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The parameters of the M-Values (coefficients a and b) were determined specifically.
===Trimix (nitrogen + helium) set of parameters===
No model can manage the de-saturation of two inert gases.
Some approaches only take into account the main inert gas (and ignore the other inert gas).
With Bühlmann,<ref name="Buhlmann-trimix" /> a weighted average of the half-times and coefficients <math>a</math> and <math>b</math> is calculated as a function of the percentage of each inert gas to calculate a specific set of parameters.
'''Example :'''
Using a 18/50 trimix (18% <math>O_2</math>, 50% <math>He</math>, 32% <math>N_2</math>), the half-time (or the <math>a</math> and <math>b</math> coefficients) of compartment #1 is calculated by taking 50% of the <math>He</math> half-time and 32% of the <math>N_2</math> half-time divided by 50% + 32% = 82%.
Example, compartment #1:
<math>t_{1/2}(\text{tx }18/50)= \frac{(1.51 \times 0.5)+ (4 \times 0.32)}{0.50 + 0.32}=\frac{(0.755 + 1.28)}{0.82}=2.48 </math> (instead of <math>1.51</math> with <math>He</math> and <math>4</math> with <math>N_2</math>)
<math>a (\text{tx }18/50)= \frac{(1.7424 \times 0.5)+ (1.2599 \times 0.32)}{0.50 + 0.32}=\frac{(0.8737 + 0.403)}{0.82}=1.5541 </math> (<math>1.7424</math> with <math>He</math> and <math>1.2599</math> with <math>N_2</math>)
<math>b (\text{tx }18/50)= \frac{(0.4245 \times 0.5)+ (0.5050 \times 0.32)}{0.50 + 0.32}=\frac{(0.2122 + 0.1616)}{0.82}=0.4559 </math> (<math>0.4245</math> with <math>He</math> and <math>0.5050</math> with <math>N_2</math>)
The same calculations can be made using partial pressures rather than percentages.
This approach is controversial with some authors<ref name="Salm-1" /> who feel that this calculation does not reflect what should be achieved. Generally speaking, the fact that desaturation with two neutral gases is not modelled encourages caution. Each trimix dive is specific, with no guarantee.
=== Constant partial pressure of oxygen<math>PpO_2</math> (closed-circuit rebreathers - CCR) ===
There are no specific model for constant <math>PpO_2</math> dives. The difference lies in the fact that, at all times, the proportion of inert gas is calculated in relation to the chosen <math>PpO_2</math> (e.g. 0.75 ou 1.3 ata (bar)).
{| class="wikitable" style="width: 80%;"
|+Table of ZH-L 16 Half-times <math>t_{1/2}</math> with <math>a</math> and <math>b</math> values for nitrogen (N<sub>2</sub>) and helium (He).<ref name="Buhlmann-a-b-2002" />
! rowspan="3" |Cpt
! colspan="5" | ZH-L 16 <math>N_2</math>
! colspan="3" | ZH-L 16 A <math>He</math>
|-
! rowspan="2" |<math>t_{1/2}</math>
(min)
! A
Experimental
! B
Tables
! C
Computers
! rowspan="2" |<math>b</math>
! rowspan="2" | <math>t_{1/2}</math>
(min)
! rowspan="2" |<math>a</math>
! rowspan="2" |<math>b</math>
|-
! <math>a</math>
! <math>a</math>
! <math>a</math>
|-
| style="text-align: center;" | {{0}}1 (1a)
| {{0|00}}4
| style="text-align: center;" | 1.2599
| style="text-align: center;" | 1.2599
| style="text-align: center;" | 1.2599
| style="text-align: center;" | 0.5050
| style="text-align: center;" | {{0|00}}1.51
| style="text-align: center;" | 1.7424
| style="text-align: center;" | 0.4245
|-
| {{0}}1b
| {{0|00}}5
| 1.1696
| 1.1696
| 1.1696
| 0.5578
| {{0|00}}
|
|
|-
| {{0}}2
| {{0|00}}8
| 1.0000
| 1.0000
| 1.0000
| 0.6514
| {{0|00}}3.02
| 1.3830
| 0.5747
|-
| {{0}}3
| {{0}}12.5
| 0.8618
| 0.8618
| 0.8618
| 0.7222
| {{0|00}}4.72
| 1.1919
| 0.6527
|-
| {{0}}4
| {{0}}18.5
| 0.7562
| 0.7562
| 0.7562
| '''0.7825'''
| {{0|00}}6.99
| 1.0458
| 0.7223
|-
| {{0}}5
| {{0}}27
| 0.6667
| 0.6667
| '''0.6200'''
| '''0.8126'''
| {{0}}10.21
| 0.9220
| 0.7582
|-
| {{0}}6
| {{0}}38.3
| 0.5933
| '''0.5600'''
| '''0.5043'''
| 0.8434
| {{0}}14.48
| 0.8205
| 0.7957
|-
| {{0}}7
| {{0}}54.3
| 0.5282
| '''0.4947'''
| '''0.4410'''
| 0.8693
| {{0}}20.53
| 0.7305
| 0.8279
|-
| {{0}}8
| {{0}}77
| 0.4701
| '''0.4500'''
| '''0.4000'''
| 0.8910
| {{0}}29.11
| 0.6502
| 0.8553
|-
| {{0}}9
| 109
| 0.4187
| 0.4187
| '''0.3750'''
| 0.9092
| {{0}}41.2
| 0.5950
| 0.8757
|-
| 10
| 146
| 0.3798
| 0.3798
| '''0.3500'''
| 0.9222
| {{0}}55.19
| 0.5545
| 0.8903
|-
| 11
| 187
| 0.3497
| 0.3497
| '''0.3295'''
| 0.9319
| {{0}}70.69
| 0.5333
| 0.8997
|-
| 12
| 239
| 0.3223
| 0.3223
| '''0.3065'''
| 0.9403
| {{0}}90.34
| 0.5189
| 0.9073
|-
| 13
| 305
| 0.2971
| '''0.2850'''
| '''0.2835'''
| 0.9477
| 115.29
| 0.5181
| 0.9122
|-
| 14
| 390
| 0.2737
| 0.2737
| '''0.2610'''
| 0.9544
| 147.42
| 0.5176
| 0.9171
|-
| 15
| 498
| 0.2523
| 0.2523
| '''0.2480'''
| 0.9602
| 188.24
| 0.5172
| 0.9217
|-
| 16
| 635
| 0.2327
| 0.2327
| 0.2327
| 0.9653
| 240.03
| 0.5119
| 0.9267
|}
===Versions===
Several versions of the Bühlmann set of parameters have been developed, both by Bühlmann and by later workers. The naming convention used to identify the set of parameters is a code starting ZH-L, from Zürich (ZH), Linear (L) followed by the number of different (a,b) couples (ZH-L 12 and ZH-L 16)<ref name="Buhlmann-a-b" />) or the number of tissue compartments (ZH-L 6, ZH-L 8), and other unique identifiers.
For example:
'''ZH-L 12 (1983)'''
* ZH-L 12: The set of parameters published in 1983 with "Twelve Pairs of Coefficients for Sixteen Half-Value Times"<ref name="Buhlmann-a-b" />
'''ZH-L 16 (1986)'''<ref name="Buhlmann-2019" />
* ZH-L 16 or ZH-L 16 A (air, nitrox): The experimental set of parameters published in 1986.
* ZH-L 16 B (air, nitrox): The set of parameters modified for printed dive table production, using slightly more conservative “a” values for tissue compartments #6, 7, 8 and 13.
* ZH-L 16 C (air, nitrox): The set of parameters with more conservative “a” values for tissue compartments #5 to 15. For use in dive computers.
* ZH-L 16 (helium): The set of parameters for use with helium.
* ZH-L 16 ADT MB: set of parameters and specific algorithm used by Uwatec for their trimix-enabled computers. Modified in the middle compartments from the original ZHL-C, is adaptive to diver workload and includes [[Decompression practice#Profile determined intermediate stops|Profile-Determined Intermediate Stops]]. Profile modification is by means of "MB Levels", personal option conservatism settings, which are not defined in the manual.<ref name="Galileo" >{{cite book|title=Technical diving software for Galilio: User manual |url=https://www.scubapro.com/sites/scubapro_site/files/trimix_user_manual-eng.pdf |author=<!--not specified--> |publisher=Scubapro |access-date = 18 September 2019 }}</ref>
'''ZH-L 6 (1988)'''
* ZH-L 6 is an adaptation<ref name="Völlm-1" /> (Albert Bühlmann, Ernst B.Völlm and Markus Mock) of the ZH-L16 set of parameters, implemented in Aladin Pro computers (Uwatec, Beuchat), with 6 tissue compartments (half-time : 6 mn / 14 mn / 34 mn / 64 mn / 124 mn / 320 mn).
'''ZH-L 8 ADT (1992)'''
* ZH-L 8 ADT: A new approach with variable half-times and supersaturation tolerance depending on risk factors.<ref name="Völlm-1" /> The set of parameters and the algorithm are not public (Uwatec property, implemented in Aladin Air-X in 1992 and presented at BOOT in 1994). This algorithm may reduce the no-stop limit or require the diver to complete a compensatory decompression stop after an ascent rate violation, high work level during the dive, or low water temperature. This algorithm may also take into account the specific nature of repetitive dives.
[[File:Repetitive-dives-2.png|1024px|left]]
* ZH-L 8 ADT MB: A version of the ZHL-8 ADT claimed to suppress MicroBubble formation.<ref name="Smart" />
* ZH-L 8 ADT MB PDIS: [[Decompression practice#Profile determined intermediate stops|Profile-Determined Intermediate Stops]].<ref name="dykcen">{{cite web|url=http://www.dykcen.dk/PDF/Instruktor%20info/PDIS_Algorithm.pdf|title=Diving with PDIS (Profile-Dependent Intermediate Stop)|last=Staff|work=Dykkercentret website|publisher=Dykkercentret ApS|access-date=5 March 2016|___location=Frederiksberg|archive-url=https://web.archive.org/web/20161017170523/http://www.dykcen.dk/PDF/Instruktor%20info/PDIS_Algorithm.pdf|archive-date=17 October 2016|url-status=dead|df=dmy-all}}</ref>
* ZH-L 8 ADT MB PMG: Predictive Multi-Gas.<ref name="Scubapro-Luna-PMG" />
==Ascent rates==
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