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<p>Mathematical models for controlled drug release are often simplified under sink boundary conditions, but non-sink conditions more accurately reflect release into a limited finite volume. This study investigates drug transport from a swelling device under non-sink conditions, where swelling alters both boundary conditions and diffusion characteristics. An advection–diffusion model is adapted accordingly, and a numerical scheme is developed to solve the problem for two swelling patterns which are the linear and logistic growth. A function <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10665_2025_10457_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(K(\tau )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is introduced to represent drug concentration at the moving boundary. The model is also tested under sink conditions to validate the numerical method in the absence of experimental data for the case of non-sink condition. The results confirm the agreement with the exact solution in the sink condition. The numerical solutions also demonstrate the reduced fractional release under non-sink conditions, consistent with drug accumulation in the surrounding medium.</p>

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Numerical solutions for controlled drug release from a swelling device with sink and non-sink boundary conditions

  • 期刊论文

  • 发表日期：

    2025年5月17日

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  • Amanina Setapa,
  • Shalela Mohd Mahali,
  • Fatimah Noor Harun,
  • Hanani Farhah Harun

摘要

Mathematical models for controlled drug release are often simplified under sink boundary conditions, but non-sink conditions more accurately reflect release into a limited finite volume. This study investigates drug transport from a swelling device under non-sink conditions, where swelling alters both boundary conditions and diffusion characteristics. An advection–diffusion model is adapted accordingly, and a numerical scheme is developed to solve the problem for two swelling patterns which are the linear and logistic growth. A function \(K(\tau )\) K ( τ ) is introduced to represent drug concentration at the moving boundary. The model is also tested under sink conditions to validate the numerical method in the absence of experimental data for the case of non-sink condition. The results confirm the agreement with the exact solution in the sink condition. The numerical solutions also demonstrate the reduced fractional release under non-sink conditions, consistent with drug accumulation in the surrounding medium.