Theoretical prediction of drug release in GI tract from spherical matrix systems

The significance of controlled release drug delivery systems (CRDDS) lies in their ability to deliver the drug at a steady rate thus reducing the dosage interval and providing a prolonged pharmacodynamic effect. But despite the steadily increasing practical importance of these devices, little is known regarding their underlying drug release mechanisms. Mathematical modeling of these drug delivery systems could help us understand the underlying mass transport mechanisms involved in the control of drug release. Mathematical modeling also plays an important role in providing us with valuable information such as the amount of drug released during a certain period of time and when the next dosage needs to be administered. Thus, potentially reducing the number of in-vitro and in-vivo experiments which in some cases are infeasible. There is a large spectrum of published mathematical models for predicting drug release from CRDDS in vitro following conventional approaches. These models describe drug release from various types of controlled delivery devices for perfect sink conditions. However in a real system (human body) a sink condition may not be applicable. For a CRDDS along with the physiochemical properties (solubility, diffusion, particle size, crystal form etc.) the physiological factors such as gastrointestinal tract (GI) pH, stomach emptying, (GI) motility, presence of food, elimination kinetics etc., also affect the rate of drug release. As the drug delivery system is expected to stay in the human body for a longer period of time when compared to a immediate release dosage form the process of drug release occurs in conjunction with the absorption (for oral delivery systems) and elimination kinetics. Earlier work by Ouruemchi et.al.[71] include prediction of the plasma drug concentration for an oral diffusion controlled drug delivery system. Amidon et.al.[68] developed several models for predicting the amount of drug absorbed within through the intestine walls for immediate release dosage forms. However none of these models study the effect of absorption rate on the rate of drug release for an oral controlled drug delivery system. In this work mathematical models are developed for prediction of drug release from both diffusion controlled and dissolution controlled drug delivery systems taking into account the affect of absorption rate. Spherical geometry of the particles is considered. The model is developed by assuming that the drug is release into a finite volume and is thereby absorbed through the intestine wall following first order kinetics. A closed form solution is obtained for the prediction of fraction of drug released for a diffusion controlled drug delivery system. The results are compared with both experimental data (taken from literature) as well as existing models in the literature. Whereas for a dissolution-diffusion controlled drug delivery system non linear dissolution kinetics are taken into consideration and the problem is solved by both numerical and analytical techniques. In addition two simple models are also presented for dissolution controlled drug delivery devices

Quantitative localized proton-promoted dissolution kinetics of calcite using scanning electrochemical microscopy (SECM)

Scanning electrochemical microscopy (SECM) has been used to determine quantitatively the kinetics of proton-promoted dissolution of the calcite (101̅4) cleavage surface (from natural “Iceland Spar”) at the microscopic scale. By working under conditions where the probe size is much less than the characteristic dislocation spacing (as revealed from etching), it has been possible to measure kinetics mainly in regions of the surface which are free from dislocations, for the first time. To clearly reveal the locations of measurements, studies focused on cleaved “mirror” surfaces, where one of the two faces produced by cleavage was etched freely to reveal defects intersecting the surface, while the other (mirror) face was etched locally (and quantitatively) using SECM to generate high proton fluxes with a 25 μm diameter Pt disk ultramicroelectrode (UME) positioned at a defined (known) distance from a crystal surface. The etch pits formed at various etch times were measured using white light interferometry to ascertain pit dimensions. To determine quantitative dissolution kinetics, a moving boundary finite element model was formulated in which experimental time-dependent pit expansion data formed the input for simulations, from which solution and interfacial concentrations of key chemical species, and interfacial fluxes, could then be determined and visualized. This novel analysis allowed the rate constant for proton attack on calcite, and the order of the reaction with respect to the interfacial proton concentration, to be determined unambiguously. The process was found to be first order in terms of interfacial proton concentration with a rate constant k = 6.3 (± 1.3) × 10–4 m s–1. Significantly, this value is similar to previous macroscopic rate measurements of calcite dissolution which averaged over large areas and many dislocation sites, and where such sites provided a continuous source of steps for dissolution. Since the local measurements reported herein are mainly made in regions without dislocations, this study demonstrates that dislocations and steps that arise from such sites are not needed for fast proton-promoted calcite dissolution. Other sites, such as point defects, which are naturally abundant in calcite, are likely to be key reaction sites

A general model of coupled drug release and tissue absorption for drug delivery devices

In this paper we present a general model of drug release from a drug delivery device and the subsequent transport in biological tissue. The model incorporates drug diffusion, dissolution and solubility in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue. Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations. One of the novelties is the generality of the model in each layer. Within the drug coating, our model includes diffusion as well as three different models of dissolution. We show that the model may also be used in cases where dissolution is rapid or not relevant, and additionally when drug release is not limited by its solubility. Within the biological tissue, the model can account for nonlinear saturable reversible binding, with linear reversible binding and linear irreversible binding being recovered as special cases. The generality of our model will allow the simulation of the release from a wide range of drug delivery devices encompassing many different applications. To demonstrate the efficacy of our model we simulate results for the particular application of drug release from arterial stents

Drug diffusion from polymeric delivery devices: a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective

On the role of specific drug binding in modelling arterial eluting stents

In this paper we consider drug binding in the arterial wall following delivery by a drug-eluting stent. Whilst it is now generally accepted that a non-linear saturable reversible binding model is required to properly describe the binding process, the precise form of the binding model varies between authors. Our particular interest in this manuscript is in assessing to what extent modelling specific and non-specific binding in the arterial wall as separate phases is important. We study this issue by extending a recently developed coupled model of drug release and arterial tissue distribution, and comparing simulated profiles of drug concentration and drug mass in each phase within the arterial tissue

Hydro-chemical modelling of in situ behaviour of bituminized radioactive waste in Boom Clay

The hydro-chemical (CH) interaction between swelling Eurobitum bituminized radioactive waste (BW) and Boom Clay was investigated to assess the feasibility of geological disposal for the long-term management of this waste. First, the long-term behaviour of BW in contact with water was studied. A CH formulation of chemically and hydraulically coupled flow processes in porous materials containing salt crystals is discussed. The formulation incorporates the strong dependence of the osmotic efficiency of the bitumen membrane on porosity and assumes the existence of high salt concentration gradients that are maintained for a long time and that influence the density and motion of the fluid. The impacts of temporal and spatial variations of key transport parameters (i.e. osmotic efficiency (s), intrinsic permeability (k), diffusion, etc.) were investigated. Porosity was considered the basic variable. For BW porosity varies in time because of the water uptake and subsequent processes (i.e. dissolution of salt crystals, swelling of hydrating layers, compression of highly leached layers). New expressions of s and k describing the dependence of these parameters on porosity are proposed. Several cases were analysed. The numerical analysis was proven to be able to furnish a satisfactory representation of the main observed patterns of the behaviour in terms of osmotic-induced swelling, leached mass of NaNO3 and progression of the hydration front when heterogeneous porosity and crystal distributions have been assumed. Second, the long-term behaviour of real Eurobitum drums in disposal conditions, and in particular its interaction with the surrounding clay, was investigated. Results of a CH analysis are presented.Peer ReviewedPostprint (published version

Dual-barrel conductance micropipet as a new approach to the study of ionic crystal dissolution kinetics

A new approach to the study of ionic crystal dissolution kinetics is described, based on the use of a dual-barrel theta conductance micropipet. The solution in the pipet is undersaturated with respect to the crystal of interest, and when the meniscus at the end of the micropipet makes contact with a selected region of the crystal surface, dissolution occurs causing the solution composition to change. This is observed, with better than 1 ms time resolution, as a change in the ion conductance current, measured across a potential bias between an electrode in each barrel of the pipet. Key attributes of this new technique are: (i) dissolution can be targeted at a single crystal surface; (ii) multiple measurements can be made quickly and easily by moving the pipet to a new location on the surface; (iii) materials with a wide range of kinetics and solubilities are open to study because the duration of dissolution is controlled by the meniscus contact time; (iv) fast kinetics are readily amenable to study because of the intrinsically high mass transport rates within tapered micropipets; (v) the experimental geometry is well-defined, permitting finite element method modeling to allow quantitative analysis of experimental data. Herein, we study the dissolution of NaCl as an example system, with dissolution induced for just a few milliseconds, and estimate a first-order heterogeneous rate constant of 7.5 (±2.5) × 10–5 cm s–1 (equivalent surface dissolution flux ca. 0.5 μmol cm–2 s–1 into a completely undersaturated solution). Ionic crystals form a huge class of materials whose dissolution properties are of considerable interest, and we thus anticipate that this new localized microscale surface approach will have considerable applicability in the future

Predicting the Drug Release Kinetics of Matrix Tablets

In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of partial differential equations. The predictions of both models show good qualitative agreement with experimental release curves. The models will provide tools for designing better controlled release devices.Comment: 17 pages, 7 figures; Elaborated at the first Workshop on the Application of Mathematics to Problems in Biomedicine, December 17-19, 2007 at the University of Otago in Dunedin, New Zealan