A fully dynamical theory for the rate of arterial gas embolism growth and dissolution

An approximation that had been widely used for more than 70 years to estimate the concentration of a dissolved volatile solute at the external surface of a gas bubble was found to be inaccurate for small bubbles. The approximation was to assume that a Henry’s law-based partition equilibrium determin...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical biosciences 2022-03, Vol.345, p.108793-108793, Article 108793
Main Author: Goldman, Saul
Format: Article
Language:English
Subjects:
Approximation
Arterial gas embolism
Arterioles
Blood flow
Bubbles
Capillaries
Decompression Sickness
Diffusion
Dissolution
Dynamic boundary condition
Embolism
Embolism, Air
Embolisms
Exchange
Gas bubble dissolution
Henrys law
Humans
Mathematical analysis
Solubility
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An approximation that had been widely used for more than 70 years to estimate the concentration of a dissolved volatile solute at the external surface of a gas bubble was found to be inaccurate for small bubbles. The approximation was to assume that a Henry’s law-based partition equilibrium determines the solute’s concentration at the bubble’s external surface. An alternative model is developed here, wherein solute exchange across the bubble surface, and solute diffusion in the medium next to the bubble, collectively determine the solute’s concentration near the bubble’s external surface. The previous model was found to predict both gas bubble growth and dissolution to be too rapid, for bubbles with a radius R≤20μ. We found that treating solute exchange across the bubble surface, and solute diffusion in the medium next to the bubble, as a collective dynamical process, was necessary to accurately model the dynamics of an arterial gas embolism (AGE) with a radius R≤20μ. An AGE of this size can block or interfere with blood flow through capillaries and arterioles. •A dynamically based solute boundary concentration and concentration gradient at a gas bubble’s surface is derived.•It is used to provide a new Dirichlet boundary condition at the bubble’s surface.•It predicts slower rates of gas bubble growth and dissolution than does the older Henry’s law-based boundary condition.•It is particularly important for small bubbles (
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2022.108793