Theoretical investigation of drug release from planar matrix systems: effects of a finite dissolution rate

Layer-by-layer assembly of nanotheranostic particles for simultaneous delivery of docetaxel and doxorubicin to target osteosarcoma

Osteosarcoma (OS) is a rare form of primary bone cancer, impacting approximately 3.4 × 106 individuals worldwide each year, primarily afflicting children. Given the limitations of existing cancer therapies, the emergence of nanotheranostic platforms has generated considerable research interest in recent decades. These platforms seamlessly integrate therapeutic potential of drug compounds with the diagnostic capabilities of imaging probes within a single construct. This innovation has opened avenues for enhanced drug delivery to targeted sites while concurrently enabling real-time monitoring of the vehicle's trajectory. In this study, we developed a nanotheranostic system employing the layer-by-layer (LbL) technique on a core containing doxorubicin (DOXO) and in-house synthesized carbon quantum dots. By utilizing chitosan and chondroitin sulfate as polyelectrolytes, we constructed a multilayered coating to encapsulate DOXO and docetaxel, achieving a coordinated co-delivery of both drugs. The LbL-functionalized nanoparticles exhibited an approximate size of 150 nm, manifesting a predominantly uniform and spherical morphology, with an encapsulation efficiency of 48% for both drugs. The presence of seven layers in these systems facilitated controlled drug release over time, as evidenced by in vitro release tests. Finally, the impact of the LbL-functionalized nanoparticles was evaluated on U2OS and Saos-2 osteosarcoma cells. The synergistic effect of the two drugs was found to be crucial in inducing cell death, particularly in Saos-2 cells treated with nanoparticles at concentrations higher than 10 μg/ml. Transmission electron microscopy analysis confirmed the internalization of the nanoparticles into both cell types through endocytic mechanisms, revealing an underlying mechanism of necrosis-induced cell death.

Controlling release from encapsulated drug-loaded devices: insights from modeling the dissolution front propagation

Dissolution of drug from its solid form to a dissolved form is an important consideration in the design and optimization of drug delivery devices, particularly owing to the abundance of emerging compounds that are extremely poorly soluble. When the solid dosage form is encapsulated, for example by the porous walls of an implant, the impact of the encapsulant drug transport properties is a further confounding issue. In such a case, dissolution and diffusion work in tandem to control the release of drug. However, the interplay between these two competing processes in the context of drug delivery is not as well understood as it is for other mass transfer problems, particularly for practical controlled-release considerations such as an encapsulant layer around the drug delivery device. To address this gap, this work presents a mathematical model that describes controlled release from a drug-loaded device surrounded by a passive porous layer. A solution for the drug concentration distribution is derived using the method of eigenfunction expansion. The model is able to track the dissolution front propagation, and predict the drug release curve during the dissolution process. The utility of the model is demonstrated through comparison against experimental data representing drug release from a cylindrical drug-loaded orthopedic fixation pin, where the model is shown to capture the data very well. Analysis presented here reveals how the various geometrical and physicochemical parameters influence drug dissolution and, ultimately, the drug release profile. It is found that the non-dimensional initial concentration plays a key role in determining whether the problem is diffusion-limited or dissolution-limited, whereas the nature of the problem is largely independent of other parameters including diffusion coefficient and encapsulant thickness. We expect the model will prove to be a useful tool for those designing encapsulated drug delivery devices, in terms of optimizing the design of the device to achieve a desired drug release profile.

Characterization of the Shells in Layer-By-Layer Nanofunctionalized Particles: A Computational Study

Drug delivery carriers are considered an encouraging approach for the localized treatment of disease with minimum effect on the surrounding tissue. Particularly, layer-by-layer releasing particles have gained increasing interest for their ability to develop multifunctional systems able to control the release of one or more therapeutical drugs and biomolecules. Although experimental methods can offer the opportunity to establish cause and effect relationships, the data collection can be excessively expensive or/and time-consuming. For a better understanding of the impact of different design conditions on the drug-kinetics and release profile, properly designed mathematical models can be greatly beneficial. In this work, we develop a continuum-scale mathematical model to evaluate the transport and release of a drug from a microparticle based on an inner core covered by a polymeric shell. The present mathematical model includes the dissolution and diffusion of the drug and accounts for a mechanism that takes into consideration the drug biomolecules entrapped into the polymeric shell. We test a sensitivity analysis to evaluate the influence of changing the model conditions on the total system behavior. To prove the effectiveness of this proposed model, we consider the specific application of antibacterial treatment and calibrate the model against the data of the release profile for an antibiotic drug, metronidazole. The results of the numerical simulation show that ∼85% of the drug is released in 230 h, and its release is characterized by two regimes where the drug dissolves, diffuses, and travels the external shell layer at a shorter time, while the drug is released from the shell to the surrounding medium at a longer time. Within the sensitivity analysis, the outer layer diffusivity is more significant than the value of diffusivity in the core, and the increase of the dissolution parameters causes an initial burst release of the drug. Finally, changing the shape of the particle to an ellipse produces an increased percentage of drugs released with an unchanged release time.

How Does Fluid Flow Influence Drug Release from Drug Filled Implants?

Drug-filled implants (DFIs) have emerged as an innovative approach to control the delivery of drugs. These devices contain the drug within the structure of the implant itself and avoid the need to include additional drug carrier materials such as a polymers, which are often associated with inflammation and delayed healing/tissue regeneration at the implant site. One common feature of in vitro experiments to generate drug release profiles is stirring or agitation of the release medium. However, the influence of the resulting fluid flow on the rate of drug release from DFIs has yet to be quantified. In this paper we consider two DFIs, which although similar in shape and size, employ different strategies to control the release of drug: a porous pin with pores on the order of μm and a pin drilled with orifices of the order of mm. We develop a multiphysics mathematical model of drug release from these DFIs, subject to fluid flow induced through stirring and show that fluid flow greatly influences the drug release profile for the orifice pin, but that the porous pin drug release profile is relatively insensitive to flow. We demonstrate that drug release from the porous pin may adequately be described through a simplified radial 1D dissolution-diffusion model, while a 3D dissolution-advection-diffusion model is required to describe drug release from the orifice pin. A sensitivity analysis reveals that that the balance of reaction-advection-diffusion in terms of key nondimensional numbers governs the overall drug release. Our findings potentially have important implications in terms of devising the most relevant experimental protocol for quantifying drug release from DFIs.

An Integrated Biophysical Model for Predicting the Clinical Pharmacokinetics of Transdermally Delivered Compounds

The delivery of therapeutic drugs through the skin is a promising alternative to oral or parenteral delivery routes because dermal drug delivery systems (D³S) offer unique advantages such as controlled drug release over sustained periods and a significant reduction in first-pass effects, thus reducing the required dosing frequency and level of patient noncompliance. Furthermore, D³S find applications in multiple therapeutic areas, including drug repurposing. This article presents an integrated biophysical model of dermal absorption for simulating the permeation and absorption of compounds delivered transdermally. The biophysical model is physiologically/biologically inspired and combines a holistic model of healthy skin with whole-body physiology-based pharmacokinetics through dermis microcirculation. The model also includes the effects of chemical penetration enhancers and hair follicles on transdermal transport. The model-predicted permeation and pharmacokinetics of select compounds were validated using in vivo data reported in the literature. We conjecture that the integrated model can be used to gather insights into the permeation and systemic absorption of transdermal formulations (including cosmetic products) released from novel depots and optimize delivery systems. Furthermore, the model can be adapted to diseased skin with parametrization and structural adjustments specific to skin diseases.

Mathematical modelling of drug delivery from pH-responsive nanocontainers

Targeted drug delivery systems represent a promising strategy to treat localised disease with minimum impact on the surrounding tissue. In particular, polymeric nanocontainers have attracted major interest because of their structural and morphological advantages and the variety of polymers that can be used, allowing the synthesis of materials capable of responding to the biochemical alterations of the environment. While experimental methodologies can provide much insight, the generation of experimental data across a wide parameter space is usually prohibitively time consuming and/or expensive. To better understand the influence of varying design parameters on the release profile and drug kinetics involved, appropriately-designed mathematical models are of great benefit. Here, we developed a continuum-scale mathematical model to describe drug transport within, and release from, a hollow nanocontainer consisting of a core and a pH-responsive polymeric shell. Our two-layer mathematical model accounts for drug dissolution and diffusion and includes a mechanism to account for trapping of drug molecules within the shell. We conduct a sensitivity analysis to assess the effect of varying the model parameters on the overall behaviour of the system. To demonstrate the usefulness of our model, we focus on the particular case of cancer treatment and calibrate the model against release profile data for two anti-cancer therapeutical agents. We show that the model is capable of capturing the experimentally observed pH-dependent release.

Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs

Amending the neglect of finite dissolution in traditional release models, this study proposed a more generalized drug release model considering the simultaneous dissolution and diffusion procedure from a drug-loaded spherical matrix. How the shape factor (n = 0, 1/2, and 2/3 for the planar, cylindrical, and spherical geometry, respectively) of dispersed drug particles affected the release from the matrix was examined for the first time. Numerical solutions of this generalized model were validated by consensus with a short-time analytical solution for planar drugs and by the approach of the diffusion-controlled limits with Higuchi’s model. The drug release rate increases with the ratio of dissolution/diffusion rate (G) and the ratio of solubility/drug loading (K) but decreases with the shape factor of drug particles. A zero-order release profile is identified for planar drugs before starting the surface depletion layer, and also found for cylindrical and spherical dispersed drugs when K and G are small, i.e. the loaded drug is mainly un-dissolved and the drug release rate is dissolution-controlled. It is also shown that for the case of a small G value, the variation of drug release profile, due to the drug particle geometry, becomes prominent. Detailed comparison with the results of the traditional Higuchi’s model indicates that Higuchi’s model can be applied only when G is large because of the assumption of an instantaneous dissolution. For K = 1/101–1/2, the present analysis suggests an error of 33–85% for drug release predicted by Higuchi’s model for G = 10⁰, 14–44% error for G = 10¹, while a less than 5% error for G ≧ 10³.

Biomimetic Nanotherapies: Red Blood Cell Based Core-Shell Structured Nanocomplexes for Atherosclerosis Management

Cardiovascular disease is the leading cause of mortality worldwide. Atherosclerosis, one of the most common forms of the disease, is characterized by a gradual formation of atherosclerotic plaque, hardening, and narrowing of the arteries. Nanomaterials can serve as powerful delivery platforms for atherosclerosis treatment. However, their therapeutic efficacy is substantially limited in vivo due to nonspecific clearance by the mononuclear phagocytic system. In order to address this limitation, rapamycin (RAP)-loaded poly(lactic-co-glycolic acid) (PLGA) nanoparticles are cloaked with the cell membrane of red blood cells (RBCs), creating superior nanocomplexes with a highly complex functionalized bio-interface. The resulting biomimetic nanocomplexes exhibit a well-defined "core-shell" structure with favorable hydrodynamic size and negative surface charge. More importantly, the biomimetic nature of the RBC interface results in less macrophage-mediated phagocytosis in the blood and enhanced accumulation of nanoparticles in the established atherosclerotic plaques, thereby achieving targeted drug release. The biomimetic nanocomplexes significantly attenuate the progression of atherosclerosis. Additionally, the biomimetic nanotherapy approach also displays favorable safety properties. Overall, this study demonstrates the therapeutic advantages of biomimetic nanotherapy for atherosclerosis treatment, which holds considerable promise as a new generation of drug delivery system for safe and efficient management of atherosclerosis.

A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix

The objective of the present study is to mathematically model the integrated kinetics of drug release in a polymeric matrix and its ensuing drug transport to the encompassing biological tissue. The model embodies drug diffusion, dissolution, solubilization, polymer degradation and dissociation/recrystallization phenomena in the polymeric matrix accompanied by diffusion, advection, reaction, internalization and specific/nonspecific binding in the biological tissue. The model is formulated through a system of nonlinear partial differential equations which are solved numerically in association with pertinent set of initial, interface and boundary conditions using suitable finite difference scheme. After spatial discretization, the system of nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations which is subsequently solved by the fourth-order Runge-Kutta method. The model simulations deal with the comparison between a drug delivery from a biodegradable polymeric matrix and that from a biodurable polymeric matrix. Furthermore, simulated results are compared with corresponding existing experimental data to manifest the efficaciousness of the advocated model. A quantitative analysis is performed through numerical computation relied on model parameter values. The numerical results obtained reveal an estimate of the effects of biodegradable and biodurable polymeric matrices on drug release rates. Furthermore, through graphical representations, the sensitized impact of the model parameters on the drug kinetics is illustrated so as to assess the model parameters of significance.

Model of dissolution in the framework of tissue engineering and drug delivery

Dissolution phenomena are ubiquitously present in biomaterials in many different fields. Despite the advantages of simulation-based design of biomaterials in medical applications, additional efforts are needed to derive reliable models which describe the process of dissolution. A phenomenologically based model, available for simulation of dissolution in biomaterials, is introduced in this paper. The model turns into a set of reaction-diffusion equations implemented in a finite element numerical framework. First, a parametric analysis is conducted in order to explore the role of model parameters on the overall dissolution process. Then, the model is calibrated and validated versus a straightforward but rigorous experimental setup. Results show that the mathematical model macroscopically reproduces the main physicochemical phenomena that take place in the tests, corroborating its usefulness for design of biomaterials in the tissue engineering and drug delivery research areas.

Integrated Stent Models Based on Dimension Reduction: Review and Future Perspectives

Stent modeling represents a challenging task from both the theoretical and numerical viewpoints, due to its multi-physics nature and to the complex geometrical configuration of these devices. In this light, dimensional model reduction enables a comprehensive geometrical and physical description of stenting at affordable computational costs. In this work, we aim at reviewing dimensional model reduction of stent mechanics and drug release. Firstly, we address model reduction techniques for the description of stent mechanics, aiming to illustrate how a three-dimensional stent model can be transformed into a collection of interconnected one-dimensional rods, called a "stent net". Secondly, we review available model reduction methods similarly applied to drug release, in which the "stent net" concept is adopted for modeling of drug elution. As a result, drug eluting stents are described as a distribution of concentrated drug release sources located on a graph that fully represents the stent geometry. Lastly, new results about the extension of these model reduction approaches to biodegradable stents are also discussed.

Pharmacokinetics of an injectable modified-release 2-hydroxyflutamide formulation in the human prostate gland using a semiphysiologically based biopharmaceutical model

The local distribution of 2-hydroxyflutamide (2-HOF) in prostate tissue after a single intraprostatic injection of a novel parenteral modified-release (MR) formulation in patients with localized prostate cancer was estimated using a semiphysiologically based biopharmaceutical model. Plasma concentration-time profiles for 2-HOF were acquired from a phase II study in 24 patients and the dissolution of the MR formulation was investigated in vitro. Human physiological values and the specific physicochemical properties of 2-HOF were obtained from the literature or calculated via established algorithms. A compartmental modeling approach was adopted for tissue and blood in the prostate gland, where the compartments were modeled as a series of concentric spherical shells contouring the centrally positioned depot formulation. Discrete fluid connections between the blood compartments were described by the representative flow of blood, whereas the mass transport of drug from tissue to tissue and tissue to blood was described by a one-dimensional diffusion approximation. An empirical dissolution approach was adopted for the release of 2-HOF from the formulation. The model adequately described the plasma concentration-time profiles of 2-HOF. Predictive simulations indicated that the local tissue concentration of 2-HOF within a distance of 5 mm from the depot formulation was approximately 40 times higher than that of unbound 2-HOF in plasma. The simulations also indicated that spreading the formulation throughout the prostate gland would expose more of the gland and increase the overall release rate of 2-HOF from the given dose. The increased release rate would initially increase the tissue and plasma concentrations but would also reduce the terminal half-life of 2-HOF in plasma. Finally, an in vitro-in vivo correlation of the release of 2-HOF from the parenteral MR formulation was established. This study shows that intraprostatic 2-HOF concentrations are significantly higher than systemic plasma concentrations and that increased distribution of 2-HOF throughout the gland, using strategic imaging-guided administration, is possible. This novel parenteral MR formulation, thus, facilitates good pharmacological effect while minimizing the risk of side effects.

Numerical modelling of transdermal delivery from matrix systems: parametric study and experimental validation with silicone matrices

A model is presented for transdermal drug delivery from single-layered silicone matrix systems. The work is based on our previous results that, in particular, extend the well-known Higuchi model. Recently, we have introduced a numerical transient model describing matrix systems where the drug dissolution can be non-instantaneous. Furthermore, our model can describe complex interactions within a multi-layered matrix and the matrix to skin boundary. The power of the modelling approach presented here is further illustrated by allowing the possibility of a donor solution. The model is validated by a comparison with experimental data, as well as validating the parameter values against each other, using various configurations with donor solution, silicone matrix and skin. Our results show that the model is a good approximation to real multi-layered delivery systems. The model offers the ability of comparing drug release for ibuprofen and diclofenac, which cannot be analysed by the Higuchi model because the dissolution in the latter case turns out to be limited. The experiments and numerical model outlined in this study could also be adjusted to more general formulations, which enhances the utility of the numerical model as a design tool for the development of drug-loaded matrices for trans-membrane and transdermal delivery.

Numerical modelling and experimental investigation of drug release from layered silicone matrix systems

Medical devices and polymeric matrix systems that release drugs or other bioactive compounds are of interest for a variety of applications. The release of the drug can be dependent on a number of factors such as the solubility, diffusivity, dissolution rate and distribution of the solid drug in the matrix. Achieving the goal of an optimal release profile can be challenging when relying solely on traditional experimental work. Accurate modelling complementing experimentation is therefore desirable. Numerical modelling is increasingly becoming an integral part of research and development due to the significant advances in computer simulation technology. This work focuses on numerical modelling and investigation of multi-layered silicone matrix systems. A numerical model that can be used to model multi-layered systems was constructed and validated by comparison with experimental data. The model could account for the limited dissolution rate and effect of the drug distribution on the release profiles. Parametric study showed how different factors affect the characteristics of drug release. Multi-layered medical silicone matrices were prepared in special moulds, where the quantity of drug in each layer could be varied, and release was investigated with Franz-diffusion cell setup. Data for long-term release was fitted to the model and the full depletion of the system predicted. The numerical model constructed for this study, whose input parameters are the diffusion, effective dissolution rate and dimensional solubility coefficients, does not require any type of steady-state approximation. These results indicate that numerical model can be used as a design tool for development of controlled release systems such as drug-loaded medical devices.

Theory of effective drug release from medical implants based on the Higuchi model and physico-chemical hydrodynamics

Combining the approach of colloid transport with the generalized Higuchi theory of drug release and with the concept of minimum inhibitory concentration (MIC) known in microbiology, the theory of effective drug release from implants has been developed. Effective release of an antibiotic at a concentration above MIC is a necessary condition to achieve protection against infection from implants such as central catheters. The Higuchi theory in its present form is not predictive of the therapeutic effect from medical implants. The theory of effective release presented in this paper specifies two release modes, namely: one with therapeutic usefulness (effective release) and another without therapeutic effect. Therapeutic usefulness may be achieved when the antibiotic concentration, C_ti , on the implant surface kills the organisms of interest and prevents the formation and propagation of biofilm when C_ti exceeds the corresponding MIC of the released antibiotic compound. Currently, neither the Higuchi theory nor any other theory can provide such prediction. The present approach requires quantification of the antibiotic transport from the drug-polymer blend implant surface into the tissue and accounts for its coupling with drug diffusion inside the blend, a task that has not been developed in existing theories. Our solution to this task resulted in the derivation of an equation for the time of duration of effective release, T_e , which depends on MIC, the Higuchi invariant and the characteristics of convective diffusion within the tissue. The latter characteristics include: diffusivity D_ti and diffusion layer thickness δ which is controlled by the velocity of the interstitial fluid in tissue. A smaller D_ti is favorable because transport from the catheter surface is weaker, while a thinner diffusion layer is harmful because this transport is stronger. The influence of the tangential component of interstitial velocity in the tissue is especially harmful because the diffusion within the incision exit site (IES) will be extremely enhanced such that it may decrease C_ti to zero. The incorporation of convective diffusion into the theory of antibacterial protection by means of antibiotic release has revealed that physicochemical mechanisms predict the effectiveness of antibiotic-loaded catheters and defines the conditions necessary to achieve better protection by means of combining the level of catheter loading with antibiotics and the use of wound (IES) dressing.

The Long-term Release of Antibiotics From Monolithic Nonporous Polymer Implants for Use as Tympanostomy Tubes

A technology is elaborated for the fabrication of a novel tympanostomy tube (TT) from solidified polymer melts (Elvax and Polyurethane) and antibiotics (Ciprofloxacin and Usnic acid) for insertion into tympanic membrane (ear drum) according to the established surgical procedure. The long-term in vitro release kinetics of the antibiotics into liquid water has been assessed using standard methods. The measured kinetic curves revealed two stages of antibiotic release into the finite space. During the first stage (fast), the fast release rate is almost invariant and is determined by the diffusion through the steady diffusion layer formed due to solution agitation. In this first stage, the influence of the initial internal transport is weak because it takes place at negligibly small distance from interface and accordingly, at negligibly concentration drop. After the antibiotic concentration decreases within the much broader layer of matrix near interface, the internal transport becomes important. This manifests itself as the second stage in measured kinetics of release curves which is characterized by a gradual decrease in rate. The minimum inhibition concentrations of three antibiotics/antimicrobial compounds for four bacterial species were measured. The first stage of fast release from the polymer implant lasts 6 days at a polymer loading by Ciprofloxacin (0.03 g/cm(3)) and this was sufficient for preventing biofilm formation on the surface of the implant material. The measured kinetic curves of drug release showed more rapid decrease in the release rate compared to the Higuchi approximation. Comparison with existing theories, which account for the finite rate of drug dissolution, showed that this may explain the observed deviation from the diffusion-controlled Higuchi model. Large dimensions of drug particles and their aggregation retard the dissolution stage and consequently the release rate. Melt blending was found to cause the drug particle aggregation within polymer matrixes which was confirmed by microscopic reexamination of the polymer implant materials.

A theoretical model for transdermal drug delivery from emulsions and its dependence upon formulation

This article presents a theoretical model of transdermal drug delivery from an emulsion-type vehicle that addresses the vehicle heterogeneity and incorporates the prediction of drug transport parameters as function of the vehicle composition. The basic mass transfer model considers interfacial and diffusion resistances within the emulsion and partition/diffusion phenomena across two skin compartments in series. Drug transport parameters are predicted as follows: partition coefficients are derived from regular solutions theory, drug diffusivity in the continuous phase is computed from a free volume theory with segmental motion, and permeability of the surfactant layer around droplets is estimated based on a free surface area model. These relationships are incorporated within the basic mass transfer model, so that the overall model is able to predict temporal profiles of drug release from the vehicle and of drug concentration in plasma, as a function of vehicle composition. In this way, the proposed model provides a sound physicochemical basis to support the development of new formulations and the planning of experiments. A simulated case study regarding a nitroglycerin ointment is presented in detail, illustrating how thermodynamic and kinetic factors inherent to the emulsion vehicle can modulate drug release and subsequent systemic absorption.

A mechanistic model of controlled drug release from polymer millirods: Effects of excipients and complex binding

The incorporation of different cyclodextrin (CD) excipients such as HPbeta-CD, beta-CD, gamma-CD or alpha-CD into polymer millirods for complexing beta-lapachone (beta-lap), a potent anti-cancer drug, significantly improved the drug release kinetics with various drug release patterns. However, such a complex system requires a mechanistically based model in order to provide a quantitative understanding of the many molecular events and processes that are essential for the rational development of millirod implants. This study focuses on mathematical modeling of drug release from PLGA cylindrical millirods. This millirod system incorporates multiple components: a PLGA matrix; excipient in free and complex forms; drug in free, bound, and crystalline forms. The model characterizes many dynamic transport and complexation processes that include radial diffusion, excipient complexation and crystalline drug dissolution. Optimal estimates of the model parameters were obtained by minimizing the difference between model simulation and experimentally measured drug release kinetics. The effects of different drug loadings on the drug release rate were simulated and compared with other data to validate this model. Whereas our model can simulate all the experimental data, the Higuchi model can simulate only some of them. Furthermore, our model incorporates mechanisms by which the processes underlying drug release from a polymer matrix can be quantitatively analyzed. These processes include drug entrapment/dissolution in the matrix, drug recrysallization, and supersaturation. This modeling study shows that complex binding capacity, which affects drug initial conditions, drug-polymer interactions, and bound drug behavior in aqueous solution, is crucial in controlling drug release kinetics.

Finite element analysis of the release of slowly dissolving drugs from cylindrical matrix systems

Drug release from matrix systems of cylindrical shape is analyzed in detail by using the finite element method. The model used combines the Noyes-Whitney and diffusion equations, and thus takes the effects of a finite dissolution rate into account. The model is valid for all drug solubilities and dissolution rates, and allows accurate predictions of the drug release to be made. Anisotropic drug transport that may result from the manufacturing process is properly accounted for. Model calculations show that a finite dissolution rate may affect the release profile significantly, producing an initial delay. The equivalence between anisotropic release and isotropic release from a matrix with different dimensions is demonstrated. Comparisons are made with the predictions of a recently proposed pseudo-steady state (PSS) analysis of drug release from cylindrical matrices [Y. Zhou, J. S. Chu, T. Zhou, X. Y. Wu, Modeling of dispersed-drug release from two-dimensional matrix tablets, Biomaterials 26 (2005) 945-952]. This comparison reveals that important discrepancies exist between the numerical and analytical results, which are attributed to the simplifying assumption made in the PSS analysis that the region containing solid drug remains cylindrical in shape throughout the release process. The proposed model is shown to describe experimental release data well.

Theoretical analysis of the release of slowly dissolving drugs from spherical matrix systems

Drug release from spherical matrix systems has been investigated theoretically, with numerical as well as analytical methods. The model used combines the Noyes-Whitney and diffusion equations, and thus takes the effects of a finite dissolution rate into account. The release profile has been determined numerically, by using well-established FORTRAN routines. An approximate analytical formula for the amount of released drug has been derived, which is valid during the early stages of the release process. This analytical short-time approximation was compared to the numerical result, and to drug release models existing in the literature. From this comparison it was concluded that the analytical approximation provided a good description of the major part of the release profile, irrespective of the dissolution rate. Existing literature models, based on instantaneous dissolution, provided a good description of the release only when drug dissolution proceeded very rapidly in comparison with the diffusion process. Consequently, the new analytical short-time approximation complements the formulas existing in the literature, since it provides a superior description of the release of slowly dissolving drugs.