Mathematical models of diffusion-limited gas bubble dynamics in tissue

Area of Science:

• Physiology
• Biophysics
• Mathematical Biology

Background:

• Mathematical models of bubble evolution in tissues are crucial for predicting decompression sickness (DCS) risk in humans after diving or flying.
• Existing models include the two-region model (unstirred tissue) and the three-region model (well-stirred tissue with a boundary layer).

Purpose of the Study:

• To analyze the structural similarity and differences between the two-region and three-region bubble dynamics models.
• To identify conditions under which these models are equivalent and when the two-region model may be misapplied.
• To provide guidance for accurate DCS risk assessment using bubble dynamics simulations.

Main Methods:

• Comparative analysis of ordinary differential equations governing bubble dynamics in the two-region and three-region models.
• Mathematical transformation of parameters to assess model equivalence.
• Evaluation of model applicability to finite tissue volumes and multi-bubble interactions.

Main Results:

• The two-region and three-region models are structurally similar and can be equivalent at large tissue volumes through parameter transformation.
• The two-region model is limited to infinite tissue extents and is not suitable for simulating multi-bubble interactions in finite tissues.
• Incorrect application of the two-region model in finite tissues can lead to substantial quantitative errors in DCS risk prediction, although results may be qualitatively correct.

Conclusions:

• Appropriate selection and application of bubble dynamics models are essential for accurate DCS risk prediction.
• Understanding the limitations and equivalencies of the two-region and three-region models can prevent significant quantitative errors.
• Improved model utilization can enhance the performance of probabilistic models for decompression sickness occurrence.