Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging

Biexponential diffusion tensor analysis of human brain diffusion data

Several studies have shown that in tissues over an extended range of b-factors, the signal decay deviates significantly from the basic monoexponential model. The true nature of this departure has to date not been identified. For the current study, line scan diffusion images of brain suitable for biexponential diffusion tensor analysis were acquired in normal subjects on a clinical MR system. For each of six noncollinear directions, 32 images with b-factors ranging from 5 to 5000 s/mm2 were collected. Biexponential fits yielded parameter maps for a fast and a slow diffusion component. A subset of the diffusion data, consisting of the images obtained at the conventional range of b-factors between 5 and 972 s/mm2, was used for monoexponential diffusion tensor analysis. Fractional anisotropy (FA) of the fast-diffusion component and the monoexponential fit exhibited no significant difference. FA of the slow-diffusion biexponential component was significantly higher, particularly in areas of lower fiber density. The principal diffusion directions for the two biexponential components and the monoexponential solution were largely the same and in agreement with known fiber tracts. The second and third diffusion eigenvector directions also appeared to be aligned, but they exhibited significant deviations in localized areas.

Diffusion magnetic resonance imaging study of a rat hippocampal slice model for acute brain injury

Diffusion magnetic resonance imaging (MRI) provides a surrogate marker of acute brain pathology, yet few studies have resolved the evolution of water diffusion changes during the first 8 hours after acute injury, a critical period for therapeutic intervention. To characterize this early period, this study used a 17.6-T wide-bore magnet to measure multicomponent water diffusion at high b-values (7 to 8,080 s/mm(2)) for rat hippocampal slices at baseline and serially for 8 hours after treatment with the calcium ionophore A23187. The mean fast diffusing water fraction (Ffast) progressively decreased for slices treated with 10-microM/L A23187 (-20.9 +/- 6.3% at 8 hours). Slices treated with 50-micromol/L A23187 had significantly reduced Ffast 80 minutes earlier than slices treated with 10-microM/L A23187 (P < 0.05), but otherwise, the two doses had equivalent effects on the diffusion properties of tissue water. Correlative histologic analysis showed dose-related selective vulnerability of hippocampal pyramidal neurons (CA1 > CA3) to pathologic swelling induced by A23187, confirming that particular intravoxel cell populations may contribute disproportionately to water diffusion changes observed by MRI after acute brain injury. These data suggest diffusion-weighted images at high b-values and the diffusion parameter Ffast may be highly sensitive correlates of cell swelling in nervous issue after acute injury.

Hypertension and neuronal degeneration in excised rat spinal cord studied by high-b value q-space diffusion magnetic resonance imaging

Hypertension is one of the major risk factors of stroke and vascular dementia (VaD). We used stroke prone spontaneous hypertensive rats (SPSHRs) as a model for neuronal degeneration frequently occurring in humans with vascular disease. Recently, high b value q-space diffusion-weighted imaging (DWI) was shown to be very sensitive to the pathophysiological state of the white matter. We studied the spinal cords of SPSHR rats ex vivo after the appearance of motor impairments using diffusion anisotropy and q-space diffusion imaging (measured at a high b value of up to 1 x 10(5) s/mm(2)). The diffusion anisotropy images computed from low b value data set (b(max) approximately 2500 s/mm(2)) showed a small but statistically significant decrease (approximately 12%, P < 0.05) in the diffusion anisotropy in the spinal cords of the SPSHR group as compared to control rats. However, more significant changes were found in the high b value q-space diffusion images. The q-space displacement values in the white matter of the SPSHR group were found to be higher by more than 70% (P < 0.002) than that of the control group. These observations concurred with electron microscopy (EM) that showed significant demyelination in the spinal cords of the SPSHR group. These results seem to indicate that high b value q-space DWI might be a sensitive method for following demyelination and axonal loss associated with vascular insults.

The evolution of the apparent diffusion coefficient in the pediatric brain at low and high diffusion weightings

PURPOSE

To evaluate the evolution of the apparent diffusion coefficient (ADC) with age for different degrees of diffusion weighting using a clinically feasible approach.

MATERIALS AND METHODS

Data was acquired using separate scans with b values in the range typically used for clinical studies (100-900 seconds/mm(2)) and higher b values (1800-3000 seconds/mm(2)). The ADC was calculated for each of the data sets by fitting the data to a monoexponential function.

RESULTS

The results from 50 children aged three years and less showed some deviations from literature values derived using a full biexponential fit, with these differences reflecting the approximations inherent in this approach. The values obtained with this technique appear to be reproducible but the resulting "institutional values" are comparable to those from other centers only if identical measurement criteria are used.

CONCLUSION

A significant decline in both components of the ADC during the first few months of life was observed; in addition, the attenuated slow ADC values seen in adult white matter were only present at birth in early myelinating regions. The subsequent development of the slow ADC in white matter suggests that it is associated with myelination or processes associated with axonal development.

High b value diffusion-weighted imaging is more sensitive to white matter degeneration in Alzheimer's disease

It has been reported that diffusion-weighted imaging (DWI) can detect white matter degeneration in the Alzheimer's disease (AD) brain. We hypothesized that imaging of the slow diffusion component using high b value DWI is more sensitive to AD-related white matter degeneration than is conventional DWI, and therefore we studied the effects of high b value on lesion-to-normal contrast and contrast-to-noise ratio (CNR). Seven AD patients and seven age-matched normal subjects were studied with full-tensor DWI at three different b values (1000, 2000, and 4000 s/mm(2)) without changing echo time or diffusion time, and the mean diffusivities in the parietal and occipital regions were measured. Statistical analyses revealed that use of higher b values significantly improves both lesion-to-normal contrast and CNR. We concluded that high b value DWI is more sensitive to AD-related white matter degeneration than is conventional DWI.

Diffusion in compartmental systems. I. A comparison of an analytical model with simulations

This article examines the way in which microscopic tissue parameters affect the signal attenuation of diffusion-weighted MR experiments. The influence of transmembrane water flux on the signal decay is emphasized using the Kärger equations, which are modified with respect to the cellular boundary restrictions for intra- and extracellular diffusion. This analytical approach is extensively compared to Monte-Carlo simulations for a tissue model consisting of two compartments. It is shown that diffusion-weighted MR methods provide a unique tool for estimation of the intracellular exchange time. Restrictions of applicability to in vivo data are examined. It is shown that the intracellular exchange time strongly depends on the size of a cell, leading to an apparent diffusion time dependence for in vivo data. Hence, an analytical model of a two-compartment system with an averaged exchange time is inadequate for the interpretation of signal curves measured in vivo over large ranges of b-values. Furthermore, differences of multiexponential signal curves, as obtained by different methods of diffusion weighting, can be explained by the influence of transmembrane water flux.

Diffusion in compartmental systems. II. Diffusion-weighted measurements of rat brain tissue in vivo and postmortem at very large b-values

Diffusion-weighted single-voxel (1)H spectroscopic measurements were performed on rat brain tissue in vivo and postmortem. Diffusion weighting was achieved by varying the diffusion time from 23 ms to 1.18 sec via the mixing time in a stimulated echo sequence. A series of constant gradient (cg-) experiments of eight effective gradient strengths q(2)(q(2) = gamma(2)delta(2)g(2)) from 24.2 x 10(3) to 490.2 x 10(3) mm(-2) was performed, resulting in a maximum attenuation factor of b = 580,000 s/mm(2). A fit of three exponential terms was found to be appropriate to represent the attenuation signal over the whole b-range. The behavior of the slowest decaying component can be fully understood in terms of a long time limit of a modified Kärger formalism for a two-compartment system. This allowed estimation of the transmembrane water exchange rate: the intracellular exchange time was determined to be 622 +/- 29 ms and 578 +/- 20 ms in vivo and postmortem, respectively.

Conventional DTI vs. slow and fast diffusion tensors in cat visual cortex

Diffusion tensor imaging (DTI) uses water diffusion anisotropy in axonal fibers to provide a tool for analyzing and tracking those fibers in brain white matter. In the present work, multidirectional diffusion MRI data were collected from a cat brain and decomposed into slow and fast diffusion tensors and directly compared with conventional DTI data from the same imaging slice. The fractional anisotropy of the slow diffusing component (D(slow)) was significantly higher than the anisotropy measured by conventional DTI while reflecting a similar directionality and appeared to account for most of the anisotropy observed in gray matter, where the fiber density is notoriously low. Preliminary results of fiber tracking based on the slow diffusion component are shown. Fibers generated based on the slow diffusion component appear to follow the vertical fibers in gray matter. D(slow)TI may provide a way for increasing the sensitivity to anisotropic structures in cortical gray matter.

Water diffusion measurements in perfused human hippocampal slices undergoing tonicity changes

Diffusion MRI has the potential to probe the compartmental origins of MR signals acquired from human nervous tissue. However, current experiments in human subjects require long diffusion times, which may confound data interpretation due to the effects of compartmental exchange. To investigate human nervous tissue at shorter diffusion times, and to determine the relevance of previous diffusion studies in rat hippocampal slices, water diffusion in 20 perfused human hippocampal slices was measured using a wide-bore 17.6-T magnet equipped with 1000-mT/m gradients. These slices were procured from five patients undergoing temporal lobectomy for epilepsy. Tissue viability was confirmed with electrophysiological measurements. Diffusion-weighted water signal attenuation in the slices was well-described by a biexponential function (R(2) > 0.99). The mean diffusion parameters for slices before osmotic perturbation were 0.686 +/- 0.082 for the fraction of fast diffusing water (F(fast)), 1.22 +/- 0.22 x 10(-3) mm(2)/s for the fast apparent diffusion coefficient (ADC), and 0.06 +/- 0.02 x 10(-3) mm(2)/s for the slow ADC. Slice perturbations with 20% hypotonic and 20% hypertonic artificial cerebrospinal fluid led to changes in F(fast) of -8.2% and +10.1%, respectively (ANOVA, P < 0.001). These data agree with previous diffusion studies of rat brain slices and human brain in vivo, and should aid the development of working models of water diffusion in nervous tissue, and thus increase the clinical utility of diffusion MRI.

Early detection of response to radiation therapy in patients with brain malignancies using conventional and high b-value diffusion-weighted magnetic resonance imaging

PURPOSE

To study the feasibility of using diffusion-weighted magnetic resonance imaging (DWMRI), which is sensitive to the diffusion of water molecules in tissues, for detection of early tumor response to radiation therapy; and to evaluate the additional information obtained from high DWMRI, which is more sensitive to low-mobility water molecules (such as intracellular or bound water), in increasing the sensitivity to response.

PATIENTS AND METHODS

Standard MRI and DWMRI were acquired before and at regular intervals after initiating radiation therapy for 10 malignant brain lesions in eight patients.

RESULTS

One week posttherapy, three of six responding lesions showed an increase in the conventional DWMRI parameters. Another three responding lesions showed no change. Four nonresponding lesions showed a decrease or no change. The early change in the diffusion parameters was enhanced by using high DWMRI. When high DWMRI was used, all responding lesions showed increase in the diffusion parameter and all nonresponding lesions showed no change or decrease. Response was determined by standard MRI 7 weeks posttherapy. The changes in the diffusion parameters measured 1 week after initiating treatment were correlated with later tumor response or no response (P <.006). This correlation was increased to P <.0006 when high DWMRI was used.

CONCLUSION

The significant correlation between changes in diffusion parameters 1 week after initiating treatment and later tumor response or no response suggests the feasibility of using DWMRI for early, noninvasive prediction of tumor response. The ability to predict response may enable early termination of treatment in nonresponding patients, prevent additional toxicity, and allow for early changes in treatment.

Effects of equilibrium exchange on diffusion-weighted NMR signals: the diffusigraphic "shutter-speed"

A general picture is presented of the implications for diffusion-weighted NMR signals of the parsimonious two-site-exchange (2SX) paradigm. In particular, it is shown that the diffusigraphic "shutter-speed," tau(-1) identical with |q(2)(D(A) - D(B))|, is a useful concept. The "wave-number" q has its standard definition (given in the text), and D(A) and D(B) are the apparent diffusion coefficients (ADCs) of molecules in the two "sites," A and B, if there is no exchange between them. At low gradient strengths (center of q-space), tau(-1) is less than rate constants for intercompartmental water molecule exchange in most tissue cases. Thus, the exchange reaction appears fast. However, q is increased during the course of most experiments and, as it is, the shutter-speed becomes "faster" and the exchange reaction, the kinetics of which do not change, appears to slow down. This causes a multiexponential behavior in the diffusion-weighting dimension, b, which also has its standard definition. This picture is found to be in substantial agreement with a number of different experimental observations. It is applied here to literature (1)H(2)O data from a yeast cell suspension and from the human and the rat brain. Since the equilibrium transcytolemmal water exchange reaction appears to be in the fast-exchange-limit at small b, the initial slope represents the weighted-average of the ADCs of intra- and extracellular water. Of course, in tissue the former is in the significant majority. Furthermore, a consideration of reasonable values for the other 2SX parameters suggests that, for resting brain tissue, the intracellular water ADC may be larger than the extracellular water ADC. There are some independent inferences of this, which would have ramifications for many applications of diffusion-weighted MRI.

Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.

Characterization of normal brain and brain tumor pathology by chisquares parameter maps of diffusion-weighted image data

OBJECTIVE

To characterize normal and pathologic brain tissue by quantifying the deviation of diffusion-related signal from a simple monoexponential decay, when measured over a wider than usual range of b-factors.

METHODS AND MATERIALS

Line scan diffusion imaging (LSDI), with diffusion weighting at multiple b-factors between 100 and 5000 s/mm(2), was performed on 1.5 T clinical scanners. Diffusion data of single slice sections were acquired in five healthy subjects and 19 brain tumor patients. In-patients, conventional T2-weighted and contrast-enhanced T1-weighted images were obtained for reference purposes. The chisquare (chi(2)) error parameter associated with the monoexponential fits of the measured tissue water signals was then used to quantify the departure from a simple monoexponential signal decay on a pixel-by-pixel basis.

RESULTS

Diffusion-weighted images over a wider b-factor range than typically used were successfully obtained in all healthy subjects and patients. Normal and pathologic tissues demonstrated signal decays, which clearly deviate from a simple monoexponential behavior. The chi(2) of cortical and deep grey matter was considerably lower than in white matter. In peritumoral edema, however, chi(2) was 68% higher than in normal white matter. In highly malignant brain tumors, such as glioblastoma multiforme (GBM) or anaplastic astrocytoma, chi(2) values were on average almost 400% higher than in normal white matter, while for one low grade astrocytoma and two cases of metastasis, chi(2) was not profoundly different from the chi(2) value of white matter. Maps of the chi(2) values provide good visualization of spatial details. However, the tumor tissue contrast generated appeared in many cases to be different from the enhancement produced by paramagnetic contrast agents. For example, in cases where the contrast agent only highlighted the rim of the tumor, chi(2) enhancement was present within the solid part of the tumor.

CONCLUSION

The deviation from a purely monoexponential diffusion signal decay becomes evident as diffusion encoding is extended well beyond the normal range. The chi(2) error parameter as a measure of this deviation seems to provide sufficient lesion contrast to permit differentiation of malignant brain tumors from normal brain tissue.

Comparison of the return-to-the-origin probability and the apparent diffusion coefficient of water as indicators of necrosis in RIF-1 tumors

Two model-independent measures of diffusion, the apparent diffusion coefficient (ADC) and return-to-the-origin probability enhancement (R) were compared for their ability to detect tissue necrosis in RIF-1 murine tumors. Both reflect the degree of restriction experienced by the endogenous water molecules; however, the ADC is calculated from the initial linear slope of the diffusion attenuation curve, while R is calculated from data that includes the non-monoexponential part of the curve. In spectroscopic studies (n = 9), neither the ADC nor R showed a strong correlation with tumor volume. In imaging studies (n = 14), ADC, R, and T(2) were calculated on a pixel-by-pixel basis. There, the mean ADC and mean R for the entire imaging slice showed reasonable correlation with necrotic tumor fraction (r(2) = 0.679 and -0.665, respectively). The mean T(2) value yielded a poor correlation (r(2) = 0.436). Regions-of-interest were chosen from areas identified as either necrotic or viable and the resulting sets of ADC and R-values were subjected to discriminant analysis to determine the identification error rate. The error was greater for R than for the ADC (P < 0.001). Therefore, in this application, the use of the non-monoexponential part of the diffusion attenuation curve does not provide additional identification power.

Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain

Oscillating gradients were used to probe the diffusion-time/frequency dependence of water diffusion in the gray matter of normal and globally ischemic rat brain. In terms of a conventional definition of diffusion time, the oscillating gradient measurements provided the apparent diffusion coefficient (ADC) of water with diffusion times between 9.75 ms and 375 micros, an order of magnitude shorter than previously studied in vivo. Over this range, ADCs increased as much as 24% in vivo and 50% postmortem, depending on the nature of the oscillating gradient waveform used. Novel waveforms were employed to sample narrow frequency bands of the so-called diffusion spectrum. This spectral description of ADC includes the effects of restriction and/or flow, and is independent of experimental parameters, such as diffusion time. The results in rat brain were found to be consistent with restricted diffusion and the known micro-anatomy of gray matter. Differences between normal and postmortem data were consistent with an increase in water restriction and/or a decrease in flow, and tentatively suggest that physical changes following the onset of ischemia occur on a scale of about 2 microm, similar to a typical cellular dimension in gray matter.

Cyclooxygenase-2 mRNA expression is associated with c-fos mRNA expression and transient water ADC reduction detected with diffusion MRI during acute focal ischemia in rats

Cyclooxygenase-2 (COX-2) plays an important role in the development of injury during cerebral ischemia and inhibition of its activity can reduce infarct size. COX-2 expression during acute ischemia is caused by activation of post-synaptic glutamate receptors, which occurs during spreading depression and ischemic depolarization. Both of these phenomena cause a reduction in the apparent diffusion coefficient of water (ADC), which can be detected with diffusion-weighted magnetic resonance imaging. The reduction is believed to be caused by cellular swelling that occurs as cells depolarize. The goal of this work was to determine the spatial relationship between cyclooxygenase-2 mRNA (cox-2) expression, c-fos mRNA expression and ADC reduction during acute focal cerebral ischemia. Adult rats were subjected to either 30- or 60-min permanent occlusion of the middle cerebral artery. A 2-Tesla scanner was used to acquire diffusion-weighted echo-planar images throughout the ischemic period, which were used to calculate ADC maps. Cox-2 and c-fos mRNA were detected with (35)S in situ hybridization. The results indicate that, for rats subjected to 60-min ischemia, cox-2 was observed in superficial layers of cortex, where transient ADC reduction and c-fos expression were observed. The same was true for most rats subjected to 30-min ischemia. However, in a small number of rats of the 30-min group, cox-2 mRNA expression was observed in regions exhibiting transient and persistent ADC reduction with no c-fos expression. The results suggest that cox-2 mRNA expression during acute MCA occlusion is caused by either or both spreading depression and transient ischemic depolarization.

Magnetic resonance microimaging of intraaxonal water diffusion in live excised lamprey spinal cord

Anisotropy of water diffusion in axon tracts, as determined by diffusion-weighted MRI, has been assumed to reflect the restriction of water diffusion across axon membranes. Reduction in this anisotropy has been interpreted as degeneration of axons. These interpretations are based primarily on a priori reasoning that has had little empirical validation. We used the experimental advantages of the sea lamprey spinal cord, which contains several very large axons, to determine whether intraaxonal diffusion is isotropic and whether anisotropy is attributable to restriction of water mobility by axon surface membranes. Through the application of magnetic resonance microimaging, we were able to measure the purely intraaxonal diffusion characteristics of the giant reticulospinal axons (20-40 microm in diameter). The intraaxonal apparent diffusion coefficients of water parallel (longitudinal ADC, l-ADC) and perpendicular (transverse ADC, t-ADC) to the long axis were 0.98 +/- 0.06 (10(-3) mm2 sec) and 0.97 +/- 0.11 (10(-3) mm2 sec), respectively. In white matter regions that included multiple axons, l-ADCs were almost identical regardless of axon density in the sampled axon tract. By comparison, t-ADCs were reduced and varied inversely with the number of axons (and thus axolemmas) in a fixed cross-sectional area. Thus, diffusion was found to be isotropic when measured entirely within a single axon and anisotropic when measured in regions that included multiple axons. These findings support the hypothesis that the cell membrane is the primary source of diffusion anisotropy in fiber tracts of the central nervous system.

Separating changes in the intra- and extracellular water apparent diffusion coefficient following focal cerebral ischemia in the rat brain

Selective intracellular (IC) and extracellular (EC) brain water apparent diffusion coefficient (ADC) values were measured in normal and ischemic rat brain. Selective T(1)-relaxation enhancement of the EC water, using intracerebroventricular (ICV) infusion of an NMR contrast reagent (CR), was used to separate the IC and EC signal contributions. In the CR-infused, normal brain (n = 4), T(1) = 235 +/- 10 ms and T(2) = 46 +/- 2 ms for IC water (85%) and T(1) = 48 +/- 8 ms and T(2) = 6 +/- 2 ms for EC water (15%). Volume-localized ADC(z) (z-gradient axis) values were 0.90 +/- 0.02 (EC+IC), 0.81 +/- 0.05 (IC), 0.51 +/- 0.02 (EC+IC), and 0.53 +/- 0.07 (IC), for normal, CR-infused, ischemic, and ischemic/CR-infused groups, respectively (ADC values are x10(-3) mm(2)/s; n = 5 for each group). Imaging ADC(z) values were 0.81 +/- 0.03 (EC+IC), 0.75 +/- 0.05 (IC), 0.51 +/- 0.04 (EC+IC), and 0.52 +/- 0.05 (IC), respectively, for the same groups. Imaging ADC(av) (average diffusivity) values for the same groups were 0.70 +/- 0.05 (EC+IC), 0.69 +/- 0.06 (IC), 0.45 +/- 0.06 (EC+IC), and 0.44 +/- 0.06 (IC), respectively. These results suggest that the IC water ADC determines the overall water ADC value in normal and ischemic rat brain.

High b-value q-space analyzed diffusion-weighted MRS and MRI in neuronal tissues - a technical review

This review deals with high b-value q-space diffusion-weighted MRI (DW-MRI) of neuronal tissues. It is well documented that at sufficiently high b-values (and high q-values) neuronal water signal decay in diffusion experiments is not mono-exponential. This implies the existence of more than one apparent diffusing component or evidence for restriction. The assignment of the different apparent diffusing components to real physical entities is not straightforward. However, the apparent slow diffusing component that was found to be restricted to a compartment of a few microns, if originating mainly from a specific pool and if assigned correctly, may potentially be used to obtain more specific MR images with regard to specific pathologies of the CNS. This review examines the utility of analyzing high b-value diffusion MRS and MRI data using the q-space approach introduced by Callaghan and by Cory and Garroway. This approach provides displacement probability maps that emphasize, at long diffusion times, the characteristics of the apparent slow diffusing component. Examples from excised spinal cord, where the experimental conditions for which the q-space analysis of MR diffusion data was developed can be met or approached will be presented. Then examples from human MS patients, where q-space requirement for the short gradient pulse is clearly violated, are presented. In the excised spinal cord studies, this approach was used to study spinal cord maturation and trauma, and was found to be more sensitive than other conventional methods in following spinal cord degeneration in an experimental model of vascular dementia (VaD). High b-value q-space DWI was also recently used to study healthy and MS diseased human brains. This approach was found to be very sensitive to the disease load in MS, compared with other conventional MRI methods, especially in the normal appearing white matter (NAWM) of MS brains. Finally, the potential diagnostic capacity embedded in high b-value q-space analyzed diffusion MR images is discussed. The potentials and caveats of this approach are outlined and experimental data are presented that show the effect of violating the short gradient pulse (SGP) approximation on the extracted parameters from the q-space analysis.

Evidence that both fast and slow water ADC components arise from intracellular space

Evaluation of water diffusion in the brain has revealed both fast- and slow-diffusing water populations. It has been suggested that these populations represent extra- and intracellular water, respectively. We have identified and characterized both populations in the intracellular space of the Xenopus oocyte. We have also determined their T(1) and T(2) relaxation properties. The fast and slow intracellular populations have diffusion coefficients of 1.06 +/- 0.05 microm(2)/ms and 0.16 +/- 0.02 microm(2)/ms, respectively, with the fast fraction representing 89% +/- 1% of the total water signal. These values are quite similar to those for total water in brain and are observed in the absence of signal from the perfusate (extracellular) water population. Volumetric swelling (16% +/- 4%) of the oocyte in hypoosmotic media increased the diffusion coefficients of both intracellular populations (fast = 1.27 +/- 0.03 microm(2)/ms, slow = 0.22 +/- 0.02 microm(2)/ms), but did not change their relative signal fractions. This phenomenon runs counter to the effects observed in brain injury, following which the apparent diffusion coefficient (ADC) decreases 30-50%. The results presented herein suggest that this ADC decrease in brain occurs despite cell swelling, which by itself would be expected to induce an increase in intracellular diffusion coefficients.

The basis of anisotropic water diffusion in the nervous system - a technical review

Anisotropic water diffusion in neural fibres such as nerve, white matter in spinal cord, or white matter in brain forms the basis for the utilization of diffusion tensor imaging (DTI) to track fibre pathways. The fact that water diffusion is sensitive to the underlying tissue microstructure provides a unique method of assessing the orientation and integrity of these neural fibres, which may be useful in assessing a number of neurological disorders. The purpose of this review is to characterize the relationship of nuclear magnetic resonance measurements of water diffusion and its anisotropy (i.e. directional dependence) with the underlying microstructure of neural fibres. The emphasis of the review will be on model neurological systems both in vitro and in vivo. A systematic discussion of the possible sources of anisotropy and their evaluation will be presented followed by an overview of various studies of restricted diffusion and compartmentation as they relate to anisotropy. Pertinent pathological models, developmental studies and theoretical analyses provide further insight into the basis of anisotropic diffusion and its potential utility in the nervous system.

Human erythrocyte ghosts: exploring the origins of multiexponential water diffusion in a model biological tissue with magnetic resonance

A tissue model composed of erythrocyte ghosts was developed to study the effects of compartmentation on the MR signal acquired from biological tissues. This simple and flexible model offers control over the biophysical parameters that contribute to multicomponent signals arising from cellular systems. Cell density, size, intra- and extracellular composition, and membrane permeability can be independently altered. The effects of cell density and cell size on water diffusion properties were assessed. The data demonstrate non-monoexponential water diffusion in ghost cell suspensions of 17-67% cell density. Data were analysed with the widely employed two-compartment (biexponential) model, and with a two-compartment model that accounted for exchange between compartments. Water exchange between the intra- and extracellular compartments appeared to be significant over the range of diffusion times studied (7-35 ms). The biexponential fit to the ghost data appeared to be underparameterised as the ADCs and relative fractions of the fast and slow components were dependent on the experimental acquisition parameters, specifically the diffusion time. However, both analysis methods proved effective at tracking changes in the ghost model when it was perturbed. This was demonstrated with cell density variation, cell swelling and shrinkage experiments, and reduction of membrane water permeability using a water channel blocker (pCMBS). We anticipate that this model system could be used to investigate compartmental diffusion effects to simulate a range of pathologies, especially ischemic stroke.

Orientational diffusion reflects fiber structure within a voxel

Several new MR techniques have been introduced to infer direction through diffusion in multiple nerve fiber bundles within a voxel. To date, however, there has been no physical model reported to evaluate these methodologies and their ability to determine fiber orientation. In this article a model of diffusion analogous to nerve fibers is presented. Diffusion measurements at multiple closely spaced angles of 15 degrees in samples with different fiber orientations are compared with theoretical calculations for restricted diffusion in cylindrical geometry. Orientational diffusion measurements are shown to reflect fiber geometry and theoretical predictions to within 10%. Simulations of fiber crossings within a voxel suggest fiber orientation does not correspond to the direction of the largest measured diffusion coefficient, but theoretical knowledge of signal decay curves can predict the shape of these diffusion coefficient contours for given fiber orientation probabilities.

Changes in axonal morphology in experimental autoimmune neuritis as studied by high b-value q-space (1)H and (2)H DQF diffusion magnetic resonance spectroscopy

Experimental autoimmune neuritis (EAN) has been studied in rat sciatic nerves by a combination of high b-value (1)H and (2)H double quantum filtered (DQF) diffusion MRS. The signal decays of water in the (1)H and (2)H DQF diffusion MRS were found to be not monoexponential and were analyzed using the q-space approach. The q-space analysis of the (1)H diffusion data detected two diffusing components, one having broad and the other having narrow displacement profiles. These components were shown to be very sensitive to the progression of EAN disease. The q-space parameters were found to be abnormal at day 9 postimmunization before the appearance of clinical signs. The assignment of the component with the narrow displacement profile to axonal water has been corroborated by the (2)H DQF diffusion MRS results. The displacement and the relative population of this slow and restricted diffusing component followed the processes of demyelination, axonal loss, and remyelination that occur in EAN. The displacements extracted from the slow-diffusing component with the narrow displacement correlated well with the average size of the axons as deduced from electron microscopy (EM). The component with the broad displacement showed significant changes which were attributed to the formation of endoneurial edema. This observation was also corroborated by the (2)H DQF diffusion MRS experiments. It seems, therefore, that q-space analysis of high b-values diffusion MRS is a promising new approach for early detection and better characterization of the different pathologies associated with EAN. This study demonstrates the utility of high-b-value q-space diffusion MRS for studying white matter-associated disorders in general.

Effects of restricted diffusion on MR signal formation

Numerous functional MRI (fMRI) and diffusion MR studies have recently boosted interest in the theory of MR signal formation in biological systems in the presence of mesoscopic magnetic field in homogeneities. Herein we report an exact solution to the problem of free induction decay (FID) and spin echo (SE) signal formation in the presence of a constant field gradient in three models of one-, two-, and three-dimensional restricted diffusion. We demonstrate the transition with increasing diffusion coefficient from the oscillating FID signal behavior in the static dephasing regime to a monotonic exponential behavior in the motional narrowing regime. Quantitative criteria are presented for applicability of the Gaussian approximation for the description of the MR signal. The spatial distribution of signal density and the edge enhancement effect are analyzed. We also demonstrate that the presence of restrictive barriers in a one-compartment model can lead to a quasi-two-compartment behavior of the MR signal. This result suggests a simple rationale for the experimental findings of biexponential echo attenuation curves in MR diffusion experiments with tissue systems.

Diffusion-weighted imaging of cerebral infarctions: are higher B values better?

PURPOSE

The purpose of this work is to determine whether high -value ( = 3,000 s/mm ) diffusion-weighted (DW) imaging is superior to low -value ( = 1,000 s/mm ) DW imaging for the detection of cerebral infarctions older than 6 h.

METHOD

Echo planar DW imaging was performed at 1.5 T in 26 consecutive patients (mean age 66 years) referred for clinical diagnosis of definite acute/subacute cerebral infarction (6 h to 14 days old). The DW imaging sequences were performed using matched parameters (TR = 10,000 ms, TE (eff)= 97 ms, FOV = 24 cm, 128 x 192 matrix, slice = 5 mm, NEX = 2) with values of 1,000 and 3,000 s/mm. Areas of infarction were compared visually by two experienced neuroradiologists. Quantitative measures of MR signal and noise levels in the infarcted areas compared with contralateral normal brain were also obtained.

RESULTS

The median time after infarction was 2.5 days (range 10 h to 14 days). By visual inspection, all infarctions were reliably identified on both the = 1,000 and the = 3,000 images. The gross signal ratio (infarct/normal brain) was approximately 33% higher in the = 3,000 images, but the = 3,000 images were rated as noticeably "noisier" by both observers in every case. This visual observation was confirmed quantitatively: The signal-to-noise (SNR) and contrast-to-noise (CNR) ratios were 70% and 51% higher in the = 1,000 than the = 3,000 images (p < 0.0005 for both).

CONCLUSION

For the evaluation of late acute/subacute cerebral infarctions, high -value ( = 3,000 s/mm(2) ) DW imaging offers no apparent diagnostic advantages compared with = 1,000 images and is significantly inferior in terms of SNR and CNR.

Deconvolution of compartmental water diffusion coefficients in yeast-cell suspensions using combined T(1) and diffusion measurements

An NMR method is presented for measuring compartment-specific water diffusion coefficient (D) values. It uses relaxography, employing an extracellular contrast reagent (CR) to distinguish intracellular (IC) and extracellular (EC) (1)H(2)O signals by differences in their respective longitudinal (T(1)) relaxation times. A diffusion-weighted inversion-recovery spin-echo (DW-IRSE) pulse sequence was used to acquire IR data sets with systematically and independently varying inversion time (TI) and diffusion-attenuation gradient amplitude (g) values. Implementation of the DW-IRSE technique was demonstrated and validated using yeast cells suspended in 3 mM Gd-DTPA(2-) with a wet/dry mass ratio of 3.25:1.0. Two-dimensional (2D) NMR data were acquired at 2.0 T and analyzed using numerical inverse Laplace transformation (2D- and sequential 1D-ILT) and sequential exponential fitting to yield T(1) and water D values. All three methods gave substantial agreement. Exponential fitting, deemed the most accurate and time efficient, yielded T(1):D (relative contribution) values of 304 ms:0.023x10(-5) cm(2)/s (47%) and 65 ms:1.24x10(-5) cm(2)/s (53%) for the IC and EC components, respectively. The compartment-specific D values derived from direct biexponential fitting of diffusion-attenuation data were also in good agreement. Extension of the DW-IRSE method to in vivo models should provide valuable insights into compartment-specific water D changes in response to injury or disease. (c) 2002 Elsevier Science (USA).

In vivo mapping of the fast and slow diffusion tensors in human brain

Recent studies have shown that the diffusional signal decay in human brain is non-monoexponential and may be described in terms of compartmentalized water fractions. Diffusion tensor imaging (DTI), which provides information about tissue structure and orientation, typically uses b values up to 1000 s x mm(-2) so that the signal is dominated by the fast diffusing fraction. In this study b factors up to 3500 s x mm(-2) are utilized, allowing the diffusion tensor properties of the more slowly diffusing fraction to be mapped for the first time. The mean diffusivity (MD) of the slow diffusion tensor was found to exhibit strong white/gray matter (WM/GM) contrast. Maps depicting the principal direction of the slow tensor indicated alignment with the fast tensor and the known orientation of the WM pathways.

In vivo diffusion tensor imaging of rat spinal cord at 7 T

In vivo diffusion tensor imaging of normal rat spinal cord was performed using a multi-segmented, blipped EPI sequence at 7 T field strength. At high diffusion weighting, the signal exhibited a non-monoexponential decay that was fitted to a biexponential function, associated with the fast and slow components of diffusion in the cord tissue, using a nonlinear regression analysis along with a constrained optimization procedure. From the measured tensors, the eigenvalues and the maps of invariant scalar measures (fractional anisotropy, relative anisotropy, volume ratio, and trace) were calculated and analyzed statistically. The results were combined to quantitatively characterize the anisotropic properties of the fast and slow diffusions in white- and gray matter of live spinal cords.

q-Space high b value diffusion MRI of hemi-crush in rat spinal cord: evidence for spontaneous regeneration

The development of the damage following hemi-crush trauma in rat spinal cord was studied ex vivo using high b value (bmax = 1 x 10(7) s cm(-2)) q-space diffusion weighted MRI (DWI) at five days, ten days and six weeks post-trauma. Rat spinal cord trauma, produced by hemi-crush of 15s and 60s duration, was studied. The water signal decay in these diffusion experiments was found to be non mono-exponential and was analyzed using the q-space approach. The q-space MRI parameters were compared with T1 and T2 MR images, behavioral tests and histopathological osmium staining. A very good anatomical correlation was found between the q-space MRI parameters and the osmium staining. Interestingly, we found that in the 15s hemi-crush model significant recovery was observed in both the q-space MR images and the osmium staining six weeks post-trauma. However, in the 60s hemi-crush trauma model very little recovery was observed. These results paralleled those obtained from behavioral tests demonstrating that partial spontaneous recovery seems to occur in the 15s hemi-crush spinal cord model, which should be taken in consideration when using it to evaluate new therapies.

Biexponential diffusion attenuation in the rat spinal cord: computer simulations based on anatomic images of axonal architecture

Water diffusion in neurological tissues is known to possess multicomponent diffusion behavior. The fractions of fast and slow apparent diffusion components have often been attributed to the volume fractions of extracellular space (ECS) and intracellular space (ICS) although diffusion fractions are at variance with the tissue compartment volume ratios. In this article this puzzle was examined with a finite difference diffusion simulation model on the basis of optical images from sectioned rat spinal cord. Here the results show that assignment of fractions obtained from biexponential fits of fast and slow diffusion attenuation to ECS and ICS volume ratios is not correct. Rather, the observed multicomponent diffusion behavior is caused by motional restriction and limited intercompartmental water exchange in that at long diffusion times diffusion attenuation is shown to become monoexponential. Although the measured apparent diffusion fractions also depend on T2 relaxation time of water protons in the various compartments, the sensitivity to T2 is small and thus T2 differences are unlikely to explain the mismatch between apparent diffusion fractions and cellular volume fractions.

High b-value diffusion imaging

Perhaps one of the greatest benefits of the development of high b-value technology has been the insight provided into the physiologic basis of diffusion imaging. The multiexponential features of the diffusion process are revealed on scans obtained with high b-value. The subsequent isotropic diffusion images have the distinct advantage of more accurately reflecting the intrinsic ADC of the tissues examined. This feature has the potential to facilitate clinical diagnosis. The degree to which this is proved to be clinically relevant is dependent on future investigation, but initial results are promising. The clinical potential of high b-value imaging at higher field strength remains to be explored. The greater signal to noise afforded by the use of 3-T scanners will likely make higher b-value imaging more practical with less costly scan time penalties necessary at lower field strengths.

Diffusion-weighted imaging of the spinal cord

Spinal cord DWI may be useful in providing information not available with conventional MR imaging. More work, however, is required to explain what the qualitative and quantitative results actually represent. Computer simulations and detailed radiologic-histologic correlations will therefore be necessary.

High b-value q-space analyzed diffusion-weighted MRI: application to multiple sclerosis

Multiple sclerosis (MS) is an inflammatory disease of the central nervous system (CNS) which affects nearly one million people worldwide, leading to a progressive decline of motor and sensory functions, and permanent disability. High b-value diffusion-weighted MR images (b of up to 14000 s/mm(2)) were acquired from the brains of controls and MS patients. These diffusion MR images, in which signal decay is not monoexponential, were analyzed using the q-space approach that emphasizes the diffusion characteristics of the slow-diffusing component. From this analysis, displacement and probability maps were constructed. The computed q-space analyzed MR images that were compared with conventional T(1), T(2) (fluid attenuated inversion recovery (FLAIR)), and diffusion tensor imaging (DTI) images were found to be sensitive to the pathophysiological state of white matter. The indices used to construct this q-space analyzed MR maps, provided a pronounced differentiation between normal tissue and tissues classified as MS plaques by the FLAIR images. More importantly, a pronounced differentiation was also observed between tissues classified by the FLAIR MR images as normal-appearing white matter (NAWM) in the MS brains, which are known to be abnormal, and the respective control tissues. The potential diagnostic capacity of high b-value diffusion q-space analyzed MR images is discussed, and experimental data that explains the consequences of using the q-space approach once the short pulse gradient approximation is violated are presented.

MR microscopy of multicomponent diffusion in single neurons

This study examines multicomponent diffusion in isolated single neurons and discusses the implications of the results for macroscopic water diffusion in tissues. L7 Aplysia neurons were isolated and analyzed using a 600 MHz Bruker wide-bore instrument with a magnetic susceptibility-matched radiofrequency microcoil. Using a biexponential fit, the apparent diffusion coefficients (ADCs) from the cytoplasm (with relative fraction) were 0.48 +/- 0.14 x 10(-3) mm2 x s(-1) (61 +/- 11%) for the fast component, and 0.034 +/- 0.017 x 10(-3) mm2 x s(-1) (32 +/- 11%) for the slow component (N = 10). Diffusion in the nucleus appears to be primarily monoexponential, but with biexponential analysis it yields 1.31 +/- 0.32 x 10(-3) mm2 x s(-1) (89 +/- 6%) for the fast component and 0.057 +/- 0.073 x 10(-3) mm2 x s(-1) (11 +/- 6%) for the slow (N = 5). The slow component in the nucleus may be explained by cytoplasmic volume averaging. These data demonstrate that water diffusion in the cytoplasm of isolated single Aplysia neurons supports a multiexponential model. The ADCs are consistent with previous measurements in the cytoplasm of single neurons and with the slow ADC measurement in perfused brain slices. These distributions may explain the multiple compartments observed in tissues, greatly aiding the development of quantitative models of MRI in whole tissues.

Application of magnetic resonance to animal models of cerebral ischemia

The present review has been compiled to highlight the role of magnetic resonance imaging (MRI) and MR spectroscopy (MRS) for the investigation of cerebral ischemia in the animal experimental field of basic research. We have focused on stroke investigations analyzing the pathomechanisms of the disease evolution and on new advances in both nuclear MR (NMR) methodology or genetic engineering of transgenic animals for the study of complex molecular relationships and causes of the disease. Furthermore, we have tried to include metabolic and genetic aspects, as well as the application of functional imaging, for the investigation of the disturbance or restitution of functional brain activation under pathological conditions as relates to controlled animal experiments.

Conductivity tensor mapping of the human brain using diffusion tensor MRI

Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self-diffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, final sigma and d) in agreement with theoretical bounds and experimental measurements presented here (final sigma/d approximately 0.844 +/- 0.0545 S small middle dots/mm(3), r(2) = 0.945). The extension to other biological transport phenomena is also discussed.

MR imaging measurement of compartmental water diffusion in perfused heart slices

Myocardial tissue slices were isolated from the left ventricular free wall (7 slices) and left ventricular papillary muscle (3 slices) of New Zealand White male rabbits (n = 4) and were subsequently superfused with a modified St. Thomas' Hospital cardioplegic solution at 19 degrees C. The diffusion-weighted images were obtained with a 600-MHz nuclear magnetic resonance spectrometer using diffusion gradient b-values that ranged from 166 to 6,408 s/mm(2); the apparent diffusion coefficient of water in the tissues were subsequently calculated. All of the tissue samples that were studied exhibited nonmonoexponential diffusion. Data from seven slices were mathematically fitted by a biexponential expression with a fast diffusion component of 0.72 +/- 0.07 x 10(-3) mm(2)/s, and a slow diffusion component of 0.060 +/- 0.033 x 10(-3) mm(2)/s. The fast component dominated the calculated apparent diffusion coefficient of the tissue, composed of 82 +/- 3% of the overall diffusion-dependent signal decay. Thus myocardial tissue exhibits characteristics consistent with multiple compartments of diffusion. This work has important implications for myocardial diffusion tensor imaging, as well as the changes in diffusion that have been reported following myocardial ischemia.

Transient decrease in water diffusion observed in human occipital cortex during visual stimulation

Using MRI, we report the observation of a transient decrease of the apparent diffusion coefficient (ADC) of water in the human brain visual cortex during activation by a black and white 8-Hz-flickering checkerboard. The ADC decrease was small (<1%), but significant and reproducible, and closely followed the time course of the activation paradigm. Based on the known sensitivity of diffusion MRI to cell size in tissues and on optical imaging studies that have revealed changes in the shape of neurons and glial cells during activation, the observed ADC findings have been tentatively ascribed to a transient swelling of cortical cells. These preliminary results suggest a new approach to produce images of brain activation with MRI from signals directly associated with neuronal activation, and not through changes in local blood flow.

Two-component diffusion tensor MRI of isolated perfused hearts

Nonmonoexponential MR diffusion decay behavior has been observed at high diffusion-weighting strengths for cell aggregates and tissues, including the myocardium; however, implications for myocardial MR diffusion tensor imaging are largely unknown. In this study, a slow-exchange-limit, two-component diffusion tensor model was fitted to diffusion-weighted images obtained in isolated, perfused rat hearts. Results indicate that there are at least two distinct components of anisotropic diffusion, characterized by a "fast" component whose principal diffusivity is comparable to that of the perfusate, and a highly anisotropic "slow" component. It is speculated that the two components correspond to tissue compartments and have a general agreement with the orientations of anisotropy, or fiber orientations, in the myocardium. Moreover, consideration of previous studies of myocardial diffusion suggests that the presently observed fast component may likely be dominated by diffusion in the vascular space, whereas the slow component may include the intracellular and interstitial compartments. The implications of the results for myocardial fiber orientation mapping and limitations of the current two-component model used are also discussed.

Biexponential apparent diffusion coefficient parametrization in adult vs newborn brain

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.

Normal Brain and Brain Tumor: Multicomponent Apparent Diffusion Coefficient Line Scan Imaging

Magnetic resonance line scan diffusion imaging of the brain, with diffusion weighting between 5 and 5,000 sec/mm(2), was performed in healthy subjects and patients with a 1.5-T machine. For each voxel, biexponential signal decay fits produced two apparent diffusion constants and respective signal amplitudes. Images based on these parameters show potential for use in the differentiation of gray and white matter, edema, and tumor.

Applications of DWI in clinical neurology

Echo planar diffusion-weighted imaging (EP DWI) provides information about the physiologic state of the brain that is not available on conventional magnetic resonance (MR) images. Specifically, it provides signal proportional to the molecular diffusion of water molecules. It has proven highly sensitive in the detection of acute infarction and it is reliable in differentiating acute stroke from other diseases that mimic acute stroke clinically and on conventional MR images. With perfusion imaging, diffusion-weighted imaging is useful in predicting final infarct size and patient outcome. Diffusion MR is also becoming increasingly useful in the evaluation of a wide variety of other disease processes including neoplasms, intracranial infections and traumatic brain injury. Because acute stroke is common in the differential diagnosis of the majority of patients who present with acute neurologic deficits, diffusion-weighted imaging has become an essential sequence.

Highly diffusion-sensitized MRI of brain: dissociation of gray and white matter

The brains of six healthy volunteers were scanned with a full tensor diffusion MRI technique to study the effect of a high b value on diffusion-weighted images (DWIs). The b values ranged from 500 to 5000 s/mm(2). Isotropic DWIs, trace apparent diffusion coefficient (ADC) maps, and fractional anisotropy (FA) maps were created for each b value. As the b value increased, ADC decreased in both the gray and white matter. Furthermore, ADC of the white matter became lower than that of the gray matter, and, as a result, the white matter became brighter than the gray matter in the isotropic DWIs. Quantitative analysis showed that these changes were due to nonmonoexponential diffusion signal decay of the brain tissue, which was more prominent in white matter than in gray matter. There was no significant change in relation to the b value in the FA maps. High b value appears to have a dissociating effect on gray and white matter in DWIs.

Acute and chronic changes of the apparent diffusion coefficient in neurological disorders--biophysical mechanisms and possible underlying histopathology

Diffusion-weighted imaging (DWI) of the brain has become a valuable tool for the reliable detection and diagnosis of several neurological disorders. Although DWI is in wide use in daily practice, the underlying biophysical mechanisms that contribute to changes in the apparent diffusion coefficient (ADC) are still under discussion. Alterations in the apparent water diffusion rate reflect pathological changes in the brain tissue state, via changes in the diffusion characteristics of the intra- and extra-cellular water compartments including restricted diffusion, water exchange across permeable boundaries, the concept of the extra-cellular tortuosity and the intra- and extra-cellular volume fraction. A reduction of the ADC has been detected in acute neurological diseases, while disease states associated with dominant acute vasogenic edema formation or chronic tissue destruction usually show elevations of the ADC. Compromise of energy metabolism is likely to contribute to a reduction of the ADC while already minor structural disintegration may contribute to elevations of the ADC.

Extracellular apparent diffusion in rat brain

The apparent diffusion coefficients (ADCs) of a series of markers concentrated in the extracellular space of normal rat brain were measured to evaluate, by inference, the ADC of water in the extracellular space. The markers (mannitol, phenylphosphonate, and polyethylene glycols) are defined as "compartment selective" because tissue culture experiments demonstrate some leakage into the intracellular space, making them less "compartment specific" than commonly believed. These primarily extracellular markers have ADCs similar to those of intracellular metabolites of comparable hydrodynamic radius, suggesting that water ADC values in the intra- and extracellular spaces are similar. If this is the case, then it is unlikely that a net shift of water from the extra- to the intracellular space contributes significantly to the reduction in water ADC detected following brain injury. Rather, this reduction is more likely due primarily to a reduction of the ADC of intracellular water associated with injury.

Analysis of partial volume effects in diffusion-tensor MRI

The diffusion tensor is currently the accepted model of diffusion in biological tissues. The measured diffusion behavior may be more complex when two or more distinct tissues with different diffusion tensors occupy the same voxel. In this study, a partial volume model of MRI signal behavior for two diffusion-tensor compartments is presented. Simulations using this model demonstrate that the conventional single diffusion tensor model could lead to highly variable and inaccurate measurements of diffusion behavior. The differences between the single and two-tensor models depend on the orientations, fractions, and exchange between the two diffusion tensor compartments, as well as the diffusion-tensor encoding technique and diffusion-weighting that is used in the measurements. The current single compartment model's inaccuracies could cause diffusion-based characterization of cerebral ischemia and white matter connectivity to be incorrect. A diffusion-tensor MRI imaging experiment on a normal human brain revealed significant partial volume effects between oblique white matter regions when using very large voxels and large diffusion-weighting (b approximately 2.69 x 10(3) sec/mm(2)). However, the apparent partial volume effects in white matter decreased significantly when smaller voxel dimensions were used. For diffusion tensor studies obtained using typical diffusion-weighting values (b approximately 1 x 10(3) sec/mm(2)) partial volume effects are much more difficult to detect and resolve. More accurate measurements of multiple diffusion compartments may lead to improved confidence in diffusion measurements for clinical applications.