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

Four-quadrant vector mapping of hybrid multidimensional MRI data for the diagnosis of prostate cancer

PURPOSE

The interpretation of prostate multiparametric magnetic resonance imaging (MRI) is subjective in nature, and there is large inter-observer variability among radiologists and up to 30% of clinically significant cancers are missed. This has motivated the development of new MRI techniques and sequences, especially quantitative approaches to improve prostate cancer diagnosis. Using hybrid multidimensional MRI, apparent diffusion coefficient (ADC) and T2 have been shown to change as a function of echo time (TE) and b-values, and that this dependence is different for cancer and benign tissue, which can be exploited for prostate cancer diagnosis. The purpose of this study is to investigate whether four-quadrant vector mapping of hybrid multidimensional MRI (HM-MRI) data can be used to diagnose prostate cancer (PCa) and determine cancer aggressiveness.

METHODS

Twenty-one patients with confirmed PCa underwent preoperative MRI prior to radical prostatectomy. Axial HM-MRI were acquired with all combinations of TE = 47, 75, 100 ms and b-values of 0, 750, 1500 s/mm2 , resulting in a 3 × 3 data matrix associated with each voxel. Prostate Quadrant (PQ) mapping analysis represents HM-MRI data for each voxel as a color-coded vector in the four-quadrant space of HM-MRI parameters (a 2D matrix of signal values for each combination of b-value and TE) with associated amplitude and angle information representing the change in T2 and ADC as a function of b-value and TE, respectively.

RESULTS

Cancers have a higher PQ4 (22.50% ± 21.27%) and lower PQ2 (69.86% ± 28.24%) compared to benign tissue: peripheral, transition, and central zone (PQ4 = 0.13% ± 0.56%, 5.73% ± 15.07%, 2.66% ± 4.05%, and PQ2 = 98.51% ± 3.05%, 86.18% ± 21.75%, 93.38% ± 9.88%, respectively). Cancers have a higher vector angle (206.5 ± 41.8°) and amplitude (0.017 ± 0.013) compared to benign tissue. PQ metrics showed moderate correlation with Gleason score (|ρ| = 0.388-0.609), with more aggressive cancers being associated with increased PQ4 and angle and reduced PQ2 and amplitude. A combination of four-quadrant analysis metrics provided an area under the curve of 0.904 (p < 0.001) for the differentiation of prostate cancer from benign prostatic tissue.

CONCLUSIONS

Four-quadrant vector mapping of HM-MRI data provides effective cancer markers, with cancers associated with high PQ4 and high vector angle and lower PQ2 and vector amplitude.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

On the Origins of Diffusion MRI Signal Changes in Stroke

Magnetic resonance imaging (MRI) is a leading diagnostic technique especially for neurological studies. However, the physical origin of the hyperintense signal seen in MR images of stroke immediately after ischemic onset in the brain has been a matter of debate since it was first demonstrated in 1990. In this article, we hypothesize and provide evidence that changes in the glial cells, comprising roughly one-half of the brain's cells and therefore a significant share of its volume, accompanying ischemia, are the root cause of the MRI signal change. Indeed, a primary function of the glial cells is osmoregulation in order to maintain homeostasis in the neurons and nerve fibers for accurate and consistent function. This realization also impacts our understanding of signal changes in other tissues following ischemia. We anticipate that this paradigm shift will facilitate new and improved models of MRI signals in tissues, which will, in turn, impact clinical utility.

Magnetic resonance measurements of cellular and sub-cellular membrane structures in live and fixed neural tissue

We develop magnetic resonance (MR) methods for real-time measurement of tissue microstructure and membrane permeability of live and fixed excised neonatal mouse spinal cords. Diffusion and exchange MR measurements are performed using the strong static gradient produced by a single-sided permanent magnet. Using tissue delipidation methods, we show that water diffusion is restricted solely by lipid membranes. Most of the diffusion signal can be assigned to water in tissue which is far from membranes. The remaining 25% can be assigned to water restricted on length scales of roughly a micron or less, near or within membrane structures at the cellular, organelle, and vesicle levels. Diffusion exchange spectroscopy measures water exchanging between membrane structures and free environments at 100 s^-1.

Comparison of diffusion-weighted MRI and anti-Stokes Raman scattering (CARS) measurements of the inter-compartmental exchange-time of water in expression-controlled aquaporin-4 cells

We performed multi-b and multi-diffusion-time diffusion-weighted magnetic resonance imaging on aquaporin-4-expressing (AQ) and -non-expressing (noAQ) cells, and demonstrated a clear difference between the signals from the two cell types. The data were interpreted using a two-compartment (intra and extracellular spaces) model including inter-compartmental exchange. It was also assumed that restricted diffusion of water molecules inside the cells leads to the intracellular diffusion coefficient being inversely proportional to the diffusion-time. Estimates of the water-exchange-times obtained with this model are compared to those measured using an independent optical imaging technique (coherent anti-Stokes Raman scattering imaging, CARS). For both techniques it was found that the exchange-time estimated for the noAQ cells was significantly longer than that for the AQ cells.

Non-invasive imaging using reporter genes altering cellular water permeability

Non-invasive imaging of gene expression in live, optically opaque animals is important for multiple applications, including monitoring of genetic circuits and tracking of cell-based therapeutics. Magnetic resonance imaging (MRI) could enable such monitoring with high spatiotemporal resolution. However, existing MRI reporter genes based on metalloproteins or chemical exchange probes are limited by their reliance on metals or relatively low sensitivity. Here we introduce a new class of MRI reporters based on the human water channel aquaporin 1. We show that aquaporin overexpression produces contrast in diffusion-weighted MRI by increasing tissue water diffusivity without affecting viability. Low aquaporin levels or mixed populations comprising as few as 10% aquaporin-expressing cells are sufficient to produce MRI contrast. We characterize this new contrast mechanism through experiments and simulations, and demonstrate its utility in vivo by imaging gene expression in tumours. Our results establish an alternative class of sensitive, metal-free reporter genes for non-invasive imaging.

Magnetic resonance imaging combined with molecular reporters can visualise cellular functions in intact organisms. Here Mukherjee et al. present a cellular imaging approach based on intracellular changes in water diffusion using human aquaporin 1 gene as a genetically encoded reporter for MRI.

Comparison of non-Gaussian and Gaussian diffusion models of diffusion weighted imaging of rectal cancer at 3.0 T MRI

Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R² = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.

Limitations and Prospects for Diffusion-Weighted MRI of the Prostate

Diffusion-weighted imaging (DWI) is the most effective component of the modern multi-parametric magnetic resonance imaging (mpMRI) scan for prostate pathology. DWI provides the strongest prediction of cancer volume, and the apparent diffusion coefficient (ADC) correlates moderately with Gleason grade. Notwithstanding the demonstrated cancer assessment value of DWI, the standard measurement and signal analysis methods are based on a model of water diffusion dynamics that is well known to be invalid in human tissue. This review describes the biophysical limitations of the DWI component of the current standard mpMRI protocol and the potential for significantly improved cancer assessment performance based on more sophisticated measurement and signal modeling techniques.

Estimation of the Number of Compartments Associated With the Apparent Diffusion Coefficient in MRI: The Theoretical and Experimental Investigations

OBJECTIVE

The goal of the present study was to estimate the number of compartments and the mean apparent diffusion coefficient (ADC) value with the use of the DWI signal curve.

MATERIALS AND METHODS

A useful new mathematic model that includes internal correlation among subcompartments with a distinct number of compartments was proposed. The DWI signal was simulated to estimate the approximate association between the number of subcompartments and the molecular density, with density corresponding to the ratio of the ADC values of the compartments, as determined using the Monte Carlo method.

RESULTS

Various factors, such as energy depletion, temperature, intracellular water accumulation, changes in the tortuosity of the extracellular diffusion paths, and changes in cell membrane permeability, have all been implicated as factors contributing to changes in the ADC of water (ADCw); therefore, one may consider them as pseudocompartments in the new model proposed in this study. The lower the coefficient is, the lower the contribution of the compartment to the net signal will be. The results of the simulation indicate that when the number of compartments increases, the signal will become significantly lower, because the gradient factor (i.e., the b value) will increase. In other words, the signal curve is approximately linear at all b values when the number of compartments in which the tissues have been severely damaged is low; however, when the number of compartments is high, the curve will become constant at high b values, and the perfusion parameters will prevail on the diffusion parameters at low b values. Therefore, normal tissues will be investigated when the number of compartments and the ADC values are high and the b values are low, whereas damaged tissues will be evaluated when the number of compartments and the ADC values are low and the b values are high.

CONCLUSION

The present study investigates damaged tissues at high b values for which the effect of eddy currents will also be compensated. These b values will probably be used in functional MRI.

Time-Dependent Influence of Cell Membrane Permeability on MR Diffusion Measurements

PURPOSE

To investigate the influence of cell membrane permeability on diffusion measurements over a broad range of diffusion times.

METHODS

Human myelogenous leukemia K562 cells were cultured and treated with saponin to selectively alter cell membrane permeability, resulting in a broad physiologically relevant range of 0.011-0.044 μm/ms. Apparent diffusion coefficient (ADC) values were acquired with the effective diffusion time (Δeff ) ranging from 0.42 to 3000 ms. Cosine-modulated oscillating gradient spin echo (OGSE) measurements were performed to achieve short Δeff from 0.42 to 5 ms, while stimulated echo acquisitions were used to achieve long Δeff from 11 to 2999 ms. Computer simulations were also performed to support the experimental results.

RESULTS

Both computer simulations and experiments in vitro showed that the influence of membrane permeability on diffusion MR measurements is highly dependent on the choice of diffusion time, and it is negligible only when the diffusion time is at least one order of magnitude smaller than the intracellular exchange lifetime.

CONCLUSION

The influence of cell membrane permeability on the measured ADCs is negligible in OGSE measurements at moderately high frequencies. By contrast, cell membrane permeability has a significant influence on ADC and quantitative diffusion measurements at low frequencies such as those sampled using conventional pulsed gradient methods.

Parsimonious continuous time random walk models and kurtosis for diffusion in magnetic resonance of biological tissue

In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.

Comparison of stretched-Exponential and monoexponential model diffusion-Weighted imaging in prostate cancer and normal tissues

BACKGROUND

To compare stretched-exponential and monoexponential model diffusion-weighted imaging (DWI) in prostate cancer and normal tissues.

METHODS

Twenty-seven patients with prostate cancer underwent DWI exam using b-values of 0, 500, 1000, and 2000 s/mm(2) . The distributed diffusion coefficients (DDC) and α values of prostate cancer and normal tissues were obtained with stretched-exponential model and apparent diffusion coefficient (ADC) values using monoexponential model. The ADC, DDC (both in 10(-3) mm(2)/s), and α values (range, 0-1) were compared among different prostate tissues. The ADC and DDC were also compared and correlated in each tissue, and the standardized differences between DDC and ADC were compared among different tissues.

RESULTS

Data were obtained for 31 cancers, 36 normal peripheral zone (PZ) and 26 normal central gland (CG) tissues. The ADC (0.71 ± 0.12), DDC (0.60 ± 0.18), and α value (0.64 ± 0.05) of tumor were all significantly lower than those of the normal PZ (1.41 ± 0.22, 1.47 ± 0.20, and 0.85 ± 0.09) and CG (1.25 ± 0.14, 1.32 ± 0.13, and 0.82 ± 0.06) (all P < 0.05). ADC was significantly higher than DDC in cancer, but lower than DDC in the PZ and CG (all P < 0.05). The ADC and DDC were strongly correlated (R(2)  = 0.99, 0.98, 0.99, respectively, all P < 0.05) in all the tissue, and standardized difference between ADC and DDC of cancer was slight but significantly higher than that in normal tissue.

CONCLUSION

The stretched-exponential model DWI provides more parameters for distinguishing prostate cancer and normal tissue and reveals slight differences between DDC and ADC values.

Avian egg latebra as brain tissue water diffusion model

PURPOSE

Simplified models of non-monoexponential diffusion signal decay are of great interest to study the basic constituents of complex diffusion behavior in tissues. The latebra, a unique structure uniformly present in the yolk of avian eggs, exhibits a non-monoexponential diffusion signal decay. This model is more complex than simple phantoms based on differences between water and lipid diffusion, but is also devoid of microscopic structures with preferential orientation or perfusion effects.

METHODS

Diffusion scans with multiple b-values were performed on a clinical 3 Tesla system in raw and boiled chicken eggs equilibrated to room temperature. Diffusion encoding was applied over the ranges 5-5,000 and 5-50,000 s/mm(2). A low read-out bandwidth and chemical shift was used for reliable lipid/water separation. Signal decays were fitted with exponential functions.

RESULTS

The latebra, when measured over the 5-5,000 s/mm(2) range, exhibited independent of preparation clearly biexponential diffusion, with diffusion parameters similar to those typically observed in in vivo human brain. For the range 5-50,000 s/mm(2), there was evidence of a small third, very slow diffusing water component.

CONCLUSION

The latebra of the avian egg contains membrane structures, which may explain a deviation from a simple monoexponential diffusion signal decay, which is remarkably similar to the deviation observed in brain tissue.

The role of tissue microstructure and water exchange in biophysical modelling of diffusion in white matter

Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange between microenvironments are reflected in diffusion MRI measurements. We focus on the use of biophysical models for extracting tissue-specific parameters from data obtained with single PGSE sequences on clinical MRI scanners, but results obtained with animal MRI scanners are also considered. While modelling of white matter is the central theme, experiments on model systems that highlight important aspects of the biophysical models are also reviewed.

Monitoring tissue development in acellular matrix-based regeneration for bladder tissue engineering: multiexponential diffusion and T2* for improved specificity

Cell-seeded acellular matrices (ACMs) are a promising approach for the tissue engineering of soft tissues and organs, such as the urinary bladder. ACM contains site-preferred structural and functional molecules, and degradation products derived from ACM play important roles in tissue remodeling. Regeneration proceeds along concurrent trajectories of cell growth and matrix degradation, characterized by evolving biophysical and biochemical properties. The assessment of tissue development through a noninvasive imaging technique, such as MRI, must therefore be capable of distinguishing these concurrent biophysical and biochemical changes. However, although MRI provides exquisite sensitivity to tissue microstructure, composition and function, specificity remains limited. In this study, multiexponential diffusion and the effective transverse relaxation time T(2)* were investigated for their ability to assess cell growth and tissue composition, respectively. Bladder ACMs prepared with and without hyaluronic acid, and ACMs seeded with smooth muscle cells, were assessed on MRI. The slow diffusion fraction from multiexponential diffusion analysis demonstrated the best correlation with cellularity, with minimal influence from underlying matrix degradation. T(2)* measurements were sensitive to macromolecular content, specifically the presence of hyaluronic acid, without confounding influence from tissue hydration. T(2)* also appeared to be sensitive to cell filling of the matrix pore space. Compared with these metrics, commonly used MRI parameters, such as T(1), T(2) and single diffusion coefficients, were more limited in specificity. The use of T(2) to measure tissue structure and composition is limited by its large dependence on water content, and single diffusion can only reflect the overall characteristics of the extra- and intracellular environment. These findings are important for further development of more specific MRI methods for the monitoring of regeneration in tissue-engineered systems.

Fractional Order Analysis of Sephadex Gel Structures: NMR Measurements Reflecting Anomalous Diffusion

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-(bD)(α)], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4,000 s-mm(-2)). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

Predictive models for pressure-driven fluid infusions into brain parenchyma

Direct infusions into brain parenchyma of biological therapeutics for serious brain diseases have been, and are being, considered. However, individual brains, as well as distinct cytoarchitectural regions within brains, vary in their response to fluid flow and pressure. Further, the tissue responds dynamically to these stimuli, requiring a nonlinear treatment of equations that would describe fluid flow and drug transport in brain. We here report in detail on an individual-specific model and a comparison of its prediction with simulations for living porcine brains. Two critical features we introduced into our model-absent from previous ones, but requirements for any useful simulation-are the infusion-induced interstitial expansion and the backflow. These are significant determinants of the flow. Another feature of our treatment is the use of cross-property relations to obtain individual-specific parameters that are coefficients in the equations. The quantitative results are at least encouraging, showing a high fraction of overlap between the computed and measured volumes of distribution of a tracer molecule and are potentially clinically useful. Several improvements are called for; principally a treatment of the interstitial expansion more fundamentally based on poroelasticity and a better delineation of the diffusion tensor of a particle confined to the interstitial spaces.

Non-Gaussian diffusion imaging: a brief practical review

The departure from purely mono-exponential decay of the signal, as observed from brain tissue following a diffusion-sensitized sequence, has prompted the search for alternative models to characterize these unconventional water diffusion dynamics. Several approaches have been proposed in the last few years. While multi-exponential models have been applied to characterize brain tissue, several unresolved controversies about the interpretations of the results have motivated the search for alternative models that do not rely on the Gaussian diffusion hypothesis. In this brief review, diffusional kurtosis imaging (DKI) and anomalous diffusion imaging (ADI) techniques are addressed and compared with diffusion tensor imaging. Theoretical and experimental issues are briefly described to allow readers to understand similarities, differences and limitations of these two non-Gaussian models. However, since the ultimate goal is to improve specificity, sensitivity and spatial localization of diffusion MRI for the detection of brain diseases, special attention will be paid on the clinical feasibility of the proposed techniques as well as on the context of brain pathology investigations.

The use of MR-detectable reporter molecules and ions to evaluate diffusion in normal and ischemic brain

As a result of the technical challenges associated with distinguishing the MR signals arising from intracellular and extracellular water, a variety of endogenous and exogenous MR-detectable molecules and ions have been employed as compartment-specific reporters of water motion. Although these reporter molecules and ions do not have the same apparent diffusion coefficients (ADCs) as water, their ADCs are assumed to be directly related to the ADC of the water in which they are solvated. This approach has been used to probe motion in the intra- and extracellular space of cultured cells and intact tissue. Despite potential interpretative challenges with the use of reporter molecules or ions and the wide variety used, the following conclusions are consistent considering all studies: (i) the apparent free diffusive motion in the intracellular space is approximately one-half of that in dilute aqueous solution; (ii) ADCs for intracellular and extracellular water are similar; (iii) the intracellular ADC decreases in association with brain injury. These findings provide support for the hypothesis that the overall brain water ADC decrease that accompanies brain injury is driven primarily by a decrease in the ADC of intracellular water. We review the studies supporting these conclusions, and interpret them in the context of explaining the decrease in overall brain water ADC that accompanies brain injury.

On high b diffusion imaging in the human brain: ruminations and experimental insights

Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber "tractography" results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,"ruminations," which have been proposed to account for the nonmonoexponentiality to date.

Aldehyde fixative solutions alter the water relaxation and diffusion properties of nervous tissue

Chemically-fixed nervous tissues are well-suited for high-resolution, time-intensive MRI acquisitions without motion artifacts, such as those required for brain atlas projects, but the aldehyde fixatives used may significantly alter tissue MRI properties. To test this hypothesis, this study characterized the impact of common aldehyde fixatives on the MRI properties of a rat brain slice model. Rat cortical slices immersion-fixed in 4% formaldehyde demonstrated 21% and 81% reductions in tissue T(1) and T(2), respectively (P < 0.001). The T(2) reduction was reversed by washing slices with phosphate-buffered saline (PBS) for 12 h to remove free formaldehyde solution. Diffusion MRI of cortical slices analyzed with a two-compartment analytical model of water diffusion demonstrated 88% and 30% increases in extracellular apparent diffusion coefficient (ADC(EX)) and apparent restriction size, respectively, when slices were chemically-fixed with 4% formaldehyde (P Collapse

Key Words

• formaldehyde
• glutaraldehyde
• water exchange
• brain slice
• mathematical model

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MESH Headings

• Animals
• Artifacts
• Brain/anatomy & histology
• Brain/drug effects
• Brain Chemistry/drug effects
• Cells, Cultured
• Diffusion/drug effects
• Diffusion Magnetic Resonance Imaging/methods
• Fixatives/pharmacokinetics
• Formaldehyde/pharmacology
• Male
• Rats
• Rats, Long-Evans
• Reproducibility of Results
• Sensitivity and Specificity
• Water/chemistry

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Grants

• R01 NS36992 NINDS NIH HHS
• R01 EB002084 NIBIB NIH HHS
• P41 RR16105 NCRR NIH HHS
• R01 NS036992 NINDS NIH HHS
• P41 RR016105 NCRR NIH HHS

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Affiliation(s)

Timothy M Shepherd Department of Radiology and Biomedical Imaging, University of California, San Francisco, San Francisco, California 94143-0628, USA.
Peter E Thelwall
Greg J Stanisz
Stephen J Blackband

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Magnetic labeling of non-phagocytic adherent cells with iron oxide nanoparticles: a comprehensive study

Small particles of iron oxide (SPIO) and ultrasmall particles of iron oxide (USPIO), inducing a strong negative contrast on T(2) and T(2)*-weighted MR images, are the most commonly used systems for the magnetic labeling of cultured cells and their subsequent detection by magnetic resonance imaging (MRI). The purpose of this work is to study the influence of iron incubation concentration, nanoparticle size and nanoparticle coating on the magnetic labeling and the viability of non-phagocytic adherent cells in culture. The magnetic labeling of 3T6 fibroblasts was studied by T(2)-weighted MRI at 4.7 T and by dosing-or cytochemical revealing-of iron through methods based on Perl's Prussian blue staining. Cells were incubated for 48 h with increasing iron concentrations of SPIO (25-1000 microg Fe/ml Endorem. Sinerem, a USPIO (20-40 nm) coated with neutral dextran, and Resovist (65 nm), a SPIO bearing an anionic carboxydextran coating, were compared with Endorem (dextran-coated, 80-150 nm) as magnetic tags. The iron loading of marrow stromal cell primary cultures (MSCs) isolated from rat femurs was compared with that of 3T6 fibroblasts. The SPIO-labeling of cells with Endorem was found to be dependent on the iron incubation concentration. MSCs, more sparsely distributed in the culture, exhibited higher iron contents than more densely populated 3T6 fibroblast cultures. A larger iron loading was achieved with Resovist than with Endorem, which in turn was more efficient than Sinerem as a magnetic tag. The magnetic labeling of cultured non-phagocytic adherent cells with iron oxide nanoparticles was thus found to be dependent on the relative concentration of the magnetic tag and of the cells in culture, on the nanoparticle size, and on the coating type. The viability of cells, estimated by methods assessing cell membrane permeability, was not affected by magnetic labeling in the conditions used in this work.

In vivo water state measurements in breast cancer using broadband diffuse optical spectroscopy

Structural changes in water molecules are related to physiological, anatomical and pathological properties of tissues. Near infrared (NIR) optical absorption methods are sensitive to water; however, detailed characterization of water in thick tissues is difficult to achieve because subtle spectral shifts can be obscured by multiple light scattering. In the NIR, a water absorption peak is observed around 975 nm. The precise NIR peak's shape and position are highly sensitive to water molecular disposition. We introduce a bound water index (BWI) that quantifies shifts observed in tissue water absorption spectra measured by broadband diffuse optical spectroscopy (DOS). DOS quantitatively measures light absorption and scattering spectra and therefore reveals bound water spectral shifts. BWI as a water state index was validated by comparing broadband DOS to magnetic resonance spectroscopy, diffusion-weighted MRI and conductivity in bound water tissue phantoms. Non-invasive DOS measurements of malignant and normal breast tissues performed in 18 subjects showed a significantly higher fraction of free water in malignant tissues (p < 0.0001) compared to normal tissues. BWI of breast cancer tissues inversely correlated with Nottingham-Bloom-Richardson histopathology scores. These results highlight broadband DOS sensitivity to molecular disposition of water and demonstrate the potential of BWI as a non-invasive in vivo index that correlates with tissue pathology.

Effects of intra- and extracellular space properties on diffusion and T(2) relaxation in a tissue model

The purpose of this study was to investigate the effects of biophysical factors on the diffusion and the relaxation time T(2) independently. Certain properties of the extracellular and the intracellular space may change radically in pathological conditions resulting in water diffusion changes. A tissue model consisting of red blood cells was studied. The extra- and intracellular spaces were modified osmotically and by suspending medium concentration. Diffusion measurements were evaluated with regard to the effective medium theory. Neither the nature of the protein in the extracellular space nor an increased level of intracellular hydration caused a significant net water diffusion change in the cell suspension. The relaxation time T(2) exhibited very little dependence on the extracellular volume fraction or the concentration or the nature of the protein in the extracellular space. An increased level of intracellular hydration resulted in systematically larger T(2) values. It seems probable that increases in extracellular protein concentrations or in the extent of intracellular hydration do not play a significant role in the diffusion changes detected in pathological conditions. T(2) appears to depend on the level of hydration or the total water content but is seemingly less dependent of the concentration and the nature of the extracellular protein in our model solutions.

Biexponential analysis of diffusion-related signal decay in normal human cortical and deep gray matter

Diffusion imaging with high-b factors, high spatial resolution and cerebrospinal fluid signal suppression was performed in order to characterize the biexponential nature of the diffusion-related signal decay with b-factor in normal cortical gray and deep gray matter (GM). Integration of inversion pulses with a line scan diffusion imaging sequence resulted in 91% cerebrospinal fluid signal suppression, permitting accurate measurement of the fast diffusion coefficient in cortical GM (1.142+/-0.106 microm2/ms) and revealing a marked similarity with that found in frontal white matter (WM) (1.155+/-0.046 microm2/ms). The reversal of contrast between GM and WM at low vs high b-factors is shown to be due to a significantly faster slow diffusion coefficient in cortical GM (0.338+/-0.027 microm2/ms) than in frontal WM (0.125+/-0.014 microm2/ms). The same characteristic diffusion differences between GM and WM are observed in other brain tissue structures. The relative component size showed nonsignificant differences among all tissues investigated. Cellular architecture in GM and WM are fundamentally different and may explain the two- to threefold higher slow diffusion coefficient in GM.

Diffusion-weighted imaging of inflammatory myopathies: polymyositis and dermatomyositis

Muscles of myositis patients examined with MRI demonstrate heterogeneous pathology ranging from unaffected muscle groups to severe inflammation, fat infiltration, and eventually, more serious fat replacement. The purpose of this investigation was to characterize myositic thigh muscles using diffusion-weighted imaging (DWI) and to examine fluid motion at various disease stages. We chose to characterize total fluid motion within the muscle using the model proposed by Le Bihan et al (6,7) in which the apparent diffusion coefficient (ADC), diffusion in the extra- and intracellular muscle compartments (D), perfusion in capillaries (pseudodiffusion) (D*), and volume fraction of capillary perfusion (f) are determined. Unaffected patient muscles have DWI coefficients equivalent to those of normal muscles. Inflamed muscles show elevated ADC and D values compared to normal muscles (P < 0.0005), and fat-infiltrated muscles have lower values than control muscles (P < 0.001). Inflamed muscles have lower f values than unaffected muscles (P < 0.009), suggesting decreased fractional volume of capillary perfusion. DWI provides quantitative data on molecular fluid motion in diseased muscles and affords the potential for longitudinal monitoring of myositic patients.

Characterization of anomalous diffusion from mr signal may be a new probe to tissue microstructure

Observation of translational self-diffusion of water molecules using magnetic resonance (MR) techniques has proven to be a powerful means to probe tissue microstructure. The collected MR signal depends on experimentally controllable parameters as well as the descriptors of tissue geometry. In order to obtain the latter, one needs to employ accurate models to characterize the dependence of the signal on the varied experimental parameters. In this work, a simple model describing diffusion in disordered media and fractal spaces is shown to describe the diffusion-time dependence of the diffusion attenuated MR signal obtained from biological specimens successfully. The model enables one to quantify the evolution of the average water displacement probabilities in terms of two exponents--dw and ds. The experiments performed on excised human neural tissue samples and human red blood cell ghosts indicate that these two parameters are sensitive to tissue microstructure. Therefore, it may be possible to use the proposed scheme to generate novel contrast mechanism for classifying and segmenting tissue.

Quantification of water compartmentation in cell suspensions by diffusion-weighted and T(2)-weighted MRI

When studying water diffusion in biological systems, any specific signal attenuation curve may be reproduced by a broad range of mathematical functions. Our goals were to quantify the diffusion and T(2) relaxation properties of water in a simple biological system and to study the changes that occur in osmotically stressed cells. Human breast cancer cells were incubated in isotonic or hypotonic osmotic buffers. Diffusion-weighted and T(2)-weighted magnetic resonance images were acquired during sedimentation over 12 h. Diffusion-weighted imaging (DWI) data were analyzed with a biexponential fit, the Kärger model for exchange between two freely diffusing populations and the Price-modified Kärger model accounting for restricted diffusion in spherical geometry. We found that only the Price model provided an accurate quantitative description for water diffusion in both cell systems, independent of acquisition parameters, over the entire density range. Model-derived cell radii, intracellular volume fractions and transmembrane water exchange times were in good agreement with results calculated from light microscopy and with model-free exchange times. T(2) data indicated two populations in fast exchange, with volume fractions clearly different from DWI populations. Hypotonic stress led to higher slow apparent diffusion coefficient, longer T(2) and lower membrane permeability. The tortuosity in a hypotonic cell suspension complied with the Wang model for spherical geometry. Quantitative characterization of biological systems is obtainable by DWI, using appropriate modeling, accounting for water restriction and exchange between compartments.

In vivo brain edema classification: New insight offered by large b-value diffusion-weighted MR imaging

PURPOSE

To assess the role of large b-value diffusion weighted imaging (DWI) in the characterization of the physicochemical properties of the water in brain edema under experimental and clinical conditions.

MATERIALS AND METHODS

Vasogenic brain edema was induced in mice by means of cold injury. A total of 17 patients with extensive peritumoral brain edema were also investigated. The longitudinal relaxation time (T(1)) and apparent diffusion coefficient (D) were measured in the edematous area both in humans and in mice. D was calculated by using both mono- (D(mono)) and biexponential (D(fast) and D(slow)) approaches in the low and overall range of b-values, respectively. The D values were correlated with the T(1) values.

RESULTS

A strong linear correlation was found between T(1) and D(mono) in vasogenic brain edema, both in humans and in mice. After breakdown of D(mono) into fast and slow diffusing components, only D(fast) exhibited a strong correlation with T(1); D(slow) was unchanged in vasogenic brain edema.

CONCLUSION

Large b-value DWI can furnish a detailed characterization of vasogenic brain edema, and may provide a quantitative approach for the differentiation of edema types on the basis of the physicochemical properties of the water molecules. Application of the DWI method may permit prediction and follow-up of the effects of antiedematous therapy.

Water diffusion heterogeneity index in the human brain is insensitive to the orientation of applied magnetic field gradients

The alpha diffusion-weighted imaging (DWI) method was developed to study heterogeneous water diffusion in the human brain using magnetic resonance imaging (MRI). An advantage of this model is that it does not require an assumption about the shape of the intravoxel distribution of apparent diffusion rates, and it has a calculable relationship to this distribution. The alpha-DWI technique is useful for detecting microstructural tissue changes associated with brain tumor invasion, and may be useful for directing therapy to invading tumor cells. In previous work, alpha-DWI was performed with magnetic field gradients applied along a single direction in order to avoid artificially introducing a source of heterogeneity to the decay. However, it is known that restricted diffusion is anisotropic in the brain, and the alpha-DWI method must take this into account to be complete. In this work the relationship between the applied magnetic field gradients and the fitted stretched-exponential model parameters was studied in the human brain. It was found the distributed diffusion coefficient (DDC) varies with the direction of applied gradients, while the heterogeneity index alpha is relatively direction-insensitive. It is proposed that in clinical use, maps of alpha can be created using diffusion-weighting gradients applied in a single direction that reflect the tissue heterogeneity.

Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal

This report introduces a novel method to characterize the diffusion-time dependence of the diffusion-weighted magnetic resonance (MR) signal in biological tissues. The approach utilizes the theory of diffusion in disordered media where two parameters, the random walk dimension and the spectral dimension, describe the evolution of the average propagators obtained from q-space MR experiments. These parameters were estimated, using several schemes, on diffusion MR spectroscopy data obtained from human red blood cell ghosts and nervous tissue autopsy samples. The experiments demonstrated that water diffusion in human tissue is anomalous, where the mean-square displacements vary slower than linearly with diffusion time. These observations are consistent with a fractal microstructure for human tissues. Differences observed between healthy human nervous tissue and glioblastoma samples suggest that the proposed methodology may provide a novel, clinically useful form of diffusion MR contrast.

Reversible and irreversible effects of chemical fixation on the NMR properties of single cells

The effects of chemical fixation are known to alter MR parameters, such as relaxation times and the apparent diffusion coefficient (ADC) of water. It is often assumed that such changes are reversible after samples have been reimmersed in a buffer solution for a sufficient period of time. In this study we characterize the changes associated with fixation of single Xenopus laevis oocytes and their subsequent reimmersion in buffer. Substantial reductions in both T(1) and T(2) values were measured for all compartments of the cell after fixation, with the cytoplasm showing larger changes than the nucleus. After reimmersion in buffer, there were small but statistically significant differences in MR parameters between fresh and reimmersed cells. Experiments with a gadolinium (Gd) contrast agent showed evidence of irreversible changes in the permeability of cellular membranes to small molecules.

Effects of temperature and aldehyde fixation on tissue water diffusion properties, studied in an erythrocyte ghost tissue model

Ex vivo biological sample imaging can complement in vivo MRI studies. Since ex vivo studies are typically performed at room temperature, and samples are frequently preserved by fixation, it is important to understand how environmental and chemical changes dictated by ex vivo studies alter the physical and MR properties of a sample. Diffusion and relaxation time measurements were used to assess the effects of temperature change and aldehyde fixation on the biophysical and MR properties of a model biological tissue comprised of erythrocyte ghosts suspended in buffer or agarose gel. Sample temperature was varied between 10 degrees C and 37 degrees C. Diffusion MRI data were analyzed with a biophysically appropriate two-compartment exchange model. Temperature change resulted in a complex alteration of water diffusion properties due to the compartmental nature of tissues and alteration in membrane permeability. Formaldehyde, Karnovsky's solution, and glutaraldehyde all caused statistically significant changes to the biophysical and MR properties of the samples. Fixation caused large decreases in water proton T2, which was restored to near prefixation values by washing free fixative from the samples. Water membrane permeability was also significantly altered by fixation. This study demonstrates that relating in vivo MR data to chemically fixed ex vivo data requires an understanding of the effects of sample preparation.

MR microscopy of rat hippocampal slice cultures: a novel model for studying cellular processes and chronic perturbations to tissue microstructure

Brain slices provide a useful nervous tissue model to investigate the relationships between magnetic resonance imaging (MRI) contrast mechanisms and tissue microstructure; yet, these acutely isolated tissues remain viable for only 10-12 h. To study slower biological processes, this work describes the first MRI microscopy characterization of organotypic rat hippocampal slice cultures that can be maintained for several weeks. Diffusion-weighted images of slice cultures acquired with a 14.1-T magnet demonstrated the laminar anatomy of the hippocampus with relatively high signal-to-noise ratios. Diffusion data analyzed using a two-compartment model with exchange indicated that cultured slices had a comparable microstructure to acute brain slices and to in vivo brain. Immunohistochemistry indicated that slice cultures tolerated the conditions required for MRI study well. MRI of cultured tissue slices is highly amenable to correlative microscopy techniques and offers great promise for future MRI investigations of pathological tissue reorganization, molecular imaging and stem cell therapies.

A model for diffusion in white matter in the brain

Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging is a powerful noninvasive method to characterize neuronal tissue in the human brain in vivo. As a first step toward understanding the relationship between the measured macroscopic apparent diffusion tensor and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the apparent diffusion tensor and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for diffusion tensor imaging and for the possible in situ estimation of microstructural parameters from diffusion-weighted MR data are discussed in the context of this modeling framework.

Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging

A new method for mapping diffusivity profiles in tissue is presented. The Bloch-Torrey equation is modified to include a diffusion term with an arbitrary rank Cartesian tensor. This equation is solved to give the expression for the generalized Stejskal-Tanner formula quantifying diffusive attenuation in complicated geometries. This makes it possible to calculate the components of higher-rank tensors without using the computationally-difficult spherical harmonic transform. General theoretical relations between the diffusion tensor (DT) components measured by traditional (rank-2) DT imaging (DTI) and 3D distribution of diffusivities, as measured by high angular resolution diffusion imaging (HARDI) methods, are derived. Also, the spherical tensor components from HARDI are related to the rank-2 DT. The relationships between higher- and lower-rank Cartesian DTs are also presented. The inadequacy of the traditional rank-2 tensor model is demonstrated with simulations, and the method is applied to excised rat brain data collected in a spin-echo HARDI experiment.

Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model

Experience with diffusion-weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so-called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched-exponential function was developed to describe diffusion-related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin-echo diffusion-weighted pulse sequence with b-values of 500-6500 s/mm(2) in six rats. Signal attenuation curves were fit to a stretched-exponential function, and 20% of the voxels were better fit to the stretched-exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity.

The existence of biexponential signal decay in magnetic resonance diffusion-weighted imaging appears to be independent of compartmentalization

It is generally believed that the apparent diffusion coefficient (ADC) changes measured by diffusion-weighted imaging (DWI) in brain pathologies are related to alterations in the water compartments. The aim of this study was to elucidate the role of compartmentalization in DWI via biexponential analysis of the signal decay due to diffusion. DWI experiments were performed on mouse brain over an extended range of b-values (up to 10,000 mm(-2) s) under intact, global ischemic, and cold-injury conditions. DWI was additionally applied to centrifuged human erythrocyte samples with a negligible extracellular space. Biexponential signal decay was found to occur in the cortex of the intact mouse brain. During global ischemia, in addition to a drop in the ADC in both components, a shift from the volume fraction of the rapidly diffusing component to the slowly diffusing one was observed. In cold injury, the biexponential signal decay was still present despite the electron-microscopically validated disintegration of the membranes. The biexponential function was also applicable for fitting of the data obtained on erythrocyte samples. The results suggest that compartmentalization is not an essential feature of biexponential decay in diffusion experiments.

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.

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.

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.