Diffusivity interfaces in lattice Monte Carlo simulations: Modeling inhomogeneous delivery and release systems.

Area of Science:

• Computational Physics
• Materials Science
• Chemical Engineering

Background:

• Lattice Monte Carlo (LMC) simulations are crucial for studying diffusion-controlled processes, including drug release.
• Inhomogeneous diffusivity environments present challenges in interpreting stochastic dynamics, known as the Ito-Stratonovich-isothermal dilemma.

Purpose of the Study:

• To develop an LMC formalism that incorporates different stochastic interpretations for modeling diffusion in space-dependent diffusivity landscapes.
• To address the "Ito-Stratonovich-isothermal dilemma" in diffusion modeling.

Main Methods:

• Proposed a novel Lattice Monte Carlo (LMC) formalism capable of handling various stochastic interpretations.
• Utilized a one-dimensional inhomogeneous system with a diffusivity interface and varied boundary conditions as a test case.
• Compared results obtained using different calculus (Ito, isothermal).

Main Results:

• The proposed LMC formalism accurately reproduces steady-state and dynamic properties of inhomogeneous diffusion systems.
• Demonstrated that system properties are dependent on the chosen stochastic calculus.
• Showcased the isothermal calculus as a more appropriate choice than Ito calculus for most drug delivery applications.

Conclusions:

• The developed LMC methodology offers an efficient alternative to Langevin simulations for diverse space-dependent diffusion problems.
• Recommends replacing the commonly used Ito calculus in LMC for drug delivery with the isothermal version for improved accuracy.
• Highlights the importance of selecting the correct stochastic interpretation for accurate modeling of diffusion phenomena.