A two-dimensional mathematical model of percutaneous drug absorption

Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1) the flow rate of the drug, (2) the flux and the cumulative amount of drug eliminated into the receptor cell, (3) the steady-state value of the flux, (4) the time to reach the steady-state value of the flux and (5) the optimal value of r, which gives the maximum absorption of the drug. The paper gives valuable information which can be obtained by this two-dimensional model, that cannot be obtained with one-dimensional models. Thus this model improves upon the much simpler one-dimensional models. Some future directions of the work based on this model and the one-dimensional non-linear models that exist in the literature, are also discussed

PCNA Retention on DNA into G2/M Phase Causes Genome Instability in Cells Lacking Elg1

Acknowledgments We thank Richard Kolodner, Grant Brown, and Daniel Durocher for strains and plasmids. We thank Anne Donaldson, Alexander Lorenz, and Shin-ichiro Hiraga from University of Aberdeen for careful reading of the manuscript. Research in T.K.’s lab is supported by Medical Research Council Career Development Fellowship L019698/1. V.K.G. was supported by Biotechnology and Biological Sciences Research Council grant K006304/1. T.S.T. was supported by grants from the Ministry of Education, Culture, Sports, Science and Technology of Japan (nos. 23131507 and 25131712).Peer reviewedPublisher PD

Efficiency of Grain Production in 18F Micro-Autoradiography

開始ページ、終了ページ: 冊子体のページ付

Distribution of 2-[18F]FDOPA in B16 Melanoma: a Double-Tracer Microautoradiographic Study

開始ページ、終了ページ: 冊子体のページ付