Modeling and numerical computation of drug transport in laminates: model case evaluation of transdermal delivery system

Recent Advances in Drug Design and Delivery Across Biological Barriers using Computational Models

Abstract:

The systemic delivery of pharmacological substances generally exhibits several significant limitations associated with the bio-distribution of active drugs in the body. As per consequence, human body’s defense mechanisms become impediments to drug delivery. Various technologies to overcome these limitations have been evolved including computational approaches and advanced drug delivery. As the body of human has evolved to defend itself from hostile biological as well as chemical invaders, along with that these biological barriers such as ocular barriers, blood-brain barriers, intestinal and skin barriers also limit the passage of drugs across desired sites. Therefore, efficient delivery remains an utmost challenge for researchers and scientists. The present review focuses on the techniques to deliver the drugs with efficient therapeutic efficacy at the targeted sites. This review article considered the insights into main biological barriers along with the application of computational or numerical methods dealing with different barriers by determining the drug flow, temperature and various other parameters. It also summarizes the advanced implantable drug delivery system to circumvent the inherent resistance showed by these biological barriers and in turn to improve the drug delivery.

Application of numerical methods for diffusion-based modeling of skin permeation

The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions.

Detailed modeling of skin penetration--an overview

In recent years, the combination of computational modeling and experiments has become a useful tool that is proving increasingly powerful for explaining biological complexity. As computational power is increasing, scientists are able to explore ever more complex models in finer detail and to explain very complex real world data. This work provides an overview of one-, two- and three-dimensional diffusion models for penetration into mammalian skin. Besides diffusive transport this includes also binding of substances to skin proteins and metabolism. These models are based on partial differential equations that describe the spatial evolution of the transport process through the biological barrier skin. Furthermore, the work focuses on analytical and numerical techniques for this type of equations such as discretization schemes or homogenization (upscaling) techniques. Finally, the work compares different geometry models with respect to the permeability.

Computational modeling of the skin barrier

A simulation environment for the numerical calculation of permeation processes through human skin has been developed. In geometry models that represent the actual cell morphology of stratum corneum (SC) and deeper skin layers, the diffusive transport is simulated by a finite volume method. As reference elements for the corneocyte cells and lipid matrix, both three-dimensional tetrakaidecahedra and cuboids as well as two-dimensional brick-and-mortar models have been investigated. The central finding is that permeability and lag time of the different membranes can be represented in a closed form depending on model parameters and geometry. This allows a comparison of the models in terms of their barrier effectiveness at comparable cell sizes. The influence of the cell shape on the barrier properties has been numerically demonstrated and quantified. It is shown that tetrakaidecahedra in addition to an almost optimal surface-to-volume ratio also has a very favorable barrier-to-volume ratio. A simulation experiment was successfully validated with two representative test substances, the hydrophilic caffeine and the lipophilic flufenamic acid, which were applied in an aqueous vehicle with a constant dose. The input parameters for the simulation were determined in a companion study by experimental collaborators.

In-silico model of skin penetration based on experimentally determined input parameters. Part II: Mathematical modelling of in-vitro diffusion experiments. Identification of critical input parameters

This work describes a framework for in-silico modelling of in-vitro diffusion experiments illustrated in an accompanying paper [S. Hansen, A. Henning, A. Naegel, M. Heisig, G. Wittum, D. Neumann, K.-H. Kostka, J. Zbytovska, C.M. Lehr, U.F. Schaefer, In-silico model of skin penetration based on experimentally determined input parameters. Part I: experimental determination of partition and diffusion coefficients, Eur. J. Pharm. Biopharm. 68 (2008) 352-367 [corrected] A mathematical model of drug permeation through stratum corneum (SC) and viable epidermis/dermis is presented. The underlying geometry for the SC is of brick-and-mortar character, meaning that the corneocytes are completely embedded in the lipid phase. The geometry is extended by an additional compartment for the deeper skin layers (DSL). All phases are modelled with homogeneous diffusivity. Lipid-donor and SC-DSL partition coefficients are determined experimentally, while corneocyte-lipid and DSL-lipid partition coefficients are derived consistently with the model. Together with experimentally determined apparent lipid- and DSL-diffusion coefficients, these data serve as direct input for computational modelling of drug transport through the skin. The apparent corneocyte diffusivity is estimated based on an approximation, which uses the apparent SC- and lipid-diffusion coefficients as well as corneocyte-lipid partition coefficients. The quality of the model is evaluated by a comparison of concentration-SC-depth-profiles of the experiment with those of the simulation. Good agreements are obtained, and by an analysis of the underlying model, critical parameters of the models can be identified more easily.

Transdermal testing: practical aspects and methods

Interest in transdermal drug delivery has increased in recent years owing to its many advantages over other routes of administration. In order to evaluate a transdermal product effectively, three main issues need to be addressed: (1) the kind of skin model that will be used to evaluate the drug permeation; (2) the mathematical model that will be used to characterize the permeation of the drug across the skin; and (3) the diffusion apparatus that will be used to conduct the permeation study.

Effect of interparticulate interaction on release kinetics of microsphere ensembles

The release kinetics of microsphere ensembles is complicated by the mutual influence of the microspheres which are entrapped in small compartments such as body cavities. This work focused on the effect of interparticulate interaction on the release kinetics of microsphere ensembles with limited spreading. Experiments and finite element modeling were conducted to investigate diffusional drug release from a single sphere, a monolayer, and multiple layers of microspheres. Poly(methyl methacrylate-co-methacrylic acid) (P(MMA/MAA)) microspheres and azidothymidine (AZT) were used in the experiments. The order of the release rate of AZT from various microsphere populations was observed to be single sphere > monolayer > multiple layers. This evidenced the importance of interparticulate interaction. The finite element simulations elucidated the influence of various factors on the release kinetics of microsphere ensembles including the separation distance, location of the spheres, and the drug accumulation in the medium. Calibration of overall release kinetics for the neighboring effect was proposed on the basis of the spreading factor. Overall release profiles of microsphere ensembles were predicted using the release profiles of individual microspheres at various locations.

Finite element analysis of diffusional drug release from complex matrix systems. II. Factors influencing release kinetics

This work concentrated on the analysis of several factors influencing the kinetics of diffusional drug release from complex matrix devices, such as convex tablets and rings, into a finite volume. These factors include initial drug concentration distribution, anisotropic matrix, and time- and concentration-dependent diffusion coefficients. The individual and comprehensive effects of these factors on the release kinetics were investigated by the finite element method. Errors introduced by neglecting drug diffusion through the ends of edges of cylindrical devices were estimated by comparison of the 1-D models with the 2-D cylinder model. The influence of side-wall coating on the accuracy of the prediction of release profiles by the 1-D slab model for cylindrical devices was studied using various coating materials of different permeabilities. The analyses carried out in this work could assist the design of the complex matrix systems required for controlled drug release.

Transdermal drug delivery and cutaneous metabolism

The delivery of drugs via the skin to achieve systemic therapeutic effect is currently under intense investigation. The skin offers unique advantages and limitations for drug input into the body. For example, while hepatic first pass may be circumvented, the excellent barrier function of the stratum corneum (the thin outermost layer of skin) precludes, at present, all but the most potent drugs from this route of administration. Examples of approved transdermally delivered drugs are scopolamine, nitroglycerin, clonidine and estradiol. The delivery systems which have been formulated for these agents have been designed to provide essentially zero-order input kinetics for between 1 and 7 days. The impact of cutaneous metabolism on transdermal drug delivery has not yet been evaluated rigorously. Limited in vivo data for nitroglycerin suggest a cutaneous first pass effect of between 10 and 20%. More work has been directed towards the use of topical prodrugs and the design of molecules better able to transport across the stratum corneum and then undergo local enzymatic activation. Further research in this area will require a more specific quantitative understanding of the metabolic capabilities of human skin in vivo.