Mathematical modeling and simulation of drug release from microspheres: Implication to drug delivery systems

Singapore-MIT Alliance, Cambridge, Massachusetts, United States
Advanced Drug Delivery Reviews (Impact Factor: 15.04). 12/2006; 58(12-13):1274-325. DOI: 10.1016/j.addr.2006.09.007
Source: PubMed


This article aims to provide a comprehensive review of existing mathematical models and simulations of drug release from polymeric microspheres and of drug transport in adjacent tissues. In drug delivery systems, mathematical modeling plays an important role in elucidating the important drug release mechanisms, thus facilitating the development of new pharmaceutical products by a systematic, rather than trial-and-error, approach. The mathematical models correspond to the known release mechanisms, which are classified as diffusion-, swelling-, and erosion-controlled systems. Various practical applications of these models which explain experimental data are illustrated. The effect of gamma-irradiation sterilization on drug release mechanism from erosion-controlled systems will be discussed. The application of existing models to nanoscale drug delivery systems specifically for hydrophobic and hydrophilic molecules is evaluated. The current development of drug transport modeling in tissues utilizing computational fluid dynamics (CFD) will also be described.

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    • "Other more complex models of release from biodegradable polymeric microspheres involve three mechanisms: drug diffusion, drug dissolution, and polymer erosion and are described by three equations that consider drug concentration in the liquid phase, a virtual solid phase, and an effective solid phase (Zhang et al., 2003). Similar complex systems model the entire drug release profile as the summation of the three mechanisms: first order burst release, first order bulk degradation of the polymer, and diffusional release, however, in a sequential time intervals for each release stage (Arifin et al., 2006; Lao et al., 2009; Siepmann et al., 2002). In this manuscript, the release of the encapsulated kinase inhibitor is analyzed by an effective mathematical drug release model that considers for the entire drug release process, a combined contribution of three mechanisms of release in a simultaneous fashion. "
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    ABSTRACT: A mathematical model of drug release that incorporates the simultaneous contributions of initial burst, nanoparticle degradation-relaxation and diffusion was developed and used to effectively describe the release of a kinase inhibitor and anticancer drug, PHT-427. The encapsulation of this drug intoPLGA nanoparticles was performed by following the single emulsion-solvent evaporation techniqueand the release wasdetermined in phosphate buffer pH 7.4 at 37°C. The size of nanoparticles was obtainedin a range of 162-254nm. The experimental release profiles showed three well definedphases: an initial fast drug release, followed by a nanoparticle degradation-relaxation slowerrelease and then a diffusion release phase. The effects of the controlled release most relevant parameters suchas drug diffusivity, initial burst constant, nanoparticle degradation-relaxation constant,and the time to achieve a maximum rate of drug release were evaluated by a parametrical analysis. The theoretical release studieswere corroborated experimentally by evaluating the cytotoxicity effectiveness of theinhibitor AKT/PDK1 loaded nanoparticles over BxPC-3 pancreatic cancer cells in vitro.These studies show that the encapsulated inhibitor AKT/PDK1 in the nanoparticles ismore accessible and thus more effective when compared with the drug alone, indicatingtheir potential use in chemotherapeutic applications. Copyright © 2015. Published by Elsevier B.V.
    Full-text · Article · Jul 2015 · International Journal of Pharmaceutics
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    • "The elevation of the lutein load in the vehicles could improve the driving force needed for the diffusion of lutein into the cornea. Fick's first law postulates that the diffusion flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient [26]. As shown in Table 2, the partition coefficient and the accumulation rate of NLC + HPβCD (4000 μg g−1 lutein) were significantly higher (P < 0.05) than those of NLC + HPβCD with 2000 μg g−1 lutein. "
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    ABSTRACT: Topical delivery has the advantages including being user friendly and cost effective. Development of topical delivery carriers for lutein is becoming an important issue for the ocular drug delivery. Quantification of the partition coefficient of drug in the ocular tissue is the first step for the evaluation of delivery efficacy. The objectives of this study were to evaluate the effects of lipid nanoparticles and cyclodextrin (CD) on the corneal lutein accumulation and to measure the partition coefficients in the porcine cornea. Lipid nanoparticles combined with 2% HP β CD could enhance lutein accumulation up to 209.2 ± 18 ( μ g/g) which is 4.9-fold higher than that of the nanoparticles. CD combined nanoparticles have 68% of drug loading efficiency and lower cytotoxicity in the bovine cornea cells. From the confocal images, this improvement is due to the increased partitioning of lutein to the corneal epithelium by CD in the lipid nanoparticles. The novel lipid nanoparticles could not only improve the stability and entrapment efficacy of lutein but also enhance the lutein accumulation and partition in the cornea. Additionally the corneal accumulation of lutein was further enhanced by increasing the lutein payload in the vehicles.
    Full-text · Article · Jul 2014 · Journal of Ophthalmology
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    • "Results of high IFP in tumors are discussed in our previous studies [2,16,17] and in the experimental results of Arifin et al. [29] and Huber et al. [30]. Maximum value of IFP in spherical tumors (1 cm radius) for baseline values in Table 1 is 1529.5 Pa which is close to the studies of Jain et al. [31], Chauhan et al. [32], and Arfin et al. [33]. "
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    ABSTRACT: Background The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor. Methods The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated. Results Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible. Conclusions This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection.
    Full-text · Article · Jun 2014 · Journal of Biological Engineering
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