A mathematical model for predicting controlled release of bioactive agents from composite fiber structures

A mathematical model for predicting bioactive agent release profiles from core/shell fiber structures was developed and studied. These new composite fibers, which combine good mechanical properties with desired protein release profiles, are designed for use in tissue regeneration and other biomedical applications. These fibers are composed of an inner dense polymeric core surrounded by a porous bioresorbable shell, which encapsulates the bioactive agent molecules. The model is based on Fick's second law of diffusion, and on two major assumptions: (a) first-order degradation kinetics of the porous shell, and (b) a nonconstant diffusion coefficient for the bioactive agent, which increases with time because of degradation of the host polymer. Three factors are evaluated and included in this model: a porosity factor, a tortuosity factor, and a polymer concentration factor. Our study indicates that the model correlates well with in vitro release results, exhibiting a mean error of less than 2.2% for most studied cases. In this study, the model was used for predicting protein release profiles from fibers with shells of various initial molecular weights and for predicting the release of proteins with various molecular weights. This new model exhibits a potential for simulating fibrous systems for a wide variety of biomedical applications.     

Scleroglucan/borax: characterization of a novel hydrogel system suitable for drug delivery

A new hydrogel, with scleroglucan using borax as a crosslinker, has been prepared. The physical gel has been loaded with a model molecule (theophylline) and the release of the drug from the gel was evaluated. The same system was used to prepare tablets and the delivery of theophylline in different environmental conditions (HCl and SIF) was determined. A recent theoretical approach has been applied to the dissolution profiles obtained from the tablets and a satisfactory agreement has been found with the experimental data. Furthermore, the diffusion coefficient of the model molecule was evaluated according to a suitable strategy that was tested on two set of data obtained with different set-ups (permeation and diffusion experiments). A simplified mathematical approach allows to reduce the two-dimensional problem of the Fick's second law in a one-dimensional system leading to a much easier handling of the data without loosing the accuracy of the original problem in two dimensions. The characterization of the gel has been also carried out following the kinetics of swelling in terms of water uptake.     

Drug controlled release from structured bioresorbable films used in medical devices--a mathematical model

A mathematical model for predicting drug release profiles from structured bioresorbable films was developed and studied. These films, which combine good mechanical properties with desired drug release profiles, are designed for use in various biomedical applications. Our structured polymer/drug films are prepared using a promising technique for controlling the drug location/dispersion in the film. The present model was used for predicting drug release profiles from two film types that is films in which the drug is located on the surface (A-type) and films in which the drug is located in the bulk (B-type). The model is based on Fick's 2nd law of diffusion and assumes that the drug release profile from the films is affected by the host polymer's characteristics, the drug location/dispersion in the film and the drug's characteristics. This semiempirical model uses the weight loss profile of the host polymers as well as the change in their degree of crystallinity with degradation. Our study indicates that the model correlates well with in vitro release results, exhibiting a mean error of less than 7% for most studied cases. It also shows that the host polymer's degradation has a greater effect on the drug release profile than the degree of crystallinity. This new model exhibits a potential for simulating the release profile of bioactive agents from structured films for a wide variety of biomedical applications.     

Characterization and behavior of anesthetic bioactive textile complex in vitro condition

In this study, a bioactive complex containing nonwoven textile material (polypropilene (PP)/viscose), chitosan hydrogel, and lidocaine hydrochloride, was designed. The purpose of such biomedical textile was in the treatment of painful sites. Mercury intrusion porosimetry was used in order to estimate the influence of medical impregnation on porous structure of nonwoven material. It was estimated that more than 97% of pores in untreated nonwoven sample were larger than 15 μm. Anesthetic treatment of nonwoven reduced total pore volume of ultramacropores and macropores, while total pore volume of mesopores slightly increased. Lidocaine hydrochloride release from the anesthetic/chitosan hydrogel/nonwoven complex was measured in vitro by Franz diffusion cell technique. Mathematical model was developed to estimate the release of the lidocaine from obtained bioactive textile material. The diffusive transport of lidocaine hydrochloride through three connected layers, i.e., polymer hydrogel, membrane, and solution is modeled based on Fick's second law. Taking all the relevant conditions, regarding this experiment, into consideration, the coefficient of lidocaine diffusion through the polymer hydrogel, as well as the concentration ratio parameter were determined by the mathematical model.     

Modeling of Diffusion with Partitioning in Stratum Corneum Using a Finite Element Model

Partitioning and diffusion of chemicals in skin is of interest to researchers in areas such as transdermal penetration and drug disposition, either for risk assessment or transdermal delivery. In this study a finite element method is used to model diffusion in the skin’s outermost layer, the stratum corneum (SC). The SC is considered to be a finite two-dimensional composite having different diffusivity values in each medium as well as a partition coefficient at the interfaces between media. A commercial finite element package with thermal analysis capabilities is selected due to the flexibility of this software to handle irregular geometries. Partitioning is accommodated through a change of variables technique. This technique is validated by comparison of model results with analytical solutions of steady-state flux, transient concentration profiles, and time lag for diffusion in laminates. Two applications are presented. Diffusion is solved in a two-dimensional “brick and mortar” geometry that is a simplification of human stratum corneum, with a partition coefficient between corneocyte and lipid. Results are compared to the diffusion in multiple laminates to examine effects of the partition coefficient. The second application is the modeling of diffusion with partitioning through an irregular geometry which is obtained from a micrograph of hairless mouse stratum corneum.     

Initial Burst Measures of Release Kinetics from Fiber Matrices

A comprehensive axisymmetric diffusion model of drug release from a fiber is developed to account for both the initial burst (IB) phenomenon as well as the later diffusion-dominated release. This model is an enhancement over previous models in that a set of four IB parameters are calculated, which both describe the initial burst phenomenon as well as improve the fit for the diffusion-dominated release phase. This model is also an enhancement over previous models in allowing: finite dissolution volumes, finite stirring levels of the medium, and user-specified initial drug dispersion within the device. Five different drug release data sets are used to verify the model and to derive values for the IB parameters. Two of the data sets are from experiments conducted in this study, and the other three sets are from previously published data. These data sets were selected to cover a wide range of possibilities, i.e., from nearly 0% to nearly 100% of the total drug release during IB, yet the model handles all cases equally well. © 2003 Biomedical Engineering Society. PAC2003: 8780-y, 8715Vv     

Drug transport mechanisms and release kinetics from molecularly designed poly(acrylic acid-g-ethylene glycol) hydrogels

Controlled drug release devices of pH-sensitive, complexing poly(acrylic acid-g-ethylene glycol) (P(AA-g-EG)) hydrogels were prepared by free radical solution UV polymerization. The effects of hydrogel composition, polymerization conditions and surrounding environment on theophylline release kinetics and drug transport mechanisms were evaluated in these P(AA-g-EG) polymer networks. Release studies indicated a dependence of the theophylline release kinetics and diffusion coefficients on the hydrogel structure, polymerization conditions and pH of the environment. The theophylline transport mechanism was studied by fitting experimental data to five different model equations and calculating the corresponding parameters. The Akaike information criterion was also considered to elucidate the best-fit equation. Results indicated that in most release cases, the drug release mechanism was anomalous (non-Fickian). This indicates that such systems may, under certain conditions, provide release characteristics approaching zero-order release. The pH of the dissolution medium appeared to have a strong effect on the drug transport mechanism. At more basic pH values, Case II transport was observed, indicating a drug release mechanism highly influenced by macromolecular chain relaxation. The results obtained in this research work lead us to the conclusion that P(AA-g-EG) hydrogels can be successfully used as drug delivery systems. Their versatility to be designed with specifically tuned release properties renders these biomaterials promising pharmaceutical carriers for therapeutic agents.     

Experimental Studies and Modeling of Drug Release from a Tunable Affinity-Based Drug Delivery Platform

An affinity-based drug delivery platform for controlling drug release is analyzed by a combination of experimental studies and mathematical modeling. This platform has the ability to form selective interactions between a therapeutic agent and host matrix that yields advantages over systems that employ nonselective methods. The incorporation of molecular interactions in drug delivery can increase the therapeutic lifetime of drug delivery implants and limit the need for multiple implants in treatment of chronic illnesses. To analyze this complex system for rational design of drug delivery implants, we developed a mechanistic mathematical model to quantify the molecular events and processes. With a β-cyclodextrin hydrogel host matrix, defined release rates were obtained using a fluorescent model drug. The key processes were the complexation between the drug and cyclodextrin and diffusion of the drug in the hydrogel. Optimal estimates of the model parameters were obtained by minimizing the difference between model simulation and experimentally measured drug release kinetics. Model simulations could predict the drug release dynamics under a wide range of experimental conditions.     

Diffuse-interface theory for structure formation and release behavior in controlled drug release systems

A common method of controlling drug release has been to incorporate the drug into a polymer matrix, thereby creating a diffusion barrier that slows the rate of drug release. It has been demonstrated that the internal microstructure of these drug–polymer composites can significantly impact the drug release rate. However, the effect of processing conditions during manufacture on the composite structure and the subsequent effects on release behavior are not well understood. We have developed a diffuse-interface theory for microstructure evolution that is based on interactions between drug, polymer and solvent species, all of which may be present in either crystalline or amorphous states. Because the theory can be applied to almost any specific combination of material species and over a wide range of environmental conditions, it can be used to elucidate and quantify the relationships between processing, microstructure and release response in controlled drug release systems. Calculations based on the theory have now demonstrated that, for a characteristic delivery system, variations in microstructure arising due to changes in either drug loading or processing time, i.e. evaporation rate, could have a significant impact on both the bulk release kinetics and the uniformity of release across the system. In fact, we observed that changes in process time alone can induce differences in bulk release of almost a factor of two and typical non-uniformities of ±30% during the initial periods of release. Because these substantial variations may have deleterious clinical ramifications, it is critical that both the system microstructure and the control of that microstructure are considered to ensure the device will be both safe and effective in clinical use.     

Development of rationally designed affinity-based drug delivery systems

Many drug delivery systems have been developed to provide sustained release of proteins in vivo. However, the ability to predict and control the rate of release from delivery systems is still a challenge. Toward this goal, we screened a random drug-binding peptide library (12 amino acids) to identify peptides of varying (i.e. low, moderate, and high) affinity for a model polysaccharide drug (heparin). Peptide domains of varying affinity for heparin identified from the library were synthesized using standard solid phase chemistry. A mathematical model of drug release from a biomaterial scaffold containing drug-binding peptide domains identified from the library was developed. This model describes the binding kinetics of drugs to the peptides, the diffusion of free drug, and the kinetics of enzymatic matrix degradation. The effect of the ratio of binding sites to drug, the effect of varying the binding kinetics and the rate of enzymatic matrix degradation on the rate of drug release was examined. The in vitro release of the model drug from scaffold containing the peptide drug-binding domains was measured. The ability of this system to deliver and modulate the biological activity of protein drugs was also assessed using nerve growth factor (NGF) in a chick dorsal root ganglia (DRG) neurite extension model. These studies demonstrate that our rational approach to drug delivery system design can be used to control drug release from tissue-engineered scaffolds and may be useful for promoting tissue regeneration in vivo.     

Preparation and Enhancing Properties of pH-Sensitive Hydrogel in Light of Gum Ghatti-cl-poly(acrylic acid)/ – o-MWCNT for Sodium Diclofenac Drug Release

Gum ghatti (GG) is used as a biopolymer, acrylic acid (AA) is used as a synthetic monomer, ammonium persulphate (APS) is used as an initiator, and methylene bis-acrylamide (MBA) is used as a cross-linker in the current study to create gum ghatti-cl-poly(acrylic acid)-o-MWCNT hydrogels. The –o-MWCNT (0, 10, 20, 30, 40, and 50 mg) is added to the hydrogel as a filler. Fourier transform infrared (FTIR), differential scanning calorimetry (DSC), scanning electron microscopy (SEM), and X-ray diffraction (XRD) analyses are used to characterize the crosslinked hydrogels. The successful polymerization of the graft is confirmed by these spectroscopic studies. Sodium diclofenac (SD) as a model drug is utilized. Swelling tests are also conducted at pH 6.8 on all prepared hydrogels. In a similar manner, all hydrogel preparations are subjected to an in vitro study at neutral (pH 7.4), acidic (pH 1.2), and basic (pH 9.2) mediums, and a higher drug release is observed at pH 7.4. The Higuchi model, the Korsmeyer–Peppas model, and various zero-order and first-order kinetics are utilized in the investigation of the drug release order mechanism from the hydrogels. The drug release data favor the Korsmeyer–Peppas model, which describes the “n” diffusion exponent that controls the drug release mechanism from synthesized hydrogels. The “n” values control the Fickian diffusion (Case-I diffusional) like coupled diffusion (0.45 ≤ n). According to the results presented here, GGAACNT-based hydrogels can be used in biomedical fields, especially for controlled drug release.     

Cellular automata model for drug release from binary matrix and reservoir polymeric devices

Kinetics of drug release from polymeric tablets, inserts and implants is an important and widely studied area. Here we present a new and widely applicable cellular automata model for diffusion and erosion processes occurring during drug release from polymeric drug release devices. The model divides a 2D representation of the release device into an array of cells. Each cell contains information about the material, drug, polymer or solvent that the domain contains. Cells are then allowed to rearrange according to statistical rules designed to match realistic drug release. Diffusion is modeled by a random walk of mobile cells and kinetics of chemical or physical processes by probabilities of conversion from one state to another. This is according to the basis of diffusion coefficients and kinetic rate constants, which are on fundamental level just probabilities for certain occurrences. The model is applied to three kinds of devices with different release mechanisms: erodable matrices, diffusion through channels or pores and membrane controlled release. The dissolution curves obtained are compared to analytical models from literature and the validity of the model is considered. The model is shown to be compatible with all three release devices, highlighting easy adaptability of the model to virtually any release system and geometry. Further extension and applications of the model are envisioned.     

A vanadium/aspirin complex controlled release using a poly(beta-propiolactone) film. Effects on osteosarcoma cells.

A delivery system for vanadium was developed using poly(beta-propiolactone) (PbetaPL) films. The release kinetics of a complex of vanadium (IV) with aspirin (VOAspi) was evaluated with films prepared from polymers of different molecular weights, as well as with variable drug load. A sustained release of vanadium over 7 days was achieved. The drug release kinetics depends on contributions from two factors: (a) diffusion of the drug; and (b) erosion of the PbetaPL film. The experimental data at an early stage of release were fitted with a diffusion model, which allowed determination of the diffusion coefficient of the drug. VOAspi does not show strong interaction with the polymer, as demonstrated by the low apparent partition coefficient (approximately 10(-2)). UMR106 osteosarcoma cells were used as a model to evaluate the anticarcinogenic effects of the VOAspi released from the PbetaPPL film. VOAspi-PbetaPL film inhibited cell proliferation in a dose-response manner and induced formation of approximately half of the thiobarbituric acid reactive substances (TBARS), an index of lipid peroxidation. compared to that with free VOAspi in solution. The unloaded PbetaPL film did not generate cytotoxicity, as evaluated by cell growth and TBARS. Thus, the polymer-embedded VOAspi retained the antiproliferative effects showing lower cytotoxicity than the free drug. Results with VOAspi-PbetaPL films suggest that this delivery system may have promising biomedical and therapeutic applications.     

Multiscale Modeling Framework of Transdermal Drug Delivery

This study addresses the modeling of transdermal diffusion of drugs to better understand the permeation of molecules through the skin, especially the stratum corneum, which forms the main permeation barrier to percutaneous permeation. In order to ensure reproducibility and predictability of drug permeation through the skin and into the body, a quantitative understanding of the permeation barrier properties of the stratum corneum (SC) is crucial. We propose a multiscale framework of modeling the multicomponent transdermal diffusion of molecules. The problem is divided into subproblems of increasing length scale: microscopic, mesoscopic, and macroscopic. First, the microscopic diffusion coefficient in the lipid bilayers of the SC is found through molecular dynamics (MD) simulations. Then, a homogenization procedure is performed over a model unit cell of the heterogeneous SC, resulting in effective diffusion parameters. These effective parameters are the macroscopic diffusion coefficients for the homogeneous medium that is “equivalent” to the heterogeneous SC, and thus can be used in finite element simulations of the macroscopic diffusion process. The resulting drug flux through the skin shows very reasonable agreement to experimental data. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Subcutaneous polymeric matrix system p(HEMA-BGA) for controlled release of an anticancer drug (5-fluorouracil). II: Release kinetics

A subcutaneous polymeric drug delivery system, which consists of a polymeric matrix of poly(hydroxyethyl methacrylate-bisglycol acrylate), was developed. 5-fluorouracil was used as the model anticancer drug. Polymer-drug beads with a diameter of 3 mm were prepared by low-temperature radiation polymerization. In order to modify the release rate, polymeric beads with different composition, drug loading and crosslinking density were obtained. The kinetics of drug release were described by the expression Mt/M infinity = ktn. The diffusional release exponent 'n', which was calculated from the release curves, indicated that the mechanism of drug release from the polymeric matrix is due to the anomalous (non-Fickian) type of diffusion.     

Drug release from ion-exchange microspheres: mathematical modeling and experimental verification

This paper presents for the first time a mathematical model for a mechanism of controlled drug release involving both ion exchange and transient counter diffusion of a drug and counterions. Numerical analysis was conducted to study the effect of different factors on drug release kinetics including environmental condition, material properties, and design parameters. The concentration profiles of counterions and drug species, the moving front of ion exchange, and three distinct regions inside a microsphere, namely unextracted region, ion-exchange region and drug diffusion region, were revealed by model prediction. The numerical results indicated that the rate of drug release increased with an increase in the initial drug concentration in the microspheres, the salt concentration in the external solution, or the valence of the counterions, whereas it decreased with increasing Langmuir isotherm constant. The mathematical and experimental procedures for determination of the equilibrium constant and the usefulness of the model were demonstrated using verapamil hydrochloride and sulfopropyl dextran microsphere system as an example. This work has provided a very useful mathematical tool for predicting kinetics and equilibrium of drug release and for optimizing the design of ion-exchange drug delivery systems.     

Sustained-release delivery systems of triclosan for treatment of Streptococcus mutans biofilm

Dental diseases are chronic infections caused by oral bacteria harboring the dental biofilm. Local sustained-release delivery systems prolong the duration of a drug in the oral cavity, thus enhancing its therapeutic potential, while reducing its side effects. Triclosan is an agent that was found to have an antibacterial effect against oral bacteria. However, its substantivity in the oral cavity is low, resulting in reduced antibacterial efficiency. The purpose of this study was to develop a local sustained release device containing triclosan and to test its antibacterial efficacy on Streptococcus mutans biofilm. Our results show that we can formulate an ethylcellulose-based, nondegradable, sustained-release device in which 80% of the loaded triclosan is released over a 10-day period. The release rate of triclosan corresponded to the Higuchi's planar homogenous diffusion release model (r2 = 0.998). A degradable local sustained-release delivery based on a methacrylate ester matrix was also developed for a faster release rate of triclosan. The release kinetics in those types of sustained-release delivery systems was erosion control. The local sustained-release delivery system significantly affected the viability of S. mutans in biofilm compared to placebo as was tested by confocal laser scanning microscopy. Our in vitro results show that triclosan can be incorporated into degradable or nondegradable sustained-release drug delivery systems. The release of triclosan from the local sustained-release delivery system can be controlled, thus extending its antibacterial properties.     

Modeling vancomycin release kinetics from microporous calcium phosphate ceramics comparing static and dynamic immersion conditions

The release kinetics of vancomycin from calcium phosphate dihydrate (brushite) matrices and polymer/brushite composites were compared using different fluid replacement regimes, a regular replacement (static conditions) and a continuous flow technique (dynamic conditions). The use of a constantly refreshed flowing resulted in a faster drug release due to a constantly high diffusion gradient between drug loaded matrix and the eluting medium. Drug release was modeled using the Weibull, Peppas and Higuchi equations. The results showed that drug liberation was diffusion controlled for the ceramics matrices, whereas ceramics/polymer composites led to a mixed diffusion and degradation controlled release mechanism. The continuous flow technique was for these materials responsible for a faster release due to an accelerated polymer degradation rate compared with the regular fluid replacement technique.     

Modeling of degradation and drug release from a biodegradable stent coating

Biodegradable polymeric coatings on cardiovascular stents can be used for local delivery of therapeutic agents to diseased coronary arteries after stenting procedures. This can minimize the occurrence of clinically adverse events such as restenosis after stent implantation. A validated mathematical model can be a very important tool in the design and development of such coatings for drug delivery. The model should incorporate the important physicochemical processes responsible for the polymer degradation and drug release. Such a model can be used to study the effect of different coating parameters and configurations on the degradation and the release of the drug from the coating. In this paper, a simultaneous transport-reaction model predicting the degradation and release of the drug Everolimus from a polylactic acid (PLA) based stent coating is presented. The model has been validated using in vitro testing data and was further used to evaluate the influence of various parameters such as partitioning coefficient of water, autocatalytic effect of the lactic acid and structural change of the matrix, on the PLA degradation and drug release. The model can be used as a tool for predicting drug delivery from other coating configurations designed using the same polymer-drug combination. In addition, this modeling methodology has broader applications and can be used to develop mathematical models for predicting the degradation and drug release kinetics for other polymeric drug delivery systems.     

The effect of composition of poly(acrylic acid)-gelatin hydrogel on gentamicin sulphate release: in vitro

Hydrogels based on poly(acrylic acid) and gelatin crosslinked with N,N'-methylene bisacrylamide (0.5mol%) and glutaraldehyde (4%), respectively, forming an interpenetrating network were employed as matrices, for studying the loading and release of gentamicin sulphate. The release kinetics of gentamicin sulphate was evaluated in water (pH approximately 5.8), phosphate buffer (pH 7.4) and citrate buffer (pH 4) at 37+/-0.1 degrees C. The drug release in phosphate buffer was faster as compared to water or citrate buffer. Fitting the data of release studies in Peppas model indicated that the release of drug from full IPNs in phosphate buffer (pH 7.4), water (pH approximately 5.8) and citrate buffer (pH 4) were diffusion controlled. However, semi-IPNs showed both anomalous and Fickian diffusion mechanisms. With increasing gelatin percentage in the polymer, rate of drug release was faster and almost 85% of the loaded drug was released within 7 days in phosphate buffer (pH 7.4).