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A statistical mechanical model for drug release: Relations between release parameters and porosity

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  • Gomes-Filho, Márcio Sampaio
  • Barbosa, Marco Aurélio Alves
  • Oliveira, Fernando Albuquerque

Abstract

A lattice gas model is proposed for investigating the release of drug molecules on devices with semi-permeable, porous membranes in two and three dimensions. The kinetic of this model was obtained through the analytical solution of the three-dimension diffusion equation for systems without membrane and with Monte Carlo simulations. Pharmaceutical data from drug release is usually adjusted to the Weibull function, exp[−(t∕τ)b], and the dependence of adjusted parameters b and τ is usually associated, in the pharmaceutical literature, with physical mechanisms dominating the drug dynamics inside the capsule. The relation of parameters τ and b with porosity λ are found to satisfy, a simple linear relation for between τ and λ−1, which can be explained through simple physically based arguments, and a scaling relation between b and λ, with the scaling coefficient proportional to the system dimension.

Suggested Citation

  • Gomes-Filho, Márcio Sampaio & Barbosa, Marco Aurélio Alves & Oliveira, Fernando Albuquerque, 2020. "A statistical mechanical model for drug release: Relations between release parameters and porosity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317819
    DOI: 10.1016/j.physa.2019.123165
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    References listed on IDEAS

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    1. Villalobos, Rafael & Cordero, Salomón & Maria Vidales, Ana & Domínguez, Armando, 2006. "In silico study on the effects of matrix structure in controlled drug release," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 305-318.
    2. Ignacio, Maxime & Chubynsky, Mykyta V. & Slater, Gary W., 2017. "Interpreting the Weibull fitting parameters for diffusion-controlled release data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 486-496.
    3. Gomes Filho, Márcio Sampaio & Oliveira, Fernando Albuquerque & Barbosa, Marco Aurélio Alves, 2016. "A statistical mechanical model for drug release: Investigations on size and porosity dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 29-37.
    4. Villalobos, Rafael & Domínguez, Armando & Ganem, Adriana & Vidales, Ana Maria & Cordero, Salomón, 2009. "One-dimensional drug release from finite Menger sponges: In silico simulation," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2875-2884.
    5. Singh, Kulveer & Satapathi, Soumitra & Jha, Prateek K., 2019. "“Ant-Wall” model to study drug release from excipient matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 98-108.
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    Cited by:

    1. Ignacio, M. & Slater, G.W., 2021. "Using fitting functions to estimate the diffusion coefficient of drug molecules in diffusion-controlled release systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Filippini, Luke P. & Simpson, Matthew J. & Carr, Elliot J., 2023. "Simplified models of diffusion in radially-symmetric geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    3. Carr, Elliot J., 2022. "Exponential and Weibull models for spherical and spherical-shell diffusion-controlled release systems with semi-absorbing boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).

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    1. Singh, Kulveer & Satapathi, Soumitra & Jha, Prateek K., 2019. "“Ant-Wall” model to study drug release from excipient matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 98-108.
    2. Ignacio, Maxime & Chubynsky, Mykyta V. & Slater, Gary W., 2017. "Interpreting the Weibull fitting parameters for diffusion-controlled release data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 486-496.
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