448
Views
36
CrossRef citations to date
0
Altmetric
Reviews

Application of mathematical modeling in sustained release delivery systems

&

Bibliography

  • Dym CL. Principles of mathematical modeling. 2nd editon. Chapter 1. Elsevier; Amsterdam: 2004
  • Israel G. Balthazar van der pol e il primo modello matematico del battito cardiaco. In: Freguglia P, editor. Modelli matematici nelle scienze biologiche. QuattroVenti; Urbino, Italy: 1998
  • Grassi M, Grassi G, Lapasin R, Colombo I. Understanding drug release and absorption mechanisms: a physical and mathematical approach. CRC Press; Boca Raton, FL, USA: 2007
  • Cartensen JT. Modeling and data treatment in the pharmaceutical sciences. Technomic Publishing Co; Lancaster, Pennsylvania, USA: 1996
  • da Vinci L. Trattato della Pittura. Carabba, editor. Lanciano (IT); 1947
  • Brigandt I. Systems biology and the integration of mechanistic explanation and mathematical explanation. Stud Hist Philos Biol Biomed Sci 2013;44:477-92
  • Peppas NA. Historical perspective on advanced drug delivery: how engineering design and mathematical modeling helped the field mature. Adv Drug Deliv Rev 2013;65:5-9
  • Wise DL. editor. Handbook of pharmaceutical controlled release technology. Marcel Dekker Inc; New York, NY, USA: 2000
  • Flynn GL, Yalkowsky SH, Roseman TJ. Mass transport phenomena and models: theoretical concepts. J Pharm Sci 1974;63:479-510
  • Grassi M, Lapasin R, Pricl S. Modeling of drug release from a swellable matrix. Chem Eng Commun 1998;169:79-109
  • Miller-Chou AA, Koening JK. A review of polymer dissolution. Prog Polym Sci 2003;28:1223-70
  • Siepmann J, Gopferich A. Mathematical modeling of bioerodible, polymeric drug delivery systems. Adv Drug Deliv Rev 2001;48:229-47
  • Mallapragada SK, Peppas NA. Unfolding and chain disentanglement during semicrystalline polymer dissolution. AIChe J 1997;43:870-6
  • Kydonieus A. editor. Treatise on controlled drug delivery. Fundamentals, optimization, applications. Marcel Dekker, Inc; New York, USA: 1992
  • Hasa D, Perissutti B, Voinovich D, et al. Nanocrystals drugs: theoretical background of solubility increase and dissolution rate enhancement. Chem Biochem Eng Q 2014; in press
  • de Smidt JH, Fokkens JG, Grijseels H, Crommelin DJ. Dissolution of theophylline monohydrate and anhydrous theophylline in buffer solutions. J Pharm Sci 1986;75:497-501
  • Hasa D, Voinovich D, Perissutti B, et al. Reduction of melting temperature and enthalpy of drug crystals: theoretical aspects. Eur J Pharm Sci 2013;50:17-28
  • Coceani N, Magarotto L, Ceschia D, et al. Theoretical and experimental analysis of drug release from an ensemble of polymeric particles containing amorphous and nano-crystalline drug. Chem Eng Sci 2012;71:345-55
  • Grassi M, Colombo I, Lapasin R. Drug release from an ensemble of swellable crosslinked polymer particles. J Control Rel 2000;68:97-113
  • Hasa D, Voinovich D, Perissutti B, et al. Enhanced oral bioavailability of vinpocetine through mechanochemical salt formation: physico-chemical characterization and in vivo studies. Pharm Res 2011;28:1870-80
  • Hasa D, Perissutti B, Grassi M, et al. Mechanochemical activation of vincamine mediated by linear polymers: assessment of some “critical steps”. Eur J Pharm Sci 2013;50:56-68
  • Grassi G, Grassi M. Mathematical modelling of nanocrystalline and amorphous drugs release and gastro-intestinal absorption from polymeric particles. In: Wilson CL, editor. Mathematical modelling, clustering algorithms and applications. NOVA Science Publishers, Inc; Hauppauge, NY, USA: 2011. p. 49-82
  • Amsden B. Solute diffusion within hydrogels. Mechanisms and models. Macromolecules 1998;31:8382-95
  • Adrover A, Giona M, Grassi M. Controlled release of theophylline from water-swollen scleroglucan matrices. J Membr Sci 1996;113:21-30
  • Singh M, Lumpkin J, Rosenblat J. Mathematical modeling of drug release from hydrogel matrices via a diffusion coupled with desorption mechanism. J Control Rel 1994;32:17-25
  • Singh M, Lumpkin J, Rosenblat J. Effect of electrostatic interactions on polylysine release rates from collagen matrices and comparison with model predictions. J Control Rel 1995;35:165-79
  • Singh MP, Stefko J, Lumpkin JA, Rosenblatt J. The effect of electrostatic charge interactions on release rates of gentamicin from collagen matrices. Pharm Res 1995;12:1205-10
  • Hilt JZ. Nanotechnology and biomimetic methods in therapeutics: molecular scale control with some help from nature. Adv Drug Deliv Rev 2004;56:1533-6
  • Byrne ME, Park K, Peppas NA. Molecular imprinting within hydrogels. Adv Drug Deliv Rev 2002;54:149-61
  • Kaunisto E, Marucci M, Borgquist P, Axelsson A. Mechanistic modelling of drug release from polymer-coated and swelling and dissolving polymer matrix systems. Int J Pharm 2011;418:54-77
  • Lee P. Effect of non-uniform initial drug concentration distribution on the kinetics of drug release from glassy hydrogel matrices. Polymer (Guildf) 1984;25:973-8
  • Lee PI. Novel approach to zero-order drug delivery via immobilized nonuniform drug distribution in glassy hydrogels. J Pharm Sci 1984;73:1344-7
  • Lee P. Initial concentration distribution as a mechanism for regulating drug release from diffusion controlled and surface erosion controlled matrix systems. J Control Rel 1986;4:1-7
  • Crank J. The mathematics of diffusion. 2nd edition. Oxford University Press; London; 1975
  • Topp EM. Principles of mass transfer. In: Amidon GL, Lee IL, Topp EM, editors. Transport processes in pharmaceutical systems, Chapter 1. Marcell Dekker, New York; 2000
  • Siepmann J, Siepmann F. Modeling of diffusion controlled drug delivery. J Control Rel 2012;161:351-62
  • Yanga R, Tuoi Vo TN, Gorelovd AV, et al. A mathematical model for pulsatile release: controlled release of rhodamine B from UV-crosslinked thermoresponsive thin films. Int J Pharm 2012;427:320-7
  • Lin CC, Metters AT. Hydrogels in controlled release formulations: network design and mathematical modeling. Adv Drug Del Rev 2006;58:1379-408
  • Siepmann J, Peppas NA. Hydrophilic matrices for controlled drug delivery: an improved mathematical model to predict the resulting drug release kinetics (the “Sequential Layer” Model). Pharm Res 2000;17:1290-8
  • Harland RS, Peppas NA. Solute diffusion in swollen networks. VII. Diffusion in semi-crystalline networks. Coll Polym Sci 1989;267:459-88
  • Narasimhan B. Accurate models in controlled drug delivery systems. In: Wise LD, editor. Handbook of pharmaceutical controlled release technology. Marcell Dekker, Inc; New York, USA: 2000. p. 155-81
  • Mandelbrot BB. The fractal geometry of nature. Freeman; San Francisco, USA: 1982
  • Stauffer D, Aharony A. Introduction to percolation theory. Taylor and Francis; London: 1992
  • Macheras P, Iliadis A. Modelling in biopharmaceutics, pharmacokinetics, and pharmacodynamics: homogeneous and heterogeneous approaches. Springer; New York, USA: 2006
  • Kosmidis K, Argyrakis P, Macheras P. A reappraisal of drug release laws using montecralo simulations: the prevalence of the weibull function. Pharm Res 2003;20:988-95
  • Martinez L, Villalobos R, Sanchez M, et al. Monte carlo simulations for the study of drug release from cylindrical matrix systems with inert nucleus. Int J Pharm 2009;369:38-46
  • Dokoumetzidis A, Kosmidis K, Macheras P. Monte carlo simulation and fractional kinetics considerations for the Higuchi equation. Int J Pharm 2011;418:100-3
  • O’Shaughnessy B, Procaccia I. Analytical solutions for diffusion on fractal objects. Phys Rev Lett 1985;54:455-8
  • Yin X, Li H, Liu R, et al. Fractal structure determines controlled release kinetics of monoliyhic osmotic pump tablets. J Pharm Pharmacol 2013;65:953-9
  • Cohen DS. Theoretical models for diffusion in glassy polymers. J Polym Sci Polym Phys Ed 1983;21:2057-65
  • Joshi S, Astarita G. Diffusion–relaxation coupling in polymers which show two-stage sorption phenomena. Polymer 1979;20:455-8
  • Astarita G, Sarti GC. A class of mathematical models for sorption of swelling solvents in glassy polymers. Polym Eng Sci 1978;18:388-95
  • Liu Q, Wang X, De Kee D. Mass transport through swelling membranes. Int J Eng Sci 2005;43:1464-70
  • Adib F, Neogi P. Sorption with oscillations in solid polymers. AIChe J 1987;33:164-6
  • Camera-Roda G, Sarti GC. Mass transport with relaxation in polymers. AIChE J 1990;36:851-60
  • Lapasin R, Pricl S. Rheology of industrial polysaccharides: theory and applications. Blackie Academic and Professional; London: 1995
  • Grassi M, Yuk SH, Cho SH. Modelling of solute transport across a temperature-sensitive polymer membrane. J Membr Sci 1999;152:241-9
  • Wu L, Brazel CS. Mathematical model to predict drug release, including the early-time burst effect, from swellable homogeneous hydrogels. Ind Eng Chem Res 2008;47:1518-26
  • Hariharan D, Peppas NA. Modelling of water transport and solute release in physiologically sensitive gels. J Control Rel 1993;23:123-35
  • Frisch HL, Wang TT, Kwel TK. Diffusion in glassy polymers II. J Polym Sci A2 1969;2, 879-87
  • Wang TT, Kwei TK, Frisch HL. D Diffusion in glassy polymers III. J Polym Sci A2 1969;2:2019-28
  • Hayes CK, Cohen DS. The evolution of steep fronts in non-Fickian polymer–penetrant systems. J Polym Sci Part B 1992;30:145-61
  • Ferreira JA, Grassi M, de Oliveira P. A 3D model for mechanistic control of drug release. SIAM J Appl Mathem 2014;74:620-33
  • Truskey GA, Yuan F, Katz DF. Transport phenomena in biological systems. Upper Saddle River. Pearson Prentice Hall; New Jersey, USA: 2004
  • Lustig SR, Caruthers JM, Peppas NA. Continuum thermodynamics and transport theory for polymer–fluid mixtures. Chem Eng Sci 1992;47:3037-57
  • Kim DJ, Caruthers JM, Peppas NA. Experimental verification of a predictive model pf penetrant transport in glassy polymers. Chem Eng Sci 1996;51:4827-41
  • Sackett CK, Narasimhan B. Mathematical modeling of polymer erosion: consequences for drug delivery. Int J Pharm 2011;418:104-14
  • Versypt AN, Pack DW, Braatz RD. Mathematical modeling of drug delivery from autocatalytically degradable PLGA microspheres — a review. J Control Rel 2013;165:29-37
  • Siepmann J, Göpferich A. Mathematical modeling of bioerodible, polymeric drug delivery systems. Adv Drug Deliv Rev 2001;48:229-47
  • Kipper MJ, Narasimhan B. Molecular description of erosion phenomena in biodegradable polymers. Macromolecules 2005;38:1989-99
  • Heller J, Baker RW. Theory and practice of controlled drug delivery from bioerodible polymers. In: Baker RW, editor. Controlled release of bioactive materials. Academic Press; New York, USA: 1980. p. 1-18
  • Soares JS, Zunino P. A mixture model for water uptake, degradation, erosion and drug release from polydisperse polymeric networks. Biomaterials 2010;31:3032-42
  • Arifin DY, Lee LY, Wang CW. Mathematical modeling and simulation of drug release from microspheres: implications to drug delivery systems. Adv Drug Deliv Rev 2006;58:1274-325
  • Siepmann J, Faisant N, Benoit JP. A new mathematical model quantifying drug release from bioerodible microparticles using Monte Carlo simulations. Pharm Res 2002;19:1887-95
  • Siepmann J, Siepmann F. Mathematical modeling of drug delivery. Int J Pharm 2008;364:328-43
  • Siepmann J, Siepmann F. Mathematical modeling of drug dissolution. Int J Pharm 2013;453:12-24
  • Wang Y, Abrahamsson B, Lindfors L, Brasseur JG. Comparison and analysis of theoretical models for diffusion-controlled dissolution. Mol Pharm 2012;9:1052-66
  • Levich VG. Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs; N.J, USA: 1962
  • Nogami H, Nagai T, Yotsuyanagi T. Dissolution phenomena of organic medicinals involving simultaneous phase changes. Chem Pharm Bull 1969;17:499-509
  • Huang J, Wigent RJ, Schwartz JB. Drug-polymer interaction and its significance on the physical stability of nifedipine amorphous dispersion in microparticles of an ammonio methacrylate copolymer and ethylcellulose binary blend. J Pharm Sci 2008;97:251-62
  • Paulsson M, Edsman K. Controlled drug release from gels using lipophilic interactions of charged substances with surfactants and polymers. J Colloid Interface Sci 2002;248:194-200
  • Kuijpers AJ, Engbers GH, van Wachem PB, et al. Controlled delivery of antibacterial proteins from biodegradable matrices. J Control Rel 1998;53:235-47
  • Kwon G, Bae YH, Cremers H, et al. Release of proteins via ion exchange from albumin-heparin microspheres. J Control Rel 1992;22:83-94
  • Brasseur N, Brault D, Couvreur P. Adsorption of hematoporphyrin onto polyalkylcyanoacrylate nanoparticles: carrier capacity and drug release. Int J Pharm 1991;70:129-35
  • Frenning G, Stromme M. Drug release modeled by dissolution, diffusion, and immobilization. Int J Pharm 2003;250:137-45
  • Desai SJ, Singh P, Simonelli AP, Higuchi WI. Investigation of factors influencing release of solid drug dispersed in inert matrices. II. Quantitation of procedures. J Pharm Sci 1966;55:1230-4
  • Muhr AH, Blanshard MV. Diffusion in gels. Polymer (Guildf) 1982;23:1012-26
  • Tzur-Balter A, Young JM, Bonanno-Young LM, Segal E. Mathematical modeling of drug release from nanostructured porous Si: combining carrier erosion and hindered drug diffusion for predicting release kinetics. Acta Biomater 2013;9:8346-53
  • Lee PI. Kinetics of drug release from hydrogel matrices. J Control Rel 1985;2:277-88
  • Bergese P, Alessandri I, Colombo I, et al. Microstructure and morphology of nimesulide/crospovidone nanocomposites by Raman and electron miscroscopies. Composites A 2005;36:443-8
  • Hasa D, Voinovich D, Perissutti B, et al. Multidisciplinary approach on characterizung a mechanochemically activated composite of vinpocetine and crospovidone. J Pharm Sci 2011;100:915-32
  • Carli F, Motta A. Characterization of drug loading in crospovidone by X-ray photoelectron spectroscopy. J Pharm Sci 1985;74:963-7
  • Zhou Y, Chu JS, Wu XY. Theoretical analysis of drug release into a finite medium from sphere ensembles with various size and concentration distributions. Eur J Pharm Sci 2004;22:251-9
  • Tapia C, Buckton G, Newton J. Factors influencing the mechanism of release from sustained release matrix pellets, produced by extrusion/spheronisation. Int J Pharm 1993;92:211-18
  • Ritger PL, Peppas NA. 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. J Control Rel 1987;5:23-36
  • Marucci M, Ragnarsson G, Nilsson B, Axelsson A. Osmotic pumping release from ethyl–hydroxypropyl–cellulose-coated pellets: a new mechanistic model. J Control Rel 2010;142:53-60
  • Noyes AA, Whitney WR. The rate of solution of solid substances in their own solutions. J Am Chem Soc 1897;19:930-4
  • Mulder M. Basic principle of membrane technology. Kluwer Academic Publishers ed; Netherlands: 1991
  • Colton CK, Smith KA, Merrill EW, Farrell PC. Permeability studies with cellulosic membranes. J Biomed Mater Res 1971;5:459-88
  • Hansen S, Lehr CM, Schaefer UF. Modeling the human skin barrier—Towards a better understanding of dermal absorption. Adv Drug Deliv Rev 2013;65:149-51
  • Selzer D, Hahn T, Naegel A, et al. Finite dose skin mass balance including the lateral part: comparison between experiment, pharmacokinetic modeling and diffusion models. J Control Rel 2013;165:119-28
  • Simon L, Ospina J. Two-dimensional transport analysis of transdermal drug absorption with a non-perfect sink boundary condition at the skin-capillary interface. Math Biosci 2013;244:58-67
  • Olatunji O, Das DB, Nassehi V. Modelling transdermal drug delivery using microneedles: effect of geometry on drug transport behaviour. J Pharm Sci 2012;101:164-75
  • Cu Y, Saltzman WS. Mathematical modeling of molecular diffusion through mucus. Adv Drug Deliv Rev 2009;61:101-14
  • Kim KS, Simon L. Transport mechanisms in oral transmucosal drug delivery: implications for pain management. Math Biosci 2011;229:93-100
  • Helbling IM, Luna JA, Cabrera MI. Mathematical modeling of drug delivery from torus-shaped single-layer devices. J Control Rel 2011;149:258-63
  • Moscicka-Studzinska A, Ciach T. Mathematical modelling of buccal iontophoretic drug delivery system. Chem Eng Sci 2012;80:182-7
  • Li CC, Chauhan A. Modeling ophthalmic drug delivery by soaked contact lenses. Ind Eng Chem Res 2006;45:3718-34
  • Zhang W, Prausnitz MR, Edwards A. Model of transient drug diffusion across cornea. J Control Rel 2004;99:241-58
  • Ferreira JA, de Oliveira P, da Silvac PM. Controlled drug delivery and ophthalmic applications. Chem Biochem Eng Q 2012;26:331-43
  • Huang J, Wong HL, Zhou Y, et al. In vitro studies and modeling of a controlled-release device for root canal therapy. J Control Rel 2000;67:293-307
  • Kreye F, Siepmann F, Siepmann J. Lipid implants as drug delivery systems. Expert Opin Drug Deliv 2008;5:291-307
  • Zunino P. Multidimensional pharmacokinetic models applied to the design of drug-eluting stents. Cardiovasc Eng Int J 2004;4:181-91
  • Davia L, Grassi G, Pontrelli G, et al. Mathematical modelling of NABD release from endoluminal gel paved stent. Comput Biol Chem 2009;33:33-40
  • Lauzon MA, Bergeron E, Marcos B, Faucheux N. Bone repair: new developments in growth factor delivery systems and their mathematical modeling. J Control Rel 2012;162:502-20
  • Modi S, Anderson BD. Determination of drug release kinetics from nanoparticles: overcoming pitfalls of the dynamic dialysis method. Mol Pharm 2013;10:3076-89
  • Pascal J, Ashley CE, Wang Z, et al. Mechanistic modeling identifies drug-uptake history as predictor of tumor drug resistance and nano-carrier-mediated response. ACS Nano 2013;7(12)):11174-82
  • Mikac U, Kristl J, Baumgartner S. Using quantitative magnetic resonance methods to understand better the gel-layer formation on polymer-matrix tablets. Expert Opin Drug Deliv 2011;8:677-92
  • Bertrand N, Leroux JC. The journey of a drug-carrier in the body: an anatomo-physiological perspective. J Control Rel 2012;161:152-63
  • Quintavalle U, Voinovich D, Perissutti B, et al. Preparation of sustained release co-extrudates by hot-melt extrusion and mathematical modelling of in vitro/in vivo drug release profiles. Eur J Pharm 2008;33:282-93
  • Milewski M, Paudel KS, Brogden NK, et al. Microneedle-assisted percutaneous delivery of naltrexone hydrochloride in yucatan minipig: in vitro−in vivo correlation. Mol Pharm 2013;10:3745-57
  • Grassi G, Hasa H, Voinovich D, et al. Simultaneous release and ADME processes of poorly water-soluble drugs: mathematical modeling. Mol Pharm 2010;7:1488-97
  • Ward JP, King JR. Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures. Math Biosci 2003;181:177-207
  • Grassi M, Lamberti G, Cascone S, Grassi G. Mathematical modeling of simultaneous drug release and in vivo absorption. Int J Pharm 2011;418:130-41
  • Wu R, Wang Z. Mathematical modeling of systems pharmacogenomics towards personalized drug delivery. Adv Drug Del Dev 2013;65:903-4

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.