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

Clarence C King1, Amelia Ann Brown1, Irmak Sargin1

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Summary

This study models oxygen diffusion in pancreatic islet cells encapsulated for artificial pancreas development. Viability is maintained for islets ≤142 µm and shells ≤283 µm, crucial for diabetes treatment.

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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.