Here is where you will find the underlying science for the SAUL model. The magazine article is written in a style that should be accessible to everybody, and probably should be read first. The Scientific Journal Articles are in prestigious high-impact peer-reviewed journals, and deal with the scientific basis of the SAUL model and other fundamental issues. They are, in general, not as universally accessible as the magazine articles, but selective components of them are. For example, the Discussion (Section IV) of the 2010 article in the Journal of Chemical Physics (in the Technical/Background section below) provides a condensed descriptive overview of issues in bubble physics, serious problems with previous treatments of this subject, and a truly modern approach and viable resolution to some of these issues.  The most recent addition, a co-authored book, involves the underlying science for the SAUL model and its application to medical practice.


Gas Bubble Dynamics in the Human Body, by Saul Goldman, Juan Manuel Solano-Altamirano, and Kenneth M. LeDez   Elsevier/Academic Press, 2017

Magazine Articles (easiest read – most relevant)

Coming Soon To A Dive Computer Near You

To Stop or Not to Stop … And Why  as published in DIVER v.37(6)

To Stop Or Not To Stop … And Why (updated)

Scientific Journal Articles

Most Relevant

This paper is the most directly relevant to the SAUL model, and contains its scientific basis. The body of the article contains the main ideas and results, and the Appendices provide the mathematical details.  The reason for providing the article in two versions – as first accepted by the journal, and as published – is that the visuals are better in the former, the latter being only black-and-white.

A new class of biophysical models for predicting the probability of decompression sickness in SCUBA diving.  Journal of Applied Physiology, 2007 (as first accepted by the journal)

Article as published in final form



Video Presentation

A video of my talk to the 17th International Congress of Hyperbaric Medicine (ICHM), 16-19 March, 2011 was posted on  Future Trend for Decompression


Technical but Important

The first article, while not directly related to the SAUL model, deals with bubbles in tissues, and their relation to decompression sickness. The main body of the article is specialized and technical, but the discussion section is descriptive, deals with relevant issues in bubble physics, and should be quite readable and informative.  At the end of this “Technical” section, there is also a press release, picked up and published by multiple online science magazines, that explains this paper and its importance.

Free energy wells for small gas bubbles in soft deformable materials.  Journal of Chemical Physics, 2010

Another article dealing with bubbles, calculating their lifetimes in relation to inner ear DCS which was referred to briefly in the October 28th. 2014 blogpost and then again in the April 28th. 2015 blogpost

The lifetimes of small arterial gas emboli, and their possible connection to Inner Ear Decompression Sickness.  Mathematical Biosciences 2014.

An article extending the 2014 arterial gas emboli research to decompression sickness in breath-hold diving, talked about in the April 28th. 2015 blogpost.

Decompression sickness in breath-hold diving and its probable connection to the growth and dissolution of small arterial gas emboli.    Mathematical Biosciences 2015

Physics of the Bends Press Release (AIP)

Press release reprinted in Science Daily

Technical/Background Papers

These are technical and mathematical.  The first paper (2008) derives the physical chemistry needed to correctly and quantitatively deal with bubble stability and bubble physics. The second paper (2009) develops the equations needed to apply the results of the first to bubbles in tissues.

The stability of bubbles formed from supersaturated solutions, and the homogeneous nucleation of gas bubbles from solution, both revisited.  Journal of Physical Chemistry, 2008

Generalizations of the Young-Laplace equation for the pressure of a mechanically stable gas bubble in a soft elastic material.  Journal of Chemical Physics, 2009

(The paper below is the one referred to in my November 21 st. blog posting)

Gas bubble dynamics in soft materials.  The Royal Society of Chemistry, 2014