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PubMed1997

Heterogeneous and anisotropic diffusion in the developing rat spinal cord.

Extrasynaptic transmission is mediated by the diffusion of transmitters, through the extracellular space (ECS) to receptors on neurons and glia. The three-dimensional diffusion of tetramethylammonium (mol. wt 74.1 kDa) was investigated in the isolated rat spinal cord at postnatal days 4-20. The diffusion parameters of the ECS, volume fraction alpha, tortuosity lambda (lambda2 = free/apparent diffusion coefficient in tissue) and nonspecific uptake k', were different in gray and white matter. In both gray and white matter, alpha decreased with neuronal development and gliogenesis by about 15% while lambda significantly increased. Diffusion in gray matter remained isotropic (lambda = 1.65), while in white matter it became anisotropic, i.e. easier along the fibers (lambda = 1.38) than across the fibers (lambda = 1.80). Anisotropy increased in the second postnatal week, during pronounced myelination. In myelinated tissue, preferential diffusion of neuroactive substances occurs along the axons.

Aging↗

PubMed2002

Diffusion tensor in posterior cingulate gyrus: correlation with cognitive decline in Alzheimer's disease.

To determine whether the diffusion abnormalities in brains with Alzheimer's disease (AD) correlate with disease severity, we studied 34 AD patients using diffusion tensor MRI. Mean diffusivity and fractional anisotropy (FA) as well as three eigenvalues (lambda1, lambda2, and lambda3) of the diffusion tensor of the posterior cingulate white matter correlated with the Mini-Mental State Examination (MMSE) score. The mean diffusivity and the three eigenvalues showed significant correlation with the MMSE score. On the other hand, no significant correlation was seen between the FA and MMSE score. Our results suggested that mean diffusivity and the eigen-values, but not FA, reflect progression of AD-related histopathlogical changes in the posterior cingulate white matter and may be useful biological indices to monitor AD.

Aged↗

PubMed1983

A time-dependent method for characterizing the diffusion of 222Rn in concrete.

The porosity and diffusion length of concrete have been determined by measuring the time-dependent diffusion of radon through a thin slab of the material. One surface of the slab is exposed to a large, fixed radon concentration beginning at t = 0. The radon that diffuses out of a portion of the opposite surface is collected during several contiguous time intervals. The total activity collected over a set of intervals beginning at t = 0 and the steady-state flux of activity are used to calculate the porosity and diffusion length. As a test of these parameters, they are then used to predict the activity collected during other time intervals and for other sample thicknesses. Samples from two types of concrete were tested: one type yielded a porosity of 0.068 and a diffusion length of 12.6 cm; the respective values for the other were 0.32 and 16.9 cm. The predicted and experimental results agreed well, thereby verifying the assumption that concrete may be treated as a homogenous diffusion medium for radon.

Construction Materials↗

PubMed1987

Determining 222Rn diffusion lengths in soils and sediments.

Radon-222 diffusion length has been measured for 28 Danish soils and sediments. Samples were placed in a diffusion column connected to a 222Rn reservoir and the transport of 222Rn through the column was measured. The diffusion length was found by comparing the measured data to time-dependent diffusion theory. Dry silt, sand and gravel materials showed diffusion lengths from 160 cm to 190 cm. For wet clay materials, diffusion lengths of about 1 cm were found.

Denmark↗

PubMedDate not supplied

MR diffusion imaging of the human brain.

Magnetic resonance diffusion imaging reflects the water mobility at each point in a tomographic image. We have studied brain water diffusion in 18 normal volunteers to identify the different factors that can influence diffusion measurements in vivo. Our results show that both the measurement accuracy and the measured diffusion coefficient strongly depend on the experimental parameters, in particular, echo and diffusion time, cardiac gating, and diffusion encoding gradient direction.

Body Water↗

PubMedDate not supplied

Canavan disease: diffusion magnetic resonance imaging findings.

A 15-month-old boy with Canavan disease is reported in whom a restricted diffusion pattern on diffusion magnetic resonance imaging (MRI) (high signal on b = 1,000 mm2/s images and low apparent diffusion coefficient [ADC] values) was evident in the affected regions of the brain, including the peripheral white matter, globi pallidi, thalami, brainstem, dorsal pons, and dentate nuclei. The ADC values at these regions ranged from 0.42 to 0.56 x 10(-3) mm2/s compared with the normal ADC values from the uninvolved deep frontal white matter (0.68-0.92 x 10(-3) mm2/s). The known histopathologic features in Canavan disease include edematous and gelatinous brain tissue associated with diffuse vacuolization. Considering these and the diffusion MRI findings in this patient, it is likely that existence of a gel (gelatinous) state rather than the usual sol state of water molecules in the affected brain regions accounted for the restricted diffusion pattern in Canavan disease.

Brain↗

PubMed1991

Transport of beta-blockers and calcium antagonists by diffusion in cat myocardium.

Beta-blockers and calcium antagonists have been claimed to possess cardioprotective properties. This study addresses the question of whether a significant amount of these drugs will reach the cardiac myocytes during no-flow ischemia, where solute transport depends solely on diffusion. In anesthetized cats the hearts were excised. Apparent diffusion coefficients in cat myocardium at 37 degrees C (D'37) for 14C-verapamil (protein bound), 3H-metoprolol (lipophilic), 3H-atenolol (hydrophilic), and 3H-propranolol (lipophilic and protein bound) were determined by means of a "true transient diffusion" method and compared with the free diffusion coefficients in water (D37). D'37 of 14C-verapamil, 3H-metoprolol, 3H-atenolol, and 3H-propranolol (in cm2 s-1 10(5)) were (mean +/- SEM) 0.025 +/- 0.002, 0.055 +/- 0.003, 0.041 +/- 0.007, and 0.025 +/- 0.002, respectively. The mean diffusive progression of the concentration profile of 3H-metoprolol and 3H-atenolol into the tissue during 20 min was calculated to be 0.36 and 0.31 mm, respectively. The protein binding of 14C-verapamil and 3H-propranolol caused a significant fall in the progression to 0.24 mm for both drugs. These results indicate that, by diffusion, these drugs traverse the tissue too slowly to reach a significant amount of myocardium before myocyte necrosis occurs during conditions of noflow. Cardioprotective drugs are probably most effective, provided sufficient amounts are present in the tissue prior to the ischemic episode or sufficient supply via collateral blood flow is achieved.

Adrenergic beta-Antagonists↗

PubMed2002

Retro-odontoid pseudotumor in diffuse idiopathic skeletal hyperostosis.

STUDY DESIGN: A rare case of retro-odontoid pseudotumor combined with diffuse idiopathic skeletal hyperostosis is presented. OBJECTIVE: To discuss the pathomechanism of retro-odontoid pseudotumor in diffuse idiopathic skeletal hyperostosis. SUMMARY OF BACKGROUND DATA: Reports describing craniovertebral manifestations of diffuse idiopathic skeletal hyperostosis are quite rare. Only two cases of an atlantoaxial subluxation and one case of an odontoid fracture have been reported. Myelopathy resulting from retro-odontoid pseudotumor combined with diffuse idiopathic skeletal hyperostosis has not been reported previously. METHODS: A 74-year-old man presented with spastic tetraparesis caused by a retro-odontoid pseudotumor combined with diffuse idiopathic skeletal hyperostosis. Transoral removal of the extradural mass combined with a dorsal atlantoaxial fusion was performed using a titanium frame with sublaminar cable wiring. RESULTS: Yellowish amorphous material extruded from between the odontoid process and the arch of C1 when the anterior capsule had been incised. The retro-odontoid mass was very firmly attached to the hypertrophied ligaments. The mass therefore had to be sharply dissected away to expose the dura. The histologic appearance of the mass consisted of poorly cell-degenerated ligament, fibrocartilage, and fibrin. There was a focal proliferation of small vessels, but no significant inflammatory component and no evidence of neoplasia. The ligaments appeared fibrillated, disintegrated, and fragmented. After surgery, the patient's neurologic function improved. CONCLUSIONS: This is the first reported case of a retro-odontoid pseudotumor combined with diffuse idiopathic skeletal hyperostosis. The secondary transfer of mechanical stress to the atlantoaxial segment was presented as a pathomechanism underlying the formation of this retro-odontoid pseudotumor.

Aged↗

PubMed2006

Osteosarcoma: preliminary results of in vivo assessment of tumor necrosis after chemotherapy with diffusion- and perfusion-weighted magnetic resonance imaging.

PURPOSE: We sought to evaluate diffusion and perfusion weighted 1.5 T magnetic resonance imaging (MRI) in detecting tumor necrosis with histologic correlation after preoperative chemotherapy. MATERIALS AND METHODS: Eight patients (ages 11-19 years) with histologic proven osteosarcoma of the limbs underwent T1- and fat-suppressed T2-weighted spin echo and diffusion-weighted EPI sequences (b value = 700) after 5 cycles of standard chemotherapy. Tumor volume and apparent diffusion coefficients (ADC) were calculated. Tumor signal intensities were measured in dynamic contrast enhanced T1-weighted fast gradient echo-sequences obtained every 3 seconds after an intravenous injection of gadolinium-DTPA. Perfusion parameters of first-pass tracing of contrast medium (time-to-peak, slope of contrast enhancement curve) were calculated, and perfusion maps were established. After MRI, all patients underwent limb resection, and the specimens were investigated macroscopically and histologically. The degree of tumor necrosis was assessed using the histologic Salzer-Kuntschik classification (grades 1-6) after chemotherapy. RESULTS: Necrotic areas, which were confirmed by macroscopic/histologic examination, showed ADC values up to 2.7 (mean, 2.3 +/- 0.2). Viable tumor areas revealed lower apparent diffusion coefficients (mean, 0.8 +/- 0.3). The differences in ADC between viable and necrotic tumor were highly significant (paired t test; P = 0.01). Slopes of necrotic areas ranged from 0.1 up to 5.2%/min (mean, 1.5%/min) and those of viable tumor areas from 2.8 to 31.5%/min (mean, 16.1%/min). The time-to-peak-values (TTPs) ranged from 40 to 210 seconds (mean, 131 seconds, SD 60 seconds) in necrotic tumors and from 30 to 96 seconds (mean, 55 seconds, SD 21) in viable areas of sarcomas. The differences in slope and TTP between viable and necrotic tumor were highly significant. In necrotic areas, the linear correlation between slope (%/min) and ADC (mm/s) and between TTP (s) and ADC were weak, respectively. CONCLUSION: Both dynamic contrast-enhanced MRI and diffusion-weighted MRI permit recognition of tumor necrosis induced by chemotherapy in osteosarcomas. We hypothesized that diffusion-weighted imaging is correlated directly with tumor necrosis. Perfusion-weighted imaging is correlated with microvessel density, vascular permeability, local blood volume, and flow. Therefore, perfusion weighed MRI depicts areas of tumor cell necrosis indirectly.

Adolescent↗

PubMed1999

Diffusion through agar blocks of finite dimensions: a theoretical analysis of three systems of practical significance in microbiology.

A number of experimental methods in biology depend on the kinetics of diffusion of a substance through a gel. This paper reviews the diffusion equations, gives the experimental limitations for some useful cases, and presents computer simulations for cases that cannot be treated analytically. While double diffusion is not considered, three single-diffusion situations are treated. (1) Systems for the study of chemotaxis in the gliding bacterium Myxococcus xanthus. Experimental designs used for this in many cases in the literature were inappropriate and mathematical analysis of these is presented. (2) The development of gradient plates. The time necessary for vertical diffusion to become substantially complete and before diffusion in the direction of the original slant has proceeded significantly is calculated. (3) The application to antimicrobial disk susceptibility tests. The basis of the measurement of antibiotic sensitivities with disks containing antimicrobial agents, as routinely used in clinical microbiological and testing laboratories, is analysed and the limitations are assessed and improvements suggested.

Agar↗

PubMed2006

Diffusion-weighted magnetic resonance imaging and its application to cancer.

Diffusion-weighted magnetic resonance imaging (DW-MRI) provides image contrast through measurement of the diffusion properties of water within tissues. Application of diffusion sensitising gradients to the MR pulse sequence allows water molecular displacement over distances of 1-20 microm to be recognised. Diffusion can be predominantly unidirectional (anisotropic) or not (isotropic). Combining images obtained with different amounts of diffusion weighting provides an apparent diffusion coefficient (ADC) map. In cancer imaging DW-MRI has been used to distinguish brain tumours from peritumoural oedema. It is also increasingly exploited to differentiate benign and malignant lesions in liver, breast and prostate where increased cellularity of malignant lesions restricts water motion in a reduced extracellular space. It is proving valuable in monitoring treatment where changes due to cell swelling and apoptosis are measurable as changes in ADC at an earlier stage than subsequent conventional radiological response indicators.

Brain Neoplasms↗

PubMed2005

Breather-induced anomalous charge diffusion.

We present results on the diffusive motion of a charge interacting with the nonlinear dynamics of a thermalized underlying lattice. Signatures of anomalous diffusive properties are found at relatively high temperatures, where highly nonlinear excitations are present. A sublinear diffusion and a plateau appear before the standard long-time diffusion during the evolution of the mean-squared displacement and a significant degree of heterogeneity is exhibited among individual trajectories. Both properties are connected with the existence of vibrational hot spots (breather or multibreather excitations). Transport parameters of the charge are strongly affected in this case, as can be exemplified by the significant suppression of the diffusion coefficient D. The variation of D with temperature follows a stretched exponential law. The results are contrasted with those of the linearized case, in the absence of breathers. Such anomalous diffusion of a charge coupled to a thermalized lattice may be relevant in low-dimensional soft materials with strong anharmonicities, such as biomolecules, conducting polymers, etc.

Biopolymers↗

PubMed2002

Analysis of the influence of coupled diffusion on transport in protein crystal growth for different gravity levels.

Diffusion has a central role in protein crystal growth both in microgravity conditions and on ground. Recently several reports have been focused on the importance to use the generalized Fick's equations in n-component systems where crystals grow. In these equations the total flux of each component is produced by the own concentration gradient (main flow) and by the concentration gradient of the other components (cross-flow) present in the system. However in literature the latter effect is often neglected, and the so-called pseudo-binary approximation is used. Lin et al. (1995) proposed a mathematical model to evaluate the concentration profile of the species present around a growing protein crystal. Although the model is reliable, it suffers of the pseudo-binary approximation (neglecting cross term diffusion coefficients and using binary diffusion coefficients), probably because of the lack of multicomponent diffusion data. The present model is based on the experimental set-up proposed by Lin et al. (1995). Nevertheless we have included the coupled diffusion effects, according to the correct description of the matter transport through the generalized Fick's equations. The crystal growth rate is calculated for different gravity levels. The model has been applied to the ternary lysozyme-NaCl-water and quaternary lysozyme-poly(ethylene glycol) (PEG)-NaCl-water systems using recent diffusion data.

Animals↗

PubMed2005

White matter fiber tractography via anisotropic diffusion simulation in the human brain.

A novel approach to noninvasively tracing brain white matter fiber tracts is presented using diffusion tensor magnetic resonance imaging (DT-MRI). This technique is based on successive anisotropic diffusion simulations over the human brain, which are utilized to construct three dimensional diffusion fronts. The fiber pathways are determined by evaluating the distance and orientation from the fronts to their corresponding diffusion seeds. Synthetic and real DT-MRI data are employed to demonstrate the tracking scheme. It is shown that the synthetic tracts are accurately replicated, and several major white matter fiber pathways can be reproduced noninvasively, with the tract branching being allowed. Since simulating the diffusion process, which is truly a physical phenomenon reflecting the underlying architecture of cerebral tissues, makes full use of the diffusion tensor data, including both the magnitude and orientation information, the proposed approach is expected to enhance robustness and reliability in white matter fiber reconstruction.

Algorithms↗

PubMed2004

Image enhancement and denoising by complex diffusion processes.

The linear and nonlinear scale spaces, generated by the inherently real-valued diffusion equation, are generalized to complex diffusion processes, by incorporating the free Schrödinger equation. A fundamental solution for the linear case of the complex diffusion equation is developed. Analysis of its behavior shows that the generalized diffusion process combines properties of both forward and inverse diffusion. We prove that the imaginary part is a smoothed second derivative, scaled by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, we develop two examples of nonlinear complex processes, useful in image processing: a regularized shock filter for image enhancement and a ramp preserving denoising process.

Algorithms↗

PubMed2006

Complex adjustments of photosynthetic potentials and internal diffusion conductance to current and previous light availabilities and leaf age in Mediterranean evergreen species Quercus ilex.

Mature non-senescent leaves of evergreen species become gradually shaded as new foliage develops and canopy expands, but the interactive effects of integrated light during leaf formation (Q(int)G), current light (Q(int)C) and leaf age on foliage photosynthetic competence are poorly understood. In Quercus ilex L., we measured the responses of leaf structural and physiological variables to Q(int)C and Q(int)G for four leaf age classes. Leaf aging resulted in increases in leaf dry mass per unit area (M(A)), and leaf dry to fresh mass ratio (D(F)) and decreases in N content per dry mass (N(M)). N content per area (N(A)) was independent of age, indicating that decreases in N(M) reflected dilution of leaf N because of accumulation of dry mass (NA = N(M) M(A)). M(A), D(F) and N(A) scaled positively with irradiance, whereas these age-specific correlations were stronger with leaf growth light than with current leaf light. Area-based maximum ribulose 1,5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylase activity (V(cmax)A), capacity for photosynthetic electron transport (J(max)A) and the rate of non-photorespiratory respiration in light (R(d)A) were also positively associated with irradiance. Differently from leaf structural characteristics, for all data pooled, these relationships were stronger with current light with little differences among leaves of different age. Acclimation to current leaf light environment was achieved by light-dependent partitioning of N in rate-limiting proteins. Mass-based physiological activities decreased with increasing leaf age, reflecting dilution of leaf N and a larger fraction of non-photosynthetic N in older leaves. This resulted in age-dependent modification of leaf photosynthetic potentials versus N relationships. Internal diffusion conductance (g(m)) per unit area (g(m)A) increased curvilinearly with increasing irradiance for two youngest leaf age classes and was independent of light for older leaves. In contrast, g(m) per dry mass (g(m)M) was negatively associated with light in current-year leaves. Greater photosynthetic potentials and moderate changes in diffusion conductance resulted in greater internal diffusion limitations of photosynthesis in higher light. Both area- and mass-based g(m) decreased with increasing leaf age. The decrease in diffusion conductance was larger than changes in photosynthetic potentials, leading to larger CO2 drawdown from leaf internal air space to chloroplasts (delta(c)) in older leaves. The increases in diffusion limitations in older leaves and at higher light scaled with age- and light-dependent increases in MA and D(F). Overall, our study demonstrates a large potential of foliage photosynthetic acclimation to changes in leaf light environment, but also highlights enhanced structural diffusion limitations in older leaves that result from leaf structural acclimation to previous rather than to current light environment and accumulation of structural compounds with leaf age.

Acclimatization↗

PubMedDate not supplied

Extended theory of the early diffusion of multiple indicators: bounds on permeability ratios, with applications to intestinal capillaries.

The determination of ratios of capillary permeabilities to multiple indicators is secured by constructing upper bounds on effects of early back-diffusion following a single arterial injection. The analysis does not exclude highly extracted indicators, and it allows for effects of asymmetric blood-tissue exchange and of tissue concentration gradients. The concept of flow limitation of uptake is delimited operationally. It is shown how to identify effects of heterogeneity of uptake for data sets extended over large ranges of rate of blood flow. These new methods are used to show, for several sets of previously published data from muscle, that back-diffusion cannot change appreciably the permeability ratios determined previously without any quantification of back-diffusion. The main application is to data published by Perry and Granger (1981) on the permeability of cat intestinal capillaries to raffinose and inulin. The permeability ratios deduced from these data imply paradoxically restricted diffusion; it is shown that this cannot be attributed to effects of back-diffusion, heterogeneity of extraction, or of solvent drag. It is shown that the paradox is removed if tissue-to-blood permeability to raffinose is at least double the blood-to-tissue permeability, possibly as part of the active transport of sugars from the intestinal lumen. It is shown that corresponding results on permeability ratios in dog gastric capillaries are not paradoxical (against the standard of unrestricted diffusion) under symmetric permeability to raffinose.

Animals↗

PubMed1997

Diffusion in axon guidance.

Axon guidance by target-derived diffusible factors plays an important role in the development of the nervous system. This paper considers the constraints imposed on this process by the mathematics of diffusion. A point source continuously producing a factor into an infinite three-dimensional volume is considered as a model for both the in vivo and in vitro situation. Basic constraints for effective guidance are assumed to be that the concentration falls between certain maximum and minimum limits, and that the percentage change in concentration across the width of the growth cone exceeds a certain minimum value. The evolution of the shape of the gradient over time is analysed. Using biologically reasonable parameter values, it is shown that the maximum range over which growth cone guidance by a diffusible factor is possible for large times (several days) after the start of the production of the factor is 500-1000 microm. This maximum distance is independent of the diffusion constant of the diffusing molecule, applies to both chemoattractants and chemorepellents, and agrees with experimental data. At earlier times, however, the constraints may be satisfied for distances up to several millimetres. The time it takes for this maximum guidance distance to fall to the asymptotic value depends on the diffusion constant. This time is a few hours for a small molecule but as much as a few days for a large molecule. The model therefore predicts that guidance over distances larger than 1000 microm is possible if the start of production of the factor is carefully matched to the time when guidance is required.

Animals↗

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