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

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.

[1]  Charles Nicholson,et al.  In vivo diffusion analysis with quantum dots and dextrans predicts the width of brain extracellular space. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Balaji Narasimhan,et al.  Molecular Description of Erosion Phenomena in Biodegradable Polymers , 2005 .

[3]  H. B. Hopfenberg,et al.  Controlled Release from Erodible Slabs, Cylinders, and Spheres , 1976 .

[4]  C. Washington,et al.  Controlled release of macromolecules from PLA microspheres: using porous structure topology. , 2000, Journal of controlled release : official journal of the Controlled Release Society.

[5]  Chi-Hwa Wang,et al.  Computer simulation of the delivery of etanidazole to brain tumor from PLGA wafers: comparison between linear and double burst release systems. , 2003, Biotechnology and bioengineering.

[6]  Robert Langer,et al.  Modeling of polymer erosion in three dimensions: Rotationally symmetric devices , 1995 .

[7]  R H Guy,et al.  Skin penetration and distribution of polymeric nanoparticles. , 2004, Journal of controlled release : official journal of the Controlled Release Society.

[8]  Marco van Vulpen,et al.  Changes in blood-brain barrier permeability induced by radiotherapy: implications for timing of chemotherapy? (Review). , 2002, Oncology reports.

[9]  Thomas Erneux,et al.  Controlled Drug Release Asymptotics , 1998, SIAM J. Appl. Math..

[10]  Yu-Ling Cheng,et al.  Diffusional release of a dispersed solute from planar and spherical matrices into finite external volume , 1997 .

[11]  S. Feng,et al.  A novel controlled release formulation for the anticancer drug paclitaxel (Taxol): PLGA nanoparticles containing vitamin E TPGS. , 2003, Journal of controlled release : official journal of the Controlled Release Society.

[12]  J. Siepmann,et al.  The effect of gamma-irradiation on drug release from bioerodible microparticles: a quantitative treatment. , 2002, International journal of pharmaceutics.

[13]  C. Nicholson,et al.  Hindered diffusion of high molecular weight compounds in brain extracellular microenvironment measured with integrative optical imaging. , 1993, Biophysical journal.

[14]  Balaji Narasimhan,et al.  Mechanistic understanding of degradation in bioerodible polymers for drug delivery , 2002 .

[15]  A. R. Kulkarni,et al.  Biodegradable polymeric nanoparticles as drug delivery devices. , 2001, Journal of controlled release : official journal of the Controlled Release Society.

[16]  Chi-Hwa Wang,et al.  Simulation of intratumoral release of Etanidazole: effects of the size of surgical opening. , 2003, Journal of pharmaceutical sciences.

[17]  W. Saltzman,et al.  Distribution of 1,3-bis(2-chloroethyl)-1-nitrosourea and tracers in the rabbit brain after interstitial delivery by biodegradable polymer implants. , 1995, The Journal of pharmacology and experimental therapeutics.

[18]  Nicholas A. Peppas,et al.  A simple equation for description of solute release II. Fickian and anomalous release from swellable devices , 1987 .

[19]  Nikolaos A. Peppas,et al.  Solute and penetrant diffusion in swellable polymers. I. Mathematical modeling , 1986 .

[20]  T Görner,et al.  Lidocaine loaded biodegradable nanospheres. II. Modelling of drug release. , 1999, Journal of controlled release : official journal of the Controlled Release Society.

[21]  V. Calhoun,et al.  Controlled release of bioactive materials. , 1980 .

[22]  T. Kissel,et al.  Gamma irradiation for terminal sterilization of 17beta-estradiol loaded poly-(D,L-lactide-co-glycolide) microparticles. , 1999, Journal of controlled release : official journal of the Controlled Release Society.

[23]  S. Schwendeman,et al.  Determination of diffusion coefficient of a small hydrophobic probe in poly(lactide-co-glycolide) microparticles by laser scanning confocal microscopy , 2003 .

[24]  Yoshito Ikada,et al.  Kinetics of diffusion-mediated drug release enhanced by matrix degradation , 1995 .

[25]  B. Narasimhan,et al.  Mathematical models describing polymer dissolution: consequences for drug delivery. , 2001, Advanced drug delivery reviews.

[26]  A. Göpferich,et al.  Why degradable polymers undergo surface erosion or bulk erosion. , 2002, Biomaterials.

[27]  S. Yuk,et al.  Biodegradable polymeric nanospheres formed by temperature-induced phase transition in a mixture of poly(lactide-co-glycolide) and poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer. , 2002, Biomacromolecules.

[28]  Robert Langer,et al.  Poly(ethylene oxide)-modified poly(beta-amino ester) nanoparticles as a pH-sensitive biodegradable system for paclitaxel delivery. , 2003, Journal of controlled release : official journal of the Controlled Release Society.

[29]  E. M. Renkin,et al.  Mechanics and thermodynamics of transcapillary exchange , 1984 .

[30]  Rakesh K. Jain,et al.  Vascular Normalization by Vascular Endothelial Growth Factor Receptor 2 Blockade Induces a Pressure Gradient Across the Vasculature and Improves Drug Penetration in Tumors , 2004, Cancer Research.

[31]  Peter M Haggie,et al.  In Vivo Measurement of Brain Extracellular Space Diffusion by Cortical Surface Photobleaching , 2004, The Journal of Neuroscience.

[32]  J. S. Vrentas,et al.  Energy effects for solvent self-diffusion in polymer-solvent systems , 1993 .

[33]  Si-Shen Feng,et al.  Nanoparticles of poly(lactide)/vitamin E TPGS copolymer for cancer chemotherapy: synthesis, formulation, characterization and in vitro drug release. , 2006, Biomaterials.

[34]  P. Costa,et al.  Modeling and comparison of dissolution profiles. , 2001, European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.

[35]  Shigeo Kojima,et al.  Drug release from poly(dl-lactide) microspheres controlled by γ-irradiation , 1995 .

[36]  Chongli Zhong,et al.  Modeling of Drug Release from Bioerodible Polymer Matrices , 2005, Drug delivery.

[37]  H Leuenberger,et al.  Dissolution properties of praziquantel--PVP systems. , 1998, Pharmaceutica acta Helvetiae.

[38]  Michael Wolff,et al.  The influence of terminal gamma-sterilization on captopril containing poly(d,l-lactide-co-glycolide) microspheres , 1994 .

[39]  A. Dokoumetzidis,et al.  Analysis of Dissolution Data Using Modified Versions of Noyes–Whitney Equation and the Weibull Function , 2006, Pharmaceutical Research.

[40]  Kyriacos Zygourakis,et al.  Development and temporal evolution of erosion fronts in bioerodible controlled release devices , 1990 .

[41]  W. G. Lloyd,et al.  Diffusion in glassy polymers , 2007 .

[42]  D J Weidler,et al.  Pharmacokinetic profile of flosequinan in patients with compromised renal function. , 1993, Journal of pharmaceutical sciences.

[43]  A. W. Hixson,et al.  Dependence of Reaction Velocity upon surface and Agitation , 1931 .

[44]  T. Higuchi.  MECHANISM OF SUSTAINED-ACTION MEDICATION. THEORETICAL ANALYSIS OF RATE OF RELEASE OF SOLID DRUGS DISPERSED IN SOLID MATRICES. , 1963, Journal of pharmaceutical sciences.

[45]  C. Nicholson,et al.  Diffusion of epidermal growth factor in rat brain extracellular space measured by integrative optical imaging. , 2004, Journal of neurophysiology.

[46]  Nikolaos A. Peppas,et al.  Prediction of polymer dissolution in swellable controlled-release systems☆ , 1987 .

[47]  Nicholas A. Peppas,et al.  Solute and penetrant diffusion in swellable polymers. II. Verification of theoretical models , 1986 .

[48]  J. Siepmann,et al.  Effect of the size of biodegradable microparticles on drug release: experiment and theory. , 2004, Journal of controlled release : official journal of the Controlled Release Society.

[49]  R. Langer,et al.  A theoretical model of erosion and macromolecular drug release from biodegrading microspheres. , 1997, Journal of pharmaceutical sciences.

[50]  M Santucci,et al.  Gamma irradiation effects on poly(DL-lactictide-co-glycolide) microspheres. , 1998, Journal of controlled release : official journal of the Controlled Release Society.

[51]  Y Zhou,et al.  Studies of diffusional release of a dispersed solute from polymeric matrixes by finite element method. , 1999, Journal of pharmaceutical sciences.

[52]  N A Peppas,et al.  Calculation of the required size and shape of hydroxypropyl methylcellulose matrices to achieve desired drug release profiles. , 2000, International journal of pharmaceutics.

[53]  Clark K. Colton,et al.  Restricted diffusion in liquids within fine pores , 1973 .

[54]  Chi-Hwa Wang,et al.  Simulation of drug release from biodegradable polymeric microspheres with bulk and surface erosions. , 2003, Journal of pharmaceutical sciences.

[55]  H. Reulen,et al.  Role of pressure gradients and bulk flow in dynamics of vasogenic brain edema. , 1977, Journal of neurosurgery.

[56]  P. Flory,et al.  STATISTICAL MECHANICS OF CROSS-LINKED POLYMER NETWORKS II. SWELLING , 1943 .

[57]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[58]  Abraham J Domb,et al.  Polyanhydrides: an overview. , 2002, Advanced drug delivery reviews.

[59]  Corinne S. Lengsfeld,et al.  Manipulation of particle size distribution of poly(l-lactic acid) nanoparticles with a jet-swirl nozzle during precipitation with a compressed antisolvent , 2003 .

[60]  Robert Langer,et al.  Polymeric controlled drug delivery , 1988 .

[61]  Pratibhash Chattopadhyay,et al.  Supercritical CO2 Based Production of Magnetically Responsive Micro- and Nanoparticles for Drug Targeting , 2002 .

[62]  W. Mark Saltzman,et al.  Chemotherapeutic Drugs Released from Polymers: Distribution of 1,3-bis(2-chloroethyl)-l-nitrosourea in the Rat Brain , 1996, Pharmaceutical Research.

[63]  N A Peppas,et al.  Molecular analysis of drug delivery systems controlled by dissolution of the polymer carrier. , 1997, Journal of pharmaceutical sciences.

[64]  W. Saltzman,et al.  Pharmacokinetics of interstitial delivery of carmustine, 4-hydroperoxycyclophosphamide, and paclitaxel from a biodegradable polymer implant in the monkey brain. , 1998, Cancer research.

[65]  Qiang Zhang,et al.  In vitro and in vivo study of two types of long-circulating solid lipid nanoparticles containing paclitaxel. , 2001, Chemical & pharmaceutical bulletin.

[66]  Richard A. Kenley,et al.  Gamma Irradiation Effects on Molecular Weight and in Vitro Degradation of Poly(D,L-Lactide-CO-Glycolide) Microparticles , 1995, Pharmaceutical Research.

[67]  V. Torchilin,et al.  Biodegradable long-circulating polymeric nanospheres. , 1994, Science.

[68]  R. Fassihi,et al.  Application of binary polymer system in drug release rate modulation. 2. Influence of formulation variables and hydrodynamic conditions on release kinetics. , 1997, Journal of pharmaceutical sciences.

[69]  J. Siepmann,et al.  HPMC-Matrices for Controlled Drug Delivery: A New Model Combining Diffusion, Swelling, and Dissolution Mechanisms and Predicting the Release Kinetics , 1999, Pharmaceutical Research.

[70]  K Zygourakis,et al.  Computer-aided design of bioerodible devices with optimal release characteristics: a cellular automata approach. , 1996, Biomaterials.

[71]  E. Starling.  On the Absorption of Fluids from the Connective Tissue Spaces , 1896, The Journal of physiology.

[72]  Nicholas A. Peppas,et al.  Solute and penetrant diffusion in swellable polymers. IV. Semicrystalline, swelling-controlled release systems of poly(ethylene-co-vinyl alcohol) , 1986 .

[73]  P. Deluca,et al.  Characterization of biodegradable poly(D,L-lactide-co-glycolide) polymers and microspheres. , 1995, Journal of pharmaceutical and biomedical analysis.

[74]  Richard W. Baker,et al.  Controlled Release of Biologically Active Agents , 1987 .

[75]  N. Peppas,et al.  Drug/Polymer Matrix Swelling and Dissolution , 2004, Pharmaceutical Research.

[76]  Shigeo Kojima,et al.  The effect of γ-irradiation on drug release from poly(lactide) microspheres , 1995 .

[77]  Donald R Paul,et al.  Diffusional release of a solute from a polymer matrix , 1976 .

[78]  Robert Langer,et al.  The influence of microstructure and monomer properties on the erosion mechanism of a class of polyanhydrides , 1993 .

[79]  Nicholas A. Peppas,et al.  A model of dissolution-controlled, diffusional drug release from non-swellable polymeric microspheres , 1988 .

[80]  Jean-Maurice Vergnaud,et al.  Controlled Drug Release Of Oral Dosage Forms , 1993 .

[81]  Juergen Siepmann,et al.  A New Mathematical Model Quantifying Drug Release from Bioerodible Microparticles Using Monte Carlo Simulations , 2002, Pharmaceutical Research.

[82]  W. Mark Saltzman,et al.  Localized Delivery of Proteins in the Brain: Can Transport Be Customized? , 1998, Pharmaceutical Research.

[83]  J. Rogers,et al.  Dissolution of fludrocortisone from phospholipid coprecipitates. , 1992, Journal of pharmaceutical sciences.

[84]  Yoshiaki,et al.  Preparations of biodegradable nanospheres of water-soluble and insoluble drugs with D, L-lactide/glycolide copolymer by a novel spontaneous emulsification solvent diffusion method, and the drug release behavior. , 1993 .

[85]  W. Saltzman,et al.  Pharmacokinetics of the Carmustine Implant , 2002, Clinical pharmacokinetics.

[86]  P. R. Nixon,et al.  Drug release from hydrophilic matrices. 2. A mathematical model based on the polymer disentanglement concentration and the diffusion layer. , 1995, Journal of pharmaceutical sciences.

[87]  Robert Langer,et al.  Modeling monomer release from bioerodible polymers , 1995 .

[88]  A. Göpferich,et al.  Mechanisms of polymer degradation and erosion. , 1996, Biomaterials.

[89]  Si-Shen Feng,et al.  PLGA/TPGS Nanoparticles for Controlled Release of Paclitaxel: Effects of the Emulsifier and Drug Loading Ratio , 2003, Pharmaceutical Research.

[90]  R. Jain.  Normalization of Tumor Vasculature: An Emerging Concept in Antiangiogenic Therapy , 2005, Science.

[91]  V. Labhasetwar,et al.  Nanosystems in Drug Targeting: Opportunities and Challenges , 2005 .

[92]  Chi-Hwa Wang,et al.  Double-walled microspheres for the sustained release of a highly water soluble drug: characterization and irradiation studies. , 2002, Journal of controlled release : official journal of the Controlled Release Society.

[93]  C. Chu,et al.  Biodegradable dextran-polylactide hydrogel network and its controlled release of albumin. , 2001, Journal of biomedical materials research.

[94]  J. Siepmann,et al.  Hydrophilic Matrices for Controlled Drug Delivery: An Improved Mathematical Model to Predict the Resulting Drug Release Kinetics (the “sequential Layer” Model) , 2004, Pharmaceutical Research.

[95]  Ick Chan Kwon,et al.  Hydrophobically modified glycol chitosan nanoparticles as carriers for paclitaxel. , 2006, Journal of controlled release : official journal of the Controlled Release Society.

[96]  Paolo Colombo,et al.  Analysis of the swelling and release mechanisms from drug delivery systems with emphasis on drug solubility and water transport , 1996 .

[97]  S. Rapoport,et al.  A two-dimensional, finite element analysis of vasogenic brain edema. , 1990, Neurologia medico-chirurgica.

[98]  R. Liggins,et al.  Paclitaxel loaded poly(L-lactic acid) (PLLA) microspheres. II. The effect of processing parameters on microsphere morphology and drug release kinetics. , 2004, International journal of pharmaceutics.

[99]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection. , 1989, Microvascular research.

[100]  Cory Berkland,et al.  Modeling small-molecule release from PLG microspheres: effects of polymer degradation and nonuniform drug distribution. , 2005, Journal of controlled release : official journal of the Controlled Release Society.

[101]  Robert Langer,et al.  Modeling of Polymer Erosion , 1993 .

[102]  Y Zhou,et al.  Modeling and analysis of dispersed-drug release into a finite medium from sphere ensembles with a boundary layer. , 2003, Journal of controlled release : official journal of the Controlled Release Society.

[103]  W. Mark Saltzman,et al.  Drugs released from polymers: diffusion and elimination in brain tissue , 1991 .

[104]  Watt W Webb,et al.  Diffusion of nerve growth factor in rat striatum as determined by multiphoton microscopy. , 2003, Biophysical journal.

[105]  Chi-Hwa Wang,et al.  In Vitro Sustained Release of Human Immunoglobulin G from Biodegradable Microspheres , 2001 .

[106]  O. I. Corrigan,et al.  Mechanisms Governing Drug Release from Poly-α-Hydroxy Aliphatic Esters: Diltiazem Base Release from Poly-Lactide-co-Glycolide Delivery Systems , 1993 .

[107]  Lisa Brannon Peppas.  Recent advances on the use of biodegradable microparticles and nanoparticles in controlled drug delivery , 1995 .

[108]  P. R. Nixon,et al.  Drug release from hydrophilic matrices. 1. New scaling laws for predicting polymer and drug release based on the polymer disentanglement concentration and the diffusion layer. , 1995, Journal of pharmaceutical sciences.

[109]  J. Siepmann,et al.  Mathematical modeling of drug release from bioerodible microparticles: effect of gamma-irradiation. , 2003, European journal of pharmaceutics and biopharmaceutics : official journal of Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V.

[110]  S. Simões,et al.  Paclitaxel-loaded PLGA nanoparticles: preparation, physicochemical characterization and in vitro anti-tumoral activity. , 2002, Journal of controlled release : official journal of the Controlled Release Society.

[111]  D. Hess,et al.  Transport models for swelling and dissolution of thin polymer films , 1989 .

[112]  John E. Hogan,et al.  MATHEMATICAL MODELLING OF DRUG RELEASE FROM HYDROXYPROPYLMETHYLCELLULOSE MATRICES : EFFECT OF TEMPERATURE , 1991 .

[113]  M. Westphal,et al.  Inhibition of glioma angiogenesis and growth in vivo by systemic treatment with a monoclonal antibody against vascular endothelial growth factor receptor-2. , 2001, Cancer research.

[114]  Chi-Hwa Wang,et al.  Simulation of the Delivery of Doxorubicin to Hepatoma , 2001, Pharmaceutical Research.

[115]  Robert Gurny,et al.  Influence of Irradiation Sterilization on Polymers Used as Drug Carriers—A Review , 1997 .

[116]  David O. Cooney,et al.  Effect of geometry on the dissolution of pharmaceutical tablets and other solids: Surface detachment kinetics controlling , 1972 .

[117]  S. Yeung,et al.  Sub‐Micrometer‐Sized Biodegradable Particles of Poly(L‐Lactic Acid) via the Gas Antisolvent Spray Precipitation Process , 1993, Biotechnology progress.

[118]  V D Calhoun,et al.  A finite element model for predicting the distribution of drugs delivered intracranially to the brain. , 1997, American journal of physiology. Regulatory, integrative and comparative physiology.

[119]  S. Feng,et al.  Vitamin E TPGS used as emulsifier in the solvent evaporation/extraction technique for fabrication of polymeric nanospheres for controlled release of paclitaxel (Taxol). , 2002, Journal of controlled release : official journal of the Controlled Release Society.

[120]  F Langenbucher,et al.  Letters to the Editor: Linearization of dissolution rate curves by the Weibull distribution , 1972, The Journal of pharmacy and pharmacology.

[121]  K. Himmelstein,et al.  A simultaneous transport-reaction model for controlled drug delivery from catalyzed bioerodible polymer matrices , 1985 .

[122]  Gordon L. Amidon,et al.  Gastrointestinal Uptake of Biodegradable Microparticles: Effect of Particle Size , 1996, Pharmaceutical Research.

[123]  R. Liggins,et al.  Paclitaxel loaded poly(L-lactic acid) microspheres: properties of microspheres made with low molecular weight polymers. , 2001, International journal of pharmaceutics.

[124]  L. E. Scriven,et al.  Percolation theory of two phase flow in porous media , 1981 .

[125]  Juergen Siepmann,et al.  How autocatalysis accelerates drug release from PLGA-based microparticles: a quantitative treatment. , 2005, Biomacromolecules.

[126]  Chi-Hwa Wang,et al.  Simulation of gentamicin delivery for the local treatment of osteomyelitis. , 2005, Biotechnology and bioengineering.

[127]  R. W. Baker,et al.  THEORY AND PRACTICE OF CONTROLLED DRUG DELIVERY FROM BIOERODIBLE POLYMERS , 1980 .

[128]  J. S. Vrentas,et al.  Solvent self-diffusion in glassy polymer-solvent systems , 1994 .

[129]  B. Narasimhan,et al.  Microphase separation in bioerodible copolymers for drug delivery. , 2001, Biomaterials.

[130]  John Crank,et al.  The Mathematics Of Diffusion , 1956 .

[131]  B. Leclerc,et al.  Release of mifepristone from biodegradable matrices: experimental and theoretical evaluations. , 2000, International journal of pharmaceutics.

[132]  Jian Li,et al.  Three-dimensional simulation of IgG delivery to tumors , 1998 .

[133]  J. S. Vrentas,et al.  Solvent self-diffusion in rubbery polymer-solvent systems , 1994 .

[134]  B Horwitz,et al.  A mathematical model for vasogenic brain edema. , 1978, Advances in neurology.

[135]  J. Siepmann,et al.  Modeling of drug release from delivery systems based on hydroxypropyl methylcellulose (HPMC). , 2001 .

[136]  Y. Song,et al.  Improved efficacy of chemotherapy for glioblastoma by radiation-induced opening of blood-brain barrier: clinical results. , 2001, International journal of radiation oncology, biology, physics.

[137]  S. Feng,et al.  Fabrication, characterization and in vitro release of paclitaxel (Taxol) loaded poly (lactic-co-glycolic acid) microspheres prepared by spray drying technique with lipid/cholesterol emulsifiers. , 2001, Journal of controlled release : official journal of the Controlled Release Society.

[138]  Nicholas A. Peppas,et al.  A simple equation for description of solute release I. Fickian and non-fickian release from non-swellable devices in the form of slabs, spheres, cylinders or discs , 1987 .

[139]  K. Whaley,et al.  Antibody diffusion in human cervical mucus. , 1994, Biophysical journal.

[140]  A La Manna,et al.  Swelling-activated drug delivery systems. , 1988, Biomaterials.

[141]  W. Deen.  Hindered transport of large molecules in liquid‐filled pores , 1987 .

[142]  Richard W. Baker,et al.  Controlled release: mechanisms and release. , 1974 .

[143]  Yu-Ling Cheng,et al.  Diffusional release of a dispersed solute from a spherical polymer matrix , 1996 .

[144]  Simon Watkins,et al.  Irradiation reduces interstitial fluid transport and increases the collagen content in tumors. , 2003, Clinical cancer research : an official journal of the American Association for Cancer Research.

[145]  Ping I. Lee.  Diffusional release of a solute from a polymeric matrix — approximate analytical solutions , 1980 .

[146]  Wim E Hennink,et al.  Mobility of model proteins in hydrogels composed of oppositely charged dextran microspheres studied by protein release and fluorescence recovery after photobleaching. , 2005, Journal of controlled release : official journal of the Controlled Release Society.

[147]  Y Zhou,et al.  Theoretical analyses of dispersed-drug release from planar matrices with a boundary layer in a finite medium. , 2002, Journal of controlled release : official journal of the Controlled Release Society.

[148]  J. Li,et al.  The delivery of BCNU to brain tumors. , 1999, Journal of controlled release : official journal of the Controlled Release Society.

[149]  N. Peppas,et al.  A simple equation for the description of solute release. III. Coupling of diffusion and relaxation , 1989 .

[150]  A. Streubel,et al.  Understanding and Predicting Drug Delivery from Hydrophilic Matrix Tablets Using the “Sequential Layer” Model , 2002, Pharmaceutical Research.

[151]  R. Langer,et al.  Transport rates of proteins in porous materials with known microgeometry. , 1989, Biophysical journal.

[152]  Lisa Brannon-Peppas,et al.  Recent advances on the use of biodegradable microparticles and nanoparticles in controlled drug delivery , 1995 .

[153]  C. Chu,et al.  Scanning electron microscopic study of the hydrolytic degradation of poly(glycolic acid) suture. , 1982, Journal of biomedical materials research.

[154]  Chi-Hwa Wang,et al.  Self-Assembled Biodegradable Nanoparticles Developed by Direct Dialysis for the Delivery of Paclitaxel , 2005, Pharmaceutical Research.

[155]  Chi-Hwa Wang,et al.  Transient interstitial fluid flow in brain tumors: Effect on drug delivery , 2005 .

[156]  S. Panomsuk,et al.  Release of medicaments from spherical matrices containing drug in suspension : theoretical aspects , 1995 .