(549i) Modeling of Diffusion in Stratified Epithelia Using Smoothed Particle Hydrodynamics

Detailed microscopic diffusion models of solute transport through stratified epithelia serve as valuable tools to understand solute flux pathways, make reasonable predictions of transport rates and tissue concentrations, and quantify transport mechanisms underlying biological function.  Thus, for instance, brick-and-mortar models of the stratum (SC, barrier) layer of skin¹ can provide the quantitative basis to predict permeation of topically applied and transdermally delivered drugs, and assess risks associated with chemical exposures.  Such models have evolved to incorporate two-dimensional cross-sectional geometries of cells and surrounding lipid membranes based on actual bitmapped microscope images,² and idealized three-dimensional  polygonal geometries,^3-7 which are usually approached by finite element and finite volume methods.^2-7  Smoothed particle hydrodynamics (SPH) is a general, mesh-free method^8-10 for solving partial differential equations in more intricate and realistic domain geometries that can overtax these grid-based numerical techniques.  As yet, it has seen essentially no application to biological diffusion problems.  This talk develops the extensions of SPH needed to realistically address such problems, and applies it to derive significant mechanistic conclusions from test problems describing dermal absorption.

Traditional SPH is based upon grid-free, inter-node interpolation of the solute concentration field using a suitable window or kernel function.  We use a non-interpolant variant of SPHthat corresponds to tracking mesoscale pseudo-particles of solute that interact via the kernels.^11-13  Kernel sums over boundary particles represent an effective “chemical potential” of the walls and allow efficient treatment of arbitrary domain shapes.^14-16  For the resultant non-interpolant boundary-sum (NIBS) SPH method, a chaining mesh reduces all sums to O(N) operations.  Three phenomena prevalent in biological systems define the extensions needed for biological applications of SPH, namely: (i) partitioning equilibria at the interfaces between aqueous and lipid phases; (ii) strong diffusional anisotropy of fluid-phase phospholipid-cholesterol bilayers in viable cell layers, and ordered gel-phase arrays of ceramides, cholesterol and long-chain fatty acids in keratinized epithelia; and (iii) binding to albumin and other binding/transporter proteins in both cytoplasm and extracellular fluid of viable cells, as well as keratin in cornified cells.  We show in detail how these three phenomena can be incorporated into the NIBS-SPH method, including kinetic rates of exchange between mobile and bound populations of particles in the case of binding.

Solute concentration profiles, effective permeability coefficients for perpendicular penetration, and effective lateral diffusion coefficients quantifying in-plane solute mobility are calculated for realistic microscopic representations of sections of (a) human stratum corneum, and (b) underlying viable epidermis, based on realistic physicochemical parameterizations for the model compounds water, hydrocortisone and glucose.  It is shown that the diffusional anisotropy of intercellular lipid phases has a dramatically affect on concentration profiles and fluxes, strongly controverting numerical results based on the assumption of an isotropic lipid phase that has commonly been made to date.^2-7

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