Hold your breath-part5
How Long Can You Really Hold Your Breath-Part5?
Part 5 - The Final Reckoning
All the posts in this series relate to the Freedive-Earth Maximum Breath-hold Calculator which is available here for you to download for free. Once again, remember that any breath-holding activity in water is potentially dangerous. Never, Ever Freedive Alone. So - we now have the following figures for our diver:
|Compartment||Oxygen Carrying Capacity (ml)|
That gives us a total oxygen carrying capacity (lungs + blood + muscle) of 2,512ml or 2.51 litres. Remember the value for BMR from way back at the beginning? Dive reflex excluded, we consume something like 250ml/min of oxygen, even when completely relaxed. So, all we have to do to find the maximum breath-hold time for our diver, is divide by 250mls: Total breath-hold time = total oxygen carrying capacity / BMR = 2512/250 =10.05mins Whoa... wait a second! That's far too long isn't it?! Well, yes, it is.
The Blackout Limit
So far we've neglected one very important fact: not all of the oxygen in the body is available for use by the diver. Remember the discrepancy when breathing air between PO2 (21kPa) and PaO2 (11kPa), and remember the tiny little bit of oxygen dissolved directly in the blood? The transfer of oxygen in the lungs to oxygen bound to haemoglobin happens via this little bit of oxygen dissolved in the blood. Oxygen from the lungs dissolves first in the blood and then is taken up by haemoglobin in proportion to the amount that's dissolved there. That's the same as saying that the saturation of haemoglobin is related to the PaO2. In fact its related in a very specific way, shown by the oxygen dissociation curve:
Notice that the maximum PaO2 is 11kPa - that reflects the inefficiency in the lungs that we talked about before. Also notice that as the PaO2 drops towards 8, the Hb saturation remains at about 95% for a long time. Below a PaO2 of 8kPa, the Hb begins to desaturate very quickly. This is good: It means that the haemoglobin is giving up oxygen to tissues that need it. Notice, though, that as the PaO2 drops towards 3kPa, the curve flattens out again. This is bad: it means that when oxygen levels get low, oxygen is no longer unbinding quickly from haemoglobin and so, although there is still oxygen in the blood (quite a lot of it, in fact) that oxygen is no longer available to the tissues (most notably the brain) and so our diver will black out long before her oxygen stores reach 0. In fact, in studies involving pilots and mountaineers, it has been found that PaO2s of 3kPa or less will typically cause blackout. During the breath-hold, the tiny amount of oxygen dissolved in the blood plasma (the PaO2) drives the diffusion of oxygen into the tissues that need it. The lungs act like a kind of reservoir, and keep topping up the blood with oxygen, maintaining the PaO2 until its stores are exhausted. In fact, all the oxygen stores we've talked about so far deplete together in a way that's determined by the PaO2. It's the PaO2 that determines the blackout point (<3kPa), not the saturation of haemoglobin, myoglobin, the amount of air in the lungs or anything else, because it's the PaO2 that determines how much oxygen gets into the tissues. This is not only a really important point but it's a useful one for us too: Unlike lots of the other oxygen stores we've talked about, PaO2 changes linearly throughout the breath-hold at a rate determined by the consumption of oxygen. All we need to do to determine the blackout point is to work out what total volume of oxygen across all 3 compartments will result in a PaO2 of 3 or less. We can do that by a simple calculation, because the change in PaO2 is linear:
So: we know the total oxygen stores of our diver at the start of the dive are 2512mls, which equates to a PaO2 of 11kPa. We also know that the blackout point will occur at 3kPa, because the oxygen stores will deplete linearly over the course of the hold (at the rate of 250ml/min) it's a simple ratio calculation: If the ratio is maintained 11:2512 Is the same as 3:(2512/11) x 3 Think I barely remembered that one from school... So the blackout limit occurs at a total oxygen content of (2512/11) x 3 = 685 ml. Our true maximum breath-hold is therefore given by: (total oxygen carrying capacity-blackout limit)/BMR = (2512-685)/250 = 7.31mins If you really want to, you can convert this into minutes and seconds by multiplying the .31mins by 60 too: .31 x 60 = 18.6 So our diver's theoretical maximum breath-hold, excluding the effect of the dive reflex (which is probably quite large!), and with more than a few little fudges thrown in, is 7'19''. Phew! We got there. But wait, don't go. You don't have to do this every time you want to know someone's theoretical maximum because...(fanfare) the freedive-earth team have put together an automatic version for you.
Have a look at the final section to see how it works.