By Laurent Simon, Juan Ospina
This publication offers ideas for 2- and 3-dimensional linear versions of controlled-release structures. It positive factors real-world purposes are taken from used to aid illustrate the tools in Cartesian, cylindrical and round coordinate structures. It covers the modeling of drug-delivery structures and offers mathematical instruments to guage and construct controlled-release units. It comprises classical and analytical options to resolve boundary-value difficulties related to - and 3-dimensional partial differential equations. It offers designated examples, case reports and step by step analytical recommendations to proper difficulties utilizing well known computational software program.
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Additional resources for Closed-form Solutions for Drug Transport through Controlled-Release Devices in Two and Three Dimensions
8) where n = 0, 1, 2, 3, … Eq. 10) Applying the principle of superposition to Eq. 11) n=0 in a discretized form. In cases where Eqs. 12) SEPARATION OF VARIABLES AND LEGENDRE POLYNOMIALS IN 2-D 41 To fully grasp the structure of Eq. 12), we take a look at the specific forms of the Legendre functions for lower values of n. The first ten Pn polynomials are P0 (x) = 1 1 3x2 P2 (x) = − + 2 2 5 3 3 P3 (x) = x − x 2 2 3 35 4 15 2 P4 (x) = + x − x 8 8 4 63 5 35 3 15 P5 (x) = x − x + x 8 4 8 5 231 6 315 4 105 2 x − x + x P6 (x) = − + 16 16 16 16 429 7 693 5 315 3 35 P7 (x) = x − x + x − x 16 16 16 16 35 6435 8 3003 6 3465 4 315 2 + x − x + x − x P8 (x) = 128 128 32 64 32 12155 9 6435 7 9009 5 1155 3 315 x − x + x − x + x P9 (x) = 128 32 64 32 128 63 46189 10 109395 8 45045 6 15015 4 3465 2 P10 (x) = − + x − x + x − x + x 256 256 256 128 128 256 The first ten Qn functions are given in Eqs.
Lin, A. , Mooney, D. J. (2007a). Integrated approach to designing growth factor delivery systems. FASEB J, 21(14), 3896–3903. Chen, R. , Silva, E. , Yuen, W. , & Mooney, D. J. (2007b). Spatio-temporal VEGF and PDGF delivery patterns blood vessel formation and maturation. Pharm Res, 24(2), 258–264. Grazul-Bilska, A. , Johnson, M. , Borowicz, P. , Bilski, J. , Reynolds, L. P. (2011). Placental development during early pregnancy in sheep: cell proliferation, global methylation, and angiogenesis in the fetal placenta.
Layer 2); ???? is the diffusivity in the polymeric matrix; k2 and kc are release and degradation rates, respectively; c10 and c20 are the initial drug concentrations. 4) are the symmetry boundary conditions at the center of the device. Perfect-sink conditions, represented by Eqs. 10), are applied at the surface; Eq. 7) is the flux continuity at the interface between the layers; Eq. 8) is a local equilibrium partition condition. 2 SOLUTION PROCEDURE FOR TRANSPORT THROUGH A TWO-LAYERED SCAFFOLD The system of Eqs.