Timely drug delivery from controlled-release devices: Dynamic analysis and novel design concepts

A method to assess dermal absorption dynamics of chemical warfare agents: Finite doses of volatile compounds

Chemical warfare agents are absorbed into the body from various entry routes and may have detrimental effects on human health. As many chemical compounds in this group are lipophilic, the outer layer of the skin is at an elevated risk. This contribution explores the dynamics of skin penetration for risk assessment. A previously validated model was applied to describe how an agent is transported across the stratum corneum following dermal exposure to a finite dose of a chemical. A mathematical construct was implemented for estimating the time constants and the cumulative amount of permeant entering the bloodstream or being released into the environment. Empirical equations were selected to determine the ratio of the steady-state evaporation rate to the steady-state dermal absorption rate and the physicochemical properties of the chemical warfare agents. Wolfram Mathematica was employed to run the simulations. The results from the newly derived expressions for the time constants matched those directly obtained from the validated model. For example, sarin gas had steady-state evaporation to an absorption rate of 991.25, and a total fractional absorption and evaporation of 5.1% and 94.9%, respectively. Combined with occupational exposure limits, the findings can help researchers assess an individual's risk level and develop protection programs.

Analysis of the absorption kinetics following dermal exposure to large doses of volatile organic compounds

A mathematical method was developed to study the skin penetration of volatile organic compounds (VOCs) after exposure to a high dose of the substance. While closed-form solutions exist to describe the diffusion and evaporation from small amounts, numerical approaches are often implemented to predict dermal transport involving large doses. This work offers a Laplace transform-based method to estimate the time constant and dynamic and steady-state behaviors. First, the process was divided into two stages, separated by the time it took for excess chemicals to be depleted from the skin surface. Series solutions were written for the percutaneous VOC concentration, absorption and evaporation in the first stage. Application of Laplace transform methods yielded transient profiles after the compound dissipated from the surface of the stratum corneum. In addition, the procedure facilitated the calculation of the time constant and steady-state values. The method was validated using benchtop and fume hood experiments conducted with N,N-diethyl-3-methylbenzamide (DEET) and air velocities of 0.165 m/s and 0.72 m/s, respectively. The increase in the flow rate decreased the total amount of VOC absorbed and reduced the period required for the surface fluid to disappear.

Finite transition times for multispecies diffusion in heterogeneous media coupled via first-order reaction networks

Calculating how long a coupled multispecies reactive-diffusive transport process in a heterogeneous medium takes to effectively reach steady state is important in many applications. In this paper, we show how the time required for such processes to transition to within a small specified tolerance of steady state can be calculated accurately without having to solve the governing time-dependent model equations. Our approach is valid for general first-order reaction networks and an arbitrary number of species. Three numerical examples are presented to confirm the analysis and investigate the efficacy of the approach. A key finding is that for sequential reactions our approach works better provided the two smallest reaction rates are well separated.

Drug delivery from microcapsules: How can we estimate the release time?

Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model. The first approach, which uses the zeroth and first temporal moments only, provides a crude approximation of the release time taking the form of a simple algebraic expression involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) while the second approach yields an asymptotic estimate of the release time that depends on consecutive higher moments. Through several test cases, we show that both approaches provide a computationally-cheap and useful tool to quantify the release time of composite microcapsule configurations.

Characteristic time scales for diffusion processes through layers and across interfaces

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

An effective time-constant algorithm for drug transport to capillaries and surrounding tissues

Expressions for a single time constant were developed in Maple (Waterloo Maple, Inc.) to calculate the rate at which a drug reaches steady-state levels in the blood capillaries and neighboring tissues. The solute concentration in the capillary region was represented by a one-dimensional convection-diffusion model. In a first case study, the plasma and the tissue reached equilibrium very quickly. Within the dynamic regime, the amount of drugs collected in both compartments increased with the Peclet number while the relaxation time to a steady-state value decreased. A similar conclusion was drawn, in a second case study, when axial and radial diffusive transports were considered important in the lungs or the skin. Also, as the mass transfer Biot number decreased, a larger amount of medication was delivered to the tissue at a given time during the transient period. Additional applications of the approach included the analysis of oxygen transport in peripheral nerves and the design of hollow fibre bioreactors.

The development of a peak-time criterion for designing controlled-release devices

This work consists of estimating dynamic characteristics for topically-applied drugs when the magnitude of the flux increases to a maximum value, called peak flux, before declining to zero. This situation is typical of controlled-released systems with a finite donor or vehicle volume. Laplace transforms were applied to the governing equations and resulted in an expression for the flux in terms of the physical characteristics of the system. After approximating this function by a second-order model, three parameters of this reduced structure captured the essential features of the original process. Closed-form relationships were then developed for the peak flux and time-to-peak based on the empirical representation. Three case studies that involve mechanisms, such as diffusion, partitioning, dissolution and elimination, were selected to illustrate the procedure. The technique performed successfully as shown by the ability of the second-order flux to match the prediction of the original transport equations. A main advantage of the proposed method is that it does not require a solution of the original partial differential equations. Less accurate results were noted for longer lag times.

Graphical process design tools for iontophoretic transdermal drug-delivery devices

A graphical procedure was proposed for the optimum design of transdermal drug-delivery systems enhanced by iontophoresis. Contour plots displayed the relationships among steady-state plasma level, current density and initial drug concentration in a vehicle. This information was combined with a closed-form expression of the process time constant, estimated as the medicament in the blood reaches a plateau after application of the electric field. Analysis was conducted using Laplace-transformed variables and did not require time-domain solutions. Simulation results show that a current density of 0.044 mA/cm(2) and a loading of 3500 μg/ml of dexamethasone sodium m-sulfobenzoate were necessary to achieve an equilibrium plasma concentration of 1.254 ng/cm(3) with a time constant of 8.34 h.