Abstract
Porous systems play a significant role in controlled release. Porous membranes and matrices can be used to store drug prior to release, and pore structure plays a significant role in determining release kinetic profiles. In this chapter we review methods used to measure pore structure and mathematical models used to relate pore structure to drug transport properties. Steric and hydrodynamic interactions between drug and pore walls, pore tortuosity, and variation in pore width are identified as factors affecting transport. Percolation theory, which addresses connectedness of random pore networks and its effect on overall releasability of drug and release rate, is discussed. Concepts developed for porous systems can be applied, with some modifications, to transport in other heterogeneous systems, such as tissue interstitium and hydrogels.
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References
Siegel RA (1989) Modeling of drug release from porous polymers. In: Rosoff M (ed) Controlled release of drugs: polymers and aggregate systems. VCH, New York, pp 1–51
Bean CP (1972) The physics of porous membranes–neutral pores. In: Eisenmann G (ed) Membranes. Marcel Dekker, New York, pp 1–54
Deen WM, Bohrer MP, Epstein NB (1981) Effects of molecular size and configuration on diffusion in microporous membranes. AIChE J 27:952–959
Madou M (2002) Fundamentals of microfabrication, 2nd edn. CRC, New York
Mueller A, Hillmyer M, Bates FS (2009) Ordered network mesostructures in block polymer materials. Macromolecules 42:7221–7250
Nuxoll EE, Hillmeyer MA, Wang R, Leighton C, Siegel RA (2009) Composite block polymer-microfabricated silicon nanoporous membrane. ACS Appl Mater Interf 1:889–893
Anglin EJ, Cheng L, Freeman WR, Sailor MJ (2008) Porous silicon in drug delivery devices and materials. Adv Drug Deliv Rev 60:1266–1277
Slowing II, Vivero-Escoto JL, Wu C-W, Lin VS-Y (2008) Mesoporous silica nanoparticles as controlled release drug delivery and gene transfection carriers. Adv Drug Deliv Rev 60:1278–1288
Cauda V, Engelke H, Sauer A, Arcizet D, Bräuchle C (2010) Colchicine-loaded lipid bilayer-coated 50 nm mesoporous nanoparticles efficiently induce microtubule depolymerization upon cell uptake. Nano Letters 10:2484–2492
Martin F, Walczak R, Boiarski A, Cohen M, West T, Cosentino C, Ferrari M (2005) Tailoring width of microfabricated nanochannels to solute size can be used to control diffusion kinetics. J Control Release 102:123–133
Baker RW (2004) Membrane technology and applications. Wiley, Chichester
Li M, Rouaud O, Poncelet D (2008) Microencapsulation by solvent evaporation: state of the art for process engineering approaches. Int J Pharm 363:26–39
Martin AN (2011) Micromeritics. In: Sinko P (ed) Martin’s physical pharmacy and pharmaceutical sciences. Kluwer, Philadelphia, pp 442–468
Chandler R, Koplik J, Lerman K, Willemsen JF (1982) Capillary displacement and percolation in porous media. J Fluid Mech 119:249–267
Lane A, Shah N, Connor WC (1986) Measurement of the morphology of high-surface-area solids: porosimetry as a percolation process. J Coll Interf Sci 109:235–242
Miller ES, Peppas NA, Winslow DN (1983) Morphological changes of ethylene/vinyl acetate-based controlled delivery systems during release of water-soluble solutes. J Membr Sci 14:79–92
Lightfoot EN, Bassingthwaighte JB, Grabowski EF (1976) Hydrodynamic models for diffusion in microporous membranes. Ann Biomed Eng 4:78–90
Malone DM, Anderson JL (1978) Hindered diffusion of particles through small pores. Chem Eng Sci 33:1429–1440
Deen WM (1989) Hindered transport of large molecules in liquid-filled pores. AIChE J 33:1409–1423
Cassasa EF (1967) Equilibrium distribution of flexible polymer chains between a macroscopic solution phase and small voids. J Poly Sci Polym Lett 5:773–777
Davidson MG, Suter UW, Deen WM (1987) Hydrodynamic partitioning of flexible macromolecules between bulk solution and cylindrical pores. Macromolecules 20:1141–1146
Brenner H, Gaydos LJ (1977) The constrained Brownian movement of spherical particles in cylindrical pores of comparable radius. J Coll Interf Sci 58:312–356
Faxen H (1923) Die Bewegung einer Einer Starren Kuegel laengs der Achse mit zaeher Fluessigkeit gefuellten Rohres. Ark Mat Astron Fys 17:1
Glandt ED (1981) Noncircular pores in model membranes: a calculation of the effect of pore geometry on the partition of a solute. J Membr Sci 8:331–336
Cosentino C, Amato F, Walczak R, Boiarski A, Ferrari M (2005) Dynamic model of biomolecular diffusion through two-dimensional nanochannels. J Phys Chem B 109:7358–7364
Pricl S, Ferrone M, Fermeglia M, Amato F, Cosentino C, Ming-Cheng Cheng M, Walczak R, Ferrari M (2006) Multiscale modeling of protein transport in silicon membrane nanochannels. Part 1. Derivation of molecular parameters from computer simulations. Biomed Microdevices 8:277–290
Amato F, Cosentino C, Pricl S, Ferrone M, Fermeglia M, Ming-Cheng Cheng M, Walczak R, Ferrari M (2006) Multiscale modeling of protein transport in silicon membrane nanochannels. Part 2. From molecular parameters to a perdictive continuum diffusion model. Biomed Microdevices 8:291–298
Higuchi T (1963) Mechanism of sustained-action medication. Theoretical analysis of solid drugs dispersed in solid matrices. J Pharm Sci 52:1145–1149
Pismen LM (1974) Diffusion in porous media of a random structure. Chem Eng Sci 29:1227–1236
Siegel RA, Langer R (1986) A new Monte Carlo approach to diffusion in constricted porous geometries. J Coll Interf Sci 109:426–440
Siegel RA, Langer R (1990) Mechanistic studies of macromolecular drug release from macroporous polymers. II. Models for the slow kinetics of drug release. J Control Release 14:153–167
Dudko OK, Berezhkovskii AM, Weiss GH (2005) Time-dependent diffusion coefficients in periodic porous media. J Phys Chem B 109:21296–21299
Maknovskii YA, Berezhkovskii AM, Zitserman VYu, Zitserman VY (2009) Time-dependent diffusion in tubes with periodic partitions. J Chem Phys 131:104705
Broadbent S, Hammersley J (1957) Percolation processes: crystals and mazes. Proc Cambr Philos Soc 53:629–641
Bollobas B, Riordan O (2006) Percolation. Cambridge University Press, Cambridge
Stauffer D, Aharony A (1994) Introduction to percolation theory. CRC, New York
Sahimi M (1994) Applications of percolation theory. Taylor and Francis, Boca Raton, FL
Saltzman M, Langer R (1989) Transport rates of proteins in porous materials with known microgeometry. Biophys J 55:163–171
Siegel RA, Kost J, Langer RA (1989) Mechanistic studies of macromolecular drug release from macroporous polymers. I. Experiments and preliminary theory concerning completeness of drug release. J Control Release 8:223–236
Hastedt JE, Wright JL (1990) Diffusion in porous materials above the percolation threshold. Pharm Res 7:893–901
Hastedt JE, Wright JL (2006) Percolative transport and cluster diffusion near and below the percolation threshold of a porous polymeric matrix. Pharm Res 23:2427–2440
Winterfeld PH, Scriven LE, Davis HT (1981) Percolation and conduction on 3D Voronoi and regular networks: a second case study in topological disorder. J Phys C Solid State Phys 17:3429–3439
Powell MJ (1979) Site percolation in randomly packed spheres. Phys Rev B 20:4194–4198
Vicsek T, Kertesz J (1981) Monte Carlo renormalization-group approach to percolation in a continuum: test of universality. J Phys A Math Gen 14:L31–L37
Boissonade J, Barreau F, Carmona F (1983) The percolation of fibers with random orientations: a Monte Carlo study. J Phys A Math Gen 16:2777–2787
Kirkpatrick S (1973) Percolation and conduction. Rev Mod Phys 574:574–588
Brandt WW (1975) Use of percolation theory to estimate effective diffusion coefficients of particles migrating on various ordered lattices and in a random network structure. J Chem Phys 63:5162–5167
Barocas V, Drasler W, Girton T, Guler I, Knapp DR, Moeller J, Parsonage E (2009) A dissolution-diffusion model for the TAXUS™ drug-eluting stent with surface burst estimated from continuum percolation. J Biomed Mater Res B Appl Biomater 90B:267–274
Schnitzer JE (1988) Analysis of steric partition behavior of molecules in membranes using statistical physics. Application to gel chromatography and electrophoresis. Biophys J 54:1065–1076
Lustig SR, Peppas NA (1988) Solute diffusion in swollen membranes. IX. Scaling laws for solute diffusion in gels. J Appl Polym Sci 36:735–747
Amsden B (1998) Solute diffusion within hydrogels. Mechanisms and models. Macromolecules 31:8382–8395
Masaro L, Zhu XX (1999) Physical models of diffusion for polymer solutions, gels, and solids. Progr Polym Sci 24:731–775
Sakiyama-Elbert SE, Hubbell JA (2000) Controlled release of nerve growth factor from a heparin-containing fibrin-based cell ingrowth matrix. J Control Release 69:149–158
Amsden BG, Cheng Y-L (1994) Enhancement of fraction released above percolation threshold from monoliths containing osmotic excipients. J Control Release 33:99–105
Eitzman DM, Melkote RR, Cussler EL (1996) Barrier membranes with tipped flakes. AIChE J 42:2–9
DeRocher JP, Gettlefinger BT, Wang J, Nuxoll EE, Cussler EL (2005) Barrier membranes with different sizes of aligned flakes. J Membr Sci 254:21–30
Lape NK, Nuxoll EE, Cussler EL (2004) Polydisperse flakes in barrier films. J Membr Sci 236:29–37
Fredrickson GH, Bicerano J (1999) Barrier properties of oriented disc composites. J Chem Phys 110:2181–2188
Liu Q, Cussler EL (2006) Barrier membranes made with lithographically printed flakes. J Membr Sci 285:56–67
Shante VKS, Kirkpatrick S (1971) An introduction to percolation theory. Adv. Phys. 20: 325–357
Nan C-W, Shen Y, Ma J (2010) Physical composites near percolation. Annu Rev Mater Res 40:131–151
Larson RG, Scriven LE, Davis HT (1977) Percolation theory of residual phases in porous media. Nature 268: 409–413
Berkowitz B, Balgerg I (1993) Percolation theory and its application to groundwater hydrology. Water Resourc Res 29:775–794
Holman LE, Leuenberger H (1988) The relationship between solid fraction and mechanical properties of compacts–the percolation theory approach. Int J Pharmaceut 46:35–44
Kuentz M, Leuenberger H (1999) Pressure susceptibility of polymer tablets as a critical property: a modified Heckel equation. J Pharm Sci 88:174–179
Balberg I, Binenbaum N, Wagner N (1984) Percolation thresholds in the three-dimensional sticks system. Phys Rev Lett 52:1465–1468
Leuenberger H, Bonny JD, Kolb M (1995) Percolation effects in matrix-type controlled release systems. Int J Pharmaceut 115:217–224
Tongwen X, Binglin H (1998) Mechanism of sustained drug release in diffusion-controlled polymer matrix--aplication of percolation theory. Int J Pharmaceut 170:139–149
Adrover A, Massimiliano G, Grassi M (1996) Analysis of controlled release in disordered structures: the percolation model. J Membr Sci 113:21–30
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Siegel, R.A. (2012). Porous Systems. In: Siepmann, J., Siegel, R., Rathbone, M. (eds) Fundamentals and Applications of Controlled Release Drug Delivery. Advances in Delivery Science and Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0881-9_9
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DOI: https://doi.org/10.1007/978-1-4614-0881-9_9
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