Water signal attenuation in diffusion-weighted 1H NMR experiments during cerebral ischemia: influence of intracellular restrictions, extracellular tortuosity, and exchange

Probing brain tissue microstructure with MRI: principles, challenges, and the role of multidimensional diffusion-relaxation encoding

Diffusion MRI uses the random displacement of water molecules to sensitize the signal to brain microstructure and to properties such as the density and shape of cells. Microstructure modeling techniques aim to estimate these properties from acquired data by separating the signal between virtual tissue 'compartments' such as the intra-neurite and the extra-cellular space. A key challenge is that the diffusion MRI signal is relatively featureless compared with the complexity of brain tissue. Another challenge is that the tissue microstructure is wildly different within the gray and white matter of the brain. In this review, we use results from multidimensional diffusion encoding techniques to discuss these challenges and their tentative solutions. Multidimensional encoding increases the information content of the data by varying not only the b-value and the encoding direction but also additional experimental parameters such as the shape of the b-tensor and the echo time. Three main insights have emerged from such encoding. First, multidimensional data contradict common model assumptions on diffusion and T2 relaxation, and illustrates how the use of these assumptions cause erroneous interpretations in both healthy brain and pathology. Second, many model assumptions can be dispensed with if data are acquired with multidimensional encoding. The necessary data can be easily acquired in vivo using protocols optimized to minimize Cramér-Rao lower bounds. Third, microscopic diffusion anisotropy reflects the presence of axons but not dendrites. This insight stands in contrast to current 'neurite models' of brain tissue, which assume that axons in white matter and dendrites in gray matter feature highly similar diffusion. Nevertheless, as an axon-based contrast, microscopic anisotropy can differentiate gray and white matter when myelin alterations confound conventional MRI contrasts.

Extra-axonal contribution to double diffusion encoding-based pore size estimates in the corticospinal tract

OBJECTIVE

To study the origin of compartment size overestimation in double diffusion encoding MRI (DDE) in vivo experiments in the human corticospinal tract. Here, the extracellular space is hypothesized to be the origin of the DDE signal. By exploiting the DDE sensitivity to pore shape, it could be possible to identify the origin of the measured signal. The signal difference between parallel and perpendicular diffusion gradient orientation can indicate if a compartment is regular or eccentric in shape. As extracellular space can be considered an eccentric compartment, a positive difference would mean a high contribution to the compartment size estimates.

MATERIALS AND METHODS

Computer simulations using MISST and in vivo experiments in eight healthy volunteers were performed. DDE experiments using a double spin-echo preparation with eight perpendicular directions were measured in vivo. The difference between parallel and perpendicular gradient orientations was analyzed using a Wilcoxon signed-rank test and a Mann-Whitney U test.

RESULTS

Simulations and MR experiments showed a statistically significant difference between parallel and perpendicular diffusion gradient orientation signals ([Formula: see text]).

CONCLUSION

The results suggest that the DDE-based size estimate may be considerably influenced by the extra-axonal compartment. However, the experimental results are also consistent with purely intra-axonal contributions in combination with a large fiber orientation dispersion.

Non-Invasive Prostate Cancer Characterization with Diffusion-Weighted MRI: Insight from In silico Studies of a Transgenic Mouse Model

Diffusion-weighted magnetic resonance imaging (DWI) enables non-invasive, quantitative staging of prostate cancer via measurement of the apparent diffusion coefficient (ADC) of water within tissues. In cancer, more advanced disease is often characterized by higher cellular density (cellularity), which is generally accepted to correspond to a lower measured ADC. A quantitative relationship between tissue structure and in vivo measurements of ADC has yet to be determined for prostate cancer. In this study, we establish a theoretical framework for relating ADC measurements with tissue cellularity and the proportion of space occupied by prostate lumina, both of which are estimated through automatic image processing of whole-slide digital histology samples taken from a cohort of six healthy mice and nine transgenic adenocarcinoma of the mouse prostate (TRAMP) mice. We demonstrate that a significant inverse relationship exists between ADC and tissue cellularity that is well characterized by our model, and that a decrease of the luminal space within the prostate is associated with a decrease in ADC and more aggressive tumor subtype. The parameters estimated from our model in this mouse cohort predict the diffusion coefficient of water within the prostate-tissue to be 2.18 × 10-3 mm2/s (95% CI: 1.90, 2.55). This value is significantly lower than the diffusion coefficient of free water at body temperature suggesting that the presence of organelles and macromolecules within tissues can drastically hinder the random motion of water molecules within prostate tissue. We validate the assumptions made by our model using novel in silico analysis of whole-slide histology to provide the simulated ADC (sADC); this is demonstrated to have a significant positive correlation with in vivo measured ADC (r2 = 0.55) in our mouse population. The estimation of the structural properties of prostate tissue is vital for predicting and staging cancer aggressiveness, but prostate tissue biopsies are painful, invasive, and are prone to complications such as sepsis. The developments made in this study provide the possibility of estimating the structural properties of prostate tissue via non-invasive virtual biopsies from MRI, minimizing the need for multiple tissue biopsies and allowing sequential measurements to be made for prostate cancer monitoring.

Separation of extra- and intracellular metabolites using hyperpolarized (13)C diffusion weighted MR

This work demonstrates the separation of extra- and intracellular components of glycolytic metabolites with diffusion weighted hyperpolarized (13)C magnetic resonance spectroscopy. Using b-values of up to 15,000smm(-2), a multi-exponential signal response was measured for hyperpolarized [1-(13)C] pyruvate and lactate. By fitting the fast and slow asymptotes of these curves, their extra- and intracellular weighted diffusion coefficients were determined in cells perfused in a MR compatible bioreactor. In addition to measuring intracellular weighted diffusion, extra- and intracellular weighted hyperpolarized (13)C metabolites pools are assessed in real-time, including their modulation with inhibition of monocarboxylate transporters. These studies demonstrate the ability to simultaneously assess membrane transport in addition to enzymatic activity with the use of diffusion weighted hyperpolarized (13)C MR. This technique could be an indispensible tool to evaluate the impact of microenvironment on the presence, aggressiveness and metastatic potential of a variety of cancers.

Exploring diffusion across permeable barriers at high gradients. II. Localization regime

We present an analytical solution of the one-dimensional Bloch-Torrey equation for diffusion across multiple semi-permeable barrier. This solution generalizes the seminal work by Stoller, Happer, and Dyson, in which the non-Gaussian stretched-exponential behavior of the pulsed-gradient spin-echo (PGSE) signal was first predicted at high gradients in the so-called localization regime. We investigate how the diffusive exchange across a semi-permeable barrier modifies this asymptotic behavior, and explore the transition between the localization regime at low permeability and the Gaussian regime at high permeability. High gradients are suitable to spatially localize the contribution of the nuclei near the barrier and to enhance the sensitivity of the PGSE signal to the barrier permeability. The emergence of the localization regime for three-dimensional domains is discussed.

Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation

The adaptive variation of the gradient intensity with the diffusion time at a constant optimal b-value is proposed to enhance the contribution of the nuclei diffusing across permeable barriers, to the pulsed-gradient spin-echo (PGSE) signal. An exact simple formula the PGSE signal is derived under the narrow pulse approximation in the case of one-dimensional diffusion across a single permeable barrier. The barrier contribution to the signal is shown to be maximal at a particular b-value. The exact formula is then extended to multiple permeable barriers, while the PGSE signal is shown to be sensitive to the permeability and to the inter-barrier distance. Potential applications of the protocol to survey diffusion in three-dimensional domains with permeable membranes are illustrated through numerical simulations.

Learning and memory alterations are associated with hippocampal N-acetylaspartate in a rat model of depression as measured by 1H-MRS

It is generally accepted that cognitive processes, such as learning and memory, are affected in depression. The present study used a rat model of depression, chronic unpredictable mild stress (CUMS), to determine whether hippocampal volume and neurochemical changes were involved in learning and memory alterations. A further aim was to determine whether these effects could be ameliorated by escitalopram treatment, as assessed with the non-invasive techniques of structural magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS). Our results demonstrated that CUMS had a dramatic influence on spatial cognitive performance in the Morris water maze task, and CUMS reduced the concentration of neuronal marker N-acetylaspartate (NAA) in the hippocampus. These effects could be significantly reversed by repeated administration of escitalopram. However, neither chronic stress nor escitalopram treatment influenced hippocampal volume. Of note, the learning and memory alterations of the rats were associated with right hippocampal NAA concentration. Our results indicate that in depression, NAA may be a more sensitive measure of cognitive function than hippocampal volume.

Apparent exchange rate mapping with diffusion MRI

Water exchange through the cell membranes is an important feature of cells and tissues. The rate of exchange is determined by factors such as membrane lipid composition and organization, as well as the type and activity of aquaporins. A method for noninvasively estimating the rate of water exchange would be useful for characterizing pathological conditions, e.g., tumors, multiple sclerosis, and ischemic stroke, expected to be associated with a change of the membrane barrier properties. This study describes the filter exchange imaging method for determining the rate of water exchange between sites having different apparent diffusion coefficients. The method is based on the filter-exchange pulsed gradient spin-echo NMR spectroscopy experiment, which is here modified to be compatible with the constraints of clinical MR scanners. The data is analyzed using a model-free approach yielding maps of the apparent exchange rate, here being introduced in analogy with the concept of the apparent diffusion coefficient. Proof-of-principle experiments are performed on microimaging and whole-body clinical scanners using yeast suspension phantoms. The limitations and appropriate experimental conditions are examined. The results demonstrate that filter exchange imaging is a fast and reliable method for characterizing exchange, and that it has the potential to become a powerful diagnostic tool.

Diffusion weighted imaging of female pelvic cancers: concepts and clinical applications

Early applications of diffusion weighted magnetic resonance imaging (DWI) were limited to neuroimaging, concentrating either on stroke or brain tumours. With recent advances in MRI hardware and software DWI is now increasingly being investigated for cancer assessment throughout the body. Clinical applications of DWI relating to female pelvic cancers have largely concentrated on detection, localisation and staging of disease. More recently investigators have started to evaluate the ability of DWI for determining tumour histology and even predicting the outcome of chemoradiation treatment. This article reviews the physical concepts of MR diffusion weighting, illustrates the biophysical basis of diffusion contrast and reports the clinical applications of DWI for cervical, endometrial, ovarian, rectal and bladder tumours.

Monte Carlo study of a two-compartment exchange model of diffusion

Multisite exchange models have been applied frequently to quantify measurements of transverse relaxation and diffusion in living tissues. Although the simplicity of such models is attractive, the precise relationship of the model parameters to tissue properties may be difficult to ascertain. Here, we investigate numerically a two-compartment exchange (Kärger) model as applied to diffusion in a system of randomly packed identical parallel cylinders with permeable walls, representing cells with permeable membranes, that may serve particularly as a model for axons in the white matter of the brain. By performing Monte Carlo simulations of restricted diffusion, we show that the Kärger model may provide a reasonable coarse-grained description of the diffusion-weighted signal in the long time limit, as long as the cell membranes are sufficiently impermeable, i.e. whenever the residence time in a cell is much longer than the time it takes to diffuse across it. For larger permeabilities, the exchange time obtained from fitting to the Kärger model overestimates the actual exchange time, leading to an underestimated value of cell membrane permeability.

How does water diffusion in human white matter change following ischemic stroke?

PURPOSE

Temporal evolution of the water apparent diffusion coefficients (ADC) parallel (ADC parallel) and perpendicular (ADC perpendicular) to the human white matter tract following ischemia has not been investigated systematically. We attempted to quantify the evolution of ADC parallel and ADC perpendicular and examine whether it can be interpreted by a model of ischemic edema.

METHODS

We retrospectively selected 53 patients with ischemic lesions involving the posterior limb of the internal capsule (PLIC) and placed regions of interest in the right and left PLIC on ADC maps. We performed regression analysis of lesion-to-contralateral ratios of ADC parallel and ADC perpendicular against the time (t = 1-1600 h) from onset. We then fitted the estimated time courses of ADC parallel and ADC perpendicular obtained from the analysis to a model of nerve tissue composed of cylinders (axons) and spheres corresponding to isotropic structures, particularly focal cytoplasmic swellings of glial cells and axons seen in ischemic white matter.

RESULTS

The evolution of ADC perpendicular and ADC parallel differed. The estimated time course of ADC parallel in microm(2)*ms(-1) was 0.64 + 0.88 exp (-0.24t) for 1 < t < 54 h and 0.00059t + 0.61 for t >or= 54 h (contralateral normal value, 1.52). That of ADC perpendicular was 0.19-0.063 exp (-0.24t) for 1 < t < 54 h and 0.00040t + 0.17 for t >or=54 h (normal value 0.22). The model fitted to these values showed that the volume of the cylinders decreased, that of the spheres increased, and extracellular volume changed little from one hour to approximately one day after stroke onset.

CONCLUSION

In the human PLIC, ADC parallel continued to decrease from one hour to a few days after stroke onset, and ADC perpendicular tended to increase. The temporal evolution could be interpreted by progression of the focal cytoplasmic swelling of glial cells and axons previously observed in animal studies.

Quantitative permeability imaging of plant tissues

A method for mapping tissue permeability based on time-dependent diffusion measurements is presented. A pulsed field gradient sequence to measure the diffusion encoding time dependence of the diffusion coefficients based on the detection of stimulated spin echoes to enable long diffusion times is combined with a turbo spin echo sequence for fast NMR imaging (MRI). A fitting function is suggested to describe the time dependence of the apparent diffusion constant in porous (bio-)materials, even if the time range of the apparent diffusion coefficient is limited due to relaxation of the magnetization. The method is demonstrated by characterizing anisotropic cell dimensions and permeability on a subpixel level of different tissues of a carrot (Daucus carota) taproot in the radial and axial directions.

Estimation of cell membrane permeability and intracellular diffusion coefficient of human gray matter

The signal intensity of diffusion-weighted imaging (DWI) is sensitive to the intra- and extracellular diffusion coefficient of water and cell membrane permeability. We applied a method we proposed in previous papers to estimate noninvasively the membrane permeability and intracellular diffusion coefficient of normal human brain (gray matter) in 3 normal volunteers. We theoretically compared predicted signals and experiment results using a 1.5-tesla magnetic resonance (MR) imaging system. We acquired images using an echo planar imaging (EPI) sequence, applying motion-probing gradient (MPG) pulses in 3 directions. We periodically performed numerical simulations for various combinations of membrane permeability and intracellular diffusion coefficients using the finite-difference method. By minimizing the difference between signals obtained experimentally and those from numerical simulation, we could estimate membrane permeability (76+/-9 mm2/s mum) and intracellular diffusion coefficient (1.0+/-0.0 mm2/s) for the human brain. The estimated membrane permeability was the criterion value for diagnosing disease in gray matter.

Evaluation of extra- and intracellular apparent diffusion coefficient of sodium in rat skeletal muscle: effects of prolonged ischemia

The mechanism of water and sodium apparent diffusion coefficient (ADC) changes in rat skeletal muscle during global ischemia was examined by in vivo 1H and 23Na magnetic resonance spectroscopy (MRS). The ADCs of Na+ and water are expected to have similar characteristics because sodium is present as an aqua-cation in tissue. The shift reagent, TmDOTP5(-), was used to separate intra- and extracellular sodium (Na+i and Na+e, respectively) signals. Water, total tissue sodium (Na+t), Na+i, and Na+e ADCs were measured before and 1, 2, 3, and 4 hr after ischemia. Contrary to the general perception, Na+i and Na+e ADCs were identical before ischemia. Thus, ischemia-induced changes in Na+e ADC cannot be explained by a simple change in the size of relative intracellular or extracellular space. Na+t and Na+e ADCs decreased after 2-4 hr of ischemia, while water and Na+i ADC remained unchanged. The correlation between Na+t and Na+e ADCs was observed because of high Na+e concentration. Similarly, the correlation between water and Na+i ADCs was observed because cells occupy 80% of the tissue space in the skeletal muscle. Ischemia also caused an increase in the Na+i and an equal decrease in Na+e signal intensity due to cessation of Na+/K+-ATPase function.

Exchange rate constants of invisible protons in proteins determined by NMR spectroscopy

Although labile protons that are exchanging rapidly with those of the solvent cannot be observed directly, their exchange rate constants can be determined by indirect detection of scalar-coupled neighboring nuclei. We have used heteronuclear NMR spectroscopy to measure the exchange rate constants of labile protons in the side chains of lysine and arginine residues in ubiquitin enriched in carbon-13 and nitrogen-15 at neutral pH. Exchange rate constants as fast as 40x10(3) s(-1) were thus measured. These results demonstrate that NMR spectroscopy is a powerful tool for the characterization of lysine NH3(+) and arginine NH groups in proteins at physiologically relevant pH values.

New perspectives on the sources of white matter DTI signal

A minimalist numerical model of white matter is presented, the objective of which is to help provide a biological basis for improved diffusion tensor imaging (DTI) analysis. Water diffuses, relaxes, and exchanges in three compartments-intracellular, extracellular, and myelin sheath. Exchange between compartments is defined so as to depend on the diffusion coefficients and the compartment sizes. Based on the model, it is proposed that an additive "baseline tensor" that correlates with intraaxonal water volume be included in the computation. Anisotropy and tortuosity calculated from such analysis may correspond better to tract ultrastructure than if calculated without the baseline. According to the model, reduced extracellular volume causes increased baseline and reduced apparent diffusion. Depending on the pulse sequence, reduced permeability can cause an increase in both the baseline and apparent diffusion.

Random-walk technique for simulating NMR measurements and 2D NMR maps of porous media with relaxing and permeable boundaries

We revisit random-walk methods to simulate the NMR response of fluids in porous media. Simulations reproduce the effects of diffusion within external inhomogeneous background magnetic fields, imperfect and finite-duration B(1) pulses, T(1)/T(2) contrasts, and relaxing or permeable boundaries. The simulation approach consolidates existing NMR numerical methods used in biology and engineering into a single formulation that expands on the magnetic-dipole equivalent of spin packets. When fluids exhibit low T(1)/T(2) contrasts and when CPMG pulse sequences are used to acquire NMR measurements, we verify that classical NMR numerical models that neglect T(1) effects accurately reproduce surface magnetization decays of saturated granular porous media regardless of the diffusion/relaxation regime. Currently, analytical expressions exist only for the case of arbitrary pore shapes within the fast-diffusion limit. However, when fluids include several components or when magnetic fields are strongly inhomogeneous, we show that simulations results obtained using the complete set of Bloch's equations differ substantially from those of classical NMR models. In addition, our random-walk formulation accurately reproduces magnetization echoes stemming from coherent-pathway calculations. We show that the random-walk approach is especially suited to generate parametric multi-dimensional T(1)/T(2)/D NMR maps to improve the characterization of pore structures and saturating fluids.

ADC measurements at low and high b values: insight into normal brain structure with clinical DWI

PURPOSE

To demonstrate drop in brain ADC measurements from low to high b values; to evaluate the structural information provided based on those changes; and to discuss the anatomical reasons for ADC differences.

METHODS

Four cerebral ROI (precuneus-PRC, hippocampus-HIP, and the genu-GCC and splenium-SCC of the corpus callosum-CC) were drawn for ADC measurements with low (1000) and high (3000) b-value DWI in 50 normal subjects. ANOVA and Bonferroni correction tested ADC differences between areas, between both hemispheres, between GCC and SCC, and between b-value related ADC drop within areas. Pearson test evaluated dependence of interhemispheric and intercallosum ADC measurements obtained with the same b-value, dependence between areas of intrazonal drop, and the interhemispheric and intercallosum dependence of intrazonal drop.

RESULTS

ADCs differed between areas (P<.0001). Interhemispheric ADC only differed in PRC with low b-value (P<.027). No HIP asymmetries occurred regardless the b-value. ADC drop within PRC and HIP was similar but differed (P<.0001) from ADC drop within both CC ROI. ADC drop was also different between GCC and SCC (P<.0001). In PRC and HIP, ADC showed a significant interhemispheric and intrazonal dependence (P<.0001). There was no GCC to SCC ADC dependence. Intrazonal dependence in the CC was only significant in the SCC (P<.001). Interhemispheric dependence of intrazonal drop was significant (PRC P=.007; HIP P<.0001) but failed to reach significance in the CC.

CONCLUSION

Low and high b-value measurements show different diffusion behaviours within different tissues, especially in a highly anisotropic structure as the corpus callosum. This fact can provide valuable information about brain structure and different diffusion compartments in clinical DWI.

Microstructural changes in ischemic cortical gray matter predicted by a model of diffusion-weighted MRI

PURPOSE

To understand the diffusion attenuated MR signal from normal and ischemic brain tissue in order to extract structural and physiological information using mathematical modeling, taking into account the transverse relaxation rates in gray matter.

MATERIALS AND METHODS

We fit our diffusion model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and exchange between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each compartment. A global optimum was found from a wide range of parameter permutations using cluster computing. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia.

RESULTS

Our model estimates an extracellular volume fraction of 0.19 in accordance with the accepted value from histology. The absolute apparent diffusion coefficient obtained from the model was similar to that of experiments. The model and the experimental results indicate significant differences in diffusion and transverse relaxation between the tissue compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms.

CONCLUSION

Our modeling suggests that transverse relaxation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling as the primary cause of the diffusion changes seen in the acute phase of brain ischemia.

Neurochemical and oedematous changes in 1,3-dinitrobenzene-induced astroglial injury in rat brain from a 1H-nuclear magnetic resonance perspective

1,3-Dinitrobenzene (1,3-DNB), an intermediate used in the chemical industry, has toxic effects in the brain and testes. It produces focal lesions with marked astroglial necrosis in the rat brain upon repeated administration. Astrocytic death occurs in parallel with elevated local blood flow and is followed by damage to the cerebral vasculature and neurones. (1)H-nuclear magnetic resonance spectroscopic analysis before the onset of astrocytic damage, showed a global elevation of lactate, whereas choline containing compounds increased in the non-vulnerable cerebral cortex, yet decreased in the vulnerable brainstem. Similarly, glutamate increased in the cerebral cortex, cerebellum and midbrain, but decreased in the susceptible brainstem. In vivo T2-weighted NMR imaging showed high signal intensities in brain nuclei shown to develop astroglial loss by conventional neuropathology at 24 hours after completion of dosing, but not at 6-10 hours. Hence the early neurochemical changes in susceptible areas contribute to the aetiology of degeneration, and those seen elsewhere may represent adaptive responses dependent on the particular phenotype of different cell groups and underlying metabolic relationships.

Quantitative measurement of leakage volume and permeability in gliomas, meningiomas and brain metastases with dynamic contrast-enhanced MRI

The spatial properties and function of the tumor vasculature differ with the tumor type and grade. T1-weighted dynamic contrast-enhanced imaging technique enables the simultaneous quantification of some functional parameters of the vasculature. These are the fractional contrast-enhancing volumes of the tissue compartments (blood volume and leakage/extravascular extracellular volume) and the exchange parameters (perfusion and permeability). The relatively long monitoring duration of 12 min used here made it necessary to divide the extravascular extracellular compartment into two subcompartments, a slowly and a fast enhancing one with different permeabilities. Forty-one gliomas (WHO grades II-IV), six meningiomas and eight distant metastases were investigated. It was shown that the technique noninvasively provides information for separating different tumor types and characterizing their microenvironment. Fast permeability describes vessel permeability and was significantly increased in meningiomas as compared with intra-axial tumors. The corresponding volume of the fast enhancing compartment was significantly increased in meningiomas compared to all gliomas taken together. Slow permeability describes diffusion within the extravascular extracellular space and was significantly reduced in low-grade gliomas, indicating short diffusion distances. The slowly enhancing extravascular extracellular space was found to be increased in high-grade gliomas and distant metastases. Blood volume differed significantly among some tumor entities and glioma grades. Perfusion was shown to increase linearly with blood volume for volumes of up to 20%, flattening out thereafter. The scatter plots of extravascular extracellular volume and blood volume were shown to differ among the tumor entities.

Assessment of axonal fiber tract architecture in excised rat spinal cord by localized NMR q-space imaging: simulations and experimental studies

NMR q-space imaging is a method designed to obtain information from porous materials where diffusion-diffraction phenomena were observed from which pore size was derived. Recently, the technique has been applied to the study of biological structures as well. Although diffusive diffraction has so far not been observed in multicellular systems, displacement profiles have been used with some success as a means to estimate structure size. However, there have been no quantitative correlations of the retrieved structure sizes with histology. Clearly, the complexity of tissue architecture poses significant challenges to the interpretation of q-space data. In this work, simulations were first performed on a two-compartment model to demonstrate the effects of interference of the diffraction patterns arising from intra and extra-axonal compartments and finite boundary permeability on q-space data. Second, q-space echo attenuation was simulated on the basis of histologic images of various rat spinal cord fiber tracts and the information obtained from the displacement profiles were compared with structural parameters computed from the histologic images. The results show that calculated mean displacements and kurtosis parallel mean axon size and axonal density. Finally, spatially localized q-space measurements were carried out at the locations where simulations had previously been performed, resulting in displacement data that support those obtained by simulation. The data suggest the NMR q-space approach has potential for nondestructive analysis of the axonal architecture in the mammalian spinal cord.

Effects of physiologic challenge on the ADC of intracellular water in the Xenopus oocyte

The biophysical determinants of the intracellular water apparent diffusion coefficient (ADC) in mammalian tissues are poorly understood. Model systems that are more amenable to physical measurements may provide insights into the behavior of more complex systems. Toward that end, we used MRI to evaluate the effects of altered microtubule concentration, nuclear breakdown, and ATP depletion on intracellular water ADC in the Xenopus oocyte. Water ADC did not change in response to polymerization of microtubules with taxol or depolymerization with nocodazole. Water ADC did not change following the breakdown of the nucleus in healthy cells. Short-term depletion of ATP (approximately 20% of normal levels following 4 hr of exposure to sodium azide and 2-deoxy-D-glucose) was not associated with a change in intracellular ADC. Long-term depletion of ATP (approximately 20% of normal levels following 2 days of exposure to antimycin A) was associated with a significant decrease in intracellular water ADC. These findings suggest that intracellular water diffusion in oocytes is not dependent on the state of microtubule polymerization or short-term ATP depletion, although long-term ATP depletion is associated with changes that lead to a decrease in intracellular water ADC.

p38 mitogen-activated protein kinase modulates expression of tumor necrosis factor-related apoptosis-inducing ligand induced by interferon-gamma in fetal brain astrocytes

This study describes the involvement of the p38 mitogen-activated protein kinase (MAPK) during interferon-gamma (IFN-gamma) signaling in fetal brain astrocytes. In some pathological conditions of brain, p38 MAPK transduces stress-related signals, increases expression of proinflammatory cytokines, and induces cellular damage or apoptosis. In astrocytes, the tumor necrosis factor (TNF)-related apoptosis-inducing ligand (TRAIL) expression level was increased by IFN-gamma. AG490, a JAK inhibitor, blocked TRAIL expression induced by IFN-gamma. SB203580, a specific p38alpha and p38beta2 MAPK inhibitor, decreased the TRAIL expression induced by IFN-gamma. The phosphorylation of the Ser727 site of STAT1, but not the Tyr701 site, was inhibited by SB203580. These results suggest that p38 MAPK modulates STAT1 phosphorylation in IFN-gamma signaling in fetal brain astrocytes.

Equilibrium water exchange between the intra- and extracellular spaces of mammalian brain

This report describes the measurement of water preexchange lifetimes and intra/extracellular content in intact, functioning mammalian brain. Intra- and extracellular water magnetic resonance (MR) signals from rat brain in vivo were quantitatively resolved in the longitudinal relaxation domain following administration of an MR relaxation agent into the extracellular space. The estimated intracellular water content fraction was 81% +/- 8%, and the intra- to extracellular exchange rate constant was 1.81 +/- 0.89 s(-1) (mean +/- SD, N = 9), corresponding to an intracellular water preexchange lifetime of approximately 550 ms. These results provide a temporal framework for anticipating the water exchange regime (fast, intermediate, or slow) underlying a variety of compartment-sensitive measurements. The method also supplies a means by which to evaluate membrane water permeability and intra/extracellular water content serially in intact tissue. The data are obtained in an imaging mode that permits detection of regional variations in these parameters.

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.

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.

In vivo excitotoxicity induced by ouabain, a Na+/K+-ATPase inhibitor

The susceptibility of immature rat brain to neurotoxicity of N-methyl-D-aspartate (NMDA) has provided a widely used paradigm to study excitotoxicity relevant to acute neurodegenerative diseases such as cerebral ischemia. In this study, excitotoxicity was induced via injection of ouabain (1 mM/0.5 microL), a Na+/K+ -ATPase-inhibitor, into neonatal rat brain and compared with NMDA injection. The aim of the study was to induce excitotoxicity secondary to cellular membrane depolarization, thereby more closely mimicking the pathophysiologic processes of ischemia-induced brain injury where NMDA-receptor overstimulation by glutamate follows, not precedes, membrane depolarization. Na+/K+ -ATPase-inhibition caused an acute, 40% +/- 8% decrease of the apparent diffusion coefficient (ADC) of water, as measured using diffusion-weighted magnetic resonance imaging (MRI), and resulted in infarctlike lesions as measured using T2-weighted MRI and histology up to 2 weeks later. Localized one- and two-dimensional 1H-magnetic resonance spectroscopy (MRS) demonstrated that the early excitotoxic diffusion changes were not accompanied by an overall metabolic disturbance. Furthermore, 31P-MRS demonstrated that energy depletion is not a prerequisite for ADC decrease or excitotoxic cell death. Treatment with the NMDA-antagonist MK-801 (1 mg/kg) attenuated the volume of tissue exhibiting a decreased ADC (P < 0.005), demonstrating that the ouabain-induced injury is indeed excitotoxic in nature. The authors argue that, compared with NMDA-injection, ouabain-induced excitotoxicity elicits more appropriate glutamate-receptor overstimulation and is better suited to detect relevant neuroprotection in that it is more sensitive to attenuation of synaptic glutamate levels.

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.

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.

Parametric imaging of tumor perfusion using flow- and permeability-limited tracers

PURPOSE

To quantitatively evaluate the spatial distribution of flow- and permeability-limited perfusion in MCF7 human breast cancer tumors orthotopically implanted in CD1-NU mice.

MATERIALS AND METHODS

Flow-limited perfusion was derived from (2)H-MRI recorded before and after infusion of deuterated water. Permeability-limited perfusion was evaluated from GdDTPA-enhanced (1)H-MRI.

RESULTS

The dominant processes in tumor perfusion, namely blood flow and capillary permeability, were mapped in orthotopically implanted MCF7 human breast cancer tumors. The dynamic data were processed according to physiological models, yielding parametric maps of intravascular volume fraction, water perfusion rate, GdDTPA permeability rate constant, and extracellular volume fraction accessible to GdDTPA. The maps exhibited the heterogeneous distribution of each perfusion parameter. Most of the tumor tissue (> or =95%) was perfused with HDO, while GdDTPA was perfused in only about 50% of it. In most loci the perfusion rate was limited by capillary permeability to GdDTPA.

CONCLUSION

The results demonstrated the instructive value of tracers with different properties used in conjunction to achieve a deeper understanding of tumor perfusion capacity. This study offers tools for the accurate, noninvasive evaluation of drug delivery efficacy.

Independence of extracellular tortuosity and volume fraction during osmotic challenge in rat neocortex

The structural properties of brain extracellular space (ECS) are summarised by the tortuosity (lambda) and the volume fraction (alpha). To determine if these two parameters were independent, we varied the size of the ECS by changing the NaCl content to alter osmolality of bathing media for rat cortical slices. Values of lambda and alpha were extracted from diffusion measurements using the real-time ionophoretic method with tetramethylammonium (TMA+). In normal medium (305 mosmol kg(-1)), the average value of lambda was 1.69 and of alpha was 0.24. Reducing osmolality to 150 mosmol kg(-1), increased lambda to 1.86 and decreased alpha to 0.12. Increasing osmolality to 350 mosmol kg(-1), reduced lambda to about 1.67 where it remained unchanged even when osmolality increased further to 500 mosmol kg(-1). In contrast, alpha increased steadily to 0.42 as osmolality increased. Comparison with previously published experiments employing 3000 M(r) dextran to measure lambda, showed the same behaviour as for TMA+, including the same constant lambda in hypertonic media but with a steeper slope in the hypotonic solutions. These data show that lambda and alpha behave differently as the ECS geometry varies. When alpha decreases, lambda increases but when alpha increases, lambda rapidly attains a constant value. A previous model allowing cellular shape to alter during osmotic challenge can account qualitatively for the plateau behaviour of lambda.

Parametric imaging of tumor perfusion with deuterium magnetic resonance imaging

Imaging of the vasculature and its functioning over the entire lesion may significantly aid in cancer diagnosis, assessment of prognosis, and therapeutic evaluation. In the current study we present a dynamic three-dimensional deuterium magnetic resonance imaging method that determines the intravascular volume fraction and water perfusion rate at a resolution of 2 mm(2)/pixel. The method was tested and utilized to characterize the vasculature of orthotopic MCF7 human breast cancer tumors in CD1-NU athymic mice. A new algorithm based on Patlak's kinetic model was developed to analyze the dynamic images acquired during and after termination of infusion with deuterated water. The resulting parametric maps spanned a wide range from 0.4 to 35.2% for the intravascular volume fraction and from 4 x 10(-6) to 3.9 x 10(-3) min(-1) for the perfusion rate and exhibited high intratumoral and intertumoral heterogeneity at both parameters. The intravascular volume fraction did not correlate with the corresponding perfusion rate, demonstrating the irregular outgrowth of tumor neovascularization. Averaging the data or analyzing at spatially degraded resolution completely masked the presence of both "hot spots" and hypoxic loci, highlighting the critical importance of high spatial resolution. The method is applicable to other types of tumors and animal models and may be extended to humans.

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.

The effects of microscopic tissue parameters on the diffusion weighted magnetic resonance imaging experiment

This review examines the way in which microscopic tissue parameters can affect MR experiments which are sensitive to diffusion. The interaction between the intra- and extravascular as well as that between the intra- and extracellular spaces is examined. Susceptibility gradients due to the presence of deoxyhemoglobin can cause diffusion-induced signal losses which are significant in functional magnetic resonance experiments, particularly at higher main magnetic field strengths. This is also true of the fast response that manifests itself as an early negative signal change in functional magnetic resonance experiments. The fields surrounding paramagnetic vessels are described and the way in which diffusion in these fields contributes to functional signal changes is examined. Flow in the capillary bed can be a confounding factor in experiments which aim to examine the diffusion characteristics of extravascular water. It is potentially also a method for assessing capillary perfusion. The intravoxel incoherent motion experiment is described in terms of how significantly this effect can influence diffusion attenuation curves from water. The major models for describing water diffusion in tissue are presented, as are the main experimental results that have contributed to an understanding of the mechanisms of diffusion contrast. The widely accepted view that changes in the diffusion characteristics are caused by a shift of water to the intracellular space and a concomitant change in extracellular tortuosity is examined critically. More recent experiments that indicate that a reduction in the intracellular diffusion may occur simultaneously with the cell swelling are described and their compatibility with existing models discussed.

Diffusion tensor imaging: concepts and applications

The success of diffusion magnetic resonance imaging (MRI) is deeply rooted in the powerful concept that during their random, diffusion-driven displacements molecules probe tissue structure at a microscopic scale well beyond the usual image resolution. As diffusion is truly a three-dimensional process, molecular mobility in tissues may be anisotropic, as in brain white matter. With diffusion tensor imaging (DTI), diffusion anisotropy effects can be fully extracted, characterized, and exploited, providing even more exquisite details on tissue microstructure. The most advanced application is certainly that of fiber tracking in the brain, which, in combination with functional MRI, might open a window on the important issue of connectivity. DTI has also been used to demonstrate subtle abnormalities in a variety of diseases (including stroke, multiple sclerosis, dyslexia, and schizophrenia) and is currently becoming part of many routine clinical protocols. The aim of this article is to review the concepts behind DTI and to present potential applications.

Displacement imaging of spinal cord using q-space diffusion-weighted MRI

Displacement MR images of water in in vitro rat spinal cord were computed from q-space analysis of high b value diffusion-weighted MRI data. It is demonstrated that q-space analysis of heavily diffusion-weighted MRI (qs-DWI) provides MR images in which physical parameters of the tissues such as the mean displacement and the probability for zero displacement of the water molecules are used as contrasts. It is shown that these MR images provide structural information surpassing the spatial resolution of conventional MRI by several orders of magnitude. This imaging methodology was used to follow spinal cord maturation in the rat. It was found that changes in the diffusion characteristics of white matter upon maturation are responsible for the emergence of gray/white matter contrast. The mean displacement of water molecules in the white and gray matter of the mature rat spinal cord was found to be 2-3, and 8-10 microns, respectively. The potential and the limitations of this new imaging methodology for early detection of white matter disorders are discussed.

Extracellular-intracellular distribution of glucose and lactate in the rat brain assessed noninvasively by diffusion-weighted 1H nuclear magnetic resonance spectroscopy in vivo

To determine the distribution of cerebral glucose and lactate between the intracellular and the extracellular space of the rat brain in vivo, the diffusion characteristic of glucose and lactate was compared with that of metabolites known to be mainly intracellular (N-acetylaspartate, choline, creatine, glutamate, myo-inositol, and taurine) using a pulsed-field-gradient 1H nuclear magnetic resonance technique. The detection of a glucose signal at large diffusion weighting provided direct experimental evidence of intracellular glucose in the rat brain. At large diffusion weighting, the apparent diffusion coefficient (ADC) of glucose and lactate was similar to that of the intracellular metabolites such as N-acetylaspartate, creatine, and glutamate. At small diffusion weighting, the ADC of glucose and lactate was increased, which was explained by a decreased relative contribution of intracellular glucose to the total signal. The calculated extracellular volume fraction of glucose (0.19 +/- 0.05) and lactate (0.17 +/- 0.06) was consistent with a substantial fraction of glucose and lactate signals being intracellular. The findings were direct in vivo evidence that the largest concentration gradient of glucose is at the blood-brain barrier and that glucose is evenly distributed in the brain in vivo between the intracellular and extracellular space.

Reduction in water and metabolite apparent diffusion coefficients during energy failure involves cation-dependent mechanisms. A proton nuclear magnetic resonance study of rat cortical brain slices

Proton (1H) nuclear magnetic resonance (NMR) diffusion spectroscopy was used to assess apparent diffusion coefficients (ADCs) in rat brain slices. Aglycemic hypoxia caused reductions in the ADC of N-acetylaspartate (NAA) (0.15 to 0.09 x 10(-3) mm2/s) and "slow" diffusion coefficient (D2) of tissue water (0.51 to 0.37 x 10(-3) mm2/s), together with a 32+/-11% increase in tissue water volume, attributable to tissue swelling. The ADC and D2 reductions were diminished, however, by removing external Ca2+, and under 10 mmol/L Mg2+, normoxic diffusion coefficients persisted until 40 minutes of hypoxia. The data suggest that the shift of water into the intracellular space alone cannot satisfactorily explain the reduced cerebral diffusion upon energy failure and that external Mg2+ and Ca2+ play crucial modulatory roles.

Water diffusion in rat brain in vivo as detected at very large b values is multicompartmental

The diffusion-weighted signal attenuation of water in rat brain was measured with pulsed-field gradient nuclear magnetic resonance methods in a single voxel under in vivo and global ischemic conditions. The diffusion-attenuated water signal was observed in vivo at b values of 300 ms/microm2 (strength of diffusion weighting) and diffusion times up to 400 ms. A series of constant diffusion time (CT) experiments with varied gradient directions and diffusion times revealed a multiexponential decay with apparent diffusion coefficients (ADC) covering two orders of magnitude from 1 to 0.01 microm2/ms. In a four-exponential fit, the observed changes during global ischemia could be fully explained by changes in the relative volume fractions only with unchanged ADCs. An anisotropy of the ADC, detected at small b values, was not observed for the ADC at large b values, but for the concomitant volume fractions. An inverse Laplace Transform of the CT curves, performed with CONTIN, resulted in continuously distributed diffusion coefficients, for which the term 'diffusogram' is proposed. This approach was more appropriate than a discrete exponential model with four to six components, being related to the morphology of brain tissue and its cell size distribution. On the basis of an analytical, quantitative model, it is suggested that the measured ADC at small b values reflects mainly properties of the restricting boundaries, i.e. the relative volume fractions and the extracellular tortuosity, while the intrinsic intracellular diffusion constant and the exchange time are predicted to have minor influence.