First Principals Article or Text on Dive Modeling

[Dr Deco]

Hello LAJim:

I am currently having a problem with a herniated cervical disk. I have trouble typing; please bear with me. Dr D.

I do not know of any book that currently describes everything. Bruce Wienke’s book is interesting but has shortcomings. The references below are original sources and are necessary for a beginning appreciation for the complexity of this field. In reality, it requires a working background knowledge of chemistry, physics, physiology and medicine.

Since there is a size limit for replies, I must break this up into smaller pieces.

Decompression Tables

Decompression tables are currently constructed based on two different concepts.

[a]The first is the limited supersaturation model initially advanced by JS Haldane at the turn of the 20th Century. It states that supersaturated solutions of solids or gases in liquids remain in a single phase if the supersaturation is small. Classical nucleation (Volmer, Doering) gives a kinetic argument for this (see references, below) although it better applies to the formation of nuclei themselves.

Most tables older than twenty years are based on the limited supersaturation model. The Buhlmann model is one example. Physically these models are all incorrect as they assume de novo microbubble formation with decompression. The supersaturations are simply too small.

The second type of table is based on a prior-existing assembly of micronuclei. These are two phase models. The model of Wienke is one example – and probably the most famous since it has been used to calculate tables. The origin of the nuclei is not known but they are simplu postulted to arise in a given distribution.

Dr Deco :doctor:


Some information - of a non mathematical nature - is available from the class listed below. The date is not firm, as I might be in Britian at that time.

Decompression Physiology :1book: http://wrigley.usc.edu/hyperbaric/advdeco.htm


References :book3:



GENERAL

Adamson, A. W. (1990). Physical Chemistry of Surfaces. 5th edition. John Wiley and Sons, New York.

Boycott AE, Damant GCC, Haldane JS. The prevention of compressed air illness. J. Hyg. (Camb). 1908; 8: 544.



BUBBLE FORMATION AND EXERCISE

Conkin J, Powell MR. Lower body adynamia as a factor to reduce the risk of hypobaric decompression sickness. Aviat. Space Environ. Med. 72, 202 – 214, (2001)

Dervay JP, Powell MR, Butler B, Fife CE. The effect of exercise and rest duration on the generation of venous gas bubbles at altitude. Aviat Space Environ Med. 2002;73(1):22-7.

Harris M, Berg WE, Whitaker DM, Twitty VC. The relation of exercise to bubble formation in animals decompressed to sea level from high barometric pressures. J. Gen. Physiol. 1944; 28: 241.



HALF TIME CHANGE

Loftin K.C., J. Conkin, MR Powell. Modeling the effects of exercise during 100% oxygen prebreathe on the risk of hypobaric decompression sickness. Aviat. Space and Environ. Med. 68, 199 - 204, (1997).

Powell, M.R., K. Loftin, and J. Conkin. An algorithm for the calculation of change of the longest half times under various metabolic work loads. Undersea and Hyperbaric Medicine, 25, (Suppl), 20, (1998).

Powell, M.R. An algorithm for the calculation of the effect of adynamia on altitude decompression risk. Undersea Hyperbaric Med., 26 (Suppl), 56, (1999).



IN VIVO NUCLEI FORMATION

Banks WH, Mill CC. Tacky adhesion - a preliminary study. J. Coll. Sci. 1955; 8: 137 - 147.

Blinks LR, Twitty VC, Whitaker DM. Bubble Formation in Frogs and Rats. In: Fulton JF, ed. Decompression Sickness. Philadelphia: Saunders, 1951: 145 - 64.

Campbell J. The tribonucleation of bubbles. Brit. J. Appl. Phys. (J Phys D) Ser 2. 1968; 18: 1085 - 1088.

Dean RB. The formation of bubbles. J. Appl. Phys. 1944; 15: 446 - 451.

Evans A, Walder DN. Significance of gas micronuclei in the aetiology of decompression sickness. Nature. 1969; 222: 251 - 252.

Gerth WA, Hemmingsen EA. Gas supersaturation thresholds for spontaneous cavitation in water with gas equilibrium pressures up to 570 atm. Z. Naturforsch. 1976; 31A: 1711 - 1716.

Harvey, E. N.; D. K. Barnes; W. D. McElroy; A. H. Whitely; D. C. Pease; and K. W. Cooper (I 944). Bubble formation in animals. 1. Physical factors. J. Cell Comp. Physiol., 24, 1.

Harvey, E.N., K. W. Cooper, A. H. Whitely, (1946). Bubble formation from contact of surfaces. J. Amer. Chem. Soc., 68, 2119 - 2120.

Harvey, E.N.; W. D. McElroy; and A. H. Whiteley, A. H.. (1947). On cavity formation in water. J. Appl. Phys., 18, 162 - 172.

Hayward ATJ. Tribonucleation of bubbles. Brit. J. Appl. Phys. 1967; 18: 641 - 644.

Hemmingsen EA. Cavitation in gas-supersaturated solutions. J. Appl. Phys. l975; 46: 213.

Hemmingsen EA. Spontaneous formation of bubbles in gas-supersaturated water. Nature. l977; 267: 213.

Hemmingsen EA. Bubble formation mechanisms. In: Vann RD, ed. The Physiological Basis of Decompression Pub. No. 75 (Phys). Bethesda: Undersea Medical Society, 1989: 153 - 176.

Hemmingsen EA, Hemmingsen BB. Bubble formation properties of hydrophobic particles in water and cells of Tetrahymena. Undersea Biomed Res. 1990; 17 (1): 67 - 78.

Ikels KG. Production of gas bubbles in fluids by tribonucleation. J Appl Physiol. 1970; 28: 524 - 527.

Vann RD, Grimstad J, Nielsen CH. Evidence for gas nuclei in decompressed rats. Undersea Biomed. Res. 1980; 19807: 107 - 112.

Weathersby PK, Homer LD, Flynn ET. Homogeneous nucleation of gas bubbles in vivo. J. Appl. Physiol. 1982; 53: 940.

Whitaker DM, Blinks LR, Berg WE, Twitty VC, Harris M. Muscular activity and bubble formation in animals decompressed to simulated altitudes. J. Gen. Physiol. 1944; 28: 213 - 223.



NUCLEATION THEORY - CLASSICAL

Becker D. and Döring W. The kinetic treatment of nuclear formation in supersaturated vapors. Annalen
der Physik. 1935, Vol. 24, p719-52.

Döring W. Die Überhitzungsgrenze und Zerreissfestigkeit vom Flussigkeiten. Phyz. Chem. 1937; B36: 371 - 386.

Volmer M. and Weber A. Keimbildung in übersättigten Gebilden. Z. Phys. Chem. 1925, Vol. 119, p277.



IN VITRO BUBBLES

Harvey EN. Physical Factors in Bubble Formation. In: Fulton JF, ed. Decompression Sickness. Philadelphia: Saunders, 1951: 90 - 114.

Pollack GL. Why gases dissolve in liquids. Science. 1991; 251: 1323-1330.

Ward CA, Johnson WR, Venter RD, Ho S, Forst TW, Fraser WD. Heterogeneous bubble formation and the conditions for growth in a liquid-gas system constrained in mass and volume. J. Appl. Phys. 1983; 54: 1833 - 1843.

Yount, D. E. (1979 b). Skins of varying permeability: a stabilization mechanism for gas cavitation nuclei. J. Acoust. Soc. Am. 65, 1429 – 1439

Yount, D.E. (1981). On the evolution, generation, and regeneration of gas cavitation nuclei. J. Acoust. Soc. Am . 71, 1473 - 1481



MODELS

Epstein, P. S. and Plesset, M. S. (1950) On the Stability of Gas Bubbles in Liquid-Gas Solutions. Journal of Chemical Physics, 18 (11). pp. 1505-1509.

Hills BA. A Kinetic and Thermodynamic Approach to Decompression Sickness. Adelaide: Library Board of South Australia, 1966 (Ph.D. Thesis).

Srinivasan, S, and MR Powell (1997). The effects of surface tension on bubble volume changes using a mathematical model. Undersea Hyperbaric Med., 24 (Suppl.): 25, 1997.

Srinivasan RS, WA Gerth, MR Powell. Mathematical models of diffusion-limited gas bubble dynamics in tissue. J. Appl. Physiol., 86 (2), 732 – 741, (1999).

Srinivasan RS, WA Gerth, MR Powell. A mathematical model of diffusion-limited gas bubble dynamics in tissue with varying diffusion region thickness. Respiration Physiology, 123, 153 – 164, (2000)

Srinivasan RS, Gerth WA, Powell MR. Mathematical model of diffusion-limited gas bubble dynamics in unstirred tissue with finite volume. Ann Biomed Eng. 2002;30(2):232-46.

Srinivasan, R.S., W. A. Gerth, and M. R. Powell. Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue, Ann. Biomed. Eng., 31:471-481, 2003.

Tikuisis P. Modeling the observation of in vivo bubble formation with hydrophobic crevices. Undersea Biomed. Res. 1986; 13: 165.
Weinke BR. Reduced gradient bubble model. Int. J. Biomed. Comput. 1990; 26: 237.


HEART VALVE NUCLEATION

Lichtenstein, O, Martinez-Val, R, Mendez, J, et al Hydrogen bubble visualization of the flow past aortic prosthetic valves. Life Support Syst 1986;4,141-149

Mackay, TG, Georgiadis, D, Grosset, DG, et al On the origin of cerebrovascular microemboli associated with prosthetic heart valves. Neurol Res 1995;17,349-352

Deklunder, G, Roussel, M, Lecroart, JL, et al Microemboli in cerebral circulation and alteration of cognitive abilities in patients with mechanical prosthetic heart valves. Stroke 1998;29,1821-1826

Milo, S, Rambod, E, Gutfinger, C, et al Mitral mechanical heart valves: in vitro studies of their closure, vortex and microbubble formation with possible medical implications. Eur J Cardiothorac Surg 2003;24,364-370

 

[Dr Deco]

Hello LAJim:


This adds to the earlier material. Certainly, this can only be an orientation since this forum would not allow for any completeness.

Limited Supersaturation Models – Single Phase Models

This was first made by Haldane. It has the characteristic of implied supersaturation and its deterministic result of DS. It also has time-invariant compartments. This concept is in virtually all models – except the NASA model – and is incorrect (see HALF TIME CHANGES, in references). This model starts with no-decompression limits [NDLs] and is therefore empirically based.

The model is simple but impossible to reconcile with physics and physiology. It does produce useful tables, though. Its virtue is simplicity and tractable calculations that easily fit in contemporary computers.

The model implies that all dissolved nitrogen remains so. From empirical studies with Doppler bubble detectors, it is known that this concept is incorrect. The method of Buhlmann has been devised to allow for two dissolved inert gases.

Professor Buhlmann ascribed DCS to exceeding supersaturation in specific halftime tissues. Not one else has ever found this to be true. I argued with him on this matter, but he was resolute. The method cannot predict deep stops unless one forces the model by imposing artificial constraints.

Starting with halftimes and NDLs, it is possible to easily construct an algorithm. This can be extrapolated to depth by the m-value approach of Workman.

Two Phase Models

These are more realistic since they acknowledge the presence of preformed nuclei. They differ in the size-number distribution. The model of Michael Gernhardt has only one representative bubble. Others such as Wienke’s model have a logistic distribution. In nature, such distributions are always power functions (see books on physical oceanography).

Thus, all current two-phase models have an incorrect nuclei distribution function – in my opinion. All models are fitted to empirical data, however. This forces the model parameters to give a good fit, although the values might be physically unrealistic.

The models will also vary as to whether they are employ mass conversation (with respect to dissolved nitrogen) or assume that the bubble density is too small for this to matter. It is an unresolved issue.

Nuclei Origin

There are probably two nuclei generators. One is the classical stochastic method (Volmer, etc) that generates the sessile free gas phase in surface asperities. This is couple with stress assisted nucleation and hydrodynamic cavitation mechanisms that enlarge these; they might also produce free-stream nuclei.

Musculoskeletal exercise was introduced by me and later incorporated into NASA decompression schemes in null gravity. It is a concept understood by every reader of DR DECO over the last seven years. It is now almost a mainstream concept.

There are numerous papers in the references section on exercise and bubble formation. The difference between then and now is the bubble lifetime. I estimate it at a few hours while EN Harvey postulated weeks.

The problem with nuclei generation is that it a non-equilibrium process and difficult to calculate. Some work has been done in the bioengineering realm with regard to heart valves. Clearly, nuclei generation is an enormous question in engineering. This started with the work of Reynolds on hydrodynamic cavitation of a ships propeller.

Dr Deco :doctor: