Water diffusion and acute stroke

Water Difhsion and Acute Stroke Peter van Gelderen, Marloes H. M. de Vleeschouwer, Daryl DesPres, James Pekar, Peter C. M. van Zijl, Chrit T. W. Moonen

The occlusion of the middle cerebral artery was used as an experimental acute stroke model in 30 cats. The diffusion of water was followed by diffusion-sensitized MRI between 1 and 15 h after induction of stroke. It is demonstrated that images representing the trace of the diffusion tensor provide a much more accurate delineation of affected area than images representing the diffusion in one direction only. The reason is that the strong contrast caused by the anisotropy and orientation of myelin fibers is completely removed in the trace of the diffusion tensor. The trace images show a small contrast between white and gray matter. The diffusion coefficient of white matter is decreased in acute stroke to approximately the same extent as gray matter. It is further shown that the average lifetime of water in extra and intracellular space is shorter than 20 ms both for healthy and ischemic tissue indicating that myelin fibers are permeable to water. The anisotropy contrast did not change before or after induction of stroke, nor after sacrifice. Together, these observations are consistent with the view that the changes in water diffusion during acute stroke are directly related to cytotoxic oedema, i.e., to the change in relative volume of intra- and extracellular spaces. Changes in membrane permeability do not appear to contribute significantly to the changes in diffusion. Key words: diffusion imaging: stroke; MR; diffusion anisotropy.

INTRODUCTION

Recently, water diffusion was introduced as an additional MRI contrast parameter (1-3). Moseley et al. (4, 5) have reported the use of diffusion MRI in the early detection of stroke and showed a drastically lowered diffusion coefficient in acute stroke areas. This is an important application of diffusion MRI, since conventional MRI has a disappointingly low contrast for ischemic insults, es- pecially in the very early, and potentially reversible, phase. The correlation of ischemia and changes in diffusion contrast have been reported in several papers (6-10). The physical basis for the lowered diffusion coefficient in acute stroke is not completely understood, but several mechanisms have been proposed, for example tempera-

MRM 31:154-163 (1994) From the Faculty of Applied Physics, University of Technology Delft, The Netherlands (P.r.G.); In vivo NMR Research Center, BEIP, NCRR, National Institutes of Health, Bethesda, Maryland (M.H.M.d.V., D.D.P., J.P., C.T.W. M.); and the Department of Radiology, Johns Hopkins University Medical School, Baltimore, Maryland (P.C.M.V.Z.). Address correspondence to: Chrit T. W. Moonen, Ph.D., In Vivo NMR Re- search Center, BEIP, NCRR, National Institutes of Health, Building 10, Room BID-125, Bethesda, MD 20892. Received June 14, 1993; revised October 4, 1993; accepted October 22, 1993. P. C. M. v.Z. is supported by NIH grant 1R01 NS31490-01. P.v.G. is supported by the Foundation for Fundamental Research on Matter and the Netherlands Technology Foundation.

Copyright 0 1994 by Williams & Wilkins All rights of reproduction in any form reserved.

0740-31 94/94 $3.00

ture effects, increased restriction by membranes, and cy- tntoxic oedema (11, 12). It is important to relate the ex: perimental MRI findings to physiological events, since the changes in diffusion may be linked to the amount of tissue damage, and possibly the reversibility of the damage. Busza et al. (13) reported that the time course of diffusion changes in acute stroke is consistent with complete loss of tissue high energy phosphates, and with the time course of increase in extracellular potassium. It was concluded that diffusion imaging is sensitive to the dis- ruption of tissue energy metabolism.

Anisotropy of the water displacement can also be studied with diffusion MRI and provides an additional probe of tissue micro structure (14). However, the large varia- tions in the measured diffusion constant of water, in particular in white matter (14), resulting from anisotropy effects may hamper clinical applications of diffusion MRI in stroke. The reason is that, in general, no reference scan will be available. As a result a local decrease in diffusion constant cannot unambiguously be assigned to a local infarct. Here, we show in theory and in an experimental animal model that the evaluation of the trace of the diffusion tensor does not suffer from this ambiguity.

In a preliminary report (15), we have evaluated restricted diffusion and its influence on the diffusion anisotropy in the displacement of brain water in the healthy cat and in an acute stroke model in a limited number of animals. Here, these initial observations are confirmed and the data analyzed in terms of compartmentation of brain water and exchange between the compartments. Also we extended the measurements to give more information on the anisotropy.

THEORY

General

A NMR experiment can be made sensitive for diffusional motion by addition of gradients, as shown by Stejskal (16), resulting in an echo attenuation of:

where S and So are the signal amplitudes with and without diffusion respectively, D is the diffusion tensor, and g is the generalized gradient function, incorporating the effects of any refocusing pulses in the experiment as an inversion of the gradient in the time previous to the respective pulses. For the traditional diffusion experiment with two gradient pulses, this leads to:

ln(S) = ln(Sn) - yzg2S2(A - S / 3 ) 0 = ln(S,) - bD [ZI 154

Water Diffusion and Acute Stroke 155

where b is a measure of the gradient effect, S is the du- ration of the gradient pulses, g is the amplitude of the gradient and A is the time between the start of the two pulses. D is now the diffusion coefficient in the direction of the gradient, as follows from Eq. [I]. Anisotropy of the diffusion can therefore be measured by applying different gradient directions. To calculate a diffusion image, a number of images have to be acquired with different diffusion attenuation, preferably by stepping the gradient amplitude. From these images the diffusion coefficient follows from a fit of the signal intensity in each voxel to Eq. [2] (3, 17,18). The root mean square (RMS) displacement A in one direction for a gaussian distribution is equal to:

[31

where tdif is the diffusion time, which, in the pulsed gradient experiment is taken equal to A - 613. In the case of restricted diffusion, where the motion of the spins is confined to a limited volume, the RMS displacement can not increase beyond a certain fraction of the dimensions of this volume, resulting in a dependence of the diffusion coefficient on the diffusion time (16). Measuring this dependence gives an indication of restriction, and the size of the volume.

Exchange

In the case of diffusion in two separated compartments, the overall diffusion attenuation becomes biexponential:

s = S,e-*D1 + S2e-bDz [41

where S, and S2 are the signal intensities from the two compartments and D, and D, the respective diffusion coefficients. If there is exchange between the two envi- ronments, the effective diffusion coefficients will be a mix of the diffusion in the two volumes V, and V,. If the exchange is fast with respect to the diffusion time, the two exponents will merge into one, with the diffusion coefficient being a weighted average of D, and D,:

[51

Anisotropy

In a homogeneous medium the diffusion is isotropic. In brain tissue however, the diffusional motion of water is influenced by the presence of the cell membranes and myelin fibers. The diffusion parallel to these structures will generally be higher then in the perpendicular direction, leading to anisotropy. The anisotropy may be caused by a different restriction size in the respective directions: as the axons of the cells in brain tissue are mostly cylindrically shaped, the diffusion in two, perpendicular, directions is much lower then the diffusion along the axon axis. Note, however, that if intra- and extracellular water exchange fast, the diffusion is not truly restricted, as the molecules can travel beyond the limits of the cell volume. The limited permeability in this case still results in an anisotropic diffusion, since the motion perpendicular to the cell axis is slowed down by

the crossing of the membranes. The effective anisotropy in imaging is an average of the range of orientations within a voxel. The resulting contrast in an image will therefore depend on the voxel size, and the angle of the applied diffusion gradient relative to the cell axis.

Permeability

MR diffusion imaging relies on a measurement of the RMS displacement A of water, as expressed in Eq. [3]. This is the MR definition of the diffusion coefficient. The measured A reflects all possible effects, including unrestricted diffusion, limited permeability (if A approaches the diameter of a restricted volume), hindrance by cell organelles and macromolecules, etc. Diffusion in systems with permeable barriers has been analyzed by Tanner (19). For equally spaced plane barriers, an analytical so- lution is only possible in the limit of fast exchange. In brain tissue, the situation is complicated by the cylindrical symmetry and the large difference in intra- and extracellular diffusion. Therefore, we do not attempt to give an analytical calculation of the permeability effects, but assume a simple model for the effects of the permeability on the displacement in the approximation of fast exchange. If there is a certain activation energy for water to cross the cell membranes, the r.m.s. displacement will be decreased by the crossing of the barrier. This results in a lower diffusion coefficient, independent of diffusion time, provided the diffusion time is long enough to average the permeability effects over all diffusing particles (fast exchange limit) (20). If the cells within a volume have a predominant orientation, the average number of crossed membranes will depend on the direction, resulting again in anisotropy, even in the case of fast exchange.

Orientation and the Trace

So far the diffusion is referred to as the diffusion perpendicular ( D J or parallel (ql) to the cell axis, that is elements of the diffusion tensor in the cell frame of reference (D). These can only be measured when the orientation of the specific cells is known and if the (ma- jority of the) cells within a single voxel are the same. The measured direction of diffusion is determined by the applied gradient, as follows from Eq. [I], which is expressed with respect to the laboratory frame of reference, with diffusion tensor (D'). The resulting diffusion coefficient is a combination of the elements of the cell frame diffusion tensor, as a result of the rotation from one frame to the other. The cell frame diffusion tensor will have only diagonal elements by symmetry. The off diagonal elements are therefore the result of the rotations involved, and give only information on the orientation of the cells (21). A single element, that is the diffusion in one direction, still shows the effects of the orientation. The contrast in a diffusion image will therefore be a combination of the anisotropy and orientation, as well as local differences in diffusion. To create an image independent of the cell orientation, the trace of the diffusion tensor can be acquired, effectively averaging out any rotations. As the trace of a tensor is invariant under rotations (see e.g., 21, 22), the result is always equal to the

156 van Gelderen et al.

sum of the three diagonal elements of the cell frame diffusion tensor:

1 Do, = - Tr(D') =

3 [61

1 1 1 - (D;* + DI, + D;,) = 5 (Dll + 2 0 , ) = - Tr(D) 3 3

The elements Dil, DL2, and Dj, are the diagonal elements of tensor D', i.e., the diffusion coefficients along the prin- cipal gradient axes, x, y, and z, respectively. This proce- dure works also in voxels with multiple cell orientations.

METHODS

The experiments were carried out on a GE 4.7 T CSI instrument equipped with shielded gradients, up to 200 mT/m.

The MRI technique is based on a stimulated echo imaging sequence, as depicted in Fig. 1. The advantage of this sequence to a spin echo method is the possibility of using long diffusion times, by increasing the middle (TM) period, without T2 relaxation losses, as the magnetization is essentially longitudinal in this period. The diffusion images were calculated from five to eight images, acquired with different diffusion gradient amplitudes (20- 160 mT/m). The diffusion time (tdjf = A - 6/3) was 48 ms and the gradient time (6) 5.5 ms, leading to a maximum b-factor of 0.26 X 10'' s/m2. In the exchange experiments, where the diffusion time was varied, the gradient amplitudes were adjusted accordingly, in order to keep the maximum b-factor at a similar value. The gradients for dephasing of unwanted coherences (the TE- and TM- spoilers, Fig. 1) were constant and always in directions different from the diffusion gradient to avoid cross-terms in the diffusion attenuation. The imaging gradients (phase, read-out) were much lower in amplitude and were always applied after the diffusion weighting, again to avoid cross terms. The images were acquired as 64 X 64 and sometimes as 128 x 128 matrices, without averaging, and the FOV was 100 X 100 mm. The repetition time (TR) was 1 s, without cardiac or respiratory gating, the echo time (TE) was 52 ms.

Cats were anesthetized with ketamine/acepromazine and maintained on isoflurane in a N,0/02 mixture (7/3), using a ventilator. The middle cerebral artery (MCA) was

TE/2 TM TWZ

RF

Slice-Select TM-rpoilar

Diffusion Phase-Encode

TE-spailer Raad-Out

exposed using a temporal approach and occluded by electrocautery or permanent clamp. Catheters were placed in the femoral vein and artery. During surgery and the MRI studies, blood gases, blood pressure, heart rate, and end tidal COz concentrations were monitored and maintained at normal levels. Succinylcholine (0.8%) was added to the infusion fluid to provide skeletal muscle relaxation during ventilation, surgery and MRI studies.

Special care was taken to prevent motion artifacts, as the sequence is extremely sensitive to motion. The animals were placed on a cradle with a stereo-tactic head holder to prevent movement of the skull. Also the muscle relaxant prevents any motion of the animals other then respiratory or due to cardiac motion. For each animal, a similar axial slice was chosen in the rostra1 part of the brain above the ventricles. The angle of the slice varied slightly due to small differences in extension of the head. At the start of each study, heavily diffusion weighted images were acquired and checked for phase encode artifacts. In general, no motion was detected. Only in ex- ceptional cases of enlarged ventricles, the CSF motion caused artifacts. In such cases, no further diffusion data were analyzed. Table 1 shows an overview of all animal experiments.

Diffusion-weighted imaging (b = 1200 s/mm2) was used for monitoring the size of the lesion starting at approximately 30 minutes following MCA occlusion. Dif- fusion trace imaging was started three hours after MCA occlusion. For each trace image, a total of 15 to 24 individual images were collected (5-8 for each gradient direction) in 20 to 30 min total time. Imaging was contin- ued up to 15 h following MCA occlusion.

Three cats were perfused with Evans blue dye before sacrifice. Brain tissue was fixed in 10% formalin, sliced and prepared for pathological evaluation. Microscopic evaluation focused on cortical areas with swelling and vacuolated cytoplasm characteristic of hypoxia.

RESULTS AND DISCUSSION

Size and Development of lnfarcted Lesions

As shown previously (4, 5), affected tissue showed a lowered diffusion constant after occlusion of the MCA, corresponding with a lowered calculated diffusion constant. Occlusion of the MCA did not lead to a detectable infarct in all the animals, probably due to a varying de- gree of collateral perfusion. In the case of a visible infarct, the size of the affected area differed drastically from animal to animal, corresponding with similar observations

Table 1 Number of Animals Involved

Successful MCA occlusions 25 Exchange studies 11 Anisotropy studies 5 Stroke lesion progression 9

Technical failures (no lesions detected or motion 3 artifacts)

Healthy (no surgery) Total

2 30 -

FIG. 1. Applied pulse sequence for diffusion images.


in the literature. The size of the affected area corre- sponded well with subsequent histological examinations ( n = 3), in agreement with literature data (12, 23-25). In addition, the onset of the hypointensity in the diffusion images varied from less than half an hour in most cases to more than 2 h. However, no further progression was seen from 3 to 15 h after occlusion.

Trace

For five animals, the diffusion maps were acquired with three different gradient directions, g,,g,,g,. For all cases, the three diffusion images were acquired within a short

period of time (less than 30 min) and using otherwise identical parameters. An example obtained from a healthy animal is shown in Fig. 2.

These images demonstrate the anisotropy of the diffusion and the large contrast arising from the different orientations of the cells in the brain tissue. As opposed to the individual diffusion images (Fig. 2a-2c), the diffusion trace map (Fig. 2d) shows little variation. The remaining contrast in the trace image reflects differences in diffusion. Interestingly, the trace image shows some small remaining contrast between white and grey matter (typi- cally, D,, for white matter is 87% D,, for grey matter).

As the trace image shows only minor true differences

FIG. 2. The calculated diffusion images (a,b,c) for three orthogonal diffusion gradients (X,Y,Z) and the resulting trace image (d). Anterior is top of image. Images represent a superior slice above the lateral ventricles. In image (c) the parallel gyri can be identified symmetrically from the midline: gyrus postlateralis, gyrus lateralis, gyrus suprasylvius medius, gyrus ectosylvius medius.


in diffusion between white and grey matter, the contrast of the individual diffusion images is dominated by ori- entational effects. Upon induction of a stroke, the ischemic area is clearly outlined on the diffusion trace image, as shown in Fig. 3. The resulting average diffusion coefficients in healthy and in stroke area are given in Table 2. After the experiments the animals were sacrificed by infusion of potassium chloride. For three animals a postmortem diffusion trace map was acquired, shortly after sacrifice ( k l 5 min). The result of one of the experiments is shown in Fig. 4 together with a trace diffusion map of the same slice, acquired with the same parameters, before sacrifice. As is clear from these images, the postmortem diffusion coefficient in the stroke area is equal to the postmortem diffusion in the rest of the brain and the affected area becomes indistinguishable. This result was obtained for all three animals.

The stroke area is not always as well defined as in Fig. 3. If the contrast between healthy and affected tissue is not as large or if the stroke area is not contiguous, the detection of the infarct area(s) can be severely hampered by the contrast arising from the anisotropy and orientation if only a single direction is measured. A diffusion trace image however, results in a better outline of the affected area(s), because the orientation has no effect in diffusion trace images. This is demonstrated in Fig. 5, showing a single diffusion map and the corresponding trace image, as in Fig. 2.

In regions affected by acute stroke, the trace of the diffusion coefficient for white matter is affected to approximately the same extent as for gray matter (see for example the white matter tracts in Fig. 4). A drop of 33% (white matter only) was detected as compared with an average drop of 36% for all regions of interest summarized in Table 2. The drop in TR(D) of white matter upon sacrifice (38%) is similar to that in acute stroke. Previous reports suggested that D in white matter is not affected (4). This may reflect the difficulties of analyzing the dif-

fusion coefficient in the presence of strong anisotropy, which is circumvented in the present study by working with the trace.

Exchange

On a microscopic scale, a volume element in the brain is inhomogeneous and contains different compartments on a cellular and subcellular level. When diffusional displacement is observed in such a system, the mobility in each compartment reflects the local viscosity, barriers like dissolved macromolecules and restriction effects. Thus in the limit of small diffusion times, the observed diffusion effect is a superposition of a wide spectrum of mobilities reflecting the different local conditions. If there is exchange between the separate compartments, the resulting diffusion behavior becomes an average of all the involved mobilities at diffusion times long with respect to the exchange rates (see Eq. [5]).

Assuming that the diffusion of all the intracellular water is uniform at the time scales of interest (e.g., tdjflonger than 20 ms), a somewhat simplified model of brain water can be used, resulting in the following possible environ- ments: intracellular, interstitial or extracellular, cerebro- spinal fluid (CSF), and vascular water. The contributions of vascular water can be neglected, since it has a low volume fraction. CSF may be present throughout the brain, but its volume fraction is also limited to a few percent, in particular in the superior slices of the cat brain. In addition, the average lifetime of water in CSF and the circulatory system is long (>300 ms), so that exchange of brain water with these compartments may be excluded in the overall description of brain water mobility. Thus, at first approximation, only extra- and intracellular water need to be considered.

To study the exchange between these two environ- ments, the diffusion was measured for a large range of diffusion times. In Fig. 6 the diffusion coefficient for one

Table 2 Summary of Studies on Diffusion Anisotropy and Trace

D,, (10-lo m2/s) Anisotropy

Cat Exp. No. Healthy Stroke Healthy Stroke

Average SD Average SD Average SD Average SD A 1 5.0 0.27 3.04 0.30 0.39 0.33 0.26 0.16

2 6.54 0.41 4.29 0.51 0.62 0.42 0.57 0.27 B 1 5.22 0.42 3.47 0.97 0.70 0.48 0.69 1.08

2 5.54 0.43 3.64 0.86 0.65 0.51 0.61 0.50 3 5.54 0.36 3.51 0.46 0.63 0.43 0.66 0.37 4 5.70 0.51 3.94 0.54 0.56 0.40 0.60 0.35 5 5.54 0.41 3.38 0.74 0.59 0.46 0.71 0.35 6 5.92 0.48 3.63 0.72 0.38 0.32 0.42 0.25

C 1 7.33 0.87 4.53 0.72 0.61 0.40 0.81 0.47 D 1 7.58 0.67 4.68 0.32 0.54 0.47 0.35 0.21 E 1 6.49 0.45 4.42 0.38 0.56 0.43 0.62 0.51

2 6.37 0.60 4.46 0.52 0.79 0.38 0.74 0.42 Total 12 6.53 0.57 4.18 0.52

The printed numbers are the average values of the stroke area and a corresponding area on the healthy side of the brain; the anisotropy is defined In Eq. [7], D,, is 1/3 Tr (D). SD is standard deviation. The values for "total" are the averages over all the animals.


FIG. 3. The calculated image of the diffusion trace after induction of a stroke. Tissue on anterior side represents the precruciate gyrus.

gradient direction is plotted versus the diffusion time, for healthy as well as affected area. It is evident that the diffusion coefficient remains similar over the large range of tdif = 20 to 2000 ms. Note that, for a diffusion coefficient of 5 x m2/s, the average displacement for a diffusion time of 20 and 2000 ms corresponds with 4.5 and 45 pm, respectively. Since the latter value largely exceeds the typical cell diameters, this clearly indicated that the myelin fibers have a high permeability for water. This may be compared with the observed values for cor- neal endothelium cells (26).

In the case of impermeable membranes, one would expect to observe unrestricted diffusion for very short diffusion times. Upon increasing diffusion time, the average intracellular diffusion coefficient would ultimately decrease to one third of the unrestricted value because of the cylindrical symmetry. This is because only the diffusion in the direction parallel to the cylinder axis remains unbounded, whereas the diffusion in the two perpendicular directions is restricted to the diameter of the cylinder. The diffusion time dependence of the diffusion coefficient for extra cellular water is more complex, as this water is not truly restricted to a (small) volume. For longer diffusion times, it is however to be expected that the diffusional motion becomes hampered by the cells and myelin fibers. The observed diffusion coefficient, which is an average of the intra- and extra cellular diffusion, would therefore change drastically for longer diffusion times, keeping in mind that the intracellular signal dominates the extracellular one. The dependence on the diffusion time is thus a good measure of restriction by the membranes (see also 19, 27).

A voxel by voxel analysis of such possible restriction effects, was performed as follows. The slope of the de- pendency of the diffusion coefficient on the diffusion time was calculated for each voxel, on the basis of ten diffusion images at various diffusion times from 20 to 2000 ms. A slope of zero indicates that the diffusion

FIG. 4. The calculated diffusion trace images before (a) and after sacrifice (b). Location of the slice is similar to that of Fig. 3 including white matter areas of centrum semiovale. Near the midbrain, the slice encompasses the precruciate gyrus, cingulate gyrus, splenia- lis.

coefficient is independent of diffusion time. The resulting “slope” image did not show any contrast between healthy and stroke tissue and an average slope of zero without further contrast corresponding to anatomical differences (data not shown). Thus, despite the profound effects on the diffusion coefficient itself, no restriction effects could be demonstrated, neither in healthy, nor in stroke tissue.

Similar experiments were done in eleven cats. The result was in all cases an indistinguishable diffusion constant for all diffusion times in the range of 20 to 2000 ms. It is concluded that exchange is fast with respect to the diffusion times used and the average lifetime of water in intra- and extracellular environment must be less than 20 ms, corresponding to values found in erythrocytes (28,


0 0 0 0

0

D [ 10-gm2/s]

0.4

0.2 . I t

0.0 0.5 1.0 1.5 2.0

t d i f [s]

FIG. 6. Dependence of the average diffusion coefficient on the diffusion time in ischemic (0) and healthy (0) area.

with diffusion times less than 20 ms. However, measurements with very short diffusion times were beyond the scope of this study.

Anisotropy

As pointed out in the theory section, the main cause for the anisotropy is the effect of the limited permeability of the cell membranes. As shown before, the average water molecule has already crossed cell membranes, even during the shortest diffusion times of 20 ms. Despite the high permeability, some activation barrier (expressed by the permeability) can be expected for crossing the rather hy- drophobic membrane. Therefore, depending on the number of membranes to be crossed in different directions, differences in displacement can be expected for different directions. The resulting anisotropy in the diffusion coefficient gives an indication of the permeability. A measure of the anisotropy can be calculated as the standard deviation of the three diffusion coefficients:

FIG. 5. The calculated diffusion image with diffusion gradient gy (a) and the trace image (b). Location of the slice is similar to that of A = 6 u(Dxx - Dav)z + - Dav)z + (Dzz - Dav)z

Fig. 2. DO, 171

29). This result implies a high permeability of membranes for water.

Apart from images, the water diffusion was also measured in a single voxel spectroscopic mode, which al- lowed a more precise determination of the diffusion attenuation as a function of the diffusion gradient, by the higher signal-to-noise ratio (SNR) and the higher repetition rate. The sequence was essentially the same as for the images, except for the imaging and selection gradients (see (30)). The resulting diffusion curves showed only small deviations from the single exponential decay. Furthermore, after fitting a biexponential decay, the fast component appeared in all cases to be most likely CSF contamination of the selected voxel, with a low volume fraction (<5%) and a high diffusion coefficient close to pure water. This also suggests that intra- and extracellular water can not be separated and the exchange is fast (lifetime <20 ms). The diffusion coefficient may change

where D,, is the average diffusion coefficient (Eq. [6]) and A the calculated anisotropy. This is scaled such that zero means isotropic diffusion and one is the maximum anisotropy (e.g., D, and Dy equal to zero).

For five animals, the anisotropy maps were calculated. Two examples are shown in Fig. 7, the first one is calculated from the images presented in Fig. 3, the second one is from the same animal and the same position, after sacrifice. The average anisotropy values are summarized in Table 2.

The anisotropy map shows no difference between the healthy side and the affected area. Also the postmortem map does not appear to be significantly different then the one before sacrifice, in spite of the differences in the diffusion coefficients. This was the case for all the calculated anisotropy maps. The anisotropy was also exam- ined for various diffusion times, and again, no effects were found. In all studies a distinct anisotropy in D was


stroke. With respect to the extracellular mobility of water, it is important to note that the macromolecular content of extracellular fluid is low, and will not change in acute stroke. The concentrations of small ions will change drastically, but this does not affect the water mobility se- riously. Therefore, the change in diffusion appears too large and too quickly to be explained by effects on the intra- and extracellular diffusion coefficients. Note the particular timing of the change of diffusion constant, i.e., immediately following the depletion of ATP and the increase in extracellular potassium (13). The changes are generally completed within less than 1 h (4).

The relative changes in intra- and extracellular volume in brain tissue upon stroke have been described in detail. In healthy tissue this volume ratio is about 82.5/17.5% (32), in ischemic tissue it becomes approximately 95/5%, as the change in intracellular volume is reported to be about 15% (in vitro) (33). Accurate values of the intra- and extracellular diffusion coefficients are largely un- known, but, as pointed out above, the difference in macromolecular content does make it reasonable to assume a low diffusion for the intracellular water and a coefficient close to that of pure water for the extracellular water.

Taking the average values found for healthy and infarcted tissue (Table 2), respectively, 0.653.10-’ mZ/s and 0.418.10-’ mz/s, the Din and D,, would have to be 0.324.10-9 m2/s, and 2.2 X lo-’ m2/s, respectively, using Eq. [5] and the quoted volume ratios, neglecting possible dilution effects of the oedema on the intracellular diffusion coefficient. The first value is in the range of those found for cytosol in different cell suspensions (29). The latter one is expected because of the low macromolecule content of the interstitial fluid.

As presented above, no effects of acute stroke on the anisotropy images were detected despite profound effects on the diffusion trace. Since the anisotropy in the diffusion of water is caused by the limited permeability of membranes, the large effects of acute stroke on diffusion can therefore not be explained by a change in permeability. A similar absence of anisotropy changes was found following sacrifice.

The results presented here do not provide unambiguous evidence of cytotoxic edema as the direct cause of the reduced diffusion coefficient. Nevertheless, all findings appear to indicate that the changed ratio of intra- and extracellular volume is the direct cause. Specifically, these findings can be summarized as:

The decrease in diffusion constant corresponds quan- titatively with the known changes in relative intra- and extracellular volume. Permeability of myelin fibers for water does not change in acute stroke. Myelin fibers are highly permeable for water in healthy and infarcted tissue, and as a result, a weighted average of diffusion constants is measured for diffusion times above 20 ms.

FIG. 7. The calculated anisotropy before (a) and after sacrifice (b).

found for white and gray matter with the larger effects found in white matter.

Possible Causes for the Change in Diffusion

The observed changes in diffusion in acute ischemia can be explained in a number of ways. Possible causes are: a change in the intra- and/or extracellular diffusion coefficient, a change in the intra- or extracellular volume ratio, a change in the permeability, or temperature effects.

As has been reported previously (13), the changes in diffusion coefficient occur in general during a few minutes only and appear to be associated with the loss of ATP. Very similar changes in diffusion coefficient occur immediately following sacrifice. Subsequently, the diffusion coefficient remains similar (31). Thus, temperature effects can be excluded as the cause of the sudden drop. A sudden change in intracellular environment does not seem likely, as the diffusion is determined mainly by the macromolecular content, which is not changing drastically upon

CONCLUSIONS

It is demonstrated that diffusion trace imaging is a pow- erful tool for the accurate delineation of damaged tissue


in acute stroke. The absence of any anisotropy and orientation effects in the trace images made the differences in healthy and affected tissue unambiguous in the animals studied. The trace images show a small contrast between white and gray matter. The diffusion coefficient of white matter is decreased in acute stroke to approximately the same extent as grey matter.

The most likely explanation for the effects on the diffusion in acute stroke is cytotoxic edema. As suggested previously, it is confirmed that myelin fibers are highly permeable to water. In addition it is demonstrated that this permeability is similar in healthy tissue, acute stroke and immediately following sacrifice.

Diffusion imaging in the clinical setting is difficult, in particular because of the motion sensitivity of the technique. However, recent advances in fast and very fast diffusion imaging have made it more feasible for routine applications. Here, we suggest that the diffusion trace is measured for each voxel, thus multiplying the number of measurements by three. However, the specificity of the information may result in an improved assessment of damage. In addition, the suggested link with cytotoxic edema may be helpful in the decision for intervention.

ACKNOWLEDGMENTS

The authors thank Joseph Frank for discussions and help in histological examinations, Jocelyne Bachevalier for advice in surgical procedures, and Joris Creyghton and Toon Mehlkopf for support and advice.

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Water diffusion and acute stroke