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PubMed1997

A cellular automata model of diffusion in aqueous systems.

A cellular automata model of a solute diffusing in water has been created and studied for the influential attributes. The results with this model are in agreement with experimental results; that is, that lipophilic solutes diffuse faster than do polar solutes. The model reveals that a solution composed of a relatively lipophilic solute permits a greater extent of diffusion of another solute. This observation is in agreement with the model showing a diffusion preference of a solute between two solutions made up of differing polarities. The solute diffuses farther into the lipophilic solution. A temperature-lipophilicity phase diagram shows the influence of these two attributes on the rate of diffusion. A model of diffusion through solutions containing stationary ingredients reveals a faster rate when the ingredient is lipophilic. We are led to a conclusion that the relative lipophilicity of solutes or stationary ingredients in a solution has a direct influence on the rates of diffusion of other solutes in their midst.

Diffusion↗

PubMed1999

General solution for diffusion-controlled dissolution of spherical particles. 1. Theory.

Three classical particle dissolution rate expressions are commonly used to interpret particle dissolution rate phenomena. Our analysis shows that an assumption used in the derivation of the traditional cube-root law may not be accurate under all conditions for diffusion-controlled particle dissolution. Mathematical analysis shows that the three classical particle dissolution rate expressions are approximate solutions to a general diffusion layer model. The cube-root law is most appropriate when particle size is much larger than the diffusion layer thickness, the two-thirds-root expression applies when the particle size is much smaller than the diffusion layer thickness. The square-root expression is intermediate between these two models. A general solution to the diffusion layer model for monodispersed spherical particles dissolution was derived for sink and nonsink conditions. Constant diffusion layer thickness was assumed in the derivation. Simulated dissolution data showed that the ratio between particle size and diffusion layer thickness (a0/h) is an important factor in controlling the shape of particle dissolution profiles. A new semiempirical general particle dissolution equation is also discussed which encompasses the three classical particle dissolution expressions. The success of the general equation in explaining limitations of traditional particle dissolution expressions demonstrates the usefulness of the general diffusion layer model.

Diffusion↗

PubMed1998

Determination of micellar self-diffusion coefficients by micellar electrokinetic chromatography.

A method is described by which the diffusion coefficients of electrically charged micelles can be determined using micellar electrokinetic chromatography (MEKC). The determination is based on a theory for the dispersion, at low electric field strengths, of analytes that are solubilized by only the micellar phase. The dispersion is represented by contributions from instrumental sources and from longitudinal diffusion. The latter depends on the micellar diffusion coefficient. The theory is used to determine the micellar diffusion coefficients of the surfactant sodium dodecyl sulfate in three solutions having different surfactant concentrations. These diffusion coefficients compare very favorably with those determined by diffusion-ordered two-dimensional NMR spectroscopy. An argument is presented justifying that the diffusion coefficients determined by MEKC are self-diffusion coefficients.

Chromatography↗

PubMed2004

A new FTIR-ATR cell for drug diffusion studies.

The drug diffusion of most compounds, particularly hydrophilic molecules through the skin is limited by the permeation of the outermost cell layers of the epidermis, the stratum corneum(SC). For this reason it is of interest to characterize drug diffusion processes through this skin layer. A new FTIR-ATR cell was developed for non-invasive real time measurements of drug diffusion. The diffusion of water through an artificial polyethyleneglycol-polydimethylsiloxane membrane was studied. Additionally the diffusion of urea in human SC was analyzed. Based on a mathematical model the diffusion coefficients were derived. We could reveal that this cell associates the advantages of the Franz diffusion cell and the FTIR-ATR spectroscopy as a new powerful method for determining drug diffusion through biological membranes.

Diffusion↗

PubMed2004

Evaluation of the diffusion coefficient for controlled release of oxytetracycline from alginate/chitosan/poly(ethylene glycol) microbeads in simulated gastrointestinal environments.

Diffusion studies of OTC (oxytetracycline) entrapped in microbeads of calcium alginate, calcium alginate coacervated with chitosan (of high, medium and low viscosity) and calcium alginate coacervated with chitosan of low viscosity, covered with PEG [poly(ethylene glycol) of molecular mass 2, 4.6 and 10 kDa, were carried out at 37+/-0.5 degrees C, in pH 7.4 and pH 1.2 buffer solutions - conditions similar to those found in the gastrointestinal system. The diffusion coefficient, or diffusivity (D), of OTC was calculated by equations provided by Crank [(1975) Mathematics in Diffusion, p. 85, Clarendon Press, Oxford] for diffusion, which follows Fick's [(1855) Ann. Physik (Leipzig) 170, 59] second law, considering the diffusion from the inner parts to the surface of the microbeads. The least-squares and the Newton-Raphson [Carnahan, Luther and Wilkes (1969) Applied Numerical Methods, p. 319, John Wiley & Sons, New York] methods were used to obtain the diffusion coefficients. The microbead swelling at pH 7.4 and OTC diffusion is classically Fickian, suggesting that the OTC transport, in this case, is controlled by the exchange rates of free water and relaxation of calcium alginate chains. In case of acid media, it was observed that the phenomenon did not follow Fick's law, owing, probably, to the high solubility of the OTC in this environment. It was possible to modulate the release rate of OTC in several types of microbeads. The presence of cracks formed during the process of drying the microbeads was observed by scanning electron microscopy.

Alginates↗

PubMed2000

Oxygen supply to contracting skeletal muscle at the microcirculatory level: diffusion vs. convection.

An adequate supply of oxygen is essential for the normal function of all cells. Because skeletal muscle cells have the ability to vary their oxygen demand by over an order of magnitude on going from rest to vigorous contraction, it is important that mechanisms be in place to ensure that the supply of oxygen is maintained at sufficient levels. Microcirculation plays a critical role in this process, as the terminal branches of this intricate network of blood vessels determine the distribution of perfusion, as well as the structural framework for diffusion. The oxygen supply depends on proper functioning of both the convective and diffusive components of the transport system. Convection is responsible for the long-range, rapid transport of oxygen by bulk flow of the blood and diffusion is the efficient mechanism for transport over the short distances between capillaries and muscle cells. Convective transport is dominated by the movement of red blood cells, as virtually all the oxygen at normal haematocrit is carried inside them, reversibly bound to haemoglobin. Over the years, specialized techniques, many of them video-based, have been developed for use in intravital microscopy to measure the parameters needed to quantify convection and diffusion in both capillaries and the larger microvessels, arterioles and venules. Most of our knowledge of oxygen transport in the microcirculation of muscle pertains to the resting condition, because one must be able to visualize the structures of interest, such as microvessels and muscle cells, and the large tissue movements that occur during contraction preclude measurements during that time. In resting muscle it has been found that the arterioles are the primary site of the diffusion of oxygen from the circulation, where the oxygen is utilized by nearby muscle cells or diffuses directly to nearby venules or capillaries. Diffusive interactions among neighbouring capillaries have also been observed. In contracting muscles, microvessels observed immediately following the period of stimulation exhibit enhancements of both convective (increased flow of red blood cells) and diffusive (increased perfused capillary surface area) transport. The use of computational models in the interpretation of experimental studies is leading to an increased understanding of the processes that underlie the oxygen transport system in skeletal muscle.

Animals↗

PubMed2002

Magnetic resonance microimaging of intraaxonal water diffusion in live excised lamprey spinal cord.

Anisotropy of water diffusion in axon tracts, as determined by diffusion-weighted MRI, has been assumed to reflect the restriction of water diffusion across axon membranes. Reduction in this anisotropy has been interpreted as degeneration of axons. These interpretations are based primarily on a priori reasoning that has had little empirical validation. We used the experimental advantages of the sea lamprey spinal cord, which contains several very large axons, to determine whether intraaxonal diffusion is isotropic and whether anisotropy is attributable to restriction of water mobility by axon surface membranes. Through the application of magnetic resonance microimaging, we were able to measure the purely intraaxonal diffusion characteristics of the giant reticulospinal axons (20-40 microm in diameter). The intraaxonal apparent diffusion coefficients of water parallel (longitudinal ADC, l-ADC) and perpendicular (transverse ADC, t-ADC) to the long axis were 0.98 +/- 0.06 (10(-3) mm2 sec) and 0.97 +/- 0.11 (10(-3) mm2 sec), respectively. In white matter regions that included multiple axons, l-ADCs were almost identical regardless of axon density in the sampled axon tract. By comparison, t-ADCs were reduced and varied inversely with the number of axons (and thus axolemmas) in a fixed cross-sectional area. Thus, diffusion was found to be isotropic when measured entirely within a single axon and anisotropic when measured in regions that included multiple axons. These findings support the hypothesis that the cell membrane is the primary source of diffusion anisotropy in fiber tracts of the central nervous system.

Animals↗

PubMed1984

Relationship between lateral diffusion, collision frequency, and electron transfer of mitochondrial inner membrane oxidation-reduction components.

Fluorescence recovery after photobleaching was used to determine the diffusion coefficients of the oxidation-reduction (redox) components ubiquinone, complex III (cytochromes b-c1), cytochrome c, and complex IV (cytochrome oxidase) of the mitochondrial inner membrane. All redox components diffuse in two dimensions as common-pool electron carriers. Cytochrome c diffuses in two and three dimensions concomitantly, and its diffusion rate, unlike that of all other redox components, is modulated along with its activity by ionic strength. The diffusion coefficients established in this study reveal that the theoretical diffusion-controlled collision frequencies of all redox components are greater than their experimental maximum (uncoupled) turnover numbers. Since electron transport is slower than the theoretical limit set by the lateral diffusion of the redox components, ordered chains, assemblies, or aggregates of redox components are not necessary to account for electron transport. Rather, mitochondrial electron transport is diffusion coupled, consistent with a "random-collision model" for electron transport.

Animals↗

PubMedDate not supplied

The effect of changing the gaseous diffusion coefficient on the mass loss pattern of Hyalophora cecropia pupae.

The importance of gas phase diffusion in insect gas exchange remains unclear. The role of diffusion in gas exchange of developing Hyalophora cecropia pupae was examined by altering the gaseous diffusion coefficient in the breathing mixture. Gaseous diffusion coefficients were manipulated by substituting helium or sulfur hexafluoride for the nitrogen usually present in air. Sensitive mass loss recordings were employed to monitor gas exchange activity. Mass loss recordings showed a two-phase cycle, open and closed-flutter. Mass loss rates during the open and closed-flutter periods were not altered in proportion to the changes induced in the rate of diffusion. Open-phase duration was inversely and proportionally related to the diffusion coefficient. These results are consistent with changes in spiracle resistance or convective flow during the open period in response to a change in the diffusion coefficient. In addition, they indicate a significant gas phase diffusive resistance within the pupal tracheal system. This previously unreported gas phase resistance appears to be a major determinant of the duration of the open period and thus of overall water loss rates in these pupae.

Animals↗

PubMed1999

Dynamics of polymerization in polyacrylamide gel (PAG) dosimeters: (II) modeling oxygen diffusion.

Oxygen contamination of a polyacrylamide gel (PAG) dosimeter can have a significant detrimental effect upon the performance characteristics of the gel as a dosimeter. Oxygen contamination can occur during preparation, but can also arise from the diffusion of atmospheric oxygen through vessel walls. Even 'trace' amounts of oxygen present in any gaseous space (usually nitrogen filled) between the surface of the PAG and the vessel seal can have a detectable effect. This paper describes a method used to quantify the detrimental effects of a range of oxygen concentrations upon the performance of the PAG. The results of diffusion studies for air and pure oxygen diffusing into the PAG over time are presented and coupled with a novel method of calculating oxygen concentrations in the PAG. Results obtained suggest that the diffusion is Fickian. The coefficient of diffusion D has been calculated to be (8+/-2) x 10(-6) cm2 s(-1) for oxygen diffusing into PAG stored at 4 degrees C, under the assumption that the diffusion mechanism is independent of the concentration of the diffusing species. In addition, a quantitative relation has been established between the transverse relaxation rate R2 of the PAG and the concentration of oxygen present. The implications of these findings for polymer gel dosimetry are discussed.

Acrylic Resins↗

PubMed1996

Diffusion measurements in the ischemic human brain with a steady-state sequence.

RATIONALE AND OBJECTIVES: The authors evaluate the clinical usefulness of a diffusion-weighted steady-state free-precession (SSFP) sequence to detect acute and subacute ischemic changes. METHODS: Twenty-four patients were examined on a 1.5-tesla scanner, using a SSFP-sequence (repetition time [TR]/ echo time [TE] = 22/3-8 mseconds). The slice thickness was 5 mm, 10 averages, 57 seconds per slice. The diffusion gradient strength was 23 millitesla/m, with b-values from 165 to 598 seconds/mm2. Diffusion-weighted images (DWI) were compared with T2-weighted images. RESULTS: The diffusion-weighted SSFP sequence produced diagnostic quality images in 23 of 24 patients. Diffusion depicted (group 1: 0-12 hours) more acute lesions (3 of 6) than T2-weighted images (2 of 6); the mean lesion diameter depicted by diffusion was 10.9 mm (standard deviation [SD], 12.3) and in T2-weighted images was 4.7 mm (SD 6.8). A significant correlation (P < 0.017) in subacute lesions was found when diffusion was compared with turbo spin echo (mean size difference/T2 = 18.5/17.5 mm, SD 13.2/12.2). CONCLUSIONS: The diffusion-weighted SSFP-sequence is more sensitive in acute ischemia and delineates likewise in subacute ischemia, when compared with T2-weighted imaging.

Adult↗

PubMed1998

Diffusion of radiotracers in normal and ischemic brain slices.

Diffusion in the extracellular space (ECS) is important in physiologic and pathologic brain processes but remains poorly understood. To learn more about factors influencing tissue diffusion and the role of diffusion in solute-tissue interactions, particularly during cerebral ischemia, we have studied the kinetics of several radiotracers in control and hypoxic 450-microm hippocampal slices and in 1,050-microm thick slices that model the ischemic penumbra. Kinetics were analyzed by nonlinear least squares methods using models that combine extracellular diffusion with tissue compartments in series or in parallel. Studies with 14C-polyethylene glycol confirmed prior measurements of extracellular volume and that ECS shrinks during ischemia. Separating diffusion from transport also revealed large amounts of 45Ca that bind to or enter brain as well as demonstrating a small, irreversibly bound compartment during ischemia. The rapidity of 3H2O entry into cells made it impossible for us to distinguish intracellular from extracellular diffusion. The diffusion-compartment analysis of 3-O-methylglucose data appears to indicate that 5 mmol/L glucose is inadequate to support glycolysis fully in thick slices. Unexpectedly, the diffusion coefficient for all four tracers rose in thick slices compared with thin slices, suggesting that ECS becomes less tortuous in the penumbra.

Animals↗

PubMed1998

Exercise tolerance in heart transplant patients with altered pulmonary diffusion capacity.

To test whether orthotopic heart transplant (OHT) patients with low pulmonary diffusion capacity have a greater limitation to exercise than OHT patients with normal pulmonary diffusion capacity, we investigated cardiorespiratory responses and blood gases in two groups of OHT patients, one with low (LdG) and the other with normal pulmonary diffusion capacity (NdG), during a graded exercise test. The results showed 1) significantly reduced peak power (P < 0.05), peak oxygen uptake (VO2, P < 0.001), peak oxygen pulse (VO2/heart rate, P < 0.01), peak minute ventilation (VE, P < 0.05), and delta PaO2 (peak PaO2 - rest PaO2, P < 0.05) in LdG versus NdG; 2) a nonsignificant decrease in peak heart rate in LdG (P < 0.13, P = 24%); and 3) significant increases in peak respiratory equivalent for oxygen (VE/VO2, P < 0.05) and delta P(A-a)O2 (peak P(A-a)O2 - resting P(A-a)O2, P < 0.05) in LdG versus NdG. No significant difference was found for PaO2 and PaCO2 at rest or at peak exercise between the groups. A strong correlation was found between pulmonary diffusion capacity (TLCO/VA) and peak VO2 (r = 0.81, P < 0.01); that is, TLCO/VA explains 66% of the variance in peak VO2. We conclude that OHT patients with decreased pulmonary diffusion capacity have a lower exercise tolerance than patients with normal pulmonary diffusion capacity. However, because of the lack of exercise-induced hypoxemia, diffusion abnormalities are not the main limiting factor for exercise tolerance in the low diffusion group.

Blood Gas Analysis↗

PubMed2006

Diffusion imaging of the prostate at 3.0 tesla.

OBJECTIVES: We sought to assess the efficacy of diffusion imaging in the differential diagnosis of prostatic carcinoma using a 3.0 T scanner and parallel imaging technology. MATERIALS AND METHODS: Diffusion-weighted images were acquired using a single shot echo-planar imaging sequence with b = 0 and 500 seconds/mm. Apparent diffusion coefficient (ADCy) values were calculated in tumor and healthy-appearing peripheral zone for 62 patients. Diffusion tensor images were also acquired in 25 patients and mean diffusivity and fractional anisotropy determined. RESULTS: Significant differences were noted between prostatic carcinoma (1.33 +/- 0.32 x 10(-3) mm2/s) and peripheral zone (1.86 +/- 0.47 x 10(-3) mm2/s) for ADCy. Significant differences between the 2 tissue types were also noted for mean diffusivity and fractional anisotropy. Utilizing a cut-off of 1.45 x 10(-3) mm/s for mean diffusivity, a sensitivity of 84% and a specificity of 80% were obtained. CONCLUSIONS: Diffusion imaging of the prostate was implemented at high magnetic field strength. Reduced ADC and increased fractional anisotropy values were noted in prostatic carcinoma.

Adult↗

PubMed2002

Morphological instability and dynamics of fronts in bacterial growth models with nonlinear diffusion.

Depending on the growth condition, bacterial colonies can exhibit different morphologies. As argued by Ben-Jacob et al. there is biological and modeling evidence that a nonlinear diffusion coefficient of the type D(b)=D(0)b(k) is a basic mechanism that underlies almost all of the patterns and generates a long-wavelength instability. We study a reaction-diffusion system with a nonlinear diffusion coefficient and find that a unique planar traveling front solution exists whose velocity is uniquely determined by k and D=D(0)/D(n), where D(n) is the diffusion coefficient of the nutrient. Due to the fact that the bacterial diffusion coefficient vanishes when b-->0, in the front solution b vanishes in a singular way. As a result the standard linear stability analysis for fronts cannot be used. We introduce an extension of the stability analysis that can be applied to singular fronts, and use the method to perform a linear stability analysis of the planar bacteriological growth front. We show that a nonlinear diffusion coefficient generates a long-wavelength instability for k>0 and D 0 and k--> infinity the dynamics of the growth zone essentially reduces to that of a sharp interface problem that is reminiscent of a so-called one-sided growth problem where the growth velocity is proportional to the gradient of a diffusion field ahead of the interface. The moving boundary approximation that we derive in these limits is quite accurate but surprisingly does not become a proper asymptotic theory in the strict mathematical sense in the limit D-->0, due to lack of full separation of scales on all dynamically relevant length scales. Our linear stability analysis and sharp interface formulation will also be applicable to other examples of interface formation due to nonlinear diffusion, like in porous media or in the problem of vortex motion in superconductors.

Bacteria↗

PubMed2003

Photoacoustic analysis indicates that chloroplast movement does not alter liquid-phase CO2 diffusion in leaves of Alocasia brisbanensis.

Light-mediated chloroplast movements are common in plants. When leaves of Alocasia brisbanensis (F.M. Bailey) Domin are exposed to dim light, mesophyll chloroplasts spread along the periclinal walls normal to the light, maximizing absorbance. Under high light, the chloroplasts move to anticlinal walls. It has been proposed that movement to the high-light position shortens the diffusion path for CO(2) from the intercellular air spaces to the chloroplasts, thus reducing CO(2) limitation of photosynthesis. To test this hypothesis, we used pulsed photoacoustics to measure oxygen diffusion times as a proxy for CO(2) diffusion in leaf cells. We found no evidence that chloroplast movement to the high-light position enhanced gas diffusion. Times for oxygen diffusion were not shorter in leaves pretreated with white light, which induced chloroplast movement to the high-light position, compared with leaves pretreated with 500 to 700 nm light, which did not induce movement. From the oxygen diffusion time and the diffusion distance from chloroplasts to the intercellular gas space, we calculated an oxygen permeability of 2.25 x 10(-)(6) cm(2) s(-)(1) for leaf cells at 20 degrees C. When leaf temperature was varied from 5 degrees C to 40 degrees C, the permeability for oxygen increased between 5 degrees C and 20 degrees C but changed little between 20 degrees C and 40 degrees C, indicating changes in viscosity or other physical parameters of leaf cells above 20 degrees C. Resistance for CO(2) estimated from oxygen permeability was in good agreement with published values, validating photoacoustics as another way of assessing internal resistances to CO(2) diffusion.

Acoustics↗

PubMed1988

Diffusion of [2-14C]diazepam across isolated hairless mouse stratum corneum/epidermal tissues.

The objective of this study was to develop a method of preparing mouse stratum corneum/epidermal (SCE) tissue without the dermis for use in drug diffusion studies. The diffusion of radiolabeled diazepam across this new preparation has been studied and the effect of the dermis on diffusion evaluated. Incubation of large pieces of mouse skin in a 20mM EDTA, 15 mM sodium phosphate buffer, pH 7.2, in normal saline for 3-4 h at 37 degrees C resulted in a tissue which easily separated at the epidermal-dermal junction. The resulting tissue contains stratum corneum and epidermis, which are the same layers used in studies with human skin in vitro. The EDTA treatment did not effect diffusion of [2-14C]diazepam across whole mouse skin (SCE and dermis) used as controls. The rate of drug diffusion was greater across SCE than SCE and dermis, however, 0.48-1.12 micrograms/cm2/h versus 0.11-0.52 microgram/cm/h, respectively. The permeability coefficients for mouse SCE ranged from 1.92-4.48 X 10(-2) cm/h. The lag times and diffusion coefficients were 0.36-0.91 h and 0.1-0.6 X 10(-6) cm2/h, respectively. The presence of the dermis decreased the diffusion rate or flux of diazepam. The dermis appears to accumulate drug until it is saturated and then the drug diffuses into the receiving chamber.

Animals↗

PubMed2005

Facilitated diffusion in chromatin lattices: mechanistic diversity and regulatory potential.

The interaction between a protein and a specific DNA site is the molecular basis for vital processes in all organisms. Location of the DNA target site by the protein commonly involves facilitated diffusion. Mechanisms of facilitated diffusion vary among proteins; they include one- and two-dimensional sliding along DNA, direct transfer between uncorrelated sites, as well as combinations of these mechanisms. Facilitated diffusion has almost exclusively been studied in vitro. This review discusses facilitated diffusion in the context of the living cell and proposes a theoretical model for facilitated diffusion in chromatin lattices. Chromatin structure differentially affects proteins in different modes of diffusion. The interplay of facilitated diffusion and chromatin structure can determine the rate of protein association with the target site, the frequency of association-dissociation events at the target site, and, under particular conditions, the occupancy of the target site. Facilitated diffusion is required in vivo for efficient DNA repair and bacteriophage restriction and has potential roles in fine-tuning gene regulatory networks and kinetically compartmentalizing the eukaryotic nucleus.

Chromatin↗