Relation between acid back -diffusion and luminal surface hydrophobicity in canine gastric mucosa: Effects of salicylate and prostaglandin

The stomach is thought to be protected from luminal acid by a gastric mucosal barrier that restricts the diffusion of acid into tissue. This study tested the hypothesis that the hydrophobic luminal surface of canine gastric mucosa incubated in Ussing chambers, impedes the back-diffusion of luminal acid into the tissue. Isolated sheets of mucosa were treated with cimetidine to inhibit spontaneous acid secretion, and incubated under conditions that prevented significant secretion of luminal bicarbonate. By measuring acid loss from the luminal compartment using the pH-stat technique, acid back-diffusion was continuously monitored; potential difference (PD) was measured as an index of tissue viability. Tissue luminal surface hydrophobicity was estimated by contact angle analysis at the end of each experiment. Addition of 16,16-dimethyl prostaglandin E$\sb2$ to the nutrient compartment enhanced luminal surface hydrophobicity, but did not reduce acid back-diffusion in tissues that maintained a constant PD. 10 mM salicylate at pH 4.00 in the luminal compartment reduced surface hydrophobicity, but this decrease did not occur if 1 ug/ml prostaglandin was present in the nutrient solution. Despite possessing relatively hydrophilic and relatively hydrophobic surface properties, respectively, acid back-diffusion in the absence of salicylate was not significantly different between these two groups. Neither group maintained a PD after incubation with salicylate. Lastly, radiolabelled salicylate was used to calculate the free (non-salicylate associated) acid loss in tissues incubated with salicylate and/or prostaglandin. No significant correlation was found between free acid back-diffusion and luminal surface hydrophobicity. These data do not support the hypothesis that acid back-diffusion in impeded by the hydrophobic surface presented by isolated canine gastric mucosa. ^

Role of tumor–host interactions in interstitial diffusion of macromolecules: Cranial vs. subcutaneous tumors

The large size of many novel therapeutics impairs their transport through the tumor extracellular matrix and thus limits their therapeutic effectiveness. We propose that extracellular matrix composition, structure, and distribution determine the transport properties in tumors. Furthermore, because the characteristics of the extracellular matrix largely depend on the tumor–host interactions, we postulate that diffusion of macromolecules will vary with tumor type as well as anatomical location. Diffusion coefficients of macromolecules and liposomes in tumors growing in cranial windows (CWs) and dorsal chambers (DCs) were measured by fluorescence recovery after photobleaching. For the same tumor types, diffusion of large molecules was significantly faster in CW than in DC tumors. The greater diffusional hindrance in DC tumors was correlated with higher levels of collagen type I and its organization into fibrils. For molecules with diameters comparable to the interfibrillar space the diffusion was 5- to 10-fold slower in DC than in CW tumors. The slower diffusion in DC tumors was associated with a higher density of host stromal cells that synthesize and organize collagen type I. Our results point to the necessity of developing site-specific drug carriers to improve the delivery of molecular medicine to solid tumors.

Life cycle of Deccan trap magma chambers: A crystal scale elemental and strontium isotopic investigation

The Deccan Trap basalts are the remnants of a massive series of lava flows that erupted at the K/T boundary and covered 1-2 million km2 of west-central India. This eruptive event is of global interest because of its possible link to the major mass extinction event, and there is much debate about the duration of this massive volcanic event. In contrast to isotopic or paleomagnetic dating methods, I explore an alternative approach to determine the lifecycle of the magma chambers that supplied the lavas, and extend the concept to obtain a tighter constraint on Deccan’s duration. My method relies on extracting time information from elemental and isotopic diffusion across zone boundaries in individual crystals. I determined elemental and Sr-isotopic variations across abnormally large (2-5 cm) plagioclase crystals from the Thalghat and Kashele “Giant Plagioclase Basalts” from the lowermost Jawhar and Igatpuri Formations respectively in the thickest Western Ghats section near Mumbai. I also obtained bulk rock major, trace and rare earth element chemistry of each lava flow from the two formations. Thalghat flows contain only 12% zoned crystals, with 87 Sr/86Sr ratios of 0.7096 in the core and 0.7106 in the rim, separated by a sharp boundary. In contrast, all Kashele crystals have a wider range of 87Sr/86Sr values, with multiple zones. Geochemical modeling of the data suggests that the two types of crystals grew in distinct magmatic environments. Modeling intracrystalline diffusive equilibration between the core and rim of Thalghat crystals led me to obtain a crystal growth rate of 2.03x10-10 cm/s and a residence time of 780 years for the crystals in the magma chamber(s). Employing some assumptions based on field and geochronologic evidence, I extrapolated this residence time to the entire Western Ghats and obtained an estimate of 25,000–35,000 years for the duration of Western Ghats volcanism. This gave an eruptive rate of 30–40 km3/yr, which is much higher than any presently erupting volcano. This result will remain speculative until a similarly detailed analytical-modeling study is performed for the rest of the Western Ghats formations.

Life Cycle of Deccan Trap Magma Chambers: A Crystal Scale Elemental and Strontium Isotopic Investigation

The Deccan Trap basalts are the remnants of a massive series of lava flows that erupted at the K/T boundary and covered 1-2 million km2 of west-central India. This eruptive event is of global interest because of its possible link to the major mass extinction event, and there is much debate about the duration of this massive volcanic event. In contrast to isotopic or paleomagnetic dating methods, I explore an alternative approach to determine the lifecycle of the magma chambers that supplied the lavas, and extend the concept to obtain a tighter constraint on Deccan’s duration. My method relies on extracting time information from elemental and isotopic diffusion across zone boundary in an individual crystal. I determined elemental and Sr-isotopic variations across abnormally large (2-5 cm) plagioclase crystals from the Thalghat and Kashele “Giant Plagioclase Basalts” from the lowermost Jawhar and Igatpuri Formations respectively in the thickest Western Ghats section near Mumbai. I also obtained bulk rock major, trace and rare earth element chemistry of each lava flow from the two formations. Thalghat flows contain only 12% zoned crystals, with 87Sr/86Sr ratios of 0.7096 in the core and 0.7106 in the rim, separated by a sharp boundary. In contrast, all Kashele crystals have a wider range of 87Sr/86Sr values, with multiple zones. Geochemical modeling of the data suggests that the two types of crystals grew in distinct magmatic environments. Modeling intracrystalline diffusive equilibration between the core and rim of Thalghat crystals led me to obtain a crystal growth rate of 2.03x10-10 cm/s and a residence time of 780 years for the crystals in the magma chamber(s). Employing some assumptions based on field and geochronologic evidence, I extrapolated this residence time to the entire Western Ghats and obtained an estimate of 25,000 – 35,000 years for the duration of Western Ghats volcanism. This gave an eruptive rate of 30 – 40 km3/yr, which is much higher than any presently erupting volcano. This result will remain speculative until a similarly detailed analytical-modeling study is performed for the rest of the Western Ghats formations.

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.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.