Modeling of reaction-diffusion transport into a core-shell geometry.

Area of Science:

• Biomedical Engineering
• Mathematical Modeling
• Cell Biology

Background:

• Pancreatic islet encapsulation is a promising strategy for type 1 diabetes treatment.
• Oxygen diffusion and consumption within encapsulated islets are critical for cell viability.
• Understanding these parameters is essential for designing functional artificial pancreas systems.

Purpose of the Study:

• To model Fickian diffusion of oxygen into a core-shell geometry mimicking encapsulated pancreatic islets.
• To investigate the impact of oxygen consumption kinetics (Michaelis-Menten) on cell viability.
• To determine critical size parameters for islet and shell dimensions to ensure cell survival.

Main Methods:

• Mathematical modeling of Fickian diffusion with Michaelis-Menten oxygen consumption.
• Transformation of the problem to dimensionless units for numerical solution.
• Development of a regression model to predict central oxygen concentration based on physical parameters.

Main Results:

• Identification of two distinct regimes: diffusion-limited and consumption-limited.
• Established critical size limits: islet radius ≤142 µm and shell radius ≤283 µm for cell viability.
• Demonstrated that 100 µm islets can survive in low oxygen environments (4.6×10⁻² mol/m⁻³).

Conclusions:

• Encapsulation strategies for artificial pancreas require careful consideration of islet and shell dimensions.
• The developed model provides a predictive tool for designing viable encapsulated islet systems.
• These findings support the potential of encapsulation for creating functional artificial pancreas to treat diabetes.