cellular lysis causes a dramatic reelevation of the diffusion coefficient but does not markedly affect the T2-weighted imaging results (39).
An understanding of the causes of the different behavior of diffusion and relaxation parameters in ischemia and development, as well as the unequivocal determination of a relationship between our diffusion results and specific structural or chemical features of the developing brain, is not simple. The MR imaging–measured water diffusivity is indeed a composite measure that reflects the contribution of multiple and heterogeneous microscopic tissue compartments. Recent analytic studies (40) and numeric simulations (41,42) of simplified models, however, have been helpful in elucidating the relative contribution of some important factors, such as the geometry, size, and intrinsic water diffusivity of the cellular and extracellular compartments. In the case of ischemia, for instance, most studies suggest that the decreased water diffusivity as measured with MR imaging is essentially related to an increased tortuosity and diminished volume fraction of the "fast-diffusivity" extracellular compartment.
To better clarify the microstructural determinants of our results, we analyzed our data by using the model recently proposed by Latour et al (40), which is applicable given our limit of long diffusion time and weak diffusion pulses. If we assume that the concentration of water is the same in both extracellular and intracellular compartments, then this model consists of an equation that relates the MR imaging–measured Doav to the extracellular diffusivity Dext, the volume fraction of the extracellular space 
, and the effective diffusivity of the cellular compartment Deffcell. Because our MR measurement was insufficient to determine all the parameters of the model, we integrated our MR imaging data with data from iontophoretic measurements (43–45), which provide selective information on the diffusion properties of the extracellular space. Unfortunately, iontophoretic measurements are available only in rats; therefore, for the sake of this discussion, we shall assume that feline brain development is sufficiently similar to that of rats. A detailed description of our approach is presented in the Appendix; here we present only the conclusion of our analysis.
Our diffusion MR imaging experiments show that between birth and adulthood, Doav in GM decreases from 1,000 to 700 µm2/sec—a 30% decrease, which is of the same magnitude as that observed after ischemia (46). By using the values of and Dext obtained from the iontophoretic measurements of Lehmenkuhler et al (44), we calculated that Deffcell changed from 650 µm2/sec at birth to 420 µm2/sec in adulthood, a decrease of about 35%. We used the same method to analyze the results in models of ischemia. By combining the iontophoretic data of Vorisek and Sykova (47) with diffusion MR imaging measurements of ischemia in cats (46), we found that Deffcell does not decrease after ischemia and shows a modest change from 380 µm2/sec in the nonischemic brain to 440 µm2/sec during ischemia.
We cannot expect the numeric values in the preceding paragraph to be accurate because the MR imaging and iontophoretic diffusion data were obtained in different species. In qualitative terms, however, the results of this analysis suggest that changes in Trace(D) during ischemia are primarily caused by changes in the diffusion properties of the extracellular space, whereas the changes during development are primarily caused by changes in the effective diffusivity of the cellular compartment.
We identify two main biologic events that could contribute to modifications in the diffusivity of the cellular compartment and consequently affect Trace(D) during development: (a) an increased concentration of macromolecules (48) and (b) a greater membrane surface–to–cell volume ratio caused by the proliferation of processes and organelles (49). Another possible factor would be a change in cell membrane permeability; however, this is difficult to asses experimentally, and we are not aware of any studies in which this possibility was investigated during brain development.
The results of our analysis also may explain why the T2 changes parallel the Trace(D) changes in development but not in ischemia. T2 relaxation is caused by fluctuations of the local magnetic field (50). These fluctuations are caused by the relative motion of the spins and the sources of local fields represented by unpaired electrons and other magnetic nuclei. Changes in the viscosity of the medium, which determine the variation in the rate of relative motion, as well as changes in the chemical composition of the medium, which affect the concentration of sources of the local field, are expected to affect T2. Of interest, the same cellular events that we suggested may cause the changes in Trace(D) during development, such as increased concentration of macromolecules and membranes, also modify the chemical composition and viscosity of the tissue, which could theoretically affect T2. In addition, experimental works (51) have shown that membranes and macromolecules shorten T2.
During acute ischemia, however, there are no such changes in tissue composition. In essence, no "new material" is created that could shorten T2; there is a change in water compartmentalization only. The resultant increased tortuosity of the extracellular compartment has a marked effect on water diffusivity but does not substantially affect T2, because it acts over large distances as compared with the nearest-neighbor distances that dominate T2 relaxation.
In conclusion, we believe that a complete understanding of the mechanisms of water diffusion and relaxation in tissues necessitates additional theoretic and experimental work. However, the results of our analysis provide a plausible explanation of how our findings are related to different tissue microstructural changes that occur in development and ischemia and suggest that the determinants of the reduced Trace(D) in development may differ profoundly from those in ischemia.
Clinical Implications of Diffusion Findings
If confirmed with studies in healthy human subjects, our finding of a surprising similarity in the information provided by the long T2 component and Trace(D) could discourage the use of diffusion MR sequences to assess brain development. We believe, however, that this conclusion is erroneous at this time for two reasons.
First, we have no assurance that analogous findings would be confirmed in pathologic conditions. Brain ischemia and stroke are clear examples of diseases where average diffusivity and T2 behave differently. Because almost no pediatric diseases have been investigated with quantitative diffusion MR imaging, we should first obtain sufficient diffusion data on pathologic conditions before concluding that the average water diffusivity provides no additional useful information in pediatric radiology.
Second, Trace(D) is not the only parameter that we can compute in a quantitative study of water diffusion in tissues. Other diffusion parameters such as diffusion anisotropy and the principal direction of diffusion may be informative even if Trace(D) is not. In the normal adult brain, it has already been demonstrated (11) that diffusion anisotropy provides anatomic and structural data that are unavailable from conventional MR imaging. Moreover, results of preliminary studies (52) indicate that in brain development, diffusion anisotropy and relaxation times show different behaviors in both WM and GM regions.
Practical applications: Various physical parameters that could potentially provide different information on the structure, chemical composition, and metabolic state of the brain can be measured with MR imaging. Our quantitative assessment of T1, T2, and Trace(D) during normal brain development has been useful for the determination of the extent to which different parameters provide independent information, as well as for the attempt to understand the biologic correlates of such changes. We believe that a quantitative approach would be particularly advantageous in pediatric neuroradiology because, in the developing brain, weighted imaging has the intrinsic limitation of no internal reference that can be considered to be invariant. We also believe that the increased availability of fast MR imaging sequences will greatly simplify the task of performing similar studies in the clinical setting.
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APPENDIX |
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
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is the volume fraction of the suspension occupied by the external medium; Deff is the effective diffusivity in the system as a whole and characterizes the diffusion properties of the system on a size scale that is large compared with the size of the cells and the separation between them; Dext is the diffusivity in the external medium and is the expected result of a diffusivity measurement in a cell-free system; cext is the fractional concentration of the diffusing molecules in the external medium; cint is the fractional concentration of the diffusing molecules inside the cells; ceff is the average concentration of the diffusing molecules in the system as a whole and is related to the other parameters by
is the permeability of the membrane that separates the cells from the external medium, a is the radius of the cells, and Dint is the diffusivity of the intracellular medium.
If we model neurons as spherical cells suspended in an extracellular medium, Equations (A1)–(A3) can describe both ion tracer measurements and MR diffusion measurements. We first apply the equations to ion tracer experiments. Analysis of data from ion tracer measurements yields values for three parameters: the volume fraction , the tortuosity 
, and the nonspecific uptake k' (see reference 43). The tortuosity is related to DMt, the measured diffusivity of the tracer in the brain, by
as defined by Equation (A4). Note that depends on the viscosity of the extracellular medium, as well as on the geometry of the extracellular space. We can use Equation (A1) to relate Dextt to D0t and therefore separate out the effect of the viscosity of the medium from the effect of geometry. If the nonspecific uptake is sufficiently small, cintt is 0 and Equation (A1) reduces to
is the same for any molecule, Equation (A6) also applies to water molecules:
We can also apply Equation (A1) to the diffusion MR imaging measurements. In this case, Deff becomes Doav, the MR imaging–measured diffusion constant, and D1 becomes Deffcell. If we assume that cint equals cext, we find that
, and intracellular water diffusivity Dintw. Dintw, in turn, is itself a composite parameter; it is not the bulk diffusivity of the intracellular medium but rather is dependent on the presence and characteristics of organelles and other intracellular constituents.
In conclusion, MR imaging measurements in the long-diffusion, weak-diffusion weighting limit give no information about the values of Dextw and Deffcell individually. However, if we use the values of and from the ion tracer measurements and Doav from the diffusion measurements, Equations (A7) and (A8) can be used to compute Dextw and Deffcell. The results for development and ischemia are given in Table A1.
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Acknowledgments |
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Footnotes |
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Abbreviations: GM = gray matter ROI = region of interest Trace(D) = trace of the diffusion tensor WM = white matter
Author contributions: Guarantors of integrity of entire study, C.B., A.S.B., C.P.; study concepts and design, C.P.; definition of intellectual content, C.B., A.S.B., C.P.; literature research, C.B.; experimental studies, C.B., A.S.B., C.P.; data acquisition, C.B.; data analysis, C.B., A.S.B., C.P.; statistical analysis, C.P.; manuscript preparation, editing, and review, C.B., A.S.B., C.P.
Received February 23, 1998;
revision requested April 15, 1998; revision received August 4, 1998;
accepted August 11, 1998.
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TOPAbstractIntroductionMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXReferences |
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), the internal capsule (
), the corpus callosum (
), the cortex (•), and the caudate nucleus (
). Error bars = SDs, ms = milliseconds, s = seconds. The time course of the changes shown in a and c are similar for all ROIs. The changes shown in b show two patterns for WM and GM ROIs.
