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PubMed2002

Ionic self-diffusion in concentrated aqueous electrolyte solutions.

A self-consistent microscopic theory is developed to understand the anomalously weak concentration dependence of ionic self-diffusion coefficient D(ion) in electrolyte solutions. The self-consistent equations are solved by using the mean spherical approximation expressions of the static pair correlation functions for unequal sizes. The results are in excellent agreement both with the known experimental results for many binary electrolytes and also with the new Brownian dynamics simulation results. The calculated velocity time correlation functions also show quantitative agreement with simulations. The theory also explains the reason for observing different D(ion) in recent NMR and neutron scattering experiments.

Journal Article↗
PubMed2003

Drag force, diffusion coefficient, and electric mobility of small particles. II. Application.

We propose a generalized treatment of the drag force of a spherical particle due to its motion in a laminar fluid media. The theory is equally applicable to analysis of particle diffusion and electric mobility. The focus of the current analysis is on the motion of spherical particles in low-density gases with Knudsen number Kn>>1. The treatment is based on the gas-kinetic theory analysis of drag force in the specular and diffuse scattering limits obtained in a preceding paper [Z. Li and H. Wang, Phys. Rev. E., 68, 061206 (2003)]. Our analysis considers the influence of van der Waals interactions on the momentum transfer upon collision of a gas molecule with the particle and expresses this influence in terms of an effective, reduced collision integral. This influence is shown to be significant for nanosized particles. In the present paper, the reduced collision integral values are obtained for specular and diffuse scattering, using a Lennard-Jones-type potential energy function suitable for the interactions of a gas molecule with a particle. An empirical formula for the momentum accommodation function, used to determine the effective, reduced collision integral, is obtained from available experimental data. The resulting treatment is shown to be accurate for interpreting the mobility experiments for particles as small as approximately 1 nm in radius. The treatment is subsequently extended to the entire range of the Knudsen number, following a semiempirical, gas-kinetic theory analysis. We demonstrate that the proposed formula predicts very well Millikan's oil-droplet experiments [R. A. Millikan, Philos. Mag. 34, 1 (1917); Phys. Rev. 22, 1 (1923)]. The rigorous theoretical foundation of the proposed formula in the Kn>>1 limit makes the current theory far more general than the semiempirical Stokes-Cunningham formula in terms of the particle size and condition of the fluid and, therefore, more attractive than the Stokes-Cunningham formula.

Journal Article↗
PubMed2002

Statistical analysis of nonlinearly reconstructed near-infrared tomographic images: Part I--Theory and simulations.

Near-infrared (NIR) diffuse tomography is an emerging method for imaging the interior of tissues to quantify concentrations of hemoglobin and exogenous chromophores non-invasively in vivo. It often exploits an optical diffusion model-based image reconstruction algorithm to estimate spatial property values from measurements of the light flux at the surface of the tissue. In this study, mean-squared error (MSE) over the image is used to evaluate methods for regularizing the ill-posed inverse image reconstruction problem in NIR tomography. Estimates of image bias and image standard deviation were calculated based upon 100 repeated reconstructions of a test image with randomly distributed noise added to the light flux measurements. It was observed that the bias error dominates at high regularization parameter values while variance dominates as the algorithm is allowed to approach the optimal solution. This optimum does not necessarily correspond to the minimum projection error solution, but typically requires further iteration with a decreasing regularization parameter to reach the lowest image error. Increasing measurement noise causes a need to constrain the minimum regularization parameter to higher values in order to achieve a minimum in the overall image MSE.

Computer Simulation↗
PubMed2003

Countercurrent exchange in the renal medulla.

The microcirculation of the renal medulla traps NaCl and urea deposited to the interstitium by the loops of Henle and collecting ducts. Theories have predicted that countercurrent exchanger efficiency is favored by high permeability to solute. In contrast to the conceptualization of vasa recta as simple "U-tube" diffusive exchangers, many findings have revealed surprising complexity. Tubular-vascular relationships in the outer and inner medulla differ markedly. The wall structure and transport properties of descending vasa recta (DVR) and ascending vasa recta (AVR) are very different. The recent discoveries of aquaporin-1 (AQP1) water channels and the facilitated urea carrier UTB in DVR endothelia show that transcellular as well as paracellular pathways are involved in equilibration of DVR plasma with the interstitium. Efflux of water across AQP1 excludes NaCl and urea, leading to the conclusion that both water abstraction and diffusion contribute to transmural equilibration. Recent theory predicts that loss of water from DVR to the interstitium favors optimization of urinary concentration by shunting water to AVR, secondarily lowering blood flow to the inner medulla. Finally, DVR are vasoactive, arteriolar microvessels that are anatomically positioned to regulate total and regional blood flow to the outer and inner medulla. In this review, we provide historical perspective, describe the current state of knowledge, and suggest areas that are in need of further exploration.

Animals↗
PubMed2006

Myoglobin translational diffusion in rat myocardium and its implication on intracellular oxygen transport.

Current theory of respiratory control invokes a role of myoglobin (Mb)-facilitated O2 diffusion in regulating the intracellular O2 flux, provided Mb diffusion can compete effectively with free O2 diffusion. Pulsed-field gradient NMR methods have now followed gradient-dependent changes in the distinct 1H NMR gamma CH3 Val E11 signal of MbO2 in perfused rat myocardium to obtain the endogenous Mb translational diffusion coefficient (D(Mb)) of 4.24 x 10(-7) cm2 s(-1) at 22 degrees C. The D(Mb) matches precisely the value predicted by in vivo NMR rotational diffusion measurements of Mb and shows no orientation preference. Given values in the literature for the Krogh's free O2 diffusion coefficient (K0), myocardial Mb concentration and a partial pressure of O2 that half saturates Mb (P50), the analysis yields an equipoise diffusion P(O2) of 1.77 mmHg, where Mb and free O2 contribute equally to the O2 flux. In the myocardium, Mb-facilitated O2 diffusion contributes increasingly more than free O2 diffusion when the P(O2) falls below 1.77 mmHg. In skeletal muscle, the P(O2) must fall below 5.72 mmHg. Altering the Mb P50 induces modest change. Mb-facilitated diffusion has a higher poise in skeletal muscle than in myocardium. Because the basal P(O2) hovers around 10 mmHg, Mb does not have a predominant role in facilitating O2 transport in myocardium but contributes significantly only when cellular oxygen falls below the equipoise diffusion P(O2).

Adenosine Triphosphate↗
PubMed1996

Drug-membrane interactions studied by molecular dynamics simulation: size dependence of diffusion.

Bioavailability, largely due to membrane permeation, is an important step in the drug delivery process and therefore drug design. In this study, a series of molecular dynamics simulations (totaling 10's of nanoseconds) of small molecules (varying in size, and functional groups) in lipid bilayer membranes were used to elucidate the mechanism of diffusion of drugs within biomembranes. These simulations accurately reproduce many experimentally observed parameters. The simulations also agree with theory that indicates the lipid bilayer has internal structure that influences the diffusion process and that even within the hydrocarbon regions there are distinct regions between which the rate and mechanism of diffusion varies. In particular, in agreement with experiment and theory the small solutes were found to diffuse by a mechanism different from that of large molecules. These variations are linked to the frequency and size of spontaneously arising voids within the bilayer as well as the rate of torsional isomerization of the hydrocarbon chains.

Biological Availability↗
PubMed2002

Electrophoresis of solid particles at large Peclet numbers.

A theory of concentration polarization of a thin electrical double layer (DL) on a spherical particle is developed for the regime of large Peclet numbers which is realized in strong electric fields. In this regime, the concentration field arising outside DL is estimated under influence of diffusion and convection. According to the theory developed, polarization of DL at large Peclet numbers causes a change in the Stern potential, the formation of a dipole moment and the long-range potential. The diffuse layer deviates strongly from spherical symmetry and electroneutrality, and the screen of the surface charge is provided not only by the diffuse atmosphere but also by the charge induced in the convective-diffusion layer. The effect of electric field on the induced charge gives rise to the additional electroosmotic slip, that was called "secondary electroosmosis". Thus, a nonlinear additional term for the Smoluchowski formula of electrophoretic velocity is based on the changes of zeta-potential and on the secondary electroosmotic slip. The comparison of theory with experimental results revealed considerable fitting.

Electrochemistry↗
PubMed1999

The relationship between water absorption characteristics and the mechanical strength of resin-modified glass-ionomer cements in long-term water storage.

The purpose of this study is to elucidate the water absorption characteristics of resin-modified glass-ionomer cements and to also investigate the relationship between the characteristics and mechanical strength after long-term water storage. The mechanism of water diffusion in these cements is also discussed. Water absorption was measured using a gravimetric analysis for 12 m, while the diffusion coefficient was calculated using Fick's law of diffusion. Water solubility was determined based on the weight of the residue in the immersed water. The compressive and diametral tensile strength were measured at 1, 2, 6, and 12 m. A correlation was observed between the diffusion coefficient and equilibrium water uptake, which thus suggests the water in the cements to diffuse through micro-voids in accordance with the 'Free volumetric theory'. A correlation was seen between the solubility and diffusion coefficient of the cements. The deterioration ratio, defined as the ratio of the strength at 12 m versus that at 1 m, was also calculated. Finally, a negative correlation was observed between the deterioration ratio of the compressive strength and the diffusion coefficients of the cements.

Absorption↗
PubMed1999

Specular and diffuse scattering of highly aligned phospholipid membranes.

We present a quantitative study of specular and diffuse (non-specular) x-ray and neutron reflectivity from highly aligned phospholipid membranes deposited on solid substrates. The height-height correlation function could be obtained from the diffuse scattering without further model assumptions. The results differ significantly from the linear theory of smectic elasticity. We argue that the diffuse scattering is dominated by static liquid-crystalline defects, rather than thermal fluctuations.

1,2-Dipalmitoylphosphatidylcholine↗
PubMed2005

Position-sensitive scanning fluorescence correlation spectroscopy.

Fluorescence correlation spectroscopy (FCS) uses a stationary laser beam to illuminate a small sample volume and analyze the temporal behavior of the fluorescence fluctuations within the stationary observation volume. In contrast, scanning FCS (SFCS) collects the fluorescence signal from a moving observation volume by scanning the laser beam. The fluctuations now contain both temporal and spatial information about the sample. To access the spatial information we synchronize scanning and data acquisition. Synchronization allows us to evaluate correlations for every position along the scanned trajectory. We use a circular scan trajectory in this study. Because the scan radius is constant, the phase angle is sufficient to characterize the position of the beam. We introduce position-sensitive SFCS (PSFCS), where correlations are calculated as a function of lag time and phase. We present the theory of PSFCS and derive expressions for diffusion, diffusion in the presence of flow, and for immobilization. To test PSFCS we compare experimental data with theory. We determine the direction and speed of a flowing dye solution and the position of an immobilized particle. To demonstrate the feasibility of the technique for applications in living cells we present data of enhanced green fluorescent protein measured in the nucleus of COS cells.

Algorithms↗
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↗
PubMed2000

Fluorescence intensity multiple distributions analysis: concurrent determination of diffusion times and molecular brightness.

Fluorescence correlation spectroscopy (FCS) has proven to be a powerful technique with single-molecule sensitivity. Recently, it has found a complement in the form of fluorescence intensity distribution analysis (FIDA). Here we introduce a fluorescence fluctuation method that combines the features of both techniques. It is based on the global analysis of a set of photon count number histograms, recorded with multiple widths of counting time intervals simultaneously. This fluorescence intensity multiple distributions analysis (FIMDA) distinguishes fluorescent species on the basis of both the specific molecular brightness and the translational diffusion time. The combined information, extracted from a single measurement, increases the readout effectively by one dimension and thus breaks the individual limits of FCS and FIDA. In this paper a theory is introduced that describes the dependence of photon count number distributions on diffusion coefficients. The theory is applied to a series of photon count number histograms corresponding to different widths of counting time intervals. Although the ability of the method to determine specific brightness values, diffusion times, and concentrations from mixtures is demonstrated on simulated data, its experimental utilization is shown by the determination of the binding constant of a protein-ligand interaction exemplifying its broad applicability in the life sciences.

Adaptor Proteins, Signal Transducing↗
PubMed1996

Interpretation of electrophoretic band shapes by a partition chromatographic model.

Measurements of the shape of electrophoretic bands of phycoerythrin and conalbumin have been made at regular intervals during migration in agarose gels. Analysis of the peak shapes suggests the existence of a significant degree of asymmetry. This is to be contrasted with the symmetry around the peak associated with the generally assumed Gaussian band. The degree of asymmetry of the bands decreased as a function of time and increased with agarose concentration. A similar experiment on DNA indicated constancy of the degree of asymmetry as a function of time. These results can be interpreted as, but do not prove the validity of, a nonlocal diffusion equation which generalizes a theory originally put forth by Giddings and Eyring (J. Am. Chem. Soc. 1955, 59, 416-420). The results may be significant in framing a measure of the resolvability of electrophoretic peaks.

Electrophoresis, Agar Gel↗
PubMed1998

Diffusion in a Fractal System.

The surface geometry of Vycor porous glass was examined by using the relative permeability (PR) technique in a H2O/He system. At a water relative pressure of approximately 0.3, a maximum is observed on the PR curve. This maximum is explained in terms of geometrical changes taking place due to the deposition of a water film on the internal Vycor surface. When the sample is dry, diffusion in a fractal system is found to be more appropriate in describing the process. When the sample is wet, the diffusion process obeys classical Knudsen theory for smooth cylinders. Copyright 1998 Academic Press.

Journal Article↗
PubMed2001

Visual filling-in for computing perceptual surface properties.

The visual system is constantly confronted with the problem of integrating local signals into more global arrangements. This arises from the nature of early cell responses, whether they signal localized measures of luminance, motion, retinal position differences, or discontinuities. Consequently, from sparse, local measurements, the visual system must somehow generate the most likely hypothesis that is consistent with them. In this paper, we study the problem of determining achromatic surface properties, namely brightness. Mechanisms of brightness filling-in have been described by qualitative as well as quantitative models, such as by the one proposed by Cohen and Grossberg. We demonstrate that filling-in from contrast estimates leads to a regularized solution for the computational problem of generating brightness representations from sparse estimates. This provides deeper insights into the nature of filling-in processes and the underlying objective function one wishes to compute. This particularly guided the proposal of a new modified version of filling-in, namely confidence-based filling-in which generates more robust brightness representations. Our investigation relates the modeling of perceptual data for biological vision to the mathematical frameworks of regularization theory and linear spatially variant diffusion. It therefore unifies different research directions that have so far coexisted in different scientific communities.

Animals↗
PubMed2006

Optical properties of ocular tissues in the near infrared region.

Near infrared characterization of optical properties of aqueous humor and vitreous humor of healthy human and bovine eyes has been performed. The indices of refraction (n) of these ocular tissues were determined using a Michelson interferometer. The total diffuse reflection (R (d)) and total transmission (T (t)) measurements had been taken for individual ocular tissue by using a double-integrating sphere setup and infrared laser diodes. The inverse adding doubling (IAD) computational method based on the diffusion approximation and radiative transport theory was applied to the measured values of n, R (d), and T (t) to calculate the optical absorption and scattering coefficients of the human and bovine ocular tissues. The scattering anisotropy value was determined by iteratively running the IAD method program and a Monte Carlo simulation of light-tissue interaction until the minimum difference in experimental and computed value for T (t) was realized. A comparison between the optical characterization of human and bovine ocular samples was also made.

Aged↗
PubMed2004

Model development and numerical simulation of electric-stimulus-responsive hydrogels subject to an externally applied electric field.

Based on a multi-phasic mixture theory with consideration of ionic diffusion and convection, a multi-physic model, called the multi-effect-coupling electric-stimulus (MECe) model, is developed for simulation of responsive behavior of the electric-sensitive hydrogels when they are immersed into a bathing solution subject to an externally applied electric field. In the developed model, with chemo-electro-mechanical coupling effects, the convection-diffusion equations for concentration distribution of diffusive ions incorporate the influence of electric potential. The electroneutrality condition is replaced by the Poisson equation for distribution of electric potential. The steady and transient analyses of hydrogel deformation are easily carried out by the continuity and momentum equations of the mixture phase. Further, the computational domain of the present model covers both the hydrogel and the surrounding solution. In order to solve the present mathematical model consisting of multi-field coupled nonlinear partial differential governing equations, a hierarchical iteration technique is proposed and a meshless Hermite-Cloud method (HCM) is employed. The steady-state simulation of the electric-stimulus responsive hydrogel is numerically conducted when it is subjected to an externally applied electric field. The hydrogel deformation and the ionic concentrations as well as electric potentials of both the hydrogel and external solution are investigated. The parameter influences on the swelling behaviors of the hydrogel are also discussed in detail. The simulating results are in good agreement with the experimental data and they validate the presently developed model.

Biosensing Techniques↗
PubMed1977

Observations upon calcium oxalate crystallization kinetics in simulated urine.

Two major etiologic theories of urinary stones are excessive saturation of urine with crystallizable substances or defects in inhibitors that allow relative supersaturation to occur. To date, it has been difficult to confirm the supersaturation theory in experiments using diffusion-limited crystallization systems because direct measurements of the nucleation process of crystallization could not be performed. We used well developed, continuous crystallizer techniques and adapted them from industrial use to the study of stone disease. Data derived from the experiments allow the absolute measurement of crystal growth rate and determination of nucleation rate. These methods were applied to study the calcium oxalate dihydrate (weddellite) system in artificial urine that lacked only proteinaceous components. Based on these experiments it was not possible to grow crystals large enough within 5 to 20 minutes to obstruct the collecting ducts of the kidney. Therefore, it appears that other processes, such as aggregation or stasis within tissues, may well be related to initiation of stone disease. Under the experimental conditions of this study nucleation rate exceeded growth rate. Therefore, multiple small particles are created at the expense of allowing larger particles to grow. Inhibitors can be tested rapidly in this system by adding them in concentrations compatible with those found in urine.

Calcium↗