Elements of decompression theory (Haldanian models)

(See also: "Notes on decompression theory" by A. Sandrucci and "Understanding M-values By E. C. Baker)

Hypothesis of the Haldanian models:

  1. The inert gases (nitrogenum...) are physically dissolved in the blood and the tissues.
  2. tissues in the human body form a parallel system with various rates of absorption and secretion
  3. saturation and desaturation proceed exponentially according to the pressure difference between ambient pressure and the pressure of nitrogen in the tissue
  4. this parallel system can be modeled by selecting a finite number of tissues (compartments).

This last statement is what really makes computer simulation possible.

In the dissolved gas or "Haldanian" decompression model, gas loading calculation for each hypothetical "tissue" compartment are compared agaist "ascent limit criteria" to determine the safe profile for ascent.

Each modeled tissue/compartment is characterized by two parameters of interest:

  1. halftime T1/2
    i.e. the time it takes to reach one half of the pressure difference between the tissue and its surroundings
  2. nitrogen supersaturation limit M0

Short halftime are tipical of "fast" tissues, like blood, that absorb and release nitrogen quickly.
Long halftimes are tipical of "slow" tissues, examples: fat, brain, spine, kidneys and liver.

For this simulation, the PADUA (Pennsylvania Analysis of Decompression for Undersea and Aerospace) model was adopted. The PADUA model uses 10 tissues, and according with the D. Workman (1960) [Baker] studies defines "nitrogen super saturation limit M0" bigger for for faster tissues and smaller for slow tissues.

Tissue T1/2[minutes] T1/2[seconds] M0[bar]
1 5 300 3,04
2 10 600 2,5536
3 20 1200 2,0672
4 40 2400 1,6112
5 80 4800 1,5808
6 120 7200 1,5504
7 160 9600 1,52
8 240 14400 1,4896
9 320 19200 1,4896
10 480 28800 1,4592

Mathematical model

Nitrogen ambient pressure [bar], calculated as portion of the inspired air gas is: 

Pa = = 0,79 (D/10+1) where:
  • D = depth in meters

Nitrogen pressure [bar] in a tissue is:

Pt  = Pt-1+ (Pa - Pt-1)(1- exp(t ln(0.5)/T1/2 )  

 where:
  • Pt = nitrogen pressure in tissue exposed for t seconds to an ambient pressure Pa
  • Pt-1= initial nitrogen pressure in tissue
  • Pa = nitrogen ambient pressure
  • t = time in seconds the tissue is exposed to Pa[*]
  • T1/2 = half-time of tissue in seconds[*]

(1) Thus nitrogen pressure change after 1 second is:

 

Pt  - Pt-1 = (Pa - Pt-1)(1- exp(ln(0.5)/T1/2 )  

 

(2) Remaining decompression time, i.e. time to reach nitrogen saturation in tissue, (also known as "No-Stop time" or "No Decompression Limit") is:

 

td  = T1/2 ln((M0 - Pa )/( Pt-1 - Pa ))/ln(0.5)  

 

 where:
  • T1/2 = half-time of tissue in seconds
  • Pt = nitrogen pressure in tissue
  • Pa = nitrogen ambient pressure
  • M0 = tissue saturation pressure

(3) Safe Ascent Depth ("ascent limit criteria"), i.e. the shallowest depth [meters] that can be safely reached during decompression, is:

SAD = 10( Pt-1 -  M0) where:
  • Pt = nitrogen pressure in tissue
  • M0 = tissue saturation pressure

Diving situations 

Once a second the computer calculates the nitrogen pressure Pt in each tissue, at the current depth, using equation (1). Depending on Pa (i.e. depth) and Pt we can have 5 possible situations:

1) Pa < M0 Safe depth, the tissue will never become saturated
2) Pt < M0 < Pa Normal condition. Tissue will become saturated after a time td that can be calculated with equation (2)
3) M0 < Pa < Pt These are no decompression situations. Tissue is saturated but will never desaturate, until Pa become below M0
4) M0 < Pt < Pa
5) Pa < M0 < Pt Decompression. Tissue is currently saturated, but will desaturate after a time td that can be calculated with equation (2). To allow for a safe decompression, Pa must not exceed certain limits, i.e. we cannot ascend above a ceiling SAD that can be calculated with equation (3)

 

WARNING/ATTENZIONE
This program is conceived as a teaching and demonstration tool only and as such it CANNOT SUBSTITUTE properly certified scuba training.
Queste informazioni e i risultati forniti dal programma sono concepiti come strumento didattico e dimostrativo, in questo senso NON POSSONO SOSTITUIRE uno specifico addestramento con un istruttore qualificato.

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