Finite element modeling of diffusion and partitioning in biological systems: the infinite composite medium problem

Area of Science:

• Computational modeling
• Biomedical engineering
• Pharmacokinetics

Background:

• Modeling diffusion in heterogeneous media presents challenges due to varying diffusion and partition coefficients across subregions.
• Existing finite element modeling (FEM) codes struggle with discontinuous concentration values at intertissue boundaries.
• Accurate modeling is crucial for predicting drug disposition in tissues and designing laminate devices.

Purpose of the Study:

• To propose and validate four novel methods for modeling diffusion in heterogeneous media.
• To address the challenge of discontinuous concentration values at tissue boundaries in FEM.
• To provide a framework for modeling drug diffusion into ocular tissues and other applications.

Main Methods:

• Developed four distinct methods to model diffusion with region-specific coefficients.
• Employed a transformation on the dependent variable to handle discontinuous concentration values.
• Validated methods against the exact solution for the infinite composite medium problem.
• Investigated a one-dimensional bolus injection simulation in the vitreous.

Main Results:

• Successfully modeled diffusion in heterogeneous media with varying coefficients.
• Method III, utilizing chemical potential, demonstrated high physical intuition.
• Method IV, a linearization of Method III, offered practical computational advantages.
• Simulations predicted drug disposition in vitreous and retina following bolus injection.

Conclusions:

• The proposed methods effectively handle diffusion in heterogeneous media with discontinuous properties.
• The chemical potential-based approach (Method III) and its linearization (Method IV) offer robust solutions for FEM.
• This modeling approach is applicable to drug delivery, organ modeling, and laminate device design.