The bends or decompression sickness in SCUBA divers is linked to fast ascents from depth. When ascending, the ambient pressure is reduced (for approximately every 33ft underwater another atmosphere of pressure is added), which causes absorbed gasses to come back out of solution and form micro-bubbles in the blood. The air consumed by SCUBA divers is pressured and consumed at depth, so as divers ascend the micro-bubbles in the blood will also start to grow larger in volume (i.e. gasses expand when pressure is reduced). If the ascent is slow enough the volume of the bubbles should not rise too high and they can safely leave the body through the lungs, as divers continuously exhale on ascent. Large bubbles of gas can impede the flow of blood to the brain, central nervous system and other vital organs. Create a model that describes the movement of gasses out of solution and back into the blood and then ultimately out of the body as a SCUBA diver ascends. Using your model, determine the maximum ascent rate from a depth of your choosing that would ensure a SCUBA diver would not get the bends. What would your model look like if the diver did not exhale on ascent? Why do deep diving mammals, like seals, dolphins, and whales, not suffer from the bends?
Theory:
- Compartment models (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 587; Stephen P. and John Guckenheimer. Dynamic Models in Biology. New Jersey: Princeton University Press, 2006. 7)
- Systems of differential equations (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 560)
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