Simulation of dynamic bubble spectra in tissues

Decompression sickness (DCS) is the result of bubble formation in the body due to excessive/rapid reduction in the ambient pressure. Existing models relate the decompression stress either to the inert gas load or to the size of a single bubble in a tissue compartment. This paper presents a model that uses the gas exchange equations combined with bubble dissolution physics and population balance equations to produce a new mathematical framework for DCS modeling. This framework, the population balance model for decompression sickness (PBMDS), simulates the number of bubbles with their corresponding size distributions in a compartmental tissue array. The model has a modular structure that enables one to explore different modeling results with respect to key aspects of DCS, such as gas exchange, nucleation, and surface tension. The paper's goal is to present the derivation of PBMDS in detail, however, three simple application case studies are provided. The aim of these case studies is to suggest that PBMDS supplies additional information on bubble distribution while supporting the results from current practice.