Modeling of drug release from matrix systems involving moving boundaries: Approximate analytical solutions

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.

Pre-clinical safety of topically administered sunitinib-loaded lipid and polymeric nanocarriers targeting corneal neovascularization

Three different types of sunitinib-loaded (SUN-loaded) nanocarriers were compared, aiming at the topical treatment of corneal neovascularization (CNV): polymeric nanospheres (NS), liposomes (LIP), and solid lipid nanoparticles (SLN). Three out of eleven formulations prepared for an optimization study - the best SUN-loaded nanocarrier of each assessed type (NS, LIP, and SLN) - were selected, based on their size, polydispersity index (PdI), drug load (DL), and encapsulation efficiency (EE). These three optimal formulations were further characterized by nanoparticle tracking analysis (NTA), electron paramagnetic resonance (EPR) spectroscopy, and zeta potential. In vitro SUN release profiles were obtained for the optimal formulations, along with ex vivo corneal permeability/retention studies, and ocular tolerance assays, namely: the bovine corneal opacity and permeability (BCOP) assay, the HET-CAM test (hen's egg test - chorioallantoic membrane), and hemolytic potential (HP) assay. None of the optimal formulations exhibited toxicity or potential for ocular irritation. SLN showed higher surface fluidity, drug release more suitable for topical ocular applications, besides greater SUN corneal retention. Our results suggest that SLN are the best CNV-targeting SUN-loaded nanocarriers for clinical translation when compared to their NS and LIP analogues.

Mucoadhesive PLGA Nanospheres and Nanocapsules for Lactoferrin Controlled Ocular Delivery

Background: the present work describes the preparation, characterization and optimization of eight types of PLGA-based nanosystems (nanospheres and nanocapsules) as innovative mucoadhesive drug delivery systems of lactoferrin, in order to achieve a preclinical consistent base as an alternative pharmacological treatment to different ocular syndromes and diseases. Methods: All different nanoparticles were prepared via two modified nanoprecipitation techniques, using a three-component mixture of drug/polymer/surfactant (Lf/PLGA/Poloxamer), as a way to overcome the inherent limitations of conventional PLGA NPs. These modified polymeric nanocarriers, intended for topical ophthalmic administration, were subjected to in vitro characterization, surface modification and in vitro and in vivo assessments. Results: An appropriate size range, uniform size distribution and negative ζ potential values were obtained for all types of formulations. Lactoferrin could be effectively included into all types of nanoparticles with appropriate encapsulation efficiency and loading capacity values. A greater, extended, and controlled delivery of Lf from the polymeric matrix was observed through the in vitro release studies. No instability or cytotoxicity was proved for all the formulations by means of organotypic models. Additionally, mucoadhesive in vitro and in vivo experiments show a significant increase in the residence time of the nanoparticles in the eye surface. Conclusions: all types of prepared PLGA nanoparticles might be a potential alternative for the topical ophthalmic administration of lactoferrin.

Designing Natural Polymer-Based Capsules and Spheres for Biomedical Applications-A Review

Natural polymers, such as polysaccharides and polypeptides, are potential candidates to serve as carriers of biomedical cargo. Natural polymer-based carriers, having a core-shell structural configuration, offer ample scope for introducing multifunctional capabilities and enable the simultaneous encapsulation of cargo materials of different physical and chemical properties for their targeted delivery and sustained and stimuli-responsive release. On the other hand, carriers with a porous matrix structure offer larger surface area and lower density, in order to serve as potential platforms for cell culture and tissue regeneration. This review explores the designing of micro- and nano-metric core-shell capsules and porous spheres, based on various functions. Synthesis approaches, mechanisms of formation, general- and function-specific characteristics, challenges, and future perspectives are discussed. Recent advances in protein-based carriers with a porous matrix structure and different core-shell configurations are also presented in detail.

Development and Optimization of Microballoons Assisted Floating Tablets of Baclofen

The objective of the present study was to develop microballoons aided gastro-retentive floating tablets of baclofen, a skeletal muscle relaxant with a low elimination half-life of ~ 3.5 h. Baclofen floating tablet was prepared to offer convenience by designing a tablet that would float in the stomach for a prolonged period and allow controlled drug release to enable once-a-day administration. Ethylcellulose microballoons (ECMBs) prepared by pseudo emulsion solvent diffusion method were employed as floating aid. The ECMBs were spherical with a size of 446.71 µm and a circularity index of 0.995. Buoyancy of 98.90 percent and good flowability reflected by an angle of repose of 23° suggested the feasibility of preparing floating tablets by direct compression. Directly compressed baclofen floating tablets comprised ECMBs, HPMC-K15M, and hydroxyl ethylcellulose as independent variables in the Box-Behnken design, however, performance characteristics of tablets such as in vitro drug release, floating lag time, and swelling index were selected as the dependent variables. Among the variables, ECMBs played a critical role in ensuring buoyancy. However, HPMC-K15M significantly influenced in vitro drug release. The optimized batch displayed Hickson-Crowell kinetics and exhibited a similar drug release profile as a marketed once-a-day formulation (f₂, 91.03). Furthermore, optimized tablets showed a swelling index of > 300, floating lag time < 3 s, and total floating time > 24 h. Microballoons assisted floating tablets exhibited great promise for assured gastric retention of tablets.

Evaluating Release Kinetics from Alginate Beads Coated with Polyelectrolyte Layers for Sustained Drug Delivery

Current approaches in stem cell-based bone tissue engineering require a release of bioactive compounds over up to 2 weeks. This study presents a polyelectrolyte-layered system featuring sustained release of water-soluble drugs with decreased burst release. The bioactive compounds adenosine 5'-triphosphate (ATP), suramin, and A740003 (a less water-soluble purinergic receptor ligand) were incorporated into alginate hydrogel beads subsequently layered with different polyelectrolytes (chitosan, poly(allyl amine), alginate, or lignosulfonate). Drug release into aqueous medium was monitored over 14 days and evaluated using Korsmeyer-Peppas, Peppas-Sahlin, Weibull models, and a Langmuir-like "Two-Stage" model. Release kinetics strongly depended on both the drug and the polyelectrolyte system. For ATP, five alternating layers of poly(allyl amine) and alginate proved to be most effective in sustaining the release. Release of suramin could be prolonged best with lignosulfonate as polyanion. A740003 showed prolonged release even without layering. Applying polyelectrolyte layers significantly slowed down the burst release. Release curves could be best described with the Langmuir-like model.

Scaling Laws in the Diffusive Release of Neutral Cargo from Hollow Hydrogel Nanoparticles: Paclitaxel-Loaded Poly(4-vinylpyridine)

We study the nonequilibrium diffusive release of electroneutral molecular cargo encapsulated inside hollow hydrogel nanoparticles. We propose a theoretical model that includes osmotic, steric, and short-range polymer-cargo attractions to determine the effective cargo-hydrogel interaction, u_eff*, and the effective diffusion coefficient of the cargo inside the polymer network, D_eff*. Using dynamical density functional theory (DDFT), we investigate the scaling of the characteristic release time, τ_1/2, with the key parameters involved in the process, namely, u_eff*, D_eff*, and the swelling ratio. This effort represents a full study of the problem, covering a broad range of cargo sizes and providing predictions for repulsive and attractive polymer shells. Our calculations show that the release time through repulsive polymer networks scales with q²e^βu_eff*/D_eff* for βu_eff* ≫ 1. In this case, the cargo molecules are excluded from the shell of the hydrogel. For attractive shells, the polymer retains the cargo molecules on its internal surface and its interior, and the release time grows exponentially with the attraction strength. The DDFT calculations are compared to an analytical model for the mean first passage time, which provides an excellent quantitative description of the kinetics for both repulsive and attractive shells without fitting parameters. Finally, we apply the method to reproduce experimental results on the release of paclitaxel from hollow poly(4-vinylpyridine) nanoparticles and find that the slow release of the drug can be explained in terms of the strong binding attraction between the drug and the polymer.

Mechanisms of water permeation and diffusive API release from stearyl alcohol and glyceryl behenate modified release matrices

This work aims to develop complimentary analytical tools for lipid formulation selection that offer insights into the mechanisms of in-vitro drug release for solid lipid modified release excipients. Such tools are envisioned to aide and expedite the time consuming process of formulation selection and development. Two pharmaceutically relevant solid lipid excipients are investigated, stearyl alcohol and glyceryl behenate, which are generally known to exhibit faster and slower relative release rates, respectively. Nuclear magnetic resonance spectroscopy and diffusometry are used, along with water uptake and dissolution experiments to help distinguish between two proposed in-vitro release mechanisms for crystalline caffeine from these matrices: 1) rate limiting movement of the wetting front through the particle, and 2) rate limiting diffusive release of the active from the wetted particle. Findings based on water permeation rates, API diffusion coefficients and kinetic modeling suggest that the rate limiting steps for caffeine release from these matrices are different, with stearyl alcohol being co-rate limited by movement of the wetting front and diffusive release of API, whereas glyceryl behenate is more strictly limited by diffusive release of API from the wetted matrix. A Peclet-like number is proposed to describe the different regimes of rate limitation for drug release. NMR spectroscopy and diffusometry are demonstrated to be useful tools for elucidating mechanisms of API release from crystalline drug/lipid mixtures and have significant potential value as screening tools in MR formulation development.

Surface Heterogeneous Nucleation-Mediated Release of Beta-Carotene from Porous Silicon

We demonstrate that the release of a poorly soluble molecule from nanoporous carriers is a complex process that undergoes heterogeneous surface nucleation events even under significantly diluted release conditions, and that those events heavily affect the dynamics of release. Using beta-carotene and porous silicon as loaded molecule and carrier model, respectively, we show that the cargo easily nucleates at the pore surface during the release, forming micro- to macroscopic solid particles at the pores surface. These particles dissolve at a much slower pace, compared to the rate of dissolution of pure beta-carotene in the same solvent, and they negatively affect the reproducibility of the release experiments, possibly because their solubility depends on their size distribution. We propose to exploit this aspect to use release kinetics as a better alternative to the induction time method, and to thereby detect heterogenous nucleation during release experiments. In fact, release dynamics provide much higher sensitivity and reproducibility as they average over the entire sample surface instead of depending on statistical analysis over a small area to find clusters.

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.

Entrapment and release kinetics study of dyes from BSA microspheres forming a matrix and a reservoir system

Two kinds of Bovine Serum Albumin (BSA)-loaded microspheres were prepared in water-organic bilayer systems using ultrasonic irradiation.

Mathematical Modeling of Release Kinetics from Supramolecular Drug Delivery Systems

Embedding of active substances in supramolecular systems has as the main goal to ensure the controlled release of the active ingredients. Whatever the final architecture or entrapment mechanism, modeling of release is challenging due to the moving boundary conditions and complex initial conditions. Despite huge diversity of formulations, diffusion phenomena are involved in practically all release processes. The approach in this paper starts, therefore, from mathematical methods for solving the diffusion equation in initial and boundary conditions, which are further connected with phenomenological conditions, simplified and idealized in order to lead to problems which can be analytically solved. Consequently, the release models are classified starting from the geometry of diffusion domain, initial conditions, and conditions on frontiers. Taking into account that practically all solutions of the models use the separation of variables method and integral transformation method, two specific applications of these methods are included. This paper suggests that "good modeling practice" of release kinetics consists essentially of identifying the most appropriate mathematical conditions corresponding to implied physicochemical phenomena. However, in most of the cases, models can be written but analytical solutions for these models cannot be obtained. Consequently, empiric models remain the first choice, and they receive an important place in the review.

Nonequilibrium Uptake Kinetics of Molecular Cargo into Hollow Hydrogels Tuned by Electrosteric Interactions

Hollow hydrogels represent excellent nano- and microcarriers due to their ability to encapsulate and release large amounts of cargo molecules (cosolutes) such as reactants, drugs, and proteins. In this work, we use a combination of a phenomenological effective cosolute-hydrogel interaction potential and dynamic density functional theory to investigate the full nonequilibrium encapsulation kinetics of charged and dipolar cosolutes by an isolated charged hollow hydrogel immersed in a 1:1 electrolyte aqueous solution. Our analysis covers a broad spectrum of cosolute valences ( z_c) and electric dipole moments (μ_c), as well as hydrogel swelling states and hydrogel charge densities. Our calculations show that, close to the collapsed state, the polar cosolutes are predominantly precluded and the encapsulation process is strongly hindered by the excluded-volume interaction exerted by the polymer network. Different equilibrium and kinetic sorption regimes (interface versus interior) are found depending on the value and sign of z_c and the value of μ_c. For cosolutes of the same sign of charge as the gel, the superposition of steric and electrostatic repulsion leads to an "interaction-controlled" encapsulation process, in which the characteristic time to fill the empty core of the hydrogel grows exponentially with z_c. On the other hand, for cosolutes oppositely charged to the gel, we find a "diffusion-controlled" kinetic regime, where cosolutes tend to rapidly absorb into the hydrogel membrane and the encapsulation rate depends only on the cosolute diffusion time across the membrane. Finally, we find that increasing μ_c promotes the appearance of metastable and stable surface adsorption states. For large enough μ_c, the kinetics enters an "adsorption-hindered diffusion", where the enhanced surface adsorption imposes a barrier and slows down the uptake. Our study represents the first attempt to systematically describe how the swelling state of the hydrogel and other leading physical interaction parameters determine the encapsulation kinetics and the final equilibrium distribution of polar molecular cargo.

Effect of hydrophilic and hydrophobic polymers on permeation of S-amlodipine besylate through intercalated polymeric transdermal matrix: 3(2) designing, optimization and characterization

OBJECTIVE

Innovation in material science has made it possible to fabricate a pharmaceutical material of modifiable characteristics and utility, in delivering therapeutics at a sustained/controlled rate. The objective of this study is to design and optimize the controlled release transdermal films of S-Amlodipine besylate by intercalating hydrophilic and hydrophobic polymers.

METHODS

3(2) factorial design and response surface methodology was utilized to prepare formulations by intercalating the varied concentration of polymers(A) and penetration enhancer(B) in solvent. The effect of these independent factors on drug release and flux was investigated to substantiate the ex-vivo, stability and histological findings of the study.

RESULTS

FTIR, DSC revealed the compatibility of drug with polymers; however, the semicrystallinity in drug was observed under PXRD. SEM micrographs showed homogeneous dispersion and entanglement of drug throughout the matrix. Results from the permeation study suggested the significant effect of factors on the ex vivo permeation of drug. It was observed that drug release was found to be increased with an increase in hydrophilic polymer concentration and PE. The formulations having polymers (EC:PVPK-30) at 7:3 showed maximum drug release with highest flux (102.60 ± 1.12 µg/cm²/h) and permeability coefficient (32.78 ± 1.38 cm/h). Significant effect of PE on lipid and protein framework of the skin was also observed which is responsible for increased permeation. The optimized formulation was found to be stable and showed no-sign of localized reactions, indicating safety and compatibility with the skin.

CONCLUSION

Thus, results indicated that the prepared intercalated transdermal matrix can be a promising nonoral carrier to deliver effective amounts of drug.

Scaffolds as Structural Tools for Bone-Targeted Drug Delivery

Although bone has a high potential to regenerate itself after damage and injury, the efficacious repair of large bone defects resulting from resection, trauma or non-union fractures still requires the implantation of bone grafts. Materials science, in conjunction with biotechnology, can satisfy these needs by developing artificial bones, synthetic substitutes and organ implants. In particular, recent advances in materials science have provided several innovations, underlying the increasing importance of biomaterials in this field. To address the increasing need for improved bone substitutes, tissue engineering seeks to create synthetic, three-dimensional scaffolds made from organic or inorganic materials, incorporating drugs and growth factors, to induce new bone tissue formation. This review emphasizes recent progress in materials science that allows reliable scaffolds to be synthesized for targeted drug delivery in bone regeneration, also with respect to past directions no longer considered promising. A general overview concerning modeling approaches suitable for the discussed systems is also provided.

Development of Itraconazole Tablets Containing Viscous KinetiSol Solid Dispersions: In Vitro and In Vivo Analysis in Dogs

The formulation factors relevant to developing immediate and controlled release dosage forms containing poorly soluble drugs dispersed in amorphous systems are poorly understood. While the utility of amorphous solid dispersions is becoming apparent in the pharmaceutical marketplace, literature reports tend to concentrate on the development of solid dispersion particulates, which then must be formulated into a tablet. Amorphous solid dispersions of itraconazole in high molecular weight hydroxypropyl methylcellulose were prepared by KinetiSol® Dispersing and tablets were formulated to immediately disintegrate or control the release of itraconazole. Formulated tablets were evaluated by two non-sink dissolution methodologies and the dosage form properties that controlled the gelling tendency of the dispersion carrier, hydroxypropyl methylcellulose, were investigated. Selected formulations were evaluated in an exploratory beagle dog pharmacokinetic study; the results of which indicate potential for a prolonged absorption phase relative to the commercially extruded control.

The Use of Cellulose Membrane to Eliminate Burst Release from Intravaginal Rings

Burst release was observed when ethylene vinyl acetate copolymer (EVA) intravaginal rings were tested for progesterone release in our previous work (Helbling et al. Pharm Res. 31(3):795-808, 2014). Burst release is undesirable in controlled delivery devices because release is uncontrollable and higher levels of active pharmaceutical ingredient could lead to the occurrence of adverse effect. The present contribution is about the use of membranes to coat EVA rings to eliminate burst release. Physicochemical state of progesterone in uncoated rings and the solubility and diffusion coefficient in membrane were studied. Hormone delivery from several rings of different sizes was compared. A mathematical model was used to analyze the effects of membrane properties on delivery rate. No chemical interactions were detected between hormone and polymer. Hormone was mainly forming amorphous aggregates inside rings, and migration to membrane was not observed during storage. Diffusion coefficient was smaller in membrane (∼10(-8) cm(2) s(-1)) than in matrix (∼10(-7) cm(2) s(-1)). Zero-order release kinetics were obtained for coated rings, and release rate decreases as the thickness of the coat increases. Cellulose membrane successfully eliminates burst release and controls the delivery from EVA rings. The equations developed can be used to determine the appropriate coat thickness to produce specific release rate.

Layered double hydroxide and sulindac coiled and scrolled nanoassemblies for storage and drug release

Systems comprising anti-inflammatory sulindac intercalated into biocompatible layered double hydroxides nanovehicles were isolated through one pot synthetic method and showed high crystallinity and curled or scrolled particles.

Quantification of swelling and erosion in the controlled release of a poorly water-soluble drug using synchrotron X-ray computed microtomography

The hydration layer plays a key role in the controlled drug release of gel-forming matrix tablets. For poorly water-soluble drugs, matrix erosion is considered as the rate limiting step for drug release. However, few investigations have reported on the quantification of the relative importance of swelling and erosion in the release of poorly soluble drugs, and three-dimensional (3D) structures of the hydration layer are poorly understood. Here, we employed synchrotron radiation X-ray computed microtomography with 9-μm resolution to investigate the hydration dynamics and to quantify the relative importance of swelling and erosion on felodipine release by a statistical model. The 3D structures of the hydration layer were revealed by the reconstructed 3D rendering of tablets. Twenty-three structural parameters related to the volume, the surface area (SA), and the specific surface area (SSA) for the hydration layer and the tablet core were calculated. Three dominating parameters, including SA and SSA of the hydration layer (SA hydration layer and SSA hydration layer ) and SA of the glassy core (SA glassy core ), were identified to establish the statistical model. The significance order of independent variables was SA hydration layer > SSA hydration layer > SA glassy core , which quantitatively indicated that the release of felodipine was dominated by a combination of erosion and swelling. The 3D reconstruction and structural parameter calculation methods in our study, which are not available from conventional methods, are efficient tools to quantify the relative importance of swelling and erosion in the controlled release of poorly soluble drugs from a structural point of view.

Higuchi's equation and beyond: overview of the formulation and application of a generalized model of drug release from polymeric matrices

An account is presented of modeling and experimental work, which complements, in many useful ways, the excellent coverage, afforded by a recent dedicated issue edited by Siepmann and Peppas (Int. J. Pharm. 2011, 418(1)), of the theoretical background and many ramifications, as well as practical applications, of the Higuchi equation. The main notable feature of the said modeling work is formulation and successful practical application, of an ab initio generalized approach, based on solving the fundamental transport equations applicable to the operation of typical matrix-controlled release (MCR) devices. This approach (i) reduces to the Higuchi equation under the pertinent restrictive conditions but can duly handle most of its more complex ramifications and (ii) can be parameterized (by the use of appropriate data from the literature or from independent experiments) to adapt itself to the physics of the particular matrix-solvent-solute system under consideration; as demonstrated here with examples from our laboratory or from the literature. A distinctive feature of the experimental work is the extensive use of simpler "model" MCR systems, chosen so as to promote better understanding of the effect of various physicochemical parameters and mechanisms on drug MCR rate and kinetics. A concept of MCR device efficiency is also discussed.

Modeling of diffusion controlled drug delivery

Mathematical modeling of drug release can be very helpful to speed up product development and to better understand the mechanisms controlling drug release from advanced delivery systems. Ideally, in silico simulations can quantitatively predict the impact of formulation and processing parameters on the resulting drug release kinetics. The aim of this article is to give an overview on the current state of the art of modeling drug release from delivery systems, which are predominantly controlled by diffusional mass transport. The inner structure of the device, the ratio "initial drug concentration:drug solubility" as well as the device geometry determine which type of mathematical equation must be applied. A straightforward "road map" is given, explaining how to identify the appropriate equation for a particular type of drug delivery system. The respective equations for a broad range of devices are indicated, including reservoir and matrix systems, exhibiting or not an initial excess of drug and the geometry of slabs, spheres and cylinders. The assumptions the models are based on as well as their limitations are pointed out. Practical examples illustrate the usefulness of mathematical modeling of diffusion controlled drug delivery. Due to the advances in information technology the importance of in silico optimization of advanced drug delivery systems can be expected to significantly increase in the future.