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Local cerebral blood flow values as estimated with diffusible tracers: validity of assumptions in normal and ischemic tissue.

A theoretical assessment is made of the validity of assumptions underlying the theory for estimating local cerebral blood flow with diffusible tracer in the tissue under normal and ischemic conditions. First, Kety's derivation of equations that have commonly been used for calculating local cerebral blood flow values is examined in order to define the problems and assumptions. Second, the brain:blood partition coefficient of diffusible tracer, lambda, and the diffusion-limited factor, m, under normal and ischemic conditions are reviewed. An examination of the literature suggested that contrary to common belief, lambda appears to change very little in ischemia if the tissue constituents remain unchanged, whereas m does change with ischemia if the diffusible tracer used is greatly diffusion-limited in the exchange between brain and blood. Even when a gas with an m value close to unity is used as the diffusible tracer, the prolonged mean transit time of blood through the ischemic tissue would make it difficult to maintain the exponential assumptions. As part of the ischemic tissue became infarcted, which is the case with most stroke patients, so the assumptions of homogeneous perfusion would become invalid. This inevitably renders it difficult to estimate local cerebral blood flow with diffusible tracer in ischemic tissue containing an infarcted mass.

Brain Ischemia↗

On the rotational brownian motion of a bacterial idle motor. I. Theory of time-dependent fluorescence depolarization.

A rotational diffusion equation and its Green's function for a spheroidal particle such as a bacterial body, to which an actively driving but idle motor is attached, are presented. As an application of the theory, general expressions for the time-dependent fluorescence depolarization caused by such a particle have been obtained. Measurement of such depolarizalion should provide a useful tool for determination of the rate of revolution of the rotating motor attached to cell bodies such as bacteria under various solution conditions, if a fluorescent (or phosphorescent) label is attached to the motor shaft.

Journal Article↗

Lateral diffusion of lipids in complex biological membranes.

Lateral diffusion of lipids in biological membranes may be influenced by polypeptides, proteins, and other nonlipid membrane constituents. Using concepts from scaled-particle theory, we extend the free-volume model for lipid diffusion to membranes having an arbitrarily large number of components. This theory clarifies the interpretation of the free-volume theory, better reproduces the free-area dependence of lipid lateral diffusion rates, and quantitatively predicts the experimental observation that the lateral diffusion rates of membrane lipids are significantly reduced when proteins or polypeptides are incorporated in the membrane.

Diffusion↗

Kinetics of shrinking of polymer gels induced by ultracentrifugal fields.

The kinetics of the shrinking of polymer gels induced by ultracentrifugal fields is investigated. A theory is proposed to describe the diffusion process of polymer networks under centrifugal fields. The initial shrinking rate is proportional to the ratio of the centrifugal force to the frictional force of networks. The shrinking attains the stationary state as a result of the balance between the centrifugal force and the swelling force of networks. The characteristic time for shrinking is of the order of a2/D where a and D are the stationary displacement and diffusion constant, respectively. We also present the experimental data for the shrinking of the poly(acrylamide) (PAAm) gels under ultracentrifugal fields. The shrinkage increases linearly with time in the initial stage whereas it reaches the steady state in the long time limit as expected by the theory. Each of longitudinal elastic modulus and friction coefficient of the PAAm gels is evaluated from the data on the basis of the theory.

Journal Article↗

Diffusion in porous materials above the percolation threshold.

The diffusion of water-soluble solutes in water-soaked porous media was studied by following the release of benzoic acid from poly(vinyl stearate) matrices. The results were analyzed using a pseudo-steady-state diffusion model coupled with the fundamental concepts of percolation theory. The results of the study indicated that the relationship between the bulk diffusion coefficient of benzoic acid in the polymer matrix and the porosity was well described by percolation scaling laws. A very low percolation threshold (0.07) was experimentally observed for this system.

Benzoates↗

Spin diffusion in double-exchange manganites.

The theoretical study of spin diffusion in double-exchange magnets by means of dynamical mean-field theory is presented. We demonstrate that the spin-diffusion coefficient becomes independent of the Hund's coupling J(H) in the range of parameters J(H)S>>W>>T, W being the bandwidth, relevant to colossal magnetoresistive manganites in the metallic part of their phase diagram. Our study reveals a close correspondence as well as some counterintuitive differences between the results on Bethe and hypercubic lattices. Our results are in accord with neutron-scattering data and with previous theoretical work for high temperatures.

Journal Article↗

The effective dispersion of nanovectors within the tumor microvasculature.

The effective longitudinal diffusion of nanovectors along non-permeable and permeable capillaries has been studied considering the contribution of molecular and convective diffusion based on the Taylor's theory of shear dispersion. The problem is of importance in the transport of nanovectors used for the intravascular delivery of drugs and contrast agents. It has been shown that for a given capillary size and hemodynamic conditions a critical radius acr exists for which the effective longitudinal diffusion along the capillary has a minimum: Nanovectors with a < acr diffuse mainly by Brownian diffusion whereas nanovectors with a < acr diffuse mainly by convection and the effective diffusion coefficient grows with a. In permeable conduits, the effective diffusion reduces significantly compared to normal non-leaky vessels and it has been derived that acr grows almost linearly with the hydraulic permeability Lp of blood vessels. It has been shown that the blood conduits with the largest effective longitudinal diffusivity could be preferentially targeted by the circulating vectors. Based on these findings, the following strategies are proposed to increase the number of nanovectors targeting the tumor vessels: (i) The use of nanovectors with a critical radius for normal vessels, (ii) the injecting of bolus of nanovectors with different radii, and (iii) the normalization of the tumor vasculature. Finally, it has been emphasized that the size of the vector should be selected depending on the body district where the tumoral mass is developing and on the type, malignancy, and state of the tumor.

Animals↗

Biological effect of paramecium in diffused ultrasonic fields.

Since the cell structure or biophysical reaction includes in the interaction between ultrasound and living matter. When multi-cell creature is exposed to ultrasound, this reaction will lead the biological effect becomes complex. Therefore, in this paper, a single cell creature is chosen to study the biological effects induced by ultrasound exposure. The paramecium, which possesses many features typical of higher-order animal cells, was considered an appropriate choice for this study. The ability shown by ultrasound in promoting and/or accelerating many reactions has been shown to be a useful field. The growth phase of paramecium by using the ultrasound irradiation is an important parameter in this study. In our experiment, the exponential and stationary phases were employed. Three important factors must be taken into account when an ultrasonic biological reaction is investigated: the medium system, the bubbles' field, and the acoustic field. The medium system involves the physical parameters of the medium field. The bubbles' field includes the reacting bubble size of the liquid and the resonance frequency of the reaction bubbles. The oscillation of the cells in response to the ultrasound radiation is simulated using Rayleigh-Plesset's bubble activation theory. The resonance frequency of the unicellular creature is then calculated. The acoustic field is about using the diffuse field theory of Sabine to create a uniform sound field for the radiation experiment. The resonance frequency of the paramecium vacuole is among 0.54-1.09 MHz. When the 0.25 and 0.5 MHz frequencies of ultrasound was irradiated in the stationary phase of the paramecium, the relative growth rate was about 20% lower than that of unexposed sample. Therefore, the phenomenon of inhibition and destruction appeared during irradiation. The exponential phase of the paramecium samples appear to be different when irradiated with 1 MHz ultrasound. As can be seen in the results, the maximum relative growth rate was increasing 18% with 1 MHz ultrasound exposure.

Animals↗

Hemoglobin affinity for 2,3-bisphosphoglycerate in solutions and intact erythrocytes: studies using pulsed-field gradient nuclear magnetic resonance and Monte Carlo simulations.

The diffusion coefficient (D) of 2,3-bisphosphoglycerate (DPG) was measured using pulsed-field gradient (PFG)-31P nuclear magnetic resonance spectroscopy in solutions containing 2.7-5.0 mM hemoglobin (Hb) and a range of DPG concentrations. The dependence of the measured values of D on the fraction of the total DPG in the sample that is bound to Hb enabled the estimation of the dissociation constants (Kd) of complexes of DPG with carbonmonoxygenated, oxygenated, and deoxygenated Hb; the values of Kd (mM), measured at 25 degrees C, pH 6.9 and in 100 mM bis Tris/50 mM KCl, were 1.98 +/- 0.26, 1.8 +/- 0.5 and 0.39 +/- 0.26, respectively. In intact erythrocytes the apparent diffusion coefficient, Dapp, of DPG was larger in oxygenated and carbonmonoxygenated cells (6.17 +/- 0.20 x 10(-11) m2s-1) than in deoxygenated cells (4.10 +/- 0.23 x 10(-11) m2s-1). Changes in intracellular DPG concentration (5-55 mM) in erythrocytes, brought about by incubation in a medium containing inosine and pyruvate, did not result in significant changes in the value of Dapp; this result supports the hypothesis that DPG binds to other sites in the erythrocyte. Monte Carlo simulations of diffusion in biconcave discs were used to test the adequacy of the values of Kd estimated in solution to describe the binding of DPG to Hb in oxygenated and deoxygenated erythrocytes. The results of the simulations implied that the value of Kd estimated for deoxygenated Hb-DPG was greater than expected from the experiments involving intact erythrocytes. This difference is surmised to be at least partly due to the difficulty of measuring D at low-ligand concentrations. Notwithstanding this shortcoming, the PFG method appears to be suitable for probing interactions between macromolecules and ligands when the Kd is in the millimolar range. It is one of the few techniques available in which these interactions can be studied in intact cells. In addition, the Monte Carlo simulations of the diffusion experiments highlighted important differences between theory and experiment relating to the nature of molecular motion inside the cells.

2,3-Diphosphoglycerate↗

Rotational viscosity, dynamic phenomena, and dielectric properties in a long-chain liquid crystal: NMR study and theoretical treatment.

The rotational diffusion constants D(perpendicular) and D(parallel), rotational viscosity coefficients gamma(i) (i=1,2), the orientational correlation times tau(L)mn, and the dielectric permittivities for nematic liquid crystals (NLCs) are investigated. gamma(i) are calculated by a combination of existing statistical-mechanical approach (SMA) and NMR relaxation theory, both based on a rotational diffusion model. In the rotational diffusion model, it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, gamma(i) are found to be a function of temperature, density, rotational diffusion constant for tumbling motions, and the orientational order parameters. The order parameters and rotational diffusion constant are obtained from an analysis of NMR measurements. Reasonable agreement between the calculated and experimental values of gamma(i) for 4-n-octyloxy-4'-cyanobiphenyl (8OCB) is obtained. The orientational correlation times, and the longitudinal and transverse components of the real chi'(j)(omega) and imaginary chi"(j)(omega) (j= parallel, perpendicular) parts of the complex susceptibility tensor for 8OCB molecules in the nematic phase are also obtained.

Journal Article↗

Chemisorption and diffusion of hydrogen on surface and subsurface sites of flat and stepped nickel surfaces.

Plane-wave density functional theory calculations were performed to investigate the binding and diffusion of hydrogen on three flat Ni surfaces, Ni(100), Ni(110), and Ni(111), and two stepped Ni surfaces, Ni(210) and Ni(531). On each surface, the favored adsorption sites were identified by considering the energy and stability of various binding sites and zero-point energy corrections were computed. Binding energies are compared with experimental and theoretical results from the literature. Good agreement with experimental and previous theoretical data is found. At surface coverages where adsorbate-adsorbate interactions are relatively weak, the binding energy of H is similar on the five Ni surfaces studied. Favorable binding energies are observed for stable surface sites, while subsurface sites have unfavorable values relative to the gas phase molecular hydrogen. Minimum energy paths for hydrogen diffusion on Ni surfaces and into subsurface sites were constructed.

Journal Article↗

"Coarse" stability and bifurcation analysis using time-steppers: a reaction-diffusion example.

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099-1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective ("coarse") bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice-Boltzmann model.

Computer Simulation↗

Dielectric and elastic properties of liquid crystals.

The structural properties, the static and relaxation dielectric coefficients [epsilon(j) and epsilon(j)(omega) (j= ||, perpendicular)], the rotational diffusion constants D( perpendicular) and D( ||), the orientational correlation times tau(1)(i0) (i=0,1), and the bulk elastic constants K(i) (i=1,2,3) are investigated for polar liquid crystals, such as 4-n-pentyl-4(')-cyanobiphenyl (5CB). epsilon(j) are calculated by a combination of the existing molecular theory and statistical-mechanical approach (SMA) that takes into account translational and orientational correlations as well as their coupling, whereas epsilon(j)(omega) are calculated by combining SMA and nuclear magnetic resonance relaxation theory, both based on a rotational diffusion model in which the reorientation of an individual molecule is assumed as stochastic Brownian motion in a potential of mean torque. Reasonable agreement between the calculated and experimental values of epsilon(j) and epsilon(j)(omega) for 5CB is obtained. The bulk Frank elastic constants K(i) (i=1,2,3), for splay, twist, and bend distortion modes, as well as their ratios K(3)/K(1) and K(2)/K(1) are also obtained.

Journal Article↗

Influence of the long-chain/short-chain amphiphile ratio on lateral diffusion of PEG-lipid in magnetically aligned lipid bilayers as measured via pulsed-field-gradient NMR.

Lateral diffusion measurements of polyethylene glycol(PEG)-lipid incorporated into magnetically aligned lipid bilayers, composed of dimyristoyl phosphatidylcholine (DMPC) plus dihexanoyl phosphatidylcholine (DHPC) plus 1 mol % (relative to DMPC) dimyristoyl phosphatidylethanolamine-n-[methoxy(polyethylene glycol)-2000] (DMPE-PEG 2000), were performed using stimulated-echo pulsed-field-gradient proton ((1)H) nuclear magnetic resonance spectroscopy. The DMPE-PEG 2000 (1 mol %, 35 degrees C) lateral diffusion coefficient D varied directly with the mole fraction of DMPC, X(DMPC) = q/(1+q) where q = DMPC/DHPC molar ratio, decreasing progressively from D = 1.65 x 10(-11) m(2) s(-1) at q approximately 4.7 to D = 0.65 x 10(-11) m(2) s(-1) at q approximately 2.5. Possible sources of this dependence, including orientational disorder, obstruction, and PEG-lipid sequestration, were simulated using, respectively, a diffusion-in-a-cone model, percolation theory, and a two-phase PEG distribution model. Orientational disorder alone was not capable of reproducing the observations, but in combination with either obstruction or PEG-lipid two-phase distribution models did so satisfactorily. A combination of all three models yielded the most reasonable fit to the observed dependence of lateral diffusion on q. These same effects would be expected to influence lateral diffusion of any bilayer-associating species in such systems.

Biophysics↗

Molecular architecture of the thylakoid membrane: lipid diffusion space for plastoquinone.

We have determined the stoichiometric composition of membrane components (lipids and proteins) in spinach thylakoids and have derived the molecular area occupied by these components. From this analysis, the lipid phase diffusion space, the fraction of lipids located in the first protein solvation shell (boundary lipids), and the plastoquinone (PQ) concentration are derived. On the basis of these stoichiometric data, we have analyzed the motion of PQ between photosystem (PS) II and cytochrome (cyt.) bf complexes in this highly protein obstructed membrane (protein area about 70%) using percolation theory. This analysis reveals an inefficient diffusion process. We propose that distinct structural features of the thylakoid membrane (grana formation, microdomains) could help to minimize these inefficiencies and ensure a non-rate limiting PQ diffusion process. A large amount of published evidence supports the idea that higher protein associations exist, especially in grana thylakoids. From the quantification of the boundary lipid fraction (about 60%), we conclude that protein complexes involved in these associations should be spaced by lipids. Lipid-spaced protein aggregations in thylakoids are qualitatively different to previously characterized associations (multisubunit complexes, supercomplexes). We derive a hierarchy of protein and lipid interactions in the thylakoid membrane.

Adenosine Triphosphatases↗

The effect of multicomponent diffusion on NAPL dissolution from spherical ternary mixtures.

This paper investigates the dissolution characteristics of ternary nonaqueous phase liquid (NAPL) mixtures with the goal of comparing the relative contributions of multicomponent (intra-NAPL) diffusion, film transfer and thermodynamic nonideality. These contributions are compared at the pore scale and intermediate scale (several centimeters downstream from the source). Trichloroethene (TCE), tetrachloroethene (PCE) and 1,1,1-trichloroethane (TCA) were selected to model a reasonably ideal mixture; TCE, PCE and octanol were selected as a relevant nonideal mixture. A multicomponent diffusion-based dissolution model incorporating hydrodynamic theory was formulated to estimate intra-NAPL concentration gradients and associated aqueous interfacial concentrations for ideally shaped (spherical) NAPL blobs. Pore scale dissolution times for this model were compared to those generated using the conventional well-mixed NAPL dissolution model, applying the same film transfer boundary condition in both cases. Activity coefficients (spatially and temporally variable for the diffusion model, temporally variable for the well-mixed model) were estimated using UNIFAC. NAPL interfacial concentration histories generated using the pore scale models were used as input in a three-dimensional groundwater transport model (MT3DMS) to compare downstream concentration distributions. For the relatively large NAPL bodies simulated (r=0.6 cm), intra-NAPL diffusion effects were found to be significant at the pore scale and were strongly impacted by the mixture's thermodynamic ideality. At the intermediate scale, and for the conditions tested, modest differences in the simulations suggested that intra-NAPL diffusion effects would be negligible compared to those associated with mixture composition uncertainty, dissolution rate processes related to NAPL-induced permeability effects and hydrodynamic issues associated with flow field heterogeneity.

Diffusion↗

Transport properties of polymer solutions. A comparative approach.

A variety of transport properties have been measured for solutions of the water soluble polymer poly(ethylene oxide)(PEO) with molecular weights ranging from 200 to 14,000, and volume fractions ranging from 0-80%. The transport properties are thermal conductivity, electrical conductivity at audio frequencies (in solutions containing dilute electrolyte), and water self-diffusion. These data, together with dielectric relaxation data previously reported, are amenable to analysis by the same mixture theory. The ionic conductivity and water self-diffusion coefficient, but not the thermal conductivity, are substantially smaller than predicted by the Maxwell and Hanai mixture relations, calculated using the known transport properties of pure liquid water. A 25% (by volume) solution of PEO exhibits an average dielectric relaxation frequency of the suspending water of one half that of pure water, with clear evidence of a distribution of relaxation times present. The limits of the cumulative distribution of dielectric relaxation times that are consistent with the data are obtained using a linear programming technique. The application of simple mixture theory, under appropriate limiting conditions, yields hydration values for the more dilute polymer solutions that are somewhat larger than values obtained from thermodynamic measurements.

Biological Transport↗