Diving with gradient factors for a new recreational diver

[goldfishtornado]

Are you sure about that?

Double checking, no. It looks like they switch from a 3% P(DCS) isopleth when talking about TDT to a 0.2% P(CNS DCS) isopleth when talking about NST. I'm not 100% sure on the translation between the two. But I think my claim is similar, the paper is showing those algorithms are below the isopleth for a given parameterization, not calculating raw probability values.

The Howle paper (doi: 10.1371/journal.pone.0172665) is a different one than I linked I guess? It looks like they are using a trinomal state model for DCS rather than a binomial, but they still follow the Weathersby & Thalman parameterization of assuming the probability of each of their subclasses of DCS are described by a P(DCS) = 1 - exp(-R), where R has a bunch of stuff, including the integrated r hazard, which is very close to proportional to the pressure gradient in the assumed compartments. I think my overall point is that the prevailing models in the literature assume exponential dependence of the probability of DCS on integrated exposure.

 

[dmaziuk]

I am also not entirely clear on the part where the risk is much higher for the dives with PRT > 25, but as special case we apply probabilities to no-stop dives with PRT <= 10..12... And then there's the latest installment of Robert's blog where he questions the wisdom of extrapolating from bent divers to not-bent divers -- without any useful measurement of "subclinical DCS stress".

Did you look at "Fraedrich follow-up" in the same blog? -- GFs under 60 seem to run the risk between zero and zip according to SAUL, the 2 models analysed give non-overlapping GF Hi ranges for "high PRT" dives (i.e. low confidence in GF-Hi) and "most uncertain" numbers for GF-Lo. He's only confident in GF-Hi of 80..90 for no-stop dives. (If he included DSAT, it'd've likely pushed that to mid-90s.)

Anyone wants to believe all that shows "linear" or even "monotonical" reduction of risk, they're welcome to it.

 

[goldfishtornado]

the latest installment of Robert's blog

I don't think I've read that one before. Robert is generally pretty precise on the blog, and I wouldn't say I strongly disagree with much of what is said their.

I have two caveats to that. The first is I don't think there is as much tension between a Bühlmann style model and a Thalmann model as might be implied. It is true that they diverge in the case where excess pressure is kept constant, but in the profiles studied people take stops a given depth. In that case the time integral over the excess pressure is an integral over an exponential, which should produce a finite probability value. Anecdotally, I do think the perception is that riding razors edge of 100%GF for a sustained period is more dangerous than a gentler slope.

The second caveat is that I think the observation that GFs under 60 seem to run effectively zero risk is evidence that the extrapolation is at least not catastrophically bad. The measurement problem Robert alludes to for small incidence rates is very real, and the BIG292 Navy data set people seem to use is 'only' ~3k observations. This would not be enough to say a lot about 1/1000 risks. That being said there probably are many hundreds of thousands of dives where people have run very conservative profiles and have effectively zero serious incidence rate. That decreases the likely hood, at least in my mind, that you face a catastrophic divergence in the extrapolation like the one illustrated in the blog post.

Edit: As an aside if anyone knows where to dig up a machine readable copy of the BIG292 data set, I would be interested.

 

[dmaziuk]

... there probably are many hundreds of thousands of dives where people have run very conservative profiles and have effectively zero serious incidence rate.

That would be why I quote DSAT all the time: from PADI RDP to Oceanic computers, it should qualify. With the caveat that it's used for multi-day multi-dive exposures -- that is yet another can of worms. (And the one that I personally care about, being a vacation diver.)

 

[scubadada]

So, just for fun I plotted the risk of DCS vs. bottom time for a dive to 100 ft on 32% nitrox. I used the SAUL recreational dive planner to calculate the risk of DCS, link kindly supplied by @tursiops post #246. The dive planner uses a descent rate of 60 ft/min, an ascent rate of 60 ft/min, and includes a 3 min safety stop. I was mainly interested in the shape of the curve.

To put this into perspective, here are the NDLs for some common decompression algorithms at 100 ft on 32% nitrox:

All bottom times of greater than 30 min would generally be deco dives. The 50 min dive would require a 2 min stop at 20 ft and a 15 min stop at 10 feet using my GFs of 80/95. Most of us would not execute these longer dives without satisfying the decompression obligation. The risk for DCS on the graph runs from 0 (less than 0.0001%, less than 1/1,000.000) at 20 min to 1.1849%, 1/84 at 50 min. The risk of DCS for the 30 min on DSAT is 0.169%, 1/592.

 

[L13]

Are you sure about that? Good thing nobody is diving 100/100 twice a day for four days in a row, then. (That wasn't the question, the question was is the reduction of risk from no-stop diving, say, near-DSAT 93/93, to, say, 70/80, is meaningful in practical terms. For bonus points: on the proposed twice a day for 4 days schedule. Since we know DSAT users don't get bent on that schedule without outside help, the 70/80 divers can rejoice in the knowledge that they're getting "exponentially more" not bent.)

Anyway, try this one Setting Gradient Factors based on published probability of DCS – The Theoretical Diver and follow the reference #3 to see how deep the rabbit hole goes.

Interesting that you quote a paper that concludes that suggests PDCS(100%) ~= 1%, while PDCS(80%) ~= 0.1%. A greater than 90% reduction in risk with only a 20% reduction in GF High. @scubadada 's graph based on SAUL sugests a reduction of PDCS of ~0.2% to ~0% or almost 100% from the same change for NDL dives with a 3min SS (the theoretical diver reference was based on Navy Deco dives with the higher PRT and therefore higher risk).

Your cute "spoiler" trick doesn't hide the fact that your 4% reduction in PDCS(50%) vs PDCS(100%) is just silly.

 

[L13]

Anyone wants to believe all that shows "linear" or even "monotonical" reduction of risk, they're welcome to it.

Every paper, blog, or article you or anyone else has referenced shows a "monotonically" reduction is risk. Every one of them shows a decidedly non-linear reduction in risk with the greatest reduction at high GF's and risk rapidly approaching zero As GF high goes below 50%.

Not a single piece of evidence suggests the the relationship is non-monotonic or that the majority of the risk reduction is not at the high end of GF's. The real UFO believer is the one who denies that.

In fact, those are probably the only two statements that every one of the sources agrees on.

 

[scubadada]

I'm sure it is not lost on readers the very small range covered by the common decompression algorithms from 20-30 minutes, all quite safe. For a single dive at a GF high of 75, the risk of DCS is around zero.

 

[dmaziuk]

I'm sure it is not lost on readers the very small range covered by the common decompression algorithms from 20-30 minutes, all quite safe. For a single dive at a GF high of 75, the risk of DCS is around zero.

"All sources agree" that it monotonically decreases with GF and thus as we decrease GF high below 75 the risk decreases to below "around" zero. Once pushed into negative numbers, it may in fact even protect the diver from future DCS on tomorrow's dive!

 

[goldfishtornado]

"All sources agree" that it monotonically decreases with GF and thus as we decrease GF high below 75 the risk decreases to below "around" zero. Once pushed into negative numbers, it may in fact even protect the diver from future DCS on tomorrow's dive!

The exponential decay curve decreases monotonically but also asymptotically towards zero. There's nothing mathematically that requires a monotonic curve to cross zero.