Halftimes????

[Bluesky65RS]

Okay so I am reading through my PADI DM Manual and in Chapter 5 on pages 113-114 it briefly discusses "Halftimes". Can someone please enlighten my small brain here. I have read it several times and it makes no sense at all. Am I just over thinking it or is it really this confusing? If possible can someone who understands it walk me through it. Maybe a sample problem or two, it would be much appreciated.

[AzAtty]

In your body, inert gas such as nitrogen moves from areas of higher pressure to areas lower pressure at a certain rate. A "half time" is the amount of time required for bodily tissues to go from equilibrium to 50% saturated for a given change in pressure.

For example, on the surface, our tissues are at equilibrium (neither taking on gas or discharging it) at a pressure of one atmosphere absolute ("1 ATA"). When we descend to 33FSW, we are now at two atmospheres absolute (2 ATA), and our regulator delivers gas to us a pressure of 2 ATA. Therefore, nitrogen is forced into the blood at a pressure of 2 ATA, and when it reaches our other tissues that are at 1 ATA of pressure, the nitrogen moves from the blood into our other tissues. This continues until the tissue pressure reaches 2 ATA and we are at equilibrium again.

Let's say that a tissue has a halftime of 10 minutes. In the first ten minutes, enough gas moves from the blood into the tissue to increase the tissue pressure by one half the "distance" between 1 ATA and 2 ATA (let's say 1.5 ATA). In the second 10 minutes, tissue pressure increases from 1.5 ATA to half the "distance" between 1.5 ATA and 2 ATA, so tissue pressure is now 1.75 ATA.

It's the old concept of: cut the distance you wish to travel in half, then half again, then half again. The distance gets increasingly smaller. This is what we call an an "exponential function." Applied to diving, it works thus: tissue pressure increases by half of the difference between an initial pressure and a subsequent pressure (surface to 33 FSW in our case above), then half of the "new" difference in pressure, then half of the "new new" difference in pressure, and so on. By general custom, we consider a tissue fully saturated after six cycles (six halftimes) have passed.

Does that make sense?

So here's how tissue pressure would look for a one-hour dive at 33FSW for a tissue having a ten minute halftime:

0 min: 1 ATA
10 min: 1.5 ATA
20 min: 1.75 ATA
30 min: 1.875 ATA
40 min: 1.9375 ATA
50 min: 1.96875 ATA
60 min: 2 ATA


This is a vast simplification of how gas exchange really works, but you have to understand the basic concepts before you can wrap your head around what we *think* actually happens. Note that "tissue" does not necessarily correspond to a particular kind of tissue found in our bodies (e.g. bone, muscle, blood). "Compartment" is most often used in place of "tissue."

[TMHeimer]

You have to start by thinking of the depth given- say 100 feet. Now deal with whatever compartment is given--say the 5 minute compartment. This compartment has a halftime of 5 minutes. That means in 5 minutes it has a pressure equal to half way to the depth given--half way to 100 ft. is 50 feet. For the 2nd halftime (the next 5 minutes) it goes half way from the 50 feet to the 100 feet which is 75 feet. Then for the 3rd 5 mins it goes half way from the 75 ft. to the 100 ft., or 87.5 ft. etc. So after 15 minutes (3 halftimes) the compartment has a pressure of 87.5 ft). It takes 6 halftimes for ANY compartment to reach saturation (or "equalibrium"). After 6 halftimes I believe the 5 minute compartment is at about 98.4 feet. This is considered saturation because it can never actually reach 100 feet as you are always taking "half way" from the feet you're at to 100 ft., so it gets really tiny but never reaches 100. It takes the 120 minute compartment 6 (6 haftimes, like all compartments) times 120=720 minutes to saturate (and 720/60 mins.= 12 hours to saturate). Has nothing to do with "half-lifes" like with the elements. Just remember to start by thinking of the depth given. Hope that helps. I take the exams myself Sat.

[AzAtty]

Originally Posted by TMHeimer

Has nothing to do with "half-lifes" like with the elements.

It's actually identical to the concept of a half life, only in reverse.

[R0gue]

I'm not going to throw anymore mud into the mix as I think the others have explained it pretty well. If you're still befuddled then my suggestion is to read the relevant section in PADI's Encyclopedia of Recreational Diving. It actually explains it pretty well.

You can also see if this link helps Scuba Diving & Other Fun Activities: Decompression & Theoretical Tissue Compartments

Ask your Instructor to help you also.

[vjanelle]

Something else I tripped on was that it was always 50% of the remaining load... imagine filling a glass with water 50%, then 50% of the remaining space, then 50% of that, etc.

Or if you want, taking 50% of the water out, then 50% of the remainder, then 50% of the remainder, etc.

[boulderjohn]

Maybe it will help if I gave a really simplistic explanation of the process of diffusion so that you can understand why it goes so fast at first and then progressively slower.

Right now you are sitting at your computer, and I assume you have been at the same altitude for quite some time. There is nitrogen in the air you breathe, in the blood flowing through your circulatory system, and in the tissues perfused by that blood. For simplicity sake, let's just talk about air and your tissues in general. The nitrogen in each is moving around in all directions, totally at random. They don't pay a lot of attention to the boundaries between the various tissues and the air. Because you have been at this pressure for a long time, things have evened out. By law of averages, there is just as many nitrogen molecules going into your tissues as there is coming out. We say your tissues are at equilibrium, or saturated.

Now you suddenly descend to 99 feet--4 atmospheres. Now there are 4 times as many nitrogen molecules in the air you are breathing than in the tissues. That means, again by law of averages, 4 times as many nitrogen molecules are flowing into the tissues as out. Your tissues are on-gassing.

The more liquid the tissue, the faster this happens. The more blood vessels in the tissues, the faster this happens. Some tissues will accept the nitrogen so rapidly that in 5 minutes they are halfway to the number of molecules in the air. Other tissues will take 10, 20, 30, 60, or more minutes to accomplish the same thing. That is their halftime.

But now that they have reached that halftime, things have changed. The difference between the air and the tissue is only half what it was before, so now, again by law of averages, the rate of exchange is cut in half. And so forth and so forth.

This is not actually a sudden shift at each half time, as the progression describes, but it is helpful to think of it that way.

Let's say you got the tissues to reach equilibrium with the air at 99 feet. That would take 30 minutes for the 5 minute tissue (compartment). The second you start to ascend, there will be more nitrogen in the tissue than the air. It is said to be supersaturated, and now the gas begins to go from tissue to air.

But you only spent 20 minutes at 99 feet, since that is the NDL. Your 5 minute compartment is about 93% saturated. As you ascend, you will very quickly reach the point at which it is saturated; that is, it is equal to the air being breathed at that depth. As you ascend further, it will be supersaturated and will begin to off gas. As you continue to ascend, the slower and slower tissues will reach their saturation point and begin to off gas.

At any point in your ascent, some of your tissues will be supersaturated and will be giving off gas, and some tissues will be below their saturation point and still on-gassing.

[scubadiver888]

Hi Bluesky65RS,

I'm going through the DM training right now as well. According to my instructor I have a pretty good explanation of half-times.

There are a few things to make sure you understand. The first is that compartments, half-times and M-values all relate to a theoretical model that has no direction correlation to the human body but that years of research have shown they seem to be a good model.

That said, different body tissues absorb/release nitrogen at different rates. Dr. Haldane decided his model would assume there are six different body tissues. So he created six compartments.

Rather than look at all the compartments at once, lets look at the 5-minute and 20-minute compartment. If we go to a depth of 60 feet for 60 minutes, here is what happens to the two compartments. First the 5-minute compartment:

After 05 minutes: 30.000' or 50% of 60'
After 10 minutes: 45.000' or 75% of 60' (50% + 25%)
After 15 minutes: 52.500' or 87.5% of 60' (50% + 25% + 12.5%)
After 20 minutes: 56.250' or 93.75% of 60' (50% + 25% + 12.5% + 6.25%)
After 25 minutes: 58.125' or 96.875% of 60' (50% + 25% + 12.5% + 6.25% + 3.125%)
After 30 minutes: 60.000' or 100% of 60'

You'll notice that 25% is half of 50%, 12.5% is half of 25%, 6.25% is half of 12.5%. In other words, every 5 minutes half as much is added. Also, half of 3.125% is 1.5625% but on the last iteration we round up to 100%. I.e. the sixth half time is always 100%.

After 30 minutes the 5-minute compartment stays at 100%. It is full and cannot hold any more. Because our example is a 60 minute dive, the 5-minute compartment will be full after 30 minutes and will stay full for the rest of the dive.

Now let's look at the 20-minute compartment:

After 20 minutes: 30.0' or 50% of 60'
After 40 minutes: 45.0' or 75% of 60'
After 60 minutes: 52.5' or 87.5% of 60'

Because it is only a 60 minute dive, the 20-minute compartment will never be full.

On top of whether or not the compartment is full, there are M-values for each compartment. If the M-value is reached then you have reached an No Deco Limit (NDL). So you might hit an NDL before any of the compartments are full.

For example, if the M-value for the 20-minute compartment was 50' (it is not) then we would hit the NDL because of the 20-minute compartment before the 60 minute mark.

You might also want to read Understanding M-Values.

Finally, the examples in the book leave out a lot of information and are based on Dr. Haldane's model. If you try comparing the examples in the book to the RDP don't bother. The RDP is based on a completely different model.

[Joe-Diver]

As a DM Candidate, also read pp 5-84 thru 5-97 in the Encyclopedia of Recreational Diving. This section, entitled Decompression Models, discusses this topic, along with M-Values and Controlling Compartments. These concepts are important to understanding half times when applying them to the model.