Molecular diffusion, tissue microdynamics and microstructure

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

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

Hemodynamic effect of iodinated high-viscosity contrast medium in the rat kidney: a diffusion-weighted MRI feasibility study

RATIONALE AND OBJECTIVES

To assess the abilities of dynamic diffusion-weighted MRI to demonstrate the effects in vivo of a high-viscosity iodinated contrast agent on medullary and cortical blood flow in the rat kidney.

METHODS

Dynamic diffusion-weighted, echoplanar MR images obtained from five b-value single-shot acquisitions and their isotropic apparent diffusion coefficient maps were obtained from nine rats anesthetized by pentobarbital sedation, before and after intravenous injection of a high-viscosity, dimeric iso-osmolar iodinated contrast medium (iodixanol), and compared with those obtained from four control rats that received saline.

RESULTS

The mean baseline apparent diffusion coefficient values were 1.64 +/- 0.05 x 10(-3) mm2/s for the cortex and 1.75 +/- 0.06 x 10(-3) mm2/s for the medulla. In the iodixanol group, a significant decrease in renal diffusion was observed at 12 minutes and lasted at least until 24 minutes. The decrease in diffusion occurred earlier for the cortex and lasted less than for the medulla. There was no significant modification in diffusion over time in the control group.

CONCLUSIONS

This preliminary experience in rats shows that dynamic diffusion-weighted MRI can be used to study noninvasively the in vivo renal hemodynamic response after injection of iodinated contrast.

The effect of aging on the apparent diffusion coefficient of normal-appearing white matter

OBJECTIVE

The purpose of our study was to test the hypothesis that the apparent diffusion coefficient (ADC) of normal-appearing white matter increases with advancing age.

SUBJECTS AND METHODS

We selected 38 patients with normal MR imaging findings from 332 patients undergoing clinical MR imaging. Diffusion-weighted MR imaging was performed with diffusion gradients applied in three orthogonal directions. For each patient, the average ADC on trace-weighted diffusion images of white matter at prespecified regions of interest and at the thalamus were compared with the patient's age.

RESULTS

For the white matter, ADC sorted by patient age in decades increased with advancing age. Patients at least 60 years old had significantly higher ADC (0.769 +/- 0.019 mm(2)/sec x 10(-3)) than patients less than 60 years old (0.740 +/- 0.013 mm(2)/sec x 10(-3)) (p < 0.001). Comparison of individual white matter ADC and age showed a significant increase with advancing age (p < 0.0001). For the thalamus, the average ADC among patients at least 60 years old (0.766 +/- 0.015 mm(2)/sec x 10(-3)) exceeded the average ADC for patients less than 60 years old (0.745 +/- 0.022 mm(2)/sec x 10(-3)) (p < 0.05). However, comparison of individual thalamic ADC and patient ages, although showing a trend to higher ADC with increasing age, did not reach statistical significance (p = 0.06).

CONCLUSION

Advancing age is associated with a small but statistically significant increase of water diffusibility in human white matter. A similar trend was present in the thalamus. These increases may reflect mild structural changes associated with normal aging.

Metabolite and water apparent diffusion coefficients in the isolated rat heart: effects of ischemia

A decrease in the apparent diffusion coefficient (ADC) of water is important in the detection of acute brain disorders, yet it is unknown whether changes in myocardial ADCs hold similar potential. Consequently, in this study a STEAM pulse sequence was modified in order to measure the ADCs of water and the (1)H-NMR detectable metabolites, taurine (an inert marker) and creatine, during perfusion, ischemia, and reperfusion in the isolated rat heart. At the short diffusion time of 50 ms, myocardial ADCs were (1.06 +/- 0. 07) x 10(-3) mm(2)/s for water, (0.29 +/- 0.01) x 10(-3) mm(2)/s for taurine and (0.26 +/- 0.01) x 10(-3) mm(2)/s for creatine. Heart water and taurine ADCs remained constant during ischemia, yet the total creatine ADC increased by 35% owing to the hydrolysis of PCr to creatine. The average cardiomyocyte diameter, calculated from taurine ADC values measured at diffusion times between 50 ms and 1510 ms, was 40 microm in the perfused heart and 27 microm by the end of ischemia. It is concluded that the taurine ADC measured at short diffusion times does not reveal ischemic injury in the heart, but at long diffusion times may be used to calculate changes in myocyte diameter. Magn Reson Med 44:208-214, 2000.

The measurement of diffusion and perfusion in biological systems using magnetic resonance imaging

The aim of this review is to describe two recent developments in the use of magnetic resonance imaging (MRI) in the study of biological systems: diffusion and perfusion MRI. Diffusion MRI measures the molecular mobility of water in tissue, while perfusion MRI measures the rate at which blood is delivered to tissue. Therefore, both these techniques measure quantities which have direct physiological relevance. It is shown that diffusion in biological systems is a complex phenomenon, influenced directly by tissue microstructure, and that its measurement can provide a large amount of information about the organization of this structure in normal and diseased tissue. Perfusion reflects the delivery of essential nutrients to tissue, and so is directly related to its status. The concepts behind the techniques are explained, and the theoretical models that are used to convert MRI data to quantitative physical parameters are outlined. Examples of current applications of diffusion and perfusion MRI are given. In particular, the use of the techniques to study the pathophysiology of cerebral ischaemia/stroke is described. It is hoped that the biophysical insights provided by this approach will help to define the mechanisms of cell damage and allow evaluation of therapies aimed at reducing this damage.

In vivo gallbladder bile diffusion coefficient measurement by diffusion-weighted echo planar imaging in hamster fed normal and lithogenic diets

It is shown that in vivo measurement of bile water apparent diffusion coefficient (ADC) by diffusion-weighted echo-planar imaging (EPI) in hamster gallbladder is possible providing motion artifact-free ADC values. These ADC values are used to estimate bile viscosity variation induced by normal diets, cholesterol gallstone-inducing diets, and an antilithiasic drug, and to determine if a link exists between bile viscosity and cholesterol gallstone formation. Measurements were performed at 4.7 T with respiratory triggering in five groups of hamsters fed a commercial (RC) or a semisynthetic (SSD) diet, a SSD containing 0.2% hyodeoxycholic acid (SSD+HDC) and two lithogenic diets (LD5, LD10). ADC decreased significantly in LD10 (2.15+/-0.07x 10(-3) mm(2)s(-1)) and SSD+HDC (2.03+/-0.04) compared to RC (2.40+/-0.05) but not in the most lithogenic LD5 diet (2.33+/-0.06). No direct relationship was found between bile viscosity and gallstone incidence; however, viscosity seems to be related to lipid contents of diets. Magn Reson Med 43:854-859, 2000.

Measurement of cell density and necrotic fraction in human melanoma xenografts by diffusion weighted magnetic resonance imaging

The aim of this study was to investigate whether apparent diffusion coefficients (ADCs) could be used as measures of cell density and necrotic fraction of tumors. Tumors of four human melanoma xenograft lines were subjected to diffusion-weighted magnetic resonance imaging (DWI). ADCs were calculated from the images and related to cell density and necrotic fraction, as determined from histological sections. A significant correlation was found between the ADC of the viable tissue and cell density, regardless of whether tumors of different lines or different regions within individual tumors were considered. Necrosis was found in two of the lines. A single region of massive necrosis that could be differentiated from the viable tissue in ADC maps was found in one line, whereas a number of smaller necrotic regions that could not be identified in ADC maps were found in the other line. Tumor ADC was significantly correlated with the necrotic fraction of the former, but not of the latter line. Our results suggest that ADCs can be used as measures of cell density and necrotic fraction of some but not of all tumors, depending on whether the individual necrotic regions are large enough to be differentiated from the viable tissue with the obtained spatial resolution of the DW images. Magn Reson Med 43:828-836, 2000.

Assignment of the water slow-diffusing component in the central nervous system using q-space diffusion MRS: implications for fiber tract imaging

Diffusion-weighted NMR spectroscopy (MRS) was performed on isolated bovine optic nerve and rat brain (in vitro) to characterize the multiexponential water signal decay in diffusion experiments. q-Space analysis of the diffusion data was used to obtain structural information about the investigated neuronal tissues. This analysis provided displacement distribution profiles of the water in the sample. Two diffusing components were identified from these profiles, thus enabling us to obtain the following information about the slow decaying component: 1) displacement of this component is restricted to a diffusing distance of approximately 2 microm; 2) it has a longer T2 than the rapidly diffusing component; and 3) the population fraction of this component depends on the orientation of the nerve fiber. When the diffusion was measured perpendicular to the long axis of the bovine optic nerve, the weighting of this population was 41 +/- 2%, whereas parallel to the long axis of the nerve it was found to be 14 +/- 2%. In the randomly oriented brain tissue, the population of this component was only 7 +/- 3%. These observations led to the conclusion that the slow-decaying component originates mainly from restricted water diffusion in the neuronal fibers. In view of these findings, in vitro and in situ diffusion-weighted images with high b values (with long delta) were acquired to obtain highly detailed images of white matter fiber tracts in the central nervous system. These images provide detailed information on white matter fiber tract location and allow spinal cord maturation to be followed with high accuracy.

Maps of self-diffusion coefficients by radiofrequency field gradient NMR microscopy

The methods of measurement of spatially resolved diffusion coefficients using radiofrequency field gradient (E. Mischler et al., J. Magn. Reson. B 106, 32, 1995; R. Kimmich et al., J. Magn. Reson. A 112, 7, 1995) produce 1D profiles whose amplitude is not only a function of the local self-diffusion coefficient but also is modulated by cosine functions of spatial coordinates. Due to this modulation diffusion-weighted images cannot be obtained unless cumbersome data processing is used. Here, we present a new sequence which avoids this modulation and yields in a straightforward manner true self-diffusion coefficient maps; this is in contrast with conventional methods which use static field gradients and which are therefore altered by background gradients. The feasibility and the reliability of the method are demonstrated with phantoms; it is also applied to different systems of interest such as solvent swelled rubber, membranes, and plants. Copyright 1999 Academic Press.

Structural information in neuronal tissue as revealed by q-space diffusion NMR spectroscopy of metabolites in bovine optic nerve

1H NMR diffusion experiments performed on the signal of the metabolites in bovine optic nerve showed that the signal decay due to diffusion is bi-exponential with a slow and a fast diffusing component. Diffusion was measured as a function of the diffusion time, and the data were analyzed as a function of b and q values. Bi-exponential fit was used to analyze the data, and the results were compared with the displacement distribution profiles obtained from the q-space analysis of the data. This q-space analysis showed that the fast diffusing component has a broad displacement distribution and appears not to be restricted. On the other hand, the slow diffusing component appears to be highly restricted to milieu in the order of 1-2 microm. The orientation of the sample with respect to the axis for which diffusion was measured affected mainly the relative sizes of the populations of each component, but had only a small effect on the extracted apparent diffusion coefficients. These results from both the b and the q value analyses suggest that the slow diffusing component is related to restricted diffusion of these metabolites in the axonal fibers, while the fast diffusing component represents diffusion of metabolites in cells and along the long axis of the nerve fibers. It is concluded that q-space analysis of metabolite diffusion enables extraction of structural information about the sample, and that the diffusion of the metabolites in optic nerve is dictated mainly by the cellular medium and microstructure of the tissue.

Anisotropic and restricted diffusion of water in the sciatic nerve: A (2)H double-quantum-filtered NMR study

The signals of water in the different compartments of rat sciatic nerve are resolved in the (2)H double-quantum-filtered NMR spectrum, due to their different quadrupolar splittings and relaxation rates. This resolution allowed the independent measurement of the water diffusion coefficients in the different compartments. The water diffusion in all three compartments, the endoneurium, the epineurium and the axon was found to be anisotropic. Parallel to the nerve fiber the average intraxonal water diffusion coefficient was 1.11 x 10(-5) cm(2)/sec, while in the perpendicular direction the diffusion is heavily restricted. The average perpendicular diffusion coefficient ranged from 0.29 x 10(-5) cm(2)/sec to 0.05 x 10(-5) cm(2)/sec for diffusion times of 7 msec and 50 msec, respectively. Assuming restricted diffusion in nonpermeable cylinders, intra-axonal mean diameters of 6.0, 7.4 and 9.0 microm were obtained for nerves taken from three different rats. Magn Reson Med 42:461-466, 1999.

Molecular aspects of magnetic resonance imaging and spectroscopy

Magnetic resonance imaging (MRI) is a well known diagnostic tool in radiology that produces unsurpassed images of the human body, in particular of soft tissue. However, the medical community is often not aware that MRI is an important yet limited segment of magnetic resonance (MR) or nuclear magnetic resonance (NMR) as this method is called in basic science. The tremendous morphological information of MR images sometimes conceal the fact that MR signals in general contain much more information, especially on processes on the molecular level. NMR is successfully used in physics, chemistry, and biology to explore and characterize chemical reactions, molecular conformations, biochemical pathways, solid state material, and many other applications that elucidate invisible characteristics of matter and tissue. In medical applications, knowledge of the molecular background of MRI and in particular MR spectroscopy (MRS) is an inevitable basis to understand molecular phenomenon leading to macroscopic effects visible in diagnostic images or spectra. This review shall provide the necessary background to comprehend molecular aspects of magnetic resonance applications in medicine. An introduction into the physical basics aims at an understanding of some of the molecular mechanisms without extended mathematical treatment. The MR typical terminology is explained such that reading of original MR publications could be facilitated for non-MR experts. Applications in MRI and MRS are intended to illustrate the consequences of molecular effects on images and spectra.

An echo-shifted gradient-echo MRI method for efficient diffusion weighting

A segmented magnetic resonance imaging (MRI) method is introduced with time-efficient diffusion weighting resulting in total imaging times similar to those of single-shot methods. The approach is based on the principles of echo shifting with a train of observations (PRESTO) MRI sequence. The time efficiency of the sequence is based on the use of diffusion gradient pulses that also serve to shift the echo train to the next TR period, resulting in TE > TR. Each diffusion gradient is therefore used twice, for dephasing one set of spins as well as rephasing a second set of spins. Diffusion weighting and acquisition are thus achieved simultaneously. The sequence is validated in vitro and in vivo on rat kidney.

Assessment of induced rat mammary tumour response to chemotherapy using the apparent diffusion coefficient of tissue water as determined by diffusion-weighted 1H-NMR spectroscopy in vivo

Chemosensitivity of N-methyl-N-nitrosourea-induced rat mammary tumours treated with 5-fluorouracil at a dose of 100 mg kg(-1) i.p. was assessed by using diffusion-weighted 1H-MRS to measure the average diffusion coefficient (ADC) of water in the tumour tissue. ADC measurements prior to any therapy correlated positively with necrotic fraction. Tumours with low initial ADC (< 0.95 x 10(9) m2 s(-1)) showed an increase in ADC 7 days after treatment, whereas tumours with a high initial ADC (> 1.2 x 10(9) m2 s(-1)) showed a decrease. All tumours decreased significantly in volume (P < 0.05) 2, 5 and 7 days after treatment. At day 7 post-treatment, tumours with a high pre-treatment ADC started to regrow. The initial ADC value, as well as changes after treatment predict tumour chemosensitivity, which could be clinically relevant.

Correlations between the apparent diffusion coefficient, water content, and ultrastructure after induction of vasogenic brain edema in cats

OBJECT

The authors examined the correlation between changes in the apparent diffusion coefficient, regional water content, and tissue ultrastructure after vasogenic brain edema.

METHODS

Vasogenic edema was induced in the white matter of six cats by cortical cold lesioning. The trace of diffusion tensor (Trace[D]) obtained from magnetic resonance imaging to measure the orientationally averaged water diffusibility was compared with the corresponding tissue water content determined by gravimetric studies and with ultrastructural water localization. Edema fluid had spread to the subcortical and deep white matter by 4.5 hours postlesioning. The increase in Trace(D) showed a significant linear correlation with the increase in tissue water content, both in the subcortical and deep white matter as follows: y = 45.5x - 2367 (r = 0.94) and y = 37.0x - 1769 (r = 0.93), respectively, where x is the water content (gram water/gram tissue) and y the Trace(D) (x 10(-6) mm2/second). On histological examination, nerve fibers were found to be dissociated in the white matter and the extracellular space was markedly enlarged with protein-rich fluid. No noticeable hydropic swelling of the cellular components was observed.

CONCLUSIONS

A linear correlation was observed between increases in Trace(D) and increases in extracellular water volume in in vivo vasogenic brain edema. A similar correlation between the subcortical and deep white matter showing different arrangements of nerve fibers (parallel compared with intermingled, respectively) indicated that measurement of Trace(D) is a suitable parameter for the evaluation of vasogenic brain edema.

Imaging the pyramidal tract in patients with brain tumors

The clinical usefulness of diffusion-weighted magnetic resonance imaging (DWI) of the pyramidal tract was evaluated in patients with brain tumors. Five normal volunteers and seven patients with glioma (n = 4) or meningioma (n = 3) near the pyramidal tract underwent coronal echo planar DWI. Greyscale DWIs in each of the three orthogonal diffusion gradients were transformed into graduations, color-coded as red, green or blue, respectively, and then composited to form a combined color image. The entire pyramidal tract was visualized on a single fiber mapping image by combining the upper half of the image slice including the primary motor cortex, the corona radiata and the internal capsule with the lower half of the image slice including the internal capsule, the cerebral peduncle and the ventral brain stem. Fiber mapping images demonstrated the pyramidal tract as a distinct band indicating nerve fiber integrity in all volunteers. The entire pyramidal tract from the primary motor subcortex to the ventral brain stem could be traced. Fiber mapping images showed the ipsilateral pyramidal tract as either discontinuous due to impaired anisotropy or compressed due to mass effect in patients with brain tumors. These findings corresponded well with the pre- and postoperative motor functions. Fiber mapping images are useful for evaluating the white matter neuronal tracts and can provide indications for determining surgical strategy.

Molecular crowding and viscosity as determinants of translational diffusion of metabolites in subcellular organelles

The role of molecular crowding and viscosity on the apparent translational diffusion coefficient (ADC) of small metabolites was investigated in different subcellular organelles using the pulse-field gradient spin-echo 1H NMR technique. ADCs of metabolites with increasing radius of gyration (0.7 A < RG < 4.5 A) were measured in the cytoplasm of rat or chicken erythrocytes, in the nucleus of chicken erythrocytes, and in isolated rat liver mitochondria. Metabolite ADCs in these systems were compared with the corresponding ADCs determined in model solutions of increasing bulk viscosity but different molecular crowding. For solutions having the same viscosity, metabolite ADCs decreased with increasing concentration of cosolutes. This effect is adequately described by the modified Stokes-Einstein relationship, ADC = k/RG (1 + 2.5Phi), where k is a constant for a given temperature and Phi is an obstruction factor reporting the fractional volume of solution occupied by cosolutes, a measure of the molecular crowding in the solution. Cytoplasmic values of Phi for metabolites of different sizes did not depend exclusively on metabolite RG but on additional factors including the chemical nature of the metabolite, the presence of diffusional barriers, and metabolite-specific binding sites. In the case of water, nuclear Phi values approached those of the extracellular space while mitochondrial Phi values were significantly higher than those of the cytoplasm. Taken together, these results reveal important differences in molecular crowding within the different subcellular compartments, suggesting considerable diffusional heterogeneity for small metabolites within the different intracellular organelles.

Towards a microMRI atlas of mouse development

This study investigates the potential of microscopic Magnetic Resonance Imaging to obtain information for 3D digital atlases of mouse development using fixed samples. Fixed samples allow direct comparison with already published atlases and provide a testing ground for future in vivo efforts. 3D MR images of mouse embryos (dpc 6.5-16) illustrate that the necessary contrast and level of detail is available with this technique. Diffusion weighted imaging, diffusion tensor imaging, and multi-valued data sets are presented as examples of uniquely MR methods of obtaining anatomical information. MRI is performed non-invasively on the intact sample, leaving open the possibility of other manipulations (e.g. classical histology, immunohistochemistry, in situ hybridization, and in vitro growth for unfixed samples) after conducting the MRI experiment.

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

The "concept of restricted intracellular water diffusion at permeable boundaries", which was recently used to model diffusion-weighted 1H NMR experiments on glioma cells, was applied to measurements on the rat brain in vivo. Combined with the "concept of extracellular tortuosity", various physiological states of the brain were simulated. Hereby, a variable intracellular volume fraction, intracellular exchange time, and extracellular tortuosity factor were considered for young, adult, and ischemic rat brains. The model simulated the cytotoxic shift of extracellular water, changes in membrane permeability and tissue morphology, and was able to explain the diffusion time dependence as well as the non-monoexponentiality of the diffusion attenuation curves. Preliminary diffusion time dependent experiments on the healthy rat brain (1H NMR imaging) agreed well with the theoretical concept. Hereby, the intracellular water signal was separated from extracellular signal contributions by large diffusion weighting. It showed the characteristic of restricted diffusion as well as a signal decay due to the exchange of intracellular water across the plasma membrane. A map of the mean intracellular exchange time for water in living animal brain was determined, and the upper limit in rat brain was evaluated to 15 ms. The presented methods can be applied to correlate local differences in a map of exchange times with tissue morphology and to detect pathological deviations of the exchange time, e.g., during ischemia.

Diffusion MR imaging during acute subarachnoid hemorrhage in rats

BACKGROUND AND PURPOSE

We analyzed the temporal and spatial pattern of water diffusion changes during acute subarachnoid hemorrhage (SAH) in rat brain to identify factors contributing to the acute pathophysiology of SAH.

METHODS

Subarachnoid hemorrhage was remotely induced via perforation of the circle of Willis with an endovascular suture during MR imaging. A fast echo-planar imaging technique was used to acquire 60 maps of the apparent diffusion coefficient (ADC) beginning 1 min before and continuing for 11 min after induction of SAH. A high-resolution spin-echo diffusion sequence was used to follow diffusion changes over 6 h after SAH. Sham-operated control (n=3), nonheparinized (n=6), and heparinized (n=5) groups were studied.

RESULTS

Sham-operated control animals did not show ADC changes over time. In both SAH groups, however, a sharp decline of ADC within 2 min of SAH was consistently observed in the ipsilateral somatosensory cortex. These decreases in diffusion then spread within minutes over the ipsilateral hemisphere. Similar ADC decreases on the contralateral side started with a further time delay of 1 to 3 min. From 30 min onward, the extent of the diffusion abnormality decreased progressively in the nonheparinized animals. No recovery was observed in heparinized rats.

CONCLUSIONS

MR diffusion imaging allows new insight into the pathophysiology of acute SAH: The spatial and temporal pattern of diffusion changes suggests the initial occurrence of acute vasospasm and subsequently "spreading depolarization" of brain tissue. Persistent hemorrhage in heparinized animals was reflected by early decline of ADC values throughout the entire brain.

Signal losses in diffusion preparation: comparison between spin-echo, stimulated echo and SEASON

Diffusion-weighted magnetic resonance imaging and spectroscopy commonly apply a spin-echo or stimulated echo preparation including sensitizing field gradients. The article reports on a systematic numerical approach to an optimum diffusion preparation considering undesired signal losses caused by relaxation. A large range of possible applications on whole-body units and animal scanners is covered. Instructions for an optimized type and timing of the diffusion preparation are provided for the readership, based on the desired diffusion weighting (b-value), the available maximum field gradient amplitudes, the RF pulse durations and gradient ramp times, and the relaxation characteristics of the specimen (or tissue) of interest. In addition, a new type of diffusion preparation named SEASON (simultaneous Spin-Echo And Stimulated echO preparatioN) is introduced and compared with spin-echo and stimulated echo diffusion preparation. It is demonstrated that spin-echo preparation is superior to stimulated echo preparation in all cases with T2 approximately T1 and in all cases with relatively low diffusion weighting resulting in short duration of diffusion sensitizing gradients delta << T2. For tissues with T2 << T1 (as musculature or red bone marrow) stimulated echo preparation becomes superior to spin-echo preparation for high ratios b/A2 (h-value indicates diffusion weighting, A is the maximum gradient amplitude). The new SEASON technique allows a higher yield in signal intensity compared to spin-echo or stimulated echo preparations in clinically relevant cases.

Dependence of apparent diffusion coefficients on axonal spacing, membrane permeability, and diffusion time in spinal cord white matter

We used a numerical simulation of water self-diffusion among permeable cylinders to predict the dependence of MR-based apparent diffusion coefficients in white matter on axonal separation, barrier permeability, and diffusion time (T). The transverse apparent diffusion coefficient (tADC), calculated with simulated diffusion-sensitizing gradients perpendicular to the axon fibers, remains a function of T down to diffusion times as short as .1 microsec for a range of diffusion barrier permeability. As the diffusion time lengthens, the response of tADC depends on axon diameter, with decreases in tADC occurring earliest, and most dramatically, for the smallest fiber diameter simulated (2 microm). For a given axonal separation, asymptotic values of ADC are determined by permeability alone and are the same for 2-microm and 11-microm fibers of equal membrane permeability. The effect of increased relative intracellular volume is manifested primarily in a decrease in tADC at short T. Increases in interaxonal spacing increase the tADC at asymptotically long diffusion times and reduce the dependence on permeability. However, at the widest plausible axonal separations, permeability remains an important determinant of tADC. These simulations may enhance interpretation of measured tADC in the context of the underlying physiologic and structural changes at the cellular level that accompany white-matter disease.

In vivo and in vitro bi-exponential diffusion of N-acetyl aspartate (NAA) in rat brain: a potential structural probe?

Diffusion measurements were performed on the N-acetyl aspartate (NAA) signal in in situ brains (in vivo and post-mortem) and on in vitro brain tissue at 37 degrees C using wide ranges of b-values (from 0 up to 4.5 x 10(6) s/cm2 and 35.8 x 10(6) s/cm2 for the in vivo and the in vitro cases, respectively). In vivo and in vitro NAA signals attenuation due to diffusion was measured at fixed diffusion times (tD). In the in vitro cases the effect of tD on the apparent diffusion coefficients (ADCs) of NAA was evaluated. From these experiments the following observations and conclusions were made: (1) NAA signal attenuation both in vivo and in vitro is not mono-exponential and could be fitted by bi-exponential fitting function; (2) analysis of the low b-value range only (up to 0.5 x 10(6) s/cm2) gives a mono-exponential decay (r = 0.999); (3) in both cases the obtained ADCs are sensitive to the diffusion time; (4) the ADCs of the pre- and post-mortem cases are nearly similar; (5) the ADCs obtained from the bi-exponential fitting function decrease when the diffusion time increases; and (6) both the fast and the slow diffusing components of NAA show a considerable restriction by what seems to be a non-permeable barrier from which two compartments were identified, one having a size of 6-8 microns and the other of approximately 1-2 microns in size. It seems conceivable that the two populations identified in the diffusion experiments represent primarily the NAA in the cell body (soma) and in the neurital space (axons and proximal dendrites).

Non-mono-exponential attenuation of water and N-acetyl aspartate signals due to diffusion in brain tissue

Diffusion measurements were performed on water and N-acetyl aspartate (NAA) molecules in excised brain tissue using a wide range of b-values (up to 28.3 x 10(6) and 35.8 x 10(6) s cm-2 for water and NAA, respectively). The attenuation of the signals of water and NAA due to diffusion was measured at fixed diffusion times (tD). These measurements, in which the echo time (TE) was set to 70 ms, were repeated for several diffusion times ranging from 35 to 305 ms. Signal attenuations were fitted to mono-, bi-, and triexponential functions to obtain the apparent diffusion coefficients (ADCs) of these molecules at each diffusion time. From these experiments the following observations and conclusions were made: (1) Signal attenuation of water and NAA due to diffusion over the entire range of b values examined is not monoexponential and the extracted ADCs depend on the diffusion time; (2) In the case of water the experimental data are best fitted by a triexponential function, while for b values up to 1 x 10(6) s cm-2, a biexponential function seems to reproduce the experimental data as well as the triexponential function; (3) If only the low range of b values are fitted (up to 0.5 x 10(6) s cm-2) signal attenuation of water is monoexponential and insensitive to tD; (4) Water ADCs decreased with the increase in tD but the relative population of the fast diffusing component increases such that at a tD of 305 ms there is nearly a single population; (5) The major fast diffusion component of the water shows only very limited restriction; (6) NAA signal attenuation is biexponential and analysis of the low b-value range gives only monoexponential decay, but the obtained ADC is sensitive to the diffusion time; (7) The ADCs obtained from fitting the data with a biexponential function decrease as diffusion time increases; (8) The relative population of the slow-diffusing component decreases with increasing tD; (9) Both the fast and the slow diffusing components of NAA show a considerable restriction by what seems to be a nonpermeable barrier from which two compartments, one of 7-8 micron and one of approximately 1 micron, were calculated using the Einstein equation. It is suggested that the two compartments represent the NAA in cell bodies and in the intra-axonal space. The effect of the range of the b value used in the diffusion experiments on the results is discussed and used to reconcile some of the apparent discrepancies obtained in different experiments concerning water diffusion in brain tissue. The potential of NAA diffusion experiments to probe cellular structure is discussed.

Restricted diffusion and exchange of intracellular water: theoretical modelling and diffusion time dependence of 1H NMR measurements on perfused glial cells

Intracellular diffusion properties of water in F98 glioma cells immobilized in basement membrane gel threads, are investigated with a pulsed-field-gradient spin-echo NMR technique at diffusion times from 6 to 2000 ms and at different temperatures. In extended model calculations the concept of 'restricted intracellular diffusion at permeable boundaries' is described by a combined Tanner-Kärger formula. Signal components in a series of ct experiments (constant diffusion time) are separated due to different diffusion properties (Gaussian and restricted diffusion), and physiological as well as morphological cell parameters are extracted from the experimental data. The intracellular apparent diffusion coefficients strongly depend on the diffusion time and are up to two orders of magnitude smaller than the self diffusion constant of water. Propagation lengths are found to be in the range of 4-7 microns. Hereby intracellular signals of compartments with a characteristic diameter could be selected by an appropriate gradient strength. With cg experiments (constant gradient) a mean intracellular residence time for water is determined to be about 50 ms, and the intrinsic intracellular diffusion constant is estimated to 1 x 10(-3)mm2/s. Studying the water diffusion in glial cells provides basic understanding of the intracellular situation in brain tissue and may elucidate possible influences on the changes in the diffusion contrast during ischemic conditions.

NMR "diffusion-diffraction" of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics

"Diffusion-diffraction" experiments on water, yielding "q-space" plots, were conducted on suspensions of oxygenated (diamagnetic) human erythrocytes. (i) These suspensions displayed diffusion-diffraction of water; (ii) the shape of the q-space plots depended on the direction along which the diffusion was measured, thus implying alignment of the cells in the magnetic field of the NMR spectrometer; (iii) the diffusion anisotropy was altered in a predictable way by converting the hemoglobin to a paramagnetic form; (iv) the shapes of the q-space plots were altered in a predictable way by inhibiting water transport; (v) the pseudo-first order rate constant characterizing the covalent inhibition of water transport, by p-chloromercuribenzenesulfonate (p-CMBS), was measured; and (vi) the cell diameter and intercellular spacing were measured from the positions of the interference minima and maxima in the q-space plots. The relevance of these findings to NMR-based histological characterization of tissues, and the implications, for magnetic resonance imaging (MRI), of erythrocyte alignment in the small vessels of the brain in particular, are noted.