Earlier models, Bühlmann’s included, assume that gas leaves a tissue the same way it enters: quickly while the pressure difference is large, then more slowly as it shrinks. Uptake and washout are symmetrical. When the US Navy tested schedules based on this assumption for a new rebreather, the decompression sickness rate showed that it was wrong for the ascent.
Edward Thalmann, a Navy medical officer at the Navy Experimental Diving Unit (NEDU), changed one part of the model. When a tissue holds more gas than the surrounding pressure, his model unloads it at a constant, limited rate instead of exponentially. This is the exponential-linear model. The US Navy’s tables and dive computers still use it.
- Bühlmann (exponential out)
- Thalmann (linear out)
Uptake is unchanged
Thalmann kept the half-time rule for uptake. During descent and at the bottom, a tissue’s pressure moves half of the remaining way towards the pressure of the gas you breathe every half-time, as in Bühlmann’s model.
The chart follows one fast tissue, with a 5-minute half-time, in both models on the same dive. While the diver is at 45 m, the two lines are identical.
Bühlmann: exponential washout
The diver ascends to 12 m and stays there. The tissue now holds much more gas than the breathing gas, so there is a large pressure difference from tissue to breathing gas.
In a symmetrical model a large difference gives fast washout. The curve falls steeply at first, then flattens as the difference shrinks. Washout follows the same exponential rule as uptake.
Thalmann: linear washout while supersaturated
Thalmann did not accept the fast initial washout. A supersaturated tissue, one holding more gas than the surrounding pressure, is where bubbles are likely to form. His reasoning was that gas in bubbles leaves more slowly than gas in solution.
In his model a supersaturated tissue therefore unloads at one constant rate, which plots as a straight line. Well into the same hold, this tissue still holds much more gas than the Bühlmann tissue.
The crossover
The linear rate applies only while the tissue is supersaturated. When its gas pressure falls to the surrounding pressure, the model returns to exponential washout. That point is the crossover.
In the Navy’s published parameter sets the crossover is exactly at the surrounding pressure. Above it, washout is linear; below it, exponential. The model’s name describes these two parts.
Origin: the MK 15 rebreather
The Navy needed a decompression computer for the MK 15, a rebreather that keeps the oxygen partial pressure at a constant 0.7 atmospheres. The mix changes with depth, so no printed table can cover it: the schedule has to be computed during the dive. Schedules from a symmetrical model gave too much decompression sickness in manned testing. Limiting washout to a linear rate lengthened the shallow stops, and the retested schedules gave better results.
The parameter set that went into service was VVal-18. The number is a version, not a count of compartments. Its later air successor, VVal-79, has 9 compartments, with half-times from 5 to 240 minutes.
- Bühlmann 100/100
- Thalmann VVal-79
The Bühlmann schedule
The example dive is 30 minutes at 40 m on air. The DiveLogic engine plans it with Bühlmann ZHL-16C and gradient factors of 100/100, so neither model has extra conservatism added.
The ladder shows each stop depth in the centre column and the minutes at that stop as a bar.
The Thalmann schedule
This is the same dive planned with Thalmann’s VVal-79 air parameters. The first stop is at the same depth. The difference is how long each stop lasts.
Where the extra time goes
The largest differences are at the last stops. Tissues are most supersaturated there, and Thalmann’s linear washout makes them slowest to clear.
Similar deep stops and longer shallow stops are characteristic of the model.
Comparing the totals
The total times differ considerably. Neither is correct in an absolute sense. Each follows from its model’s assumption about how fast gas leaves, fitted to the dives its authors tested.
Navy schedules are also planned to an explicit, stated risk of decompression sickness, set for working divers with a chamber on site. A Thalmann runtime and a Bühlmann runtime therefore answer different questions.
Try it
Change the depth and bottom time and note which stops Thalmann lengthens. Then give the Bühlmann plan gradient factors that divers commonly use. Low gradient factors add time at both deep and shallow stops. Thalmann has no equivalent setting: its conservatism depends only on the parameter set you choose.
- Bühlmann 100/100
- Thalmann VVal-79
What to remember
- Thalmann’s model loads gas the same way as Bühlmann’s, with exponential uptake and the same half-time rule.
- A supersaturated tissue unloads at a constant, linear rate, which is slower than a symmetrical model allows.
- The crossover is where the model changes from linear to exponential washout. In the Navy’s parameter sets it is at the surrounding pressure.
- Compared with Bühlmann, deep stops are similar and shallow stops are longer.
- The model was developed for the MK 15 rebreather (VVal-18). The US Navy’s air tables have used it since Revision 6, and the Navy’s dive computers run it.
Thalmann in the planner
DiveLogic plans with Thalmann’s model as well as Bühlmann’s. Choose Thalmann E-L as the algorithm and a parameter set, then plan the same dive with each model. The tissue view shows the model’s own compartments and their linear washout.
Sources
- Thalmann E. D. (1984). Phase II testing of decompression algorithms for use in the U.S. Navy underwater decompression computer. NEDU Report 1-84. Navy Experimental Diving Unit, Panama City, FL.
- Thalmann E. D. (1985). Development of a decompression algorithm for constant 0.7 ata oxygen partial pressure in helium diving. NEDU Report 1-85.
- Thalmann E. D. (1997, issued 2003). Suitability of the USN MK 15 (VVAL18) decompression algorithm for air diving. NEDU TR 03-12.
- Gerth W. A., Doolette D. J. (2007). VVal-18 and VVal-18M Thalmann Algorithm air decompression tables and procedures. NEDU TR 07-09.
- Gerth W. A. (2010). Thalmann Algorithm decompression table generation software design document. NEDU TR 10-09.
- Doolette D. J., Murphy F. G., Gerth W. A. (2018). Thalmann Algorithm parameter sets for support of constant 1.3 atm PO₂ He-O₂ diving to 300 fsw. NEDU TR 18-05.
- Naval Sea Systems Command (2016). U.S. Navy Diving Manual, Revision 7. SS521-AG-PRO-010.