Water diffusion and acute stroke

Numerical model for calculation of apparent diffusion coefficients (ADC) in permeable cylinders--comparison with measured ADC in spinal cord white matter

We have implemented a numerical method for calculation of the apparent diffusion coefficient (ADC) in spinal cord injury, which takes into account the distribution of axon diameters and permeability found in spinal cord white matter, as well as relative axonal volume. We propose a procedure for determining the status of axonal integrity from measured ADC values. These methods have been applied to a well characterized rat spinal cord injury model, affording a prediction of the increase in axonal permeability which is presumed to be closely related to functional deficit. ADC values are compared to those calculated from analytical formulas in the literature, and possible factors underlying the ADC behavior are explored. Calculated results indicate both axonal swelling and cell membrane permeability to be important factors contributing to ADC in traumatic spinal cord injury.

Water household of the common carp, Cyprinus carpio, when submitted to an osmotic challenge, as determined by diffusion-weighted magnetic resonance imaging at 7 T

In vivo diffusion-weighted magnetic resonance imaging (MRI) was used to determine the effects of an osmotic challenge (1% NaCl) to a freshwater fish, the common carp (Cyprinus carpio). The imaged region covered organs such as the swimbladder, the liver, the kidney, the intestine, the spinal cord, and muscle tissue. A striking difference between salt-treated and control fish was found in the liver. The apparent diffusion coefficient value of livers from control fish was (0.39 +/- 0.16) 10(-9) m2/s and of salt-treated fish was (1.23 +/- 0.14) 10(-9) m2/s, which points to an increase in extracellular water content. These results were partially confirmed by a decrease in dry/wet weight ratio of the liver tissue. We also found increased levels of stress proteins in liver tissue. The Q factor of the applied radiofrequency coil dropped dramatically when we performed experiments with salt-exposed fish, indicating an increased conductivity resulting from the increased ion concentration and osmolarity of the fish. The data on plasma osmolarity of salt-exposed fish confirm a significant osmolarity increase upon salt exposure (from 334 to 430 mOsm/kg) and exceeded the osmolarity of the salt water (324 mOsm/kg), indicating that carp tend to cope with an increased salinity by increasing the internal osmolarity (hyperosmotic regulation). These data demonstrate that diffusion-weighted MRI might be a useful and noninvasive tool in the study of osmotic challenges of aquatic organisms.

An analytical model of restricted diffusion in bovine optic nerve

An analytical model of restricted diffusion in bovine optic nerve is presented. The nerve tissue model is composed of two different objects: prolate ellipsoids (axons) and spheres (glial cells) surrounded by partially permeable membranes. The free diffusion coefficients of intracellular and extracellular water may differ. Analytical formulas for signal loss due to diffusion in the pulsed gradient spin echo (PGSE) experiment for this tissue model are derived. The model is fitted to experimental data for bovine optic nerve. The obtained model parameters are shown to be reasonable. The model describes all of the characteristics of the PGSE data: anisotropy, upward curvature of decay curves, and diffusion time dependence. The validity and sensitivity of the model are also discussed.

The normal and pathological physiology of brain water

The physicochemical properties of water enable it to act as a solvent for electrolytes, and to influence the molecular configuration and hence the function--enzymatic in particular--of polypeptide chains in biological systems. The association of water with electrolytes determines the osmotic regulation of cell volume and allows the establishment of the transmembrane ion concentration gradients that underlie nerve excitation and impulse conduction. Fluid in the central nervous system is distributed in the intracellular and extracellular spaces (ICS, ECS) of the brain parenchyma, the cerebrospinal fluid, and the vascular compartment--the brain capillaries and small arteries and veins. Regulated exchange of fluid between these various compartments occurs at the blood-brain barrier (BBB), and at the ventricular ependyma and choroid plexus, and, on the brain surface, at the pia mater. The normal BBB is relatively permeable to water, but considerably less so to ions, including the principal electrolytes Brain fluid regulation takes place within the context of systemic fluid volume control, which depends on the mutual interaction of osmo-, volume-, and pressure-receptors in the hypothalamus, heart and kidney, hormones such as vasopressin, renin-angiotensin, aldosterone, atriopeptins, and digitalis-like immunoreactive substance, and their respective sites of action. Evidence for specific transport capabilities of the cerebral capillary endothelium, for example high Na+K(+)-ATPase activity and the presence at the abluminal surface of a Na(+)--H+ antiporter, suggests that cerebral microvessels play a more active part in brain volume regulation and ion homoeostasis than do capillaries in other vascular beds. The normal brain ECS amounts to 12-19% of brain volume, and is markedly reduced in anoxia, ischaemia, metabolic poisoning, spreading depression, and conventional procedures for histological fixation. The asymmetrical distributions of Na+ K+ and Ca2+ between ICS and ECS underlie the roles of these cations in nerve excitation and conduction, and in signal transduction. The relatively large volume of the CSF, and extensive diffusional exchange of many substances between brain ECS and CSF, augment the ion-homeostasing capacity of the ECS. The choroid plexus, in addition to secreting CSF principally by biochemical mechanisms (there is an additional small component from the extracellular fluid), actively transports some substances from the blood (e.g. nucleotides and ascorbic acid), and actively removes others from the CSF. In contrast with CSF secretion, CSF reabsorption is principally a biomechanical process, passively dependent on the CSF-dural sinus pressure gradient. Pathological increases in intracranial water content imply development of an intracranial mass lesion. The additional water may be distributed diffusely within the brain parenchyma as brain oedema, as a cyst, or as increase in ventricular volume due to hydrocephalus. Brain oedema is classified on the basis of pathophysiology into four categories, vasogenic, cytotoxic, osmotic and hydrostatic. The clinical conditions in which brain oedema presents the greatest problems are tumour, ischaemia, and head injury. Peritumoural oedema is predominantly vasogenic and related to BBB dysfunction. Ischaemic oedema is initially cytotoxic, with a shift of Na+ and CI- ions from ECS to ICS, followed by osmotically obliged water, this shift can be detected by diffusion-weighted MRI. Later in the evolution of an ischaemic lesion the oedema becomes vasogenic, with disruption of the BBB. Recent imaging studies in patients with head injury suggest that the development of traumatic brain oedema may follow a biphasic time course similar to that of ischaemic oedema. Hydrocephalus is associated in the great majority of cases with an obstruction to the circulation or drainage of CSF, or, occasionally, with overproduction of CSF by a choroid plexus papilloma. In either case, the consequence is a ris

Unraveling diffusion constants in biological tissue by combining Carr-Purcell-Meiboom-Gill imaging and pulsed field gradient NMR

A diffusion-weighted multi-spin-echo pulse sequence is presented, which allows for simultaneous measurement of T2, the fractional amplitude, and the diffusion constant of different fractions. Monte Carlo simulations demonstrate an improvement of this sequence with respect to the accuracy of diffusion constant and fractional amplitude for slow exchange. Examples are shown for a simple phantom containing two fractions. In addition, experiments on cat brain in healthy condition and following occlusion of the middle cerebral artery show that the fractional amplitude and the diffusion constant of cerebral spinal fluid and normal brain tissue can be analyzed within each pixel with acceptable accuracy.

Toward a quantitative assessment of diffusion anisotropy

Indices of diffusion anisotropy calculated from diffusion coefficients acquired in two or three perpendicular directions are rotationally variant. In living monkey brain, these indices severely underestimate the degree of diffusion anisotropy. New indices calculated from the entire diffusion tensor are rotationally invariant (RI). They show that anisotropy is highly variable in different white matter regions depending on the degree of coherence of fiber tract directions. In structures with a regular, parallel fiber arrangement, water diffusivity in the direction parallel to the fibers (Dparallel approximately 1400-1800 x 10(-6) mm2/s) is almost 10 times higher than the average diffusivity in directions perpendicular to them (D + D)/2 [corrected] approximately 150-300 x 10(-6) mm2/s), and is almost three times higher than previously reported. In structures where the fiber pattern is less coherent (e.g., where fiber bundles merge), diffusion anisotropy is significantly reduced. However, RI anisotropy indices are still susceptible to noise contamination. Monte Carlo simulations show that these indices are statistically biased, particularly those requiring sorting of the eigenvalues of the diffusion tensor based on their magnitude. A new intervoxel anisotropy index is proposed that locally averages inner products between diffusion tensors in neighboring voxels. This "lattice" RI index has an acceptably low error variance and is less susceptible to bias than any other RI anisotropy index proposed to date.

Diffusion of metabolites in normal and ischemic rat brain measured by localized 1H MRS

The apparent diffusion coefficient (ADC) of choline-containing compounds (Cho), creatine and phosphocreatine (Cre), N-acetyl-aspartate (NAA), lactate, and water was measured in normal rat brain, and in the ischemic and contralateral region of rat brain approximately 3 and 24 h after induction of focal cerebral ischemia. After 3 h of ischemia, the ADC of Cre and NAA in the ischemic region had significantly decreased by 29% and 19%, respectively (P < 0.05). Lactate ADC was also obtained in the ischemic region. After 24 h of focal ischemia, no ADC values could be measured for NAA, Cre and Cho in the ischemic region because their concentrations had become too low. The ADCs of lactate and water in the ischemic volume were virtually identical at 3 and 24 h after occlusion. The experiments suggest that the ADC decrease of water after induction of ischemia is partly caused by changes in the diffusion characteristics of the intracellular compartment.

Analysis and comparison of motion-correction techniques in diffusion-weighted imaging

Motion continues to be a significant problem in MRI, producing image artifacts that can severely degrade image quality. In diffusion-weighted imaging (DWI), the problem is amplified by the presence of large gradient fields used to produce the diffusion weighting. Three correction methods applicable for correction of specific classes of motion are described and compared. The first is based on a generalised projection onto convex sets (GPOCS) postprocessing algorithm. The second technique uses the collection of navigator echoes to track phase errors. The third technique is based on a radial-scan data acquisition combined with a modified projection-reconstruction algorithm. Although each technique corrects well for translations, the radial-scan method proves to be more robust when more complex motions are present. A detailed description of the causes of MR data errors caused by rigid body motion is included as an appendix.

Evolution of photochemically induced focal cerebral ischemia in the rat. Magnetic resonance imaging and histology

BACKGROUND AND PURPOSE

Magnetic resonance imaging (MRI) is increasingly used to study the pathophysiological evolution of cerebral ischemia in humans and animals. We have investigated photochemically induced (rose bengal) focal cerebral ischemia, a relatively noninvasive, reproducible model for stroke, and compared the evolution of the ischemic response in vivo and postmortem with MRI and histology, respectively.

METHODS

MR images weighted for T2, diffusion, and T2* and parallel histological sections stained with cresyl fast violet (CFV) and for glial fibrillary acid protein were obtained from 34 adult male Hooded Lister rats at seven time points (3.75 to 196 hours) after bilateral ischemia induction. From CFV histology, lesion volumes and cell counts were calculated; from diffusion-weighted and T2-weighted images, apparent diffusion coefficients and lesion volumes were determined.

RESULTS

Both MRI and histology revealed a well-defined lesion at 3.75 hours after irradiation and a consistent pattern of temporal evolution; lesion apparent diffusion coefficients decreased significantly by 3.75 hours, increased significantly by day 2, and correlated strikingly with the decline in lesion CFV-positive cell numbers. After day 2, astrocytes and connective tissue cells invaded the infarct. Throughout the time course, lesion volumes determined in vivo and postmortem (after shrinkage correction) agreed well.

CONCLUSIONS

MRI changes quantitatively reflect histopathology, revealing reproducible primary and secondary damage characteristics noninvasively. These changes essentially replicate those reported for other animal stroke models and clinically, emphasizing the value both of MRI and the photochemically induced focal cerebral ischemia model in stroke research.

Line scan diffusion imaging

A novel line scan diffusion imaging sequence (LSDI) is introduced. LSDI is inherently insensitive to motion artifacts and high quality diffusion maps of the brain can be obtained rapidly without the use of head restraints or cardiac gating. Results from a stroke study and abdominal diffusion images are presented. The results indicate that it is feasible to use the LSDI technique for clinical evaluation of acute ischemic stroke. In contrast to echo-planar diffusion imaging, LSDI does not require modified gradient hardware and can be implemented on conventional scanners. Thus, LSDI should dramatically increase the general availability of robust clinical diffusion imaging.

Severe transient hypoglycemia causes reversible change in the apparent diffusion coefficient of water

BACKGROUND AND PURPOSE

The aim of this study was to determine the effects of temporary severe hypoglycemia on the apparent diffusion coefficient (ADC) acquired by diffusion-weighted MRI of brain water with the use of serial multislice ADC mapping in rats. Severe hypoglycemia reduces the extracellular space volume, as does ischemia. Demonstrating a reduction of ADC with hypoglycemia should increase our understanding of the mechanisms underlying ADC changes in ischemia and other conditions.

METHODS

Fasted rats were given regular insulin (15 IU/kg IP). Rats were subjected to 15 minutes (n = 5) and 50 minutes (n = 5) of temporary severe hypoglycemia, causing a transiently isoelectric electroencephalogram (EEG). ADC mapping was performed every 30 seconds beginning at the onset of isoelectricity for 8.5 minutes. ADC maps were also obtained later during the isoelectric EEG period and 10, 20, 30, and 40 minutes after glucose infusion. Control images were obtained from a separate group of animals suffering cardiac arrest (n = 5).

RESULTS

Abnormal ADC values were not observed before the onset of cerebral isoelectricity, except for isolated areas in the cortex and periventricular regions. Cortical ADC values globally declined at the onset of EEG isoelectricity. The ADC decline spread to subcortical regions within a few minutes. During the isoelectric period, significant declines of ADC values (27% to 45%) occurred in the entire brain. Glucose infusion normalized most of the ADC changes, even after a 50-minute period of isoelectricity.

CONCLUSIONS

ADC mapping during hypoglycemia clearly demonstrates changes likely related to energy depletion. Most of these ADC declines were reversible. Hypoglycemia is a condition known to be associated with shrinkage of the extracellular space. These observations support the hypothesis that ADC reductions observed in ischemia are also related to shifts of water from the extracellular to the intracellular compartment.

Correlation of the average water diffusion constant with cerebral blood flow and ischemic damage after transient middle cerebral artery occlusion in cats

Magnetic resonance water diffusion imaging can detect early ischemic changes in stroke. Using a middle cerebral artery occlusion model, we examined which range of values of the orientation-independent diffusion quantity Dav = 1/3Trace(D) = 1/3(Dxx + Dyy + Dzz) is an early noninvasive indicator of reduced cerebral perfusion and focal brain injury. Cats underwent either a 30-min occlusion followed by 3.5 h reperfusion (n = 7) or a 60-min occlusion followed by 4-h reperfusion (n = 6). Repeated measurements of CBF were made with radiolabeled microspheres, and acute focal injury was measured with triphenyltetrazolium chloride (TTC) staining. During occlusion, the decrease in Dav correlated with CBF for caudate [30-min occlusion (n = 13): p < 0.0001: 60-min occlusion (n = 6): p < 0.02] and for cortex [30-min occlusion (n = 12): p < 0.0001: 60-min occlusion (n = 5): p < 0.04]. Variable caudate and hemispheric injury levels were found among cats in both groups. The area of tissue injury demarcated by TTC began to correlate with the area of reduced Dav by 30 min of occlusion (p < 0.02), and this correlation improved (p < 0.0001) at 1, 1.5, and 2.0 h after the onset of occlusion. The time necessary to reach a one-to-one correspondence between the percent of hemisphere injured and the percent of hemispheric area with Dav < 0.65 x 10(-9) m2/s was 2 h after occlusion. Thus, the absolute value of Dav is a good indicator of the risk of tissue injury, whereas the combination of Dav and the length of time of Dav reduction is an excellent predictor of acute focal tissue injury demarcated by TTC staining.

Hemodialysis increases apparent diffusion coefficient of brain water in nephrectomized rats measured by isotropic diffusion-weighted magnetic resonance imaging

The nature of brain edema in dialysis disequilibrium syndrome (DDS) was investigated by diffusion-weighted magnetic resonance imaging (DWI). DWI was performed on normal or bilaterally nephrectomized rats before, and immediately after, hemodialysis. Hemodialysis was performed with a custom-made dialyzer (surface area 150 cm2) against a bicarbonate-buffered bath for 90 min with or without 70 mM urea. Hemodialysis with non-urea bath decreased plasma urea by 21 mM, and plasma osmolality by 22 mosmol/kg H2O, and increased brain water content by 8.0% (all < 0.05), while hemodialysis with urea bath did not affect plasma urea, osmolality, or brain water content. Three sets of axial DWI images of the brain were obtained at different gradient weighing factors with an in-plane resolution of 0.39 mm2. The apparent diffusion coefficient (Dapp) of the brain water was not affected by bilateral nephrectomy, or by hemodialysis in normal rats. In nephrectomized rats, brain Dapp was significantly increased after dialysis with non-urea bath (1.15 +/- 0.08 vs 0.89 +/- 0.07 x 10(-9)m2/sec, P < 0.01). No significant changes of brain water Dapp could be observed after dialysis with urea bath. The increased Dapp associated with DDS indicates that brain extracellular water increases and/or intracellular water decreases after hemodialysis. Our results strongly suggest that the brain edema induced by hemodialysis in uremic rats is due to interstitial edema rather than cytotoxic edema. Furthermore, our results support a primary role for the "reverse urea effect" in the pathogenesis of brain edema in DDS.DWI may be a useful diagnostic tool for DDS in patients with end-stage renal disease.

Dynamic changes in water ADC, energy metabolism, extracellular space volume, and tortuosity in neonatal rat brain during global ischemia

To obtain a better understanding of the mechanisms underlying early changes in the brain water apparent diffusion coefficient (ADC) observed in cerebral ischemia, dynamic changes in the ADC of water and in the energy status were measured at postnatal day 8 or 9 in neonatal rat brains after cardiac arrest using 1H MRS/MRI and 31P MRS, respectively. The time courses of the MR parameters were compared with changes in the extracellular space (ECS) volume fraction (alpha) and tortuosity (lambda), determined from concentration-time profiles of tetramethylammonium applied by iontophoresis. The data show a decrease of the ADC of tissue water after induction of global ischemia of which the time course strongly correlates with the time course of the decrease in the ECS volume fraction and the increase in ECS tortuosity. This indicates that cell swelling is an important cause for the ADC decrease of water.

Single-shot diffusion MRI of human brain on a conventional clinical instrument

A single-shot diffusion MRI technique on a standard clinical 1.5T scanner is presented. The method incorporates the following elements: (a) an inversion RF pulse followed by a delay of 1.3 s to null cerebral spinal fluid (CSF) signal, (b) a stimulated echo sequence (TE = 56 ms, TM = 100 ms) to obtain strong diffusion weighting, (c) a single-shot gradient- and spin-echo (GRASE) sequence for imaging with a modified k-space trajectory and Carr-Purcell Meiboom-Gill (CPMG)-phase cycle. The trace of the diffusion coefficient obtained with this approach is in good agreement with values reported for animal brain, and for recent human studies. It is demonstrated that single-shot diffusion imaging of human brain is feasible on an unmodified standard instrument without high-gradient slew rate or extreme field homogeneity.

Encoding of anisotropic diffusion with tetrahedral gradients: a general mathematical diffusion formalism and experimental results

A diffusion imaging method with a tetrahedral sampling pattern has been developed for high-sensitivity diffusion analysis. The tetrahedral gradient pattern consists of four different combinations of x, y, and z gradients applied simultaneously at full strength to uniformly measure diffusion in four different directions. Signal-to-noise can be increased by up to a factor of about three using this approach, compared with diffusion measurements made using separately applied x, y, and z gradients. A mathematical formalism is presented describing six fundamental parameters: the directionally averaged diffusion coefficient D and diffusion element anisotropies eta and epsilon which are rotationally invariant, and diffusion ellipsoid orientation angles theta, phi, and omega which are rotationally variant. These six parameters contain all the information in the symmetric diffusion tensor D. Principal diffusion coefficients, reduced anisotropies, and other rotational invariants are further defined. It is shown that measurement of off-diagonal tensor elements is essential to assess anisotropy and orientation, and that the only parameter which can be measured with the orthogonal method is D. In cases of axial diffusion symmetry (e.g., fibers), the four tetrahedral diffusion measurements efficiently enable determination of D, eta, theta, and phi which contain all the diffusion information. From these four parameters, the diffusion parallel and perpendicular to the symmetry axis (D and D) and the axial anisotropy A can be determined. In more general cases, the six fundamental parameters can be determined with two additional diffusion measurements. Tetrahedral diffusion sequences were implemented on a clinical MR system. A muscle phantom demonstrates orientation independence of D, D, D, and A for large changes in orientation angles. Sample background gradients and diffusion gradient imbalances were directly measured and found to be insignificant in most cases.

Evaluation of intracellular diffusion in normal and globally-ischemic rat brain via 133Cs NMR

The question of whether the apparent diffusion coefficient (ADC) of intracellular water changes after brain injury was addressed by using 133Cs as an indicator to report on the state of the intracellular environment. Cesium is an NMR-detectable potassium analog that accumulates in the intracellular space and is detectable in rat brain after being added to the animal's diet. The ADC of cesium was measured before and after the death of the rat. The cesium ADC fell from 0.91 +/- 0.05 x 10(-3) mm2/s (mean +/- SEM, n=5) in the alive rat to 0.71 +/- 0.05 x 10(-3) mm2/s within 20 min (the best time resolution of the experiment) of the death of the animal and stayed at this value for at least 3 h (p < 0.001). Assuming that the ADC of cesium reflects motion in the intracellular environment, these results support the idea that there are changes associated with cell injury that would cause a reduction in the ADC of intracellular water. Hence, one factor contributing to the decrease in water ADC after brain injury is a change in the ADC of intracellular water.

Effects of osmotically driven cell volume changes on diffusion-weighted imaging of the rat optic nerve

The apparent diffusion coefficient (ADC) of the rat optic nerve was measured in vitro, using magnetic resonance imaging, to determine the effects of changes in cellular volume fraction on the diffusion of tissue water. Nerve ADC was determined under conditions of cell membrane depolarization and (i) increased intracellular volume, (ii) decreased intracellular volume, and (iii) negligible volume change. Depolarization alone had little affect on ADC, whereas volume changes produced strong, reversible effects. Increased cell volume decreased ADC and vice versa. These results are consistent with the view that changes in the extracellular space are the major source of ADC changes in brain tissue.

Imaging focal reperfusion injury following global ischemia with diffusion-weighted magnetic resonance imaging and 1H-magnetic resonance spectroscopy

The purpose of the study was to determine whether diffusion-weighted magnetic resonance imaging (DWI) could identify focal lesions that develop in ischemia-sensitive cerebral tissues during reperfusion following global brain ischemia. Localized 1H-Magnetic Resonance Spectroscopy (1H-MRS) measurements were also obtained to determine whether abnormal spectroscopic markers were associated with focal lesions and to define time correlations between DWI and metabolic changes. Brain diffusion-weighted magnetic resonance imaging measurements were made in a cat model of repetitive global cerebral ischemia and reperfusion. Five animals were exposed to three episodes of 10 min vascular occlusions at hourly intervals. Three animals were evaluated as controls. DWI, T2WI, and 1H-MRS data were acquired for up to 12 h. Transient focal DWI hyperintensity was detected in the hippocampus, basal ganglia, and cortical watershed areas. These focal abnormalities usually appeared during the final reperfusion and eventually spread to encompass all of the gray matter. Spectroscopic measurements demonstrated the expected elevation of the lactate signal intensity during vessel occlusion, which returned to normal during early reperfusion. A subsequent rise in the lactate signal occurred approximately 3-4 h after the beginning of the third reperfusion. This late lactate elevation occurred after focal hyperintensities were identified by DWI. No significant signal changes were seen in spectroscopic metabolites other than lactate. The study illustrates that DWI and 1H-MRS are sensitive to focal cerebral lesions that occur during reperfusion following global cerebral ischemia.

Inferring microstructural features and the physiological state of tissues from diffusion-weighted images

We review several methods that have been developed to infer microstructural and physiological information about isotropic and anisotropic tissues from diffusion weighted images (DWIs). These include Diffusion Imaging (DI), Diffusion Tensor Imaging (DTI), isotropically weighted imaging, and q-space imaging. Just as DI provides useful information about molecular displacements in one dimension with which to characterize diffusion in isotropic tissues, DTI provides information about molecular displacements in three dimensions needed to characterize diffusion is anisotropic tissues. DTI also furnishes scalar parameters that behave like quantitative histological or physiological 'stains' for different features of diffusion. These include Trace(D), which is related to the mean diffusivity, and a family of parameters derived from the diffusion tensor, D, which characterize different features of anisotropic diffusion. Simple thought experiments and geometrical constructs, such as the diffusion ellipsoid, can be used to understand water diffusion in isotropic and anisotropic media, and the NMR experiments used to characterize it.

Diffusion MRI: precision, accuracy and flow effects

After a decade of evolution and application of diffusion imaging, a large body of literature has been accumulated. It is in this context that the accuracy and precision of diffusion-weighted and quantitative diffusion MRI are reviewed. The emphasis of the review is on practical methods for clinical human imaging, particularly in the brain. The requirements for accuracy and precision are reviewed for various clinical and basic science applications. The methods of measuring and calculating diffusion effects with MRI are reviewed. The pulse gradient spin echo (PGSE) methods are emphasized as these methods are used most commonly in the clinical setting. Processing of PGSE data is reviewed. Various PGSE encoding schemes are also reviewed in terms of the accuracy and precision of isotropic and anisotropic diffusion measurements. The broad range of factors impacting the accuracy of the PGSE methods and other encoding schemes is then considered. Firstly, system inaccuracies such as background imaging gradients, gradient linearity, refocusing RF pulses, eddy currents, image misregistration, noise and dynamic range are considered. A second class of inaccuracies is contributed by the bulk effects of the imaged object, and include sample background gradients, subject motion of cerebrospinal fluid and organs, and aperiodic organ motion. A final category of potential inaccuracies is classified as being contributed by microscopic, biophysical tissue properties and include partial volume effects, anisotropy, restriction, diffusion distance, compartmentation, exchange, multiexponential diffusion decay, T2 weighting and microvascular perfusion. Finally, the application of diffusion methods to studies of blood flow in the microvasculature (i.e. the arterioles, capillaries and venules) are reviewed in detail, particularly in terms of feasibility and the stringent accuracy and precision requirements. Recent provocative studies examining the use of PGSE approaches to suppress microvascular signals in brain functional MRI (fMRI) are also reviewed.

Diffusion-weighted imaging in tissues: theoretical models

Typical diffusion measurements use Stejskal-Tanner pulsed gradient spin echo sequences to provide information about the average diffusion and displacement profiles of particles in a sample. To derive structural information, a measured displacement profile has to be related by means of a model to the physical and geometrical properties of the tissue, such as diffusion coefficients and shapes of semi-permeable membranes of compartments in the system. The behavior of the NMR signal and the measured ADC are greatly affected by the cellular architecture of a tissue, mainly because cellular membranes are relatively impermeable to water. For long diffusion times, and small signal attenuations, ADC is relatively insensitive to how it is measured. In general, however, ADC values are not readily interpreted unless the measuring conditions are specified in detail. For given measuring conditions, ADC depends on intra- and extracellular diffusion coefficients, membrane permeabilities, cell sizes and the cellular volume fraction. If intra- and extracellular T2 relaxation rates are different enough, ADC may also depend on the relaxation properties of the system and the echo time. An improved understanding of the precise influence of these factors has been obtained by detailed consideration of theoretical and computer models that can be related to experimental data in simple systems. Further refinements of such models should advance our understanding of water diffusion in tissues.

Molecular diffusion, tissue microdynamics and microstructure

Diffusion NMR is the only method available today that noninvasively provides information on molecular displacements over distances comparable to cell dimensions. This information can be used to infer tissue microstructure and microdynamics. However, data may be fairly difficult to interpret in biological tissues which differ markedly from the theoretical "infinite isotrope medium", as many factors may affect the NMR signal. The object of this paper is to analyze the expected effects of temperature, restriction, hindrance, membrane permeability, anisotropy and tissue inhomogeneity on the diffusion measurements. Powerful methods, such as q-space imaging, diffusion tensor imaging and diffusion spectroscopy of metabolites further enhance the specificity of the information obtained from diffusion NMR experiments.

Clinical aspects of DWI

Diffusion-weighted MR imaging (DWI) is capable of imaging ischemia-induced changes in water protons in either animal or man. Technical developments are described that allow the routine clinical utility of DWI in a stroke setting to provide objective criteria beyond the neurological exam by which the pathophysiology of stroke can be evaluated. To date, DWI has provided unique information concerning detection and evaluation of acute, symptomatic lesions from older, chronic strokes, detection and localization of small deep infarcts and reversible ischemic neurologic deficits and transient ischemia. Clinical DWI studies suggest that the temporal behaviour of ADC can critically improve the evaluation of clinical ischemia.

Alteration of intracellular metabolite diffusion in rat brain in vivo during ischemia and reperfusion

BACKGROUND AND PURPOSE

Diffusion-weighted MRI can demonstrate decreases of the apparent diffusion coefficient (ADC) of brain tissue water shortly after the onset of ischemia. To further elucidate underlying mechanisms, this study extended diffusion assessment to intracellular metabolites in rat brain in vivo before, during, and after ischemia.

METHODS

Changes in molecular mobility were studied in a rat model of global forebrain ischemia (n = 8, 20-minute occlusion, 120-minute reperfusion) with the use of diffusion-weighted localized proton MR spectroscopy. During ischemia and early reperfusion the time course of ADC changes was monitored by strongly diffusion-weighted spectra. ADC values of N-acetylaspartate, creatines, cholines, and myo-inositol were evaluated from series of differently diffusion-weighted spectra before ischemia, 90 minutes after reperfusion, and 60 minutes postmortem.

RESULTS

Parallel to a rise in diffusion-weighted water signal (133 +/- 20%), pertinent intensities of all brain metabolites increased during ischemia. Changes were most pronounced for myo-inositol (46 +/- 9%) and smallest for N-acetylaspartate (12 +/- 4%). During reperfusion water ADC values returned to basal values, whereas metabolite ADC values were decreased by 22% (after 40 minutes). Postmortem ADC values (after 60 minutes) were reduced by 46% for water and 38% for metabolites.

CONCLUSIONS

The present findings indicate that water ADC changes during ischemic stroke are accompanied by significant alterations in intracellular mobility in both neuronal and glial cell populations as reflected by N-acetylaspartate and myo-inositol, respectively. Altered metabolite ADC values during reperfusion are consistent with irreversible tissue damage in this model and offer new means to assess circulatory and metabolic compromise.

Correlation of early reduction in the apparent diffusion coefficient of water with blood flow reduction during middle cerebral artery occlusion in rats

To determine the relationship between reductions in the apparent diffusion coefficient of water (ADC) and in cerebral blood flow (CBF) during focal ischemia, we used diffusion-weighted magnetic resonance (D-MR) imaging and autoradiographic CBF analysis to examine rats subjected to 30 or 90 min of permanent middle cerebral artery (MCA) occlusion. In the 30-min occlusion group (n = 10), the area with substantially reduced ADC (15% or more below the contralateral level [ADC15]) corresponded best to the area with CBF below 25 ml/100 g/min and was significantly smaller than the area with CBF below 50 ml/100 g/min (CBF50), a level associated with reduced protein synthesis and delayed necrosis (40 +/- 13% versus 74 +/- 8% of the ischemic hemisphere; P < 0.0001). In the 90-min occlusion group (n = 6), the ADC15 area corresponded best to the CBF30 to CBF35 area and was again significantly smaller than the CBF50 area (54 +/- 13% versus 73 +/- 20%, P < 0.05). Thus, the area of substantially reduced ADC at 30 and 90 min represents only 53% and 74%, respectively, of the tissue at risk for infarction. These findings indicate a potential limitation in using early D-MR imaging to predict stroke outcome.

Correlation of rapid changes in the average water diffusion constant and the concentrations of lactate and ATP breakdown products during global ischemia in cat brain

Rapid changes in the average water diffusion constant, Dav = 1/3[Dxx+Dyy+Dzz], and in the concentrations of lactate and purine nucleotides and nucleosides were measured upon global ischemia (cardiac arrest) in cat brain, at a combined time resolution of 36 s (n = 7). At this time resolution, the normalized time curves of 1 - Dav and the increase in ATP breakdown product did not coincide, with the changes in Dav being most rapid. The normalized curves of 1 - Dav and the lactate increase coincided for the first 2-2.5 min after which the change in Dav was more rapid. After this time point, an excellent correlation was found between the drop in Dav and the decrease in energy utilization rate, which was calculated from the measured time curves of lactate formation and ATP breakdown, and from the time curve for phosphocreatine use reported in the literature. These results are in agreement with the expected biphasic changes in ion and water homeostasis during ischemia and with the model of diffusional changes being a consequence of a water shift from interstitial to intracellular space.

Optimized isotropic diffusion weighting

The authors introduce several sets of time-efficient gradient waveforms for applying isotropic diffusion weighting in NMR experiments. This creates signal attenuation that depends on the trace of the diffusion tensor and is therefore rotationally invariant. Numerical methods for the calculation of such gradient sets are outlined, and results are shown for isotropic and anisotropic gradient hardware and first order flow moment nulled diffusion weighting gradients. Preliminary experimental results from the human brain validate this new technique.

Analytical expressions for the NMR apparent diffusion coefficients in an anisotropic system and a simplified method for determining fiber orientation

NMR measurements of anisotropic diffusion were studied using a three-dimensional random-walk model. It was found that the apparent diffusion coefficient can be expressed in a canonical form as the product of a diagonal matrix, an orthonormal rotation matrix, and a vector representing the encoding magnetic field gradient. The diffusion coefficient can be interpreted as the sum of the corresponding coefficients measured along the principal diffusion axes, weighted by the squares of the directional cosines of the encoding direction with respect to the principal axes. The analysis revealed that determining the orientation of anisotropy, in a cylindrically symmetric system, requires a minimum of four diffusion measurements. A special pulse sequence which minimized gradient cross-terms and possible restricted diffusion effects was used to characterize diffusion anisotropy in cut chicken gizzards. Diffusion coefficients parallel to the muscle fibers were found to be approximately two to three times larger than those in the transverse direction. Furthermore, the method was successful in detecting the angular change when the sample was rotated by 30 degrees. Results indicate that the proposed approach to measure fiber orientation is valid and may be used to improve the time efficiency of diffusion anisotropy measurements.

Limitations of stimulated echo acquisition mode (STEAM) techniques in cardiac applications

Stimulated echoes are widely used for imaging functional tissue parameters such as diffusion coefficient, perfusion, and flow rates. They are potentially interesting for the assessment of various cardiac functions. However, severe limitations of the stimulated echo acquisition mode occur, which are related to the special dynamic properties of the beating heart and flowing blood. To the well-known signal decay due to longitudinal relaxation and through-plane motion between the preparation and the read-out period of the stimulated echoes, additional signal loss is often observed. As the prepared magnetization is fixed with respect to the tissue, this signal loss is caused by the tissue deformation during the cardiac cycle, which leads to a modification of the modulation frequency of the magnetization. These effects are theoretically derived and corroborated by phantom and in vivo experiments.

Navigated diffusion imaging of normal and ischemic human brain

The principal barrier to clinical application of diffusion-weighted MR imaging is the severe image degradation caused by patient motion. One way to compensate for motion effects is the use of a "navigator echo" phase correction scheme. In this work, a modification of this technique is introduced, in which the phase correction step is performed in the frequency domain (i.e., after the readout Fourier transform). This significantly improves the robustness of the navigator echo approach and, when combined with cardiac gating, allows diagnostic quality diffusion-weighted images of the brain to be routinely obtained on standard clinical scanner hardware. The technique was evaluated in phantom studies and in 23 humans (3 normal volunteers and 20 patients). Diffusion anisotropy and apparent diffusion coefficient maps were generated from the image data and showed decreased apparent diffusion in acute stroke lesions and, in several cases, increased apparent diffusion in chronic stroke lesions.

Theoretical model for water diffusion in tissues

Water diffusion in a tissue model is studied both analytically and numerically. Tissue is regarded as a periodic array of boxes surrounded by partially permeable membranes (cells), embedded in an extracellular medium. intracellular and extracellular diffusion coefficients may differ. Expressions for the apparent diffusion coefficients (ADC) in isotropic and nonisotropic tissues are derived and compared with Monte Carlo simulations. Calculated ADCs disagree with values obtained from the widely used "fast exchange" formula. Effects of differences between intracellular and extracellular T2 relaxation times on measured values of ADC and T2 are discussed. The general analysis is specifically applied to the changes occurring in ADC following ischemic insults to brain tissue. It is found that although membranes affect ADC significantly, the observed changes in diffusion cannot be due to reduced membrane permeabilities. They may result from the combined effect of changes in cellular volume fraction, extracellular and intracellular diffusion.

Barbiturate-reversible reduction of water diffusion coefficient in flurothyl-induced status epilepticus in rats

Rat brains (n = 17) with flurothyl-induced status epilepticus (SE) have been imaged with a gradient-echo diffusion-weighted imaging sequence at 2.0 T. The apparent water diffusion coefficient (ADC) decreased during seizure discharges. The magnitude of the ADC reduction correlated well with the duration of flurothyl exposure. A 17% reduction in the water ADC compared with preseizure condition was observed in rats with the longest flurothyl exposure time. In 13 rats, pentobarbital was used to arrest the electrographic seizure activity. ADC values began to return to normal a few minutes after the injection. In four rats with no pentobarbital administration, ADC values remained depressed up to 1 h after seizure onset. The results suggest that diffusion-weighted MR imaging may be useful for mapping recent intense seizure activity in human patients with medically intractable epilepsy.

Novel MR image contrast mechanisms in epilepsy

A range of magnetic resonance (MR) parameters are introduced, which can give rise to image contrast by using suitable pulse sequences, and that can be measured quantitatively. Their relationship to tissue pathology is given as far as possible. Techniques for their measurement, and results from multiple sclerosis, stroke, and epilepsy are given. The parameters are proton density, T1, T2, transverse magnetisation decay, which gives estimates of extracellular water and myelin concentrations, magnetisation transfer ratio and T1sat, and diffusion (including trace and anisotropy measured from the tensor matrix).

Diffusion weighting by the trace of the diffusion tensor within a single scan

The anisotropy of the water diffusion tensor inside brain causes contrast in diffusion images, which depends on the relative orientation of the diffusion gradients and the subject. Because the trace of a tensor is invariant upon rotation, measurement of this trace can reduce the orientation effect. A family of imaging pulse sequences is presented in which the signal intensity is weighted by the trace of the diffusion tensor in a single scan. The methods are demonstrated for chicken gizzard in several orientations with respect to the gradient frame of reference, and for ischemic injury in cat brain after middle cerebral artery occlusion. The sensitivity of the techniques to the presence of background gradients is measured and discussed in detail. As a result, pulse sequences are suggested that provide reliable diffusion constants in both homogeneous and inhomogeneous magnetic fields. The efficiency of the techniques for clinical application is also evaluated.

Rapid monitoring of changes in water diffusion coefficients during reversible ischemia in cat and rat brain

Changes in the diffusion constant of water during reversible brain ischemia and cardiac arrest were monitored with a 10-s time resolution. Results (five cats, three rats) indicate that these changes are reversible and that the bulk of the changes are not caused by temperature or motion related to brain pulsations and blood flow. The rapid time course of the changes corresponds to the known time course for changes in energy state, signal transduction, and ionic homeostasis.