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Drug Release Kinetics from Biodegradable Polymers via Partial Differential Equations Models

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In order to achieve prescribed drug release kinetics some authors have been investigating bi-phasic and possibly multi-phasic releases from blends of biodegradable polymers. Recently, experimental data for the release of paclitaxel have been published by Lao et al. (Lao and Venkatraman in J. Control. Release 130:9–14, 2008; Lao et al. in Eur. J. Pharm. Biopharm. 70:796–803, 2008). In Blanchet et al. (SIAM J. Appl. Math. 71(6):2269–2286, 2011) we validated a two-parameter quadratic ordinary differential equation (ODE) model against their experimental data from three representative neat polymers. In this paper we provide a gradient flow interpretation of the ODE model. A three-dimensional partial differential equation (PDE) model for the drug release in their experimental set up is introduced and its parameters are related to the ones of the ODE model. The gradient flow interpretation is extended to the study of the asymptotic concentrations that are solutions of the PDE model to determine the range of parameters that are suitable to simulate complete or partial drug release.

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  1. Intravascular ultrasound (IVUS) is a medical imaging methodology using a specially designed catheter with a miniaturized ultrasound probe attached to the distal end of the catheter.

  2. Bare Metal Stent (BMS).

  3. A bi-phasic strategy consists in delivering the treatment in two phases. For instance, in the first phase of drug release, the immediate release dose fraction reaches a therapeutic drug level, while the second extended release phase provides the dose fraction required to maintain an effective therapeutic level for a prolonged period.

  4. Cf. [1, 2, 6, 12, 13, 1618, 25, 2830].

  5. The capacity of a set is a mathematical notion. For instance a finite segment in the plane has zero area but finite capacity. Roughly speaking, the capacity is a “measure” of the cracks.

  6. See also the more recent comprehensive paper [7, Theorem 5.5] using the very neat theory of periodic unfolding.


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This research was supported by a Discovery Grant from the National Sciences and Engineering Research Council of Canada (NSERC).

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Correspondence to Michel C. Delfour.

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Delfour, M.C. Drug Release Kinetics from Biodegradable Polymers via Partial Differential Equations Models. Acta Appl Math 118, 161–183 (2012).

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