Haldane, Workman, Bühlmann and Thalmann all model gas dissolved in the tissues. None of these models includes bubbles, although bubbles are what injure a diver. From the 1970s onwards, some researchers built models that aim to control bubble formation directly.
The best known are David Yount’s Varying Permeability Model (VPM) and Bruce Wienke’s Reduced Gradient Bubble Model (RGBM). Both put the first decompression stop deeper than a dissolved-gas model does. For a decade this was widely treated as an improvement, until the US Navy tested it.
- Nucleus
- Growing bubble
- Critical radius
Gas nuclei
Forming a bubble where no gas is already present takes far more supersaturation than divers ever reach. Divers still form bubbles, so bubble models assume the body always contains tiny pockets of gas, called nuclei, from which bubbles grow.
Yount proposed that each nucleus is coated with surface-active molecules whose permeability to gas changes with pressure. This is the “varying permeability” in the model’s name.
Crushing on descent
Descent compresses every nucleus. Bubble modellers call this crushing.
Size matters because of surface tension: the smaller a nucleus, the more supersaturation it needs to grow. In this model, the size of a diver’s nuclei depends on how much and how fast they were compressed.
The critical radius
During the ascent, nuclei larger than a critical radius grow into bubbles and smaller ones do not. VPM limits supersaturation so that only the few largest nuclei exceed that radius.
This is where VPM differs from dissolved-gas models. A dissolved-gas M-value allows more supersaturation the deeper you are, while VPM’s allowance is much the same at every depth. Early in the ascent, when the diver is still deep, VPM’s limit is the tighter of the two, so the model starts the stops deeper.
The critical volume
Yount and Hoffman added one more rule: some bubbles are acceptable, provided their total volume stays under a critical volume.
VPM limits the total volume of gas that comes out of solution over the whole decompression. Deep stops keep bubble growth small early in the ascent, so the model allows more supersaturation in the shallower part and the shallow stops can be shorter. A typical VPM schedule has a deeper first stop, shorter shallow stops and a similar total time.
RGBM
Wienke’s RGBM, from the same period, starts from dissolved-gas limits and reduces them with bubble factors in situations thought to produce more bubbles: repetitive dives, dives deeper than the previous one, and diving on many consecutive days. Simplified versions ran in several recreational dive computers. Its schedules also start with deeper stops.
- Deep-stop shape (GF 10/85)
- Shallow-weighted (GF 70/85)
A deep-stop profile
DiveLogic does not run a bubble model, so it cannot plot a real VPM schedule. It can show the shape of one. Bühlmann with a very low GF low also stops deep, and many divers used low GF low settings to approximate bubble-model profiles.
Unlike a bubble model, it adds the deep stops without taking time from the shallow ones, so its total time is longer.
Slow tissues keep loading
During a deep stop the fast tissues release gas. The slow tissues do not: the breathing gas at that depth still holds far more nitrogen than they do, so they continue to load.
Deep stops reduce supersaturation in the fast tissues and increase the gas load in the slow ones. A model cannot say whether that exchange is worthwhile. It has to be tested on divers.
The NEDU trial
The US Navy Experimental Diving Unit (NEDU) tested the idea directly and published the results in 2011. The dive was 30 minutes at 52 m on air. Two schedules were compared, each with 174 minutes of stops. The deep-stop schedule, from a bubble model, had its first stop at 21 m; the shallow-stop schedule had its first stop at 12 m.
The dive and the total stop time were the same. Only the distribution of the stop time differed.
Trial size
Navy divers made 198 dives on the deep-stop schedule and 192 on the shallow-stop schedule.
Results
Decompression sickness occurred after 10 dives with deep stops and 3 with shallow stops. Moving stop time from shallow to deep stops made decompression sickness more likely.
Try it
Move GF low and note the depth of the first stop. A low GF low makes the first stop deep. As GF low approaches GF high, the profile moves onto the white line, which is the same dive with no deep-stop shaping. Change the dive as well: deeper and longer dives show a larger difference.
- GF 20/85
- GF 85/85
What to remember
- Bubble models assume that nuclei, tiny pockets of gas, are always present, and that only nuclei larger than a critical radius grow during the ascent.
- VPM’s permitted supersaturation changes little with depth, so its schedules stop deeper than dissolved-gas models. Its critical-volume limit then shortens the shallow stops.
- RGBM reduces dissolved-gas limits with bubble factors, and its schedules also start deeper.
- Deep stops keep the slow tissues loading. In NEDU’s 2011 trial, moving stop time deeper gave more decompression sickness: 10 cases in 198 dives against 3 in 192.
- Since the trial, practice has moved towards shallower first stops, most visibly through higher GF low settings.
First stop depth in the planner
DiveLogic plans with Bühlmann and gradient factors, or with Thalmann. It does not run a bubble model. Plan a dive with a low GF low and then a higher one, and compare the first stop depth and the slow-tissue loading in the tissue view.
Sources
- Yount D. E. (1979). Skins of varying permeability: a stabilization mechanism for gas cavitation nuclei. Journal of the Acoustical Society of America 65(6): 1429-1439.
- Hennessy T. R., Hempleman H. V. (1977). An examination of the critical released gas volume concept in decompression sickness. Proceedings of the Royal Society of London B 197: 299-313.
- Yount D. E., Hoffman D. C. (1986). On the use of a bubble formation model to calculate diving tables. Aviation, Space, and Environmental Medicine 57(2): 149-156.
- Wienke B. R. (1990). Reduced gradient bubble model. International Journal of Bio-Medical Computing 26(4): 237-256.
- Marroni A., Bennett P. B., Cronje F. J., et al. (2004). A deep stop during decompression from 82 fsw (25 m) significantly reduces bubbles and fast tissue gas tensions. Undersea and Hyperbaric Medicine 31(2): 233-243.
- Doolette D. J., Gerth W. A., Gault K. A. (2011). Redistribution of decompression stop time from shallow to deep stops increases incidence of decompression sickness in air decompression dives. NEDU TR 11-06. Navy Experimental Diving Unit, Panama City, FL.