Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue

Area of Science:

• Biomedical Engineering
• Physiology
• Diving Medicine

Background:

• Existing models for gas bubble dynamics in decompression sickness lack the ability to account for interactions between multiple bubbles.
• Previous models simulated diffusion-limited gas exchange but assumed a fixed diffusion region volume, preventing analysis of bubble competition for available gas.

Purpose of the Study:

• To extend a previous diffusion-limited gas bubble model to incorporate interactions among multiple bubbles.
• To develop a more comprehensive model for probabilistic analysis of decompression sickness incidence.

Main Methods:

• Modified an existing ordinary differential equation model for gas bubble dynamics.
• Allowed the diffusion region volume around each bubble to vary dynamically.
• Investigated the relationship between bubble number density, tissue volume, and sustained bubble growth under given decompression conditions.

Main Results:

• The extended model successfully accommodates interactions between multiple gas bubbles.
• Bubble growth is sustained only when the bubble number density is below a specific maximum for a given tissue volume and decompression profile.
• This allows for more realistic simulations of gas bubble evolution in tissues.

Conclusions:

• The enhanced model provides a more accurate representation of gas bubble dynamics relevant to decompression sickness.
• It enables the study of bubble interactions and competition for gas, improving probabilistic analyses.
• The findings suggest a critical threshold for bubble number density to prevent sustained bubble growth.