Multilevel 1.9 PDA

5. Decompression in theory and practice (kindly supported by Wendell Crogan!)

It was always a dream of humans to be able to move like a fish for a long time under water. But only with compressed air technology did this desire became reality.Unfortunately it soon turned out however that the nitrogen of the breathing air can become dangerous in two regards here. On the one hand it causes a dangerous narcosis, on the other hand it punishes too rapid ascent with caisson illness.

The beginning of serious decompression research is closely linked with the name Haldane. Haldane experimented with goats, which he pressurized.With rapid decompression these developed severe symptoms, which resembled the caisson illness of humans. By further experiments Haldane could determine that the goats remained symptom-free whenever the pressures were reduced max. to half. Thus if an animal had been below an equivalent depth of 40 m of water (500 kPa), then one could bring it without visible symptoms to 15 m water depth (250 kPa). With shorter exposure one could bring the goats immediately problem-free to the surface or at least into a still smaller depth. From this 2:1 relation and this single observations, which can be reproduced very easily, Haldane developed the first decompression computer model based on kinetics. He had already noticed that inert gas kinetics were not linear, but rather it follows an exponential function, i.e. that the uptake and saturation take place not evenly but rather faster at the start of a exposure and toward end more slowly. He now introduced a model with five tissues with variable tissue half times (5, 10, 20, 40, 75 min). Thus Haldane had already established the central dogmas, which are still valid today, still with many common multi-tissue models in the year 1908 (although modern concepts are naturally far more differentiated):
 

• Inert gas uptake and decompression can be described simply as exponentially running processes with model tissues of variable tissue half-times.
• After more than 6 tissue half times it takes up no more additional inert gas.
• The relation between ambient pressure and symptom-free tolerated inert gas positive pressure is constant for each tissue (linear function)

5.2 Bühlmann's multi-tissue model

Since the beginning of decompression research an indeterminable variety of models was presented. I would like to be limited here however quite consciously to the multi-tissue models, which are often used today still due to their many advantages.

The Swiss dive physician Professor Bühlmann structured together with the mathematician Hannes Keller fundamental Haldane concepts and modified it according to their own observations. With the caisson work in Swiss tunnel construction Bühlmann observed that joint complaints of the workers mostly accumulated after mid week, while the workers had fewer problems at the start of the week. Bühlmann attributed this to cumulative effects, which could not be explained with the tissue half times used thus far.

Together with the test results of volunteers in the pressure chamber this led to the 16 - tissue model (ZH-L16), whose longest tissue half time was with 635 min - more than twice as long as the longest tissue half time of 240 minutes, used so far. Also Bühlmann observed, like Haldane before him, a constant relation between ambient pressure and tolerated positive pressure (linear function), however this applied in ZH-L16 only within an individual tissue.

Each tissue thus had another constant relation between ambient pressure and tolerated inert gas positive pressure. This, according to Bühlmanns theory was small with slow (badly supplied with blood) tissues e.g. joint cartilages and great with fast (well supplied with blood) tissues. Now one could have determined conditions for each tissue empirically, but the large number of model tissues (Bühlmann spoke also of "Compartments") it was almost impossible to assign individual real tissues to certain symptoms. Bühlmann simplified the process as he introduced two coefficients a and b, the size of which he derived by an empirical formula directly from the nitrogen tissue half time ( t 1/2 N 2):

Coefficient a=2.0 bar * (t 1/2 N 2 [ min ]) 1/3

Coefficient b=1.005-1 * (t 1/2 N 2 [ min ]) 1/2

We remember that a straight line in a 2-dimensional graph with x- and y-axis can be determined by the above linear function. The mathematician describes this as follows: f(x)=ax+b. Thus this is exactly the function of the two coefficients a and b. Bühlmann exchanged the designation of the two coefficients. Its function reads therefore f(x)=bx+a , whereby x is for the ambient pressure and f(x) for the symptom-freely tolerated inert gas positive pressure.

Therefore with his empirical formula Buehlmann could determine thus 16 coefficients a and 16 coefficients b for 16 tissues and derive 16 different straight lines according to the respective tissue half time (see following table). As a result the fast tissue are characterized by great increased values for a and  small values for b, while it behaves exactly in reverse with the slow tissues.

In connection with exponential tissue kinetics it is thus possible to create a differentiated decompression plan. This would be however only grey theory, if Bühlmann had not undertaken innumerable chamber dives, in order to test the usefulness of its model in practice. This led partially also to a slight modification of its two coefficients, which he published then in 1983 for the first edition of the book " Dive Medicine ".

How accurate is the model now? Bühlmann concluded from his observations that diminishing the deco stops generated with the pure ZH-L16 - algorithm (without safety addition) by only 4 -  5 % leads to the first symptoms of a CNS decompression illness!

We can calculate with Multilevel an example of a CNS accident published by Bühlmann (safety addition 0 % and no deep stops). 8 military divers undertook a 20 minute high-altitude dive to a depth of 30 m depth. The elevation amounted to 1800 mNN. If we use the Bühlmann model without tissue No. 0, we will see  that the program with 0% safety addition asks still for another short stop of 2 min on the 3 m level in order to desaturate the tissues with  half-times of 4 - 12.5 min. If we calculate the same dive on sea level the program will however display no decompression stops.  2 of the 8 divers developed paralyses and sensitivity failures in both legs after the end of the no-stop dive which regressed immediately after recompression. This was the cause to develop particularly adapted tables for mountain dives.

A crucial problem was not solved yet: how does the decompression look with dive profiles with helium mixtures? Here Bühlmann developed a simple method due to the fact that helium is a smaller molecule with approx. 2.65 times faster vague ion kinetics than nitrogen: the nitrogen tissue half times were divided by 2,65 and the coefficients a and b with the empirical formula were calculated again. During the chamber dives it showed up however that the a - coefficient had to be improved with the slow tissues.

Here the tissue half times and coefficients used in Multilevel, which correspond to the data published by Bühlmann under the name ZH-L16B with exception of the tissue 0:
 

Compartment	t1/2N2 [min]	a (N2)	b (N2)	t1/2He [min]	a (He)	b (He)
0	2.0	0.3	0.83	0.75	0.5	0.6
1	4.0	1.2599	0.5050	1.51	1.7424	0.4245
2	8.0	1.0000	0.6514	3.02	1.3830	0.5747
3	12.5	0.8618	0.7222	4.72	1.1919	0.6527
4	18.5	0.7562	0.7825	6.99	1.0458	0.7223
5	27.0	0.6667	0.8126	.0.21	0.9220	0.7582
6	38.3	0.5600	0.8434	14.48	0.8205	0.7957
7	54.3	0.4947	0.8693	20.53	0.7305	0.8279
8	77.0	0.4500	0.8910	29.11	0.6502	0.8553
9	109.0	0.4187	0.9092	41.20	0.5950	0.8757
10	146.0	0.3798	0.9222	55.19	0.5545	0.8903
11	187.0	0.3497	0.9319	70.69	0.5333	0.8997
12	239.0	0.3223	0.9403	90.34	0.5189	0.9073
13	305.0	0.2850	0.9477	115.29	0.5181	0.9122
14	390.0	0.2737	0.9544	147.42	0.5176	0.9171
15	498.0	0.2523	0.9602	188.24	0.5172	0.9217
16	635.0	0.2327	0.9653	240.03	0.5119	0.9267

Note: with Multilevel the possibility exists to use either the more liberal coefficients for helium (Bühlmann original values) or the more conservative being derived from nitrogen kinetics. The latter have a substantially better empirical testing. A word still about difficult safety addition: Bühlmann only suggested in his book to add 2 m depth to each level. Thus however deco schedules are generated, which are compared with today's deco schemes still quite short. Strangely enough however the deco tables published in the Bühlmann-Hahn table are clearly more conservative. At the same time Buehlmann however suggested that a conceivable safety gain could go over a lowering of the tissue tolerance limits embodied in the model (coefficient a). It is not meaningful however to modify the slope of the relationship between ambient pressure and tolerated inert gas positive pressure, given by the coefficient b, since this is experimentally quite well proven over far distances. Therefore I tried to reproduce the Bühlmann - Hahn - tables (due to good empirical testing) with a linear reduction of the a-coefficients. This succeeded to me with a reduction of around 30  %. However the term safety addition is quite problematic, since the empirical base is often missing, as Bill Hamilton stated recently. It is probably the best strategy to use a particular deco scheme as long as it prooves to be practical. The Bühlmann model is still very widely used. New developments led to addition of so-called adaptive models, simulating micro bubbles and shunts.

The concept of the deep deco stops
In the context of the evaluation of long and deep dives with mixed gas it was demonstrated again and again that the decompression quality could by dramatically improved by introducing deep deco stops. Due to the observations and publications of George Irvine, Richard Pyle and Bill Hamilton (just to name a few) empirical concepts received more attention in recent time. Multilevel simulates the deep stops by a very inert gas-positive pressure-sensitive tissue 0 (tissue half time 2 min), that was added to the Bühlmann algorithm ZH-L16 as 17th tissue (model ZH-L17B_TS) and comes very close to the Pyle' concept  (but generates however slightly flatter stops). I decided to insert the tissue 0 in order to simulate the alveolar region of the lung (ventilation perfusion area) in a kinetic model. The Pyle' general rule for the calculation of the deep stops of 2 min in the middle between your max. achieved depth and your first regular decostop  is practical for "bounce dives ", however it will be difficult to apply such a general rule to complex multi-level dives. These considerations led to the concept of tissue 0.
Why do deep stops improve the decompression quality? While there is plenty of room for speculation,  this concept most probably reduces the growth of micro bubbles at a very early point in time strongly, before they achieve a critical size. Thus also the lung shunt does not reach dimensions as large, as one would normally expect it after such a dive. The progressive lung shunt at the end of the dive is one of the reasons why the decompression of the tissues precedes more slowly than compression.
But to be  sure: no matter how the theoretical concept reads: Main thing is it functions!