Random walk diffusion simulations in semi-permeable layered media with varying diffusivity

Area of Science:

• Computational Physics
• Biophysics
• Image Analysis

Background:

• Diffusion in semi-permeable layered media is crucial in biological systems.
• Existing models struggle with abrupt changes in diffusivity across membranes.
• Accurate simulation is vital for applications like diffusion tensor cardiovascular magnetic resonance (DT-CMR) imaging.

Purpose of the Study:

• To develop and validate a novel hybrid random walk model for diffusion in layered media.
• To compare the hybrid model's performance against a standard reference model.
• To assess the model's applicability to DT-CMR imaging and other fields.

Main Methods:

• Development of a hybrid transit model treating membrane permeability and diffusivity changes as sequential interactions.
• Analytical flux analysis to compare model performance.
• Numerical simulations in a histology-based domain relevant to DT-CMR.
• Assessment across a range of membrane permeabilities.

Main Results:

• The hybrid model effectively overcomes limitations of the reference model in handling step changes in diffusivity.
• Numerical simulations confirm the hybrid model's accuracy and computational efficiency.
• The model demonstrates suitability for DT-CMR imaging simulations.
• The hybrid model shows promise for broader applications beyond biological tissues.

Conclusions:

• The novel hybrid random walk model provides a more accurate and efficient solution for simulating diffusion in complex layered media.
• This advancement is particularly relevant for enhancing DT-CMR imaging analysis.
• The model's flexibility supports its application in diverse scientific and engineering fields.