The Bühlmann decompression model is a Haldanian which models the way inert gases enter and leave the human body as the ambient pressure changes. [1] Versions are used to create decompression tables and in personal dive computers to compute no-decompression limits and decompression schedules for dives in real-time, allowing divers to plan the depth and duration for dives and the required decompression stops.
The model (Haldane, 1908) [2] assumes perfusion limited gas exchange and multiple parallel tissue compartments and uses an inverse exponential model for in-gassing and out-gassing, both of which are assumed to occur in the dissolved phase.
Multiple sets of parameters were developed by Swiss physician Dr. Albert A. Bühlmann, who did research into decompression theory at the Laboratory of Hyperbaric Physiology at the University Hospital in Zürich, Switzerland. [3] [4] The results of Bühlmann's research that began in 1959 were published in a 1983 German book whose English translation was entitled Decompression-Decompression Sickness. [1] The book was regarded as the most complete public reference on decompression calculations and was used soon after in dive computer algorithms.
Building on the previous work of John Scott Haldane [2] (The Haldane model, Royal Navy, 1908) and Robert Workman [5] (M-Values, US-Navy, 1965) and working off funding from Shell Oil Company, [6] Bühlmann designed studies to establish the longest half-times of nitrogen and helium in human tissues. [1] These studies were confirmed by the Capshell experiments in the Mediterranean Sea in 1966. [6] [7]
The basic idea (Haldane, 1908) [2] is to represent the human body by multiple tissues (compartments) of different saturation half-times and to calculate the partial pressure of the inert gases in each of the compartments (Haldane's equation):
with the initial partial pressure , the partial pressure in the breathing gas (minus the vapour pressure of water in the lung of about 60 mbar), the time of exposure and the compartment-specific saturation half-time .
When the gas pressure drops, the compartments start to off-gas.
To calculate the maximum tolerable pressure , the constants and , which are derived from the saturation half-time as follows (ZH-L 16 A):
are used to calculate M-Value ():
The values calculated do not correspond to those used by Bühlmann for tissue compartments 4 (0.7825 instead of 0.7725) and 5 (0.8126 instead of 0.8125). [8]
Versions B and C have manually modified [8] the coefficient .
The modified values of and are shown in bold in the table below.
According to Graham's Law, the speed of diffusion (or effusion) of two gases under the same conditions of temperature and pressure is inversely proportional to the square root of their molar mass (28.0184 g/mol for and 4.0026 g/mol for , i.e. ), which means that molecules diffuse 2.645 times faster than molecules.
Bühlmann took this into account and divided all the tissue compartment half-time for air (nitrogen) by 2.645 to obtain a helium-specific set of parameters with the longest compartment set at
The parameters of the M-Values (coefficients a and b) were determined specifically.
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, [9] a weighted average of the half-times and coefficients and 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% , 50% , 32% ), the half-time (or the and coefficients) of compartment #1 is calculated by taking 50% of the half-time and 32% of the half-time divided by 50% + 32% = 82%.
Example, compartment #1:
(instead of with and with )
( with and with )
( with and with )
The same calculations can be made using partial pressures rather than percentages.
This approach is controversial with some authors [10] 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.
There are no specific model for constant dives. The difference lies in the fact that, at all times, the proportion of inert gas is calculated in relation to the chosen (e.g. 0.75 or 1.3 ata (bar)).
Cpt | ZH-L 16 | ZH-L 16 A | ||||||
---|---|---|---|---|---|---|---|---|
(min) |
A
Experimental |
B
Tables |
C
Computers |
(min) |
||||
1 (1a) | 4 | 1.2599 | 1.2599 | 1.2599 | 0.5050 | 1.51 | 1.7424 | 0.4245 |
1b | 5 | 1.1696 | 1.1696 | 1.1696 | 0.5578 | |||
2 | 8 | 1.0000 | 1.0000 | 1.0000 | 0.6514 | 3.02 | 1.3830 | 0.5747 |
3 | 12.5 | 0.8618 | 0.8618 | 0.8618 | 0.7222 | 4.72 | 1.1919 | 0.6527 |
4 | 18.5 | 0.7562 | 0.7562 | 0.7562 | 0.7825 | 6.99 | 1.0458 | 0.7223 |
5 | 27 | 0.6667 | 0.6667 | 0.6200 | 0.8126 | 10.21 | 0.9220 | 0.7582 |
6 | 38.3 | 0.5933 | 0.5600 | 0.5043 | 0.8434 | 14.48 | 0.8205 | 0.7957 |
7 | 54.3 | 0.5282 | 0.4947 | 0.4410 | 0.8693 | 20.53 | 0.7305 | 0.8279 |
8 | 77 | 0.4701 | 0.4500 | 0.4000 | 0.8910 | 29.11 | 0.6502 | 0.8553 |
9 | 109 | 0.4187 | 0.4187 | 0.3750 | 0.9092 | 41.2 | 0.5950 | 0.8757 |
10 | 146 | 0.3798 | 0.3798 | 0.3500 | 0.9222 | 55.19 | 0.5545 | 0.8903 |
11 | 187 | 0.3497 | 0.3497 | 0.3295 | 0.9319 | 70.69 | 0.5333 | 0.8997 |
12 | 239 | 0.3223 | 0.3223 | 0.3065 | 0.9403 | 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 |
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) [11]) or the number of tissue compartments (ZH-L 6, ZH-L 8), and other unique identifiers. For example:
ZH-L 12 (1983)
ZH-L 16 (1986) [12]
ZH-L 6 (1988)
ZH-L 8 ADT (1992)
Ascent rate is intrinsically a variable, and may be selected by the programmer or user for table generation or simulations, and measured as real-time input in dive computer applications.
The rate of ascent to the first stop is limited to 3 bar per minute for compartments 1 to 5, 2 bar per minute for compartments 6 and 7, and 1 bar per minute for compartments 8 to 16. Chamber decompression may be continuous, or if stops are preferred they may be done at intervals of 1 or 3 m. [18]
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{{
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Many articles on the Bühlmann tables are available on the web.
The Bühlmann decompression model is a Haldanian which models the way inert gases enter and leave the human body as the ambient pressure changes. [1] Versions are used to create decompression tables and in personal dive computers to compute no-decompression limits and decompression schedules for dives in real-time, allowing divers to plan the depth and duration for dives and the required decompression stops.
The model (Haldane, 1908) [2] assumes perfusion limited gas exchange and multiple parallel tissue compartments and uses an inverse exponential model for in-gassing and out-gassing, both of which are assumed to occur in the dissolved phase.
Multiple sets of parameters were developed by Swiss physician Dr. Albert A. Bühlmann, who did research into decompression theory at the Laboratory of Hyperbaric Physiology at the University Hospital in Zürich, Switzerland. [3] [4] The results of Bühlmann's research that began in 1959 were published in a 1983 German book whose English translation was entitled Decompression-Decompression Sickness. [1] The book was regarded as the most complete public reference on decompression calculations and was used soon after in dive computer algorithms.
Building on the previous work of John Scott Haldane [2] (The Haldane model, Royal Navy, 1908) and Robert Workman [5] (M-Values, US-Navy, 1965) and working off funding from Shell Oil Company, [6] Bühlmann designed studies to establish the longest half-times of nitrogen and helium in human tissues. [1] These studies were confirmed by the Capshell experiments in the Mediterranean Sea in 1966. [6] [7]
The basic idea (Haldane, 1908) [2] is to represent the human body by multiple tissues (compartments) of different saturation half-times and to calculate the partial pressure of the inert gases in each of the compartments (Haldane's equation):
with the initial partial pressure , the partial pressure in the breathing gas (minus the vapour pressure of water in the lung of about 60 mbar), the time of exposure and the compartment-specific saturation half-time .
When the gas pressure drops, the compartments start to off-gas.
To calculate the maximum tolerable pressure , the constants and , which are derived from the saturation half-time as follows (ZH-L 16 A):
are used to calculate M-Value ():
The values calculated do not correspond to those used by Bühlmann for tissue compartments 4 (0.7825 instead of 0.7725) and 5 (0.8126 instead of 0.8125). [8]
Versions B and C have manually modified [8] the coefficient .
The modified values of and are shown in bold in the table below.
According to Graham's Law, the speed of diffusion (or effusion) of two gases under the same conditions of temperature and pressure is inversely proportional to the square root of their molar mass (28.0184 g/mol for and 4.0026 g/mol for , i.e. ), which means that molecules diffuse 2.645 times faster than molecules.
Bühlmann took this into account and divided all the tissue compartment half-time for air (nitrogen) by 2.645 to obtain a helium-specific set of parameters with the longest compartment set at
The parameters of the M-Values (coefficients a and b) were determined specifically.
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, [9] a weighted average of the half-times and coefficients and 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% , 50% , 32% ), the half-time (or the and coefficients) of compartment #1 is calculated by taking 50% of the half-time and 32% of the half-time divided by 50% + 32% = 82%.
Example, compartment #1:
(instead of with and with )
( with and with )
( with and with )
The same calculations can be made using partial pressures rather than percentages.
This approach is controversial with some authors [10] 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.
There are no specific model for constant dives. The difference lies in the fact that, at all times, the proportion of inert gas is calculated in relation to the chosen (e.g. 0.75 or 1.3 ata (bar)).
Cpt | ZH-L 16 | ZH-L 16 A | ||||||
---|---|---|---|---|---|---|---|---|
(min) |
A
Experimental |
B
Tables |
C
Computers |
(min) |
||||
1 (1a) | 4 | 1.2599 | 1.2599 | 1.2599 | 0.5050 | 1.51 | 1.7424 | 0.4245 |
1b | 5 | 1.1696 | 1.1696 | 1.1696 | 0.5578 | |||
2 | 8 | 1.0000 | 1.0000 | 1.0000 | 0.6514 | 3.02 | 1.3830 | 0.5747 |
3 | 12.5 | 0.8618 | 0.8618 | 0.8618 | 0.7222 | 4.72 | 1.1919 | 0.6527 |
4 | 18.5 | 0.7562 | 0.7562 | 0.7562 | 0.7825 | 6.99 | 1.0458 | 0.7223 |
5 | 27 | 0.6667 | 0.6667 | 0.6200 | 0.8126 | 10.21 | 0.9220 | 0.7582 |
6 | 38.3 | 0.5933 | 0.5600 | 0.5043 | 0.8434 | 14.48 | 0.8205 | 0.7957 |
7 | 54.3 | 0.5282 | 0.4947 | 0.4410 | 0.8693 | 20.53 | 0.7305 | 0.8279 |
8 | 77 | 0.4701 | 0.4500 | 0.4000 | 0.8910 | 29.11 | 0.6502 | 0.8553 |
9 | 109 | 0.4187 | 0.4187 | 0.3750 | 0.9092 | 41.2 | 0.5950 | 0.8757 |
10 | 146 | 0.3798 | 0.3798 | 0.3500 | 0.9222 | 55.19 | 0.5545 | 0.8903 |
11 | 187 | 0.3497 | 0.3497 | 0.3295 | 0.9319 | 70.69 | 0.5333 | 0.8997 |
12 | 239 | 0.3223 | 0.3223 | 0.3065 | 0.9403 | 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 |
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) [11]) or the number of tissue compartments (ZH-L 6, ZH-L 8), and other unique identifiers. For example:
ZH-L 12 (1983)
ZH-L 16 (1986) [12]
ZH-L 6 (1988)
ZH-L 8 ADT (1992)
Ascent rate is intrinsically a variable, and may be selected by the programmer or user for table generation or simulations, and measured as real-time input in dive computer applications.
The rate of ascent to the first stop is limited to 3 bar per minute for compartments 1 to 5, 2 bar per minute for compartments 6 and 7, and 1 bar per minute for compartments 8 to 16. Chamber decompression may be continuous, or if stops are preferred they may be done at intervals of 1 or 3 m. [18]
{{
cite journal}}
: CS1 maint: unfit URL (
link)
{{
cite journal}}
: CS1 maint: unfit URL (
link)
Many articles on the Bühlmann tables are available on the web.