A study of the diffusion characteristics of normal, delipidized and relipidized articular cartilage using magnetic resonance imaging

This paper assesses the capacity to provide semipermeability of the synthetic layer of surface-active phospholipids created to replace the depleted surface amorphous layer of articular cartilage. The surfaces of articular cartilage specimens in normal, delipidized, and relipidized conditions following incubation in dipalmitoyl-phosphatidylcholine and palmitoyl-oleoyl-phosphatidylcholine components of the joint lipid mixture were characterized nanoscopically with the atomic force microscope and also imaged as deuterium oxide (D2O) diffused transiently through these surfaces in a magnetic resonance imaging enclosure. The MR images were then used to determine the apparent diffusion coefficients in a purpose-built MATLAB®-based algorithm. Our results revealed that all surfaces were permeable to D2O, but that there was a significant difference in the semipermeability of the surfaces under the different conditions, relative to the apparent diffusion coefficients. Based on the results and observations, it can be concluded that the synthetic lipid that is deposited to replace the depleted SAL of articular cartilage is capable of inducing some level of semipermeability.

Delivering crushed tablets using thickened fluids : is drug diffusion into gastric fluids restricted?

Solid medications are often crushed and mixed with food or thickened water to aid drug delivery for those who cannot or prefer not to swallow whole tablets or capsules. Dysphagic patients have the added problem of being unable to safely swallow thin fluids so water thickened with polysaccharides is used to deliver crushed medications and ensure safe swallowing. It is postulated that these polysaccharide systems may restrict drug release by reducing the diffusion of the drug into gastric fluids. METHODS By using a vertical diffusion cell separated with a synthetic membrane, the diffusion of a model drug (atenolol) was studied from a donor system containing the drug dispersed into thickened water with xanthan gum (concentration range from 0.005%-2.2%) into a receptor system containing simulated gastric fluid (SGF) at 37°C. The amount of drug transferred was measured over 8 hours and diffusion coefficients estimated using the Higuchi model approach. RESULTS Atenolol diffusion decreased with increasing xanthan gum concentration up to 1.0%, above which diffusion remained around 300 μ2s-1. The rheological measurements captured the influence of the structure and conformation of the polysaccharide in water on the movement and availability of the drug in SGF. DISCUSSION Dose form administration for dysphagic patients’ needs special attention from general practitioners, pharmacist and patients. Improving drug release of crushed tablets from thickening agents requires a reduction in the diffusion pathway (e.g. by decreasing drop size radius). This approach could make the drug available in SGF in a short time without compromising the mechanical aspects of thickening agents that guarantee safe swallowing.

Comparing charge transport predictions for a ternary electrolyte using the Maxwell–Stefan and Nernst–Planck equations

In this work, we investigate and compare the Maxwell–Stefan and Nernst–Planck equations for modeling multicomponent charge transport in liquid electrolytes. Specifically, we consider charge transport in the Li+/I−/I3−/ACN ternary electrolyte originally found in dye-sensitized solar cells. We employ molecular dynamics simulations to obtain the Maxwell–Stefan diffusivities for this electrolyte. These simulated diffusion coefficients are used in a multicomponent charge transport model based on the Maxwell– Stefan equations, and this is compared to a Nernst–Planck based model which employs binary diffusion coefficients sourced from the literature. We show that significant differences between the electrolyte concentrations at electrode interfaces, as predicted by the Maxwell–Stefan and Nernst–Planck models, can occur. We find that these differences are driven by a pressure term that appears in the Maxwell–Stefan equations. We also investigate what effects the Maxwell–Stefan diffusivities have on the simulated charge transport. By incorporating binary diffusivities found in the literature into the Maxwell–Stefan framework, we show that the simulated transient concentration profiles depend on the diffusivities; however, the simulated equilibrium profiles remain unaffected.

A cell migration device that maintains a defined surface with no cellular damage during wound edge generation

Studying the rate of cell migration provides insight into fundamental cell biology as well as a tool to assess the functionality of synthetic surfaces and soluble environments used in tissue engineering. The traditional tools used to study cell migration include the fence and wound healing assays. In this paper we describe the development of a microchannel based device for the study of cell migration on defined surfaces. We demonstrate that this device provides a superior tool, relative to the previously mentioned assays, for assessing the propagation rate of cell wave fronts. The significant advantage provided by this technology is the ability to maintain a virgin surface prior to the commencement of the cell migration assay. Here, the device is used to assess rates of mouse fibroblasts (NIH 3T3) and human osteosarcoma (SaOS2) cell migration on surfaces functionalized with various extracellular matrix proteins as a demonstration that confining cell migration within a microchannel produces consistent and robust data. The device design enables rapid and simplistic assessment of multiple repeats on a single chip, where surfaces have not been previously exposed to cells or cellular secretions.

Dynamic Micromapping of CO2 Sorption in Coal

We have applied X-ray and neutron small-angle scattering techniques (SAXS, SANS, and USANS) to study the interaction between fluids and porous media in the particular case of subcritical CO2 sorption in coal. These techniques are demonstrated to give unique, pore-size-specific insights into the kinetics of CO2 sorption in a wide range of coal pores (nano to meso) and to provide data that may be used to determine the density of the sorbed CO2. We observed densification of the adsorbed CO2 by a factor up to five compared to the free fluid at the same (p, T) conditions. Our results indicate that details of CO2 sorption into coal pores differ greatly between different coals and depend on the amount of mineral matter dispersed in the coal matrix: a purely organic matrix absorbs more CO2 per unit volume than one containing mineral matter, but mineral matter markedly accelerates the sorption kinetics. Small pores are filled preferentially by the invading CO2 fluid and the apparent diffusion coefficients have been estimated to vary in the range from 5 × 10-7 cm2/min to more than 10-4 cm2/min, depending on the CO2 pressure and location on the sample.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Diffusion indices on magnetic resonance imaging and neuropsychological performance in amnestic mild cognitive impairment

Background: Magnetic resonance diffusion tensor imaging (DTI) shows promise in the early detection of microstructural pathophysiological changes in the brain. Objectives: To measure microstructural differences in the brains of participants with amnestic mild cognitive impairment (MCI) compared with an age-matched control group using an optimised DTI technique with fully automated image analysis tools and to investigate the correlation between diffusivity measurements and neuropsychological performance scores across groups. Methods: 34 participants (17 participants with MCI, 17 healthy elderly adults) underwent magnetic resonance imaging (MRI)-based DTI. To control for the effects of anatomical variation, diffusion images of all participants were registered to standard anatomical space. Significant statistical differences in diffusivity measurements between the two groups were determined on a pixel-by-pixel basis using gaussian random field theory. Results: Significantly raised mean diffusivity measurements (p<0.001) were observed in the left and right entorhinal cortices (BA28), posterior occipital-parietal cortex (BA18 and BA19), right parietal supramarginal gyrus (BA40) and right frontal precentral gyri (BA4 and BA6) in participants with MCI. With respect to fractional anisotropy, participants with MCI had significantly reduced measurements (p<0.001) in the limbic parahippocampal subgyral white matter, right thalamus and left posterior cingulate. Pearson's correlation coefficients calculated across all participants showed significant correlations between neuropsychological assessment scores and regional measurements of mean diffusivity and fractional anisotropy. Conclusions: DTI-based diffusivity measures may offer a sensitive method of detecting subtle microstructural brain changes associated with preclinical Alzheimer's disease.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.