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Controlled Drug Release Asymptotics

Cohen, Donald S. and Erneux, Thomas (1998) Controlled Drug Release Asymptotics. SIAM Journal on Applied Mathematics, 58 (4). pp. 1193-1204. ISSN 0036-1399. doi:10.1137/S0036139995293269.

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The solution of Higushi's model for controlled release of drugs is examined when the solubility of the drug in the polymer matrix is a prescribed function of time. A time-dependent solubility results either from an external control or from a change in pH due to the activation of pH immobilized enzymes. The model is described as a one-phase moving boundary problem which cannot be solved exactly. We consider two limits of our problem. The first limit considers a solubility much smaller than the initial loading of the drug. This limit leads to a pseudo-steady-state approximation of the diffusion equation and has been widely used when the solubility is constant. The second limit considers a solubility close to the initial loading of the drug. It requires a boundary layer analysis and has never been explored before. We obtain simple analytical expressions for the release rate which exhibits the effect of the time-dependent solubility.

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Additional Information:©1998 Society for Industrial and Applied Mathematics. Received by the editors October 23, 1995; accepted for publication (in revised form) January 3, 1997; published electronically May 27, 1998. [D.S.C.] was supported in part by NSF grant DMS-9501511 and the Department of Energy grant W-7405-ENG-36 at the Center for Nonlinear Studies at Los Alamos. [T.E.] was supported in part by NSF grant DMS-9625843, U.S. Air Force Office of Scientific Research grant F49620-95-0065, and the Fonds National de La Recherche Scientique (Belgium).
Funding AgencyGrant Number
National Science FoundationDMS-9501511
Department of EnergyW-7405-ENG-36
National Science FoundationDMS-9625843
Air Force Offce of Scientific ResearchF49620-95-0065
Fonds National de La Recherche Scientique (Belgium)UNSPECIFIED
Subject Keywords:moving boundary problem; boundary layer; exponentially small asymptotics; controlled drug release; nonlinear diffusion
Issue or Number:4
Record Number:CaltechAUTHORS:COHsiamjam98
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12833
Deposited On:09 Jan 2009 05:31
Last Modified:08 Nov 2021 22:33

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