Mathematical Modeling of Oxygen Diffusion from Capillary to Tissues during Hypoxia through Multiple Points Using...

Area of Science:

• Biomedical Engineering
• Mathematical Biology
• Physiology

Background:

• Clinical studies often investigate oxygen diffusion from capillaries to tissues, driven by conditions like hypoxia.
• Analytical and numerical studies on this phenomenon are less common.
• Existing models may not fully capture multi-point diffusion dynamics.

Purpose of the Study:

• To develop a novel mathematical model for multi-point oxygen diffusion from capillaries.
• To complement existing physiological investigations with a rigorous analytical approach.
• To analyze the spatial and temporal variations in oxygen concentration.

Main Methods:

• Developed a fractional dynamical system using balance equations with memory.
• Applied the Routh-Hurwitz stability criterion for stability analysis.
• Obtained analytical solutions using Henkel transformations.

Main Results:

• Oxygen diffusion decreases along the capillary length, with higher concentrations near the capillary entrance.
• The effective diffusion radius diminishes with distance along the capillary.
• Model simulations show close correlation with simpler diffusion models.

Conclusions:

• The proposed fractional dynamical model accurately describes multi-point oxygen diffusion.
• The findings provide insights into oxygen transport limitations in tissue.
• The model serves as a benchmark for advanced computational fluid dynamics simulations.