M Values and Gradient Factors - Explained

[Gareth Burrows]

I posted this "in another place" but someone has asked me to put it here too". Everything correct in this post is down to Mark Powell. Everything incorrect is down to me playing pool with finn whilst Mark's students listen in to the lecture


Gradient Factors explained.....

OK

Now we all know that as you descend the ambient pressure of the gas you are breathing increases. Also as you descend, the pressure of Nitrogen, or other inert gases, in your tissues increases, as your tissues become saturated. Stay at a given depth for long enough, and some of your tissues become fully saturated, IE the pressure of gas in your tissues has equalised with ambient pressure of gas you are breathing. this is the point where you stop ongassing. As you begin to ascend, the pressure of gas in your tissues becomes larger than the ambient pressure in the gas you are breathing, and you begin to offgas.

Let's imagine you have a graph, like the one below. Its really crap, so bear with me.




The line marked "saturation" - the blue one at the bottom which really should be in the middle of the graph - indicates the point where the ambient pressure meets the tissue pressure. This means you are not ongassing or offgassing, but have reached a point where thepressure of ambient gas (eg Nitrogen) around you has equalised with the pressure of ambient gas in your tissues. This will obviously be a different depth for each tissue compartment but let's just pretend the body has one tissue compartment to make it simple.

Now everything below that line to the right hand side of the graph means you have greater ambient pressure than tissue pressure. This means you are ongassing becuase your tissues have not equalised with the pressure of inert gas in the gas you are breathing. Everywhere above that line means the tissue pressure is greater than the ambient pressure. Hence you are offgassing. This is known as the "deco zone", as when we are in this zone we are decompression. We get to this zone by lowering the ambient pressure -ascending.

Now, obviously, we all need to offgas during the ascent on a dive, and the more into the decozone we go, the faster we offgas. However, there comes a point where you are offgassing too much. This is the point where the tissue pressure is so much greater than the ambient pressure that bubbles begin to form in your tissues - ie you get bent. Now, the point where this happens is a theoretical line called supersaturation, or the "M value".

Now ye old buhlmann tables took you straight up from a deep dive to the M value, and kept you there until offgassing was complete, hence the reason many people refer to them as a "bend and mend model". This had the advantage of getting you shallow fast, and offgassing fast, but really took you to the edge of being bent. This is why buhlmann tables, and buhlmann based computers, such as the suuntos, get you very shallow, very fast. This is also why many people consider Suuntos to be far too aggressive for decompression diving.

Now, lets call the point of saturation, where everything is equal as being 0%, and the point of supersaturation, or M value, where we are on the point of being bent, as being 100. The fact that buhlmann tables take you straight to the M value means that you are being taken immediately to 100% of the distance between saturation and the M value, hence the reason buhlmann tables are often called 100/100, becuase all of the stops are done at this 100% point. However. There is a "grey area" around the M value, as it is only a theoretical line, and the problem is the many people feel like shit diving buhlmann tables, and indeed people got bent. So Gradient factors were introduced as a fudge to make the model safer. Gradient factors are represented by a LOW factor figure and a HIGH factor figure, which sit as two lines betweem the point of saturation (equilibrium) and the point of supersaturation (whoops I'm bent). the intention is to keep you in the deco zone but stop you getting too close to the M Value

The LOW figure represents the percentage of the distance from the equilibrium to the M Value at which we will start our stops. Thus 10/90 gradient factors mean we start our stops very deep indeed at only 10% of the distance to the M Value. 30/70 gradient factors mean we start our stops 30% of the way towards the M value, ie a little shallower. The lower the value is, the more deep stops we will do during our ascent.

The HIGH gradient factor represents the maximum percentage we are willing to go between the point of saturation and point of supersaturation before hitting the surface. For example, 20/80 means we will never go above 80% of the way towards the M value during our stops, and will break the surface without going over that 80% limit. 10/90 means we go a little closer to the M Valu. Obviously, the higher this figure, the greater the difference between tissue and ambient pressure, and the faster you will be offgassing, but the close you are to that theoretical "bend" point, and let's not forget about that grey zone around the M Value, so its in our interest to hang back from it a bit.

What factors you use is purely empircal, at least in the non-DIR world. Whatever makes you feel good are the right factors to use. A very low LOW factors will mean you will make lots of deep stops, but will not be offgassing quickly so will have a longer deco. A very high HIGH factor will mean you are offgassing quickly, but are moving towards the M value, a bad place to be. the most popular combinations are things like 20/80 and 10/90, which sort of combine the best of both worlds, although you do hear of people doing mad combintations of greater than 100%. If it works for them, great, its only a theoretical model after all.



Anyway, that's gradient factors.



Garf

[Janos]

Erik Baker's explanation (available from the e-aquanauts website here is also well worth a read.

Janos

[Gareth Burrows]

If you mean this ... http://www.e-aquanauts.co.uk/2006/do...g_M-values.pdf and this ... http://www.e-aquanauts.co.uk/2006/do...0deepstops.pdf

yes its excellent reading

[KeyLimePie]

Well worth another post, Garf

[neilh]

Can anyone help me get my head around M-Values for a couple of models?

My understanding of Haldane's 2:1 ratio is that a given compartment can tolerate a tissue tension of up to twice the ambient pressure. I.e. at 20M the M-Value is 6 bar (3 ATA x 2) - so you could get from 50M (6 ATA) with saturated tissues up to 20M. Is that right?

For Workman's model I'm not entirely clear about how whether the result of M0 + (dM x depth) is the absolute tissue tension or not. From some of the bits I've read it seems that relative pressures might come into play with this model rather than absolute (i.e. 10M is 1 bar relative to surface pressure rather than 2 bar asbsolute) - but I'm not sure!

Can anyone shed any light?

[Gene_Hobbs]

Originally Posted by neilh

Workman's model

I found these worked well:

CALCULATION OF DECOMPRESSION SCHEDULES FOR NITROGEN-OXYGEN AND HELIUM-OXYGEN DIVES.
Workman, 1965.
RRR ID: 3367

Systematic Guide to Decompression Schedule Calculations.
Braithwaite, 1972
RRR ID: 3945

[neilh]

Originally Posted by Gene_Hobbs

I found these worked well:

Thanks Gene - certainly cleared up my question around Haldane which is great, but I'm still a bit confused about Workman's M-Values

Taking an example of breathing air at 20M for compartment 1:
M0 = 31.7, deltaM = 1.8, so:
M = 31.7 + (1.8 x 20) = 67.7msw = 6.77 bar

Taking a simple view of nitrogen uptake (i.e. ignoring water vapour, etc) to calculate ppN2 in the tissues, does this mean that you could come up from 75 M without exceeding the M-Value for this compartment?

75M = 8.5 ATA
ppN2 = 0.79 x 8.5 = 6.72 bar

[GLOC]

Originally Posted by neilh

Thanks Gene - certainly cleared up my question around Haldane which is great, but I'm still a bit confused about Workman's M-Values

Taking an example of breathing air at 20M for compartment 1:
M0 = 31.7, deltaM = 1.8, so:
M = 31.7 + (1.8 x 20) = 67.7msw = 6.77 bar

Taking a simple view of nitrogen uptake (i.e. ignoring water vapour, etc) to calculate ppN2 in the tissues, does this mean that you could come up from 75 M without exceeding the M-Value for this compartment?

75M = 8.5 ATA
ppN2 = 0.79 x 8.5 = 6.72 bar

67.7msw is 5.77 bar, does that make a difference to what you were looking at?

[John Touhig]

Originally Posted by GLOC

67.7msw is 5.77 bar, does that make a difference to what you were looking at?

did you mean 7.77 bar....


and you run DECO on the fly... tut tut tut

[wilbo]