Sunday, 12 February 2012

Scuba Diving Decompression Sickness: The Bends & Caisson Disease: Formula - Formulae


Formula

Pt = P1 + P2 + P3 ...
(Where Pt is total pressure, P1 is the partial pressure of gas one, P2 of gas two, etc.)
For example, the simplified composition of air is 21% oxygen and 79% nitrogen. If the total air pressure equals 1 ATA, then the partial pressure of the two gases will be 0.21 ATA and 0.79 ATA respectively - i.e. 21% of 1 ATA equals 0.21 ATA.
At a depth of 50 msw, the pressure equals 6 ATA. Therefore, the partial pressure of nitrogen (pN2) will be 79% of 6 ATA, which is 4.74 ATA - i.e. there are six times as many N2 molecules in a SCUBA diver’s air supply at a depth of 50 msw than at the surface.
This explains how a diver is exposed to an increase in inert gas simply by breathing at depth. Henry’s law goes on to explain how the gas spreads through the body’s tissues.
When a liquid is exposed to a gas, some of the gas molecules will dissolve into it. The number of molecules that dissolve into the liquid depends on factors such as the mass of the liquid, the partial pressure of the gas, its solubility and the surface area of contact.
Oxygen is normally carried by haemoglobin and only dissolves into the liquid plasma in small amounts. If the partial pressure of oxygen is increased, as with hyperbaric therapy or SCUBA diving, then more oxygen molecules will dissolve. Unfortunately, this is also the case for other gases in a diver’s breathing gas supply - including nitrogen. Because nitrogen is not utilised by the body, it will accumulate in the tissues until they can absorb no more molecules at that pressure, i.e. until they become ‘saturated’.
The body consists of various types of tissue. The rate at which an inert gas is absorbed (loaded) by each tissue during hyperbaric exposure, and subsequently released (off-loaded or off-gassed) during decompression, depends on several factors. These include the blood perfusion in the tissue and the solubility of the gas in each particular tissue type. A simplified description of tissues is that they can be fast or slow at absorbing and releasing inert gas. The table below gives examples of the 'speed' at which this process can occur for several tissue types exposed to both nitrogen and helium - the two most commonly used inert gasses in diving.
 

Tissue

Half-time, Nitrogen (mins)
Half-time, Helium (mins)
Spinal Cord
12.5
12.5
 
Skin, Muscle
37 - 79
14 - 30
 
Inner Ear
146 - 238
55 - 90
 
Joints, Bones
304 - 635
115 - 240
 
Edmonds, Lowry and Pennefather (1991)

As pressure is reduced, the inert gas in the tissues is carried away only slowly by the blood to the lungs where it can leave the body.
Off-gassing can be carried out more quickly by breathing an oxygen enriched atmosphere. However, oxygen becomes toxic at high partial pressures. Long term effects include pulmonary damage, but of greater concern to divers is the effect oxygen has on the central nervous system. At a pO2 greater than about 2ATA there is a risk of seizures. This equates to a depth of just 10msw, and the risk increases with depth. A pO2 limit of 1.6ATA is generally recommended for in-water diving, although much higher pO2 levels are routinely used for supervised treatment sessions in hyperbaric chambers, where there is no risk of drowning.
Boyle's law states that if a fixed mass of a gas such as oxygen or nitrogen is compressed then the volume of that gas will decrease.

Formulae

P x V = k         OR       P1 x V1 = P2 x V2      
(Where P1, P2 are pressure, V1, V2 are volume and k is a constant.)
For example, the volume in a diver's lungs equals 4 litres of air at the surface. What would the volume of air be at 10 msw if the diver held his breath? Firstly, the pressure at the surface equals 1 ATA. At 10 msw it is 2 ATA.
P1 x V1 = P2 x V2
V2 = P1 x V1 / P2
V2 = 1 ATA x 4 / 2
V2 = 2 litres.
The formula can be used to show that the gas volume will continue to fall as pressure increases. Conversely, during decompression the volume of any bubbles (including microscopic ones) will increase. Note that the change in volume is greatest nearer the surface.
This can be demonstrated with a large syringe filled with a carbonated drink without obvious bubbles. Cap the syringe and pull the plunger to simulate a drop in pressure – the gas in the liquid will come out of solution to form bubbles. Notice that when the plunger is released, despite a return to the original pressure, the bubbles in the liquid remain. In fact, even when pressure is increased by pushing the plunger, the bubbles do not all immediately dissolve back into the liquid.
Rather than spontaneously forming in a liquid, bubbles are ‘seeded’ by areas of slight imperfections on a surface. This can be seen when looking at a glass of carbonated drink – bubbles tend to appear on the inside surface of the glass at the same points. The internal structure of the human body is more irregular than the seemingly smooth surface of glass, and the potential for bubble formation is greater at areas where there is damaged tissue. 

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