## Notes On Decompression Theory

J.S. Haldane first theorized a decompression model for the Royal Navy, from which most modern decompression models originate.
It consisted of the following postulates:

1. tissues absorb and secrete nitrogen at an exponential rate, based on the pressure difference between ambient pressure and the pressure of nitrogen in the tissue
2. tissues in the human body form a continuous spectrum with varoius rates of absorption and secretion
3. this continuous spectrum can be modeled by selecting a finite number of tissues

This last statement is what really makes computer simulation possible.

Each modeled tissue is characterized by two parameters of interest:

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

Short half-time are tipical of "fast" tissues, like blood, that absorb and release nitrogen quickly.
Long half-times are tipical of "slow" tissues like fat.

For this simulation, the PADUA (Pennsylvania Analysis of Decompression for Undersea and Aerospace) model was adopted. The PADUA model uses 10 tissues, and is considered more accurate and safe than the U.S. Navy model which uses only 6 tissues.

 Tissue T1/2[minutes] M0[bar] 1 5 3,04 2 10 2,5536 3 20 2,0672 4 40 1,6112 5 80 1,5808 6 120 1,5504 7 160 1,52 8 240 1,4896 9 320 1,4896 10 480 1,4592

### Relevant Formulas

Nitrogen ambient pressure [bar] is: where: D = depth in meters

Nitrogen pressure [bar] in a tissue is: 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 minutes

(1) Thus nitrogen pressure change after 1 second is: (2) Remaining decompression time, i.e. time to reach nitrogen saturation in tissue, is: where: T1/2 = half-time of tissue in minutes Pt = nitrogen pressure in tissue Pa = nitrogen ambient pressure M0 = tissue saturation pressure

(3) Safe Ascent Depth, i.e. the shallowest depth [meters] that can be safely reached during decompression, is: where: Pt = nitrogen pressure in tissue M0 = tissue saturation pressure

### Algorythm

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, so we must ascend in order to bring Pa 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)