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Interpreting the Weibull fitting parameters for diffusion-controlled release data

Author

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  • Ignacio, Maxime
  • Chubynsky, Mykyta V.
  • Slater, Gary W.

Abstract

We examine the diffusion-controlled release of molecules from passive delivery systems using both analytical solutions of the diffusion equation and numerically exact Lattice Monte Carlo data. For very short times, the release process follows a t power law, typical of diffusion processes, while the long-time asymptotic behavior is exponential. The crossover time between these two regimes is determined by the boundary conditions and initial loading of the system. We show that while the widely used Weibull function provides a reasonable fit (in terms of statistical error), it has two major drawbacks: (i) it does not capture the correct limits and (ii) there is no direct connection between the fitting parameters and the properties of the system. Using a physically motivated interpolating fitting function that correctly includes both time regimes, we are able to predict the values of the Weibull parameters which allows us to propose a physical interpretation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:486-496
    DOI: 10.1016/j.physa.2017.05.033
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    References listed on IDEAS

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    1. Casault, Sébastien & Slater, Gary W., 2008. "Systematic characterization of drug release profiles from finite-sized hydrogels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5387-5402.
    2. 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.
    3. 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.
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    Citations

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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. 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.
    3. 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).
    4. Ignacio, M. & Slater, G.W., 2022. "A Lattice Kinetic Monte Carlo method to study drug release from swelling porous delivery systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    5. 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).
    6. 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).

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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. 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).
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