Spisni study

[UWSojourner]

Hey Daniel,

I would say the following about ISS:

1. It is clearly NOT the only variable on which DCS depends. Nobody ever stated that. So picking one quote from Dr. Mitchell (from among the literally thousands of posts on this deep stop topic spread across multiple forums) might not be a reliable indicator of the nuances of the topic.
2. ISS is clearly an important variable. Supersaturation is a condition of bubble formation so more supersaturation implies more bubble formation (all other things equal). So if you have profiles that are EXACTLY the same except for their distribution of stop time and one profile has 30+% more supersaturation exposure (as measured by ISS), I think it's fair to ask "what is this profile giving me that justifies the additional exposure"? In my opinion the only likely answer is "higher P(DCS)".
3. A fairer reading of what has been said is this: For similar profiles (same runtimes, same depths, same gases) that only vary by how they distribute the same stop time, ISS is a pretty good index of the relative decompression stresses between the profiles. Yes, you can come up with profiles where ascending to 1 fsw and spending all your time there will generate a lower ISS. But we have other reasons to believe that the "Ascend to 1-fsw and stop there" Deco Method is likely sub-optimal in most decompression settings so we're really not too interested in that method.
4. ISS is a principal "ingredient" in many decompression models, VPM included. So clearly it's not irrelevant. The US Navy believes the difference in supersaturation exposure is the most plausible explanation of the NEDU study results.
5. The simple ISS measure was predictive (i.e. gives the right signal) in both the NEDU study and the Spisni study. Blind luck? I doubt it.

If what you're saying is that ISS isn't perfect, then I would agree (and have said as much). But are you really trying to defend models that produce 30+% more supersaturation exposure for identical stop time? What do you believe the models are providing the divers in those situations that justifies the increased exposure?

 

[David Doolette]

So I ended up implementing the actual calculation. A few notes on the implementation:
* Integration is numeric, in 10s intervals during the dive, followed by 40s intervals for 1 hour after surfacing, and another 23 hours after that with 200s integration steps. The reason I'm having longer steps post dive is merely because I'm using code I had written before, were performance was important. Happy to calculate this again with 10s intervals throughout the dive + 24 hour surface time interval if you want, but it shouldn't make a difference.
* I'm using 9 tissues in this calculation with the following half-times: 2min, 5min, 10min, 20min, 40min, 80min, 120min, 240min, 480min. Again, this is what I had already implemented (I was implementing the RGBM). Happy to change it to ZHL16 tissues or whatever else if you think it's important. Tissues on- and off-gas proportional to the pressure differential in this calculation.

What I found was that which profile has the lowest ISS depends on how oxygen is considered in the calculation.

a) Ignoring oxygen alltogether (i.e. assuming oxygen partial pressure is 0atm in all tissues at all time):
* NEDU shallow profile: 9,684 atm s
* NEDU deep profile: 10,624 atm s
* NEDU bottom time, then ascending within a minute to the surface: 17,681 atm s

-> NEDU shallow best, followed by NEDU deep. No decompression worst by far.

b) Assuming oxygen partial pressures proportional to nitrogen partial pressures (ppO2 = ppN2 / 0.21):
* NEDU shallow profile: 55,022 atm s
* NEDU deep profile: 62,150 atm s
* NEDU bottom time, then ascending within a minute to the surface: 51,302 atm s

-> No decompression best, followed by NEDU shallow, with NEDU deep being the worst

All three have a descent of 3 minutes from 0 to 170 fsw, followed by 30 minutes bottom time at that depth. (I realize this thread is not about the NEDU dive profile or even air diving per se, I just use these as an example here)


So you are right that my intuition was incorrect here. I did not consider the oxygen window when I speculated about the outcome. I believe that this is because the oxygen window adds a non-linear factor to the supersaturation at a given time. The non-linearity comes from the fact that supersaturation is max(0, pressureGradient), and doing a staged decompression can keep more tissues in the 0-case (undersaturation). Hence ISS with oxygen window does not behave the way that I expected.




I'm not missing this point, that is exactly the point I'm making! Thank you for putting it into clearer words than I did. (my argument for this point was by contradiction, so I can see why it was a little obscured)

That being said, ISS by itself seems to be a comparably poor way of providing an indication of decompression stress, given that under the right circumstances it will tell you that going straight to the surface after 30 minutes at 170ft results in less decompression stress than a reasonably safe, staged decompression.



That is literally what he says in the quote I included in my post. Let me quote him here again:


He seems to be saying that for two dive profiles that differ only in their decompression staging, the one that has lower ISS has lower risk of DCS and vice versa. I'm not going to give you a mathematical proof about ordered sets here, but I'm pretty sure that Simon's statement that for any two decompressions A, B
ISS(A) < ISS(B) => P(DCS(A)) < P(DCS(B))
implies that there exists a monotonic function f, such that for any decompression x (from the same dive), we have
DCS(x) = f(ISS(x))

Hence ISS, according to Simon's statement, when taken literally, would indeed be the *only* thing that is important for the risk of DCS when it comes to choosing from a number of alternative decompression schedules for a given dive.

I'm pretty sure that Simon did not mean this. That's why I asked him to clarify how to exactly interpret this statement.

Hi Daniel, it has been a while since we chatted, or that I logged into SB. There is lot to answer in your posts. I am away diving, and I am waiting for my buddy to wake up so we can get out, so this might be overly brief and not completely thought through.

You suggestion that PDCS=f(ISS) and you could minimize f(ISS) to find an optimum decompression schedule is exactly how USN ‘gas content’ (as opposed to ‘bubble’) probabilistic decompression models work. However, the USN models are a little different than just the raw ISS. Instead of just SS, the function we use is:
w(Ptis-Pamb-Pthr)/Pamb
So there is a threshold term (Pthr) which is greater than zero in some compartments, and although this is not a particularly influential parameter (you can get good model fits without it), it does contribute to the models not giving large PDCS for e.g. a ski trip. There is weighting term (w). Also, it is ‘relative’ supersaturation (Pamb in the denominator) but this was chosen in the original work and we have stuck with it, although you can get good model fits without it. I did not use relative SS in the NEDU deep stops report to compare deep stops skew, because it penalizes deep stop schedules which skew the SS towards lower Pamb. The exact form of the function is less important than the fact that the models are calibrated by optimizing the parameters - Pthr, and the compartment half-time – by fit to a large database of dive profiles and outcomes. You are correct that the choice of half-times matter, e.g. if you had all very short half-times, that might favor deep stops. For all of these reasons, I have cautioned, and I think Kevin as heeded in stuff he has posted that the ISS needs to be used cautiously. First is to only compare dive profiles of the same length, and second is to use a broad and reasonable spread of half-times – and Kevin has been using the “standard” ZH-L16 collection, the same or similar to the algorithms we dive.


Moving on, I am curious about your finding that adding oxygen to your model made a no-stop dive the lowest ISS. Intuitively, that should not be the case (but we both know trying to intuit these things can be wrong), but I am not sure exactly what you mean (I don’t think you are using the term “oxygen window” correctly, but that is for another post). Are you treating some of the oxygen as if it where an inert gas, i.e. it can contribute to the ISS? That is appropriate (because all gases contribute to SS). A simple way to include oxygen is for it to be fixed value approximating PvO2 (venous PO2) in the Ptis calculation (that is common for USN models, using a value of about 0.18atm representing PvO2+PvCO2+PH2O). But I cannot think of why that would give the result you found. Is your equation PO2=PN2/0.21 a typo? It is not correct, and would result inappropriately large values for PO2, increasingly so with depth, which might be why you got the no-stop result.

Cheers

David

 

[Dr Simon Mitchell]

Hello Daniel,

My apologies for the late reply; I have been travelling solidly for the last couple of weeks.

Hi Simon, I am very confused by this statement. This cannot possibly be true. Otherwise we could get perfect decompression schedules for a given decompression time simply by optimizing the ascent for the lowest integral supersaturation. Decades of decompression research and comparative studies such as the NEDU deep stop study would have been pointless.

David has largely addressed this, and has made the point that ISS is applied in the way I suggested in some US Navy decompression models. Nevertheless, when I wrote the statement you quoted I should probably have qualified it in a way to mitigate overly-literal interpretations. There may be examples of application of the principle where it does not work as well as expected. Moreover, any assumption about the best way to plan decompression should be tested across the range of dive profiles which the plan is applied to, and sometimes unexpected results will arise. That is exactly what we are seeing now that we are getting around to actually testing the previous assumption that bubble models would produce the most efficient decompression. But as a general principle, I stand by what I said; and particularly in respect to ISS as a means of performing the sorts of comparisons (and drawing relevant conclusions) about the deep vs shallow stop approaches to decompression that have been debated across these forums.

David has made some points about your ISS calculations. They don't seem intuitively correct to me either; particularly the 5-fold increase you report for the same profiles when oxygen is included. Oxygen does not behave like an inert gas (by accumulating significantly in tissues); at least not at the inspired pressures we can tolerate during diving.

Simon M

 

[danielmewes]

Thank you UWSojourner and David for your responses. (enjoy your diving David!)

I'll clarify a few things David brought up:

However, the USN models are a little different than just the raw ISS. Instead of just SS, the function we use is:
w(Ptis-Pamb-Pthr)/Pamb

[...]
So there is a threshold term (Pthr) which is greater than zero in some compartments, and although this is not a particularly influential parameter (you can get good model fits without it)

I do think the Pthr term is relevant, even if it might not have as much impact in practice.

ISS as an integral merely over max(0, Ptis-Pamb) is a strictly linear operation within the area of positive tissue gradients, given that integration is linear and max(0, Ptls-Pamb) is linear in both inputs in the range where Ptls-Pamb>0. I still believe that in the positive gradient domain, you will get the lowest ISS value by going straight to the surface after any dive. I could be wrong, since I don't have a mathematical proof for it.

Here is my intuition for it though: If we ignore the fact that oxygen is different for a moment, and e.g. assume that the breathing gas is 100% inert, then upon reaching the surface, Ptls-Pamb_surface will always be positive for all compartments. For a non-saturation dive, we can avoid it getting positive for the slower compartments during part of the decompression, by staying at a depth where Pamb is lower than Ptis. However doing so would imply that those compartments are still on-gassing during those stops. Attributing for the gradient Ptis-Pamb_surface would merely be delayed until later in the decompression. And since we were on-gassing for longer, it would have gotten even worse at that point.

Having the Pthr changes the dynamics here, because "Ptls-Pthr-Pamb_surface will always be positive" no longer holds. You can now gain a meaningful advantage from introducing an intermediate stop where Ptis-Pthr-Pamb is still non-positive, but Ptis-Pamb is already positive, and hence you off-gas a compartment without incurring the "penalty" on the ISS. The more of your deco time you can spend in that region, the lower your total ISS will be.

Now I made another big assumption above "assume that the breathing gas is 100% inert", which obviously doesn't hold in reality. This brings me to your other point:

Moving on, I am curious about your finding that adding oxygen to your model made a no-stop dive the lowest ISS. [...] Is your equation PO2=PN2/0.21 a typo? It is not correct, and would result inappropriately large values for PO2, increasingly so with depth, which might be why you got the no-stop result.

(Edit: Actually the PO2=PN2/0.21 *was* a typo. It should have been Ptis=PtisN2/0.79, or PtisO2=PtisN2/0.79*0.21. Sorry for the confusion.)

Yes, absolutely right. It wasn't a typo, but another way of expressing the "assume that the breathing gas is 100% inert" assumption (in this case assuming oxygen behaved just like nitrogen). Obviously this isn't correct. The point I was trying to make (and probably didn't express very well), was that if ISS gives clearly bad predictions if oxygen behaved like an inert gas, then whatever predictions it makes if you assume that oxygen is different from an inert gas will depend extremely heavily on how exactly you model oxygen behavior and its contribution to deco stress.
I'm having a hard time expressing precisely why this bothers me, but it feels like ISS can be used to find the best profile that exploits oxygen-related inherent tissue undersaturation. But my observation put in doubt the predictive power that ISS has beyond a schedule that keeps tissues strictly undersaturated throughout the whole decompression (including subsequent surface time).

Now circling back to the points on Pthr above: Oxygen-related undersaturation has roughly the same effect as the introduction of Pthr on the dynamics of ISS.

If you get good correlation for ISS without any additional Pthr, then that might mean that using ISS to measure how well a dive profile exploits oxygen-related undersaturation is effective. I think the addition of data-fitted Pthr moves the model beyond that simplistic view, and makes sense to me. Though in the end, I would argue that this is creating "just another model", and there isn't anything universal or "inherently right" about ISS as an indicator of deco stress. Bubble model X with good correlation to dive outcomes might be used equally well to extrapolate deco stress to additional profiles outside the training/fitting data.
Does that sound fair to say?

 

[danielmewes]

Hi Simon, thanks so much for replying as well. I really appreciate the time that you, David and others spend on these forums to discuss topics like these.

David has made some points about your ISS calculations. They don't seem intuitively correct to me either; particularly the 5-fold increase you report for the same profiles when oxygen is included. Oxygen does not behave like an inert gas (by accumulating significantly in tissues); at least not at the inspired pressures we can tolerate during diving.

I hope my response to David that I just posted clears this up a bit. Let me know if it is still unclear.

I unfortunately can't publish the full source code that I used for the calculations, because I wrote the initial version with a friend during a company Hackathon and don't hold the full copyright on it. While I double-checked things a fair bit, it's certainly possible that there's some unintended bug in my calculations. I can try to rewrite it in an open format, but not sure when I'd have time for that. Note that the particular increase in ISS in the case of assumed-inert oxygen I think is expected, and doesn't indicate a bug.

 

[UWSojourner]

I still believe that in the positive gradient domain, you will get the lowest ISS value by going straight to the surface after any dive.

This isn't true even in the simplest case of air-only dives. Once the dive is long enough to get several compartments involved, you get a pretty dynamic problem. And you can find stops that reduce ISS.

Clearly ISS isn't the only thing to consider in a proposed decompression profile. But it is an interesting metric (under the kinds of limits Dr. Doolette discussed above), especially given the results of the NEDU study and the conclusion that the difference in supersaturation exposure was the best explanation of the results.

 

[huwporter]

At the very least, it should also be obvious that peak supersaturation 'might' be something you want to consider...

 

[David Doolette]

Hi Daniel

I can see how you might get the no-stop result if you assume 100% inert gas (as did Haldane), but I do not know if a no-stop dive will always give the lowest ISS (assuming 100% inert gas).

Now circling back to the points on Pthr above: Oxygen-related undersaturation has roughly the same effect as the introduction of Pthr on the dynamics of ISS.

In fact, typically (but not always) the optimized value for Pthr is equivalent to the value chosen for the “fixed" gases (PO2+PCO2+PH2O) so it takes you back to an inert gas only model. Any contribution of oxygen to decompression stress is not firmly established, but the experimental evidence to date leans towards oxygen having little or no contribution to decompression stress if breathed at the partial pressures typical in normal diving operations (see for instance
Weathersby PK, Hart BL, Flynn ET, Walker WF. Role of oxygen in the production of human decompression sickness. J Appl Physiol 1987;63:2380-7 and Doolette DJ, Gault KA, Gerth WA. Manipulating the duration and frequency of air breaks during oxygen-decompression did not identify a direct contribution of oxygen to decompression stress. Panama City (FL): Navy Experimental Diving Unit; 2017. Report No.: NEDU TR 17-13.)

If you get good correlation for ISS without any additional Pthr, then that might mean that using ISS to measure how well a dive profile exploits oxygen-related undersaturation is effective. I think the addition of data-fitted Pthr moves the model beyond that simplistic view, and makes sense to me. Though in the end, I would argue that this is creating "just another model", and there isn't anything universal or "inherently right" about ISS as an indicator of deco stress. Bubble model X with good correlation to dive outcomes might be used equally well to extrapolate deco stress to additional profiles outside the training/fitting data.
Does that sound fair to say?

Setting aside that there are some awful publications purporting to "correlate" bubble models with dive outcomes, this is a fair statement. ISS is just another model, and obviously not the “true model”. One of its attractions is it has fewer unknown parameters than bubble models which assume values for many unknowns. Since bubbles are the putative cause of DCS, a bubble model could potentially work better than a gas content model – if you can get the model structure right and find good values for the parameters, e.g. by optimization around right reliable diving outcome data. This is why the US Navy continues to pursue this approach. This gets to the motivation for including mechanism in models rather than using purely empirical functions.

David

 

[danielmewes]

Thanks David for the reference on effects of oxygen and your additional thoughts on ISS and bubble models. (and apologies for me taking such a long time to respond back)

I think we're on the same page (at least on a high level), and thanks for bearing with me through this conversation.

For what it's worth, my use of the term "correlation" in this context wasn't meant to reference any specific bubble models and/or methods for computing said correlation

We've had a similar discussion before, and you obviously have a ton more practical experience with this than I have, but I do still think that there's an appeal in reducing the number of *fitted* model parameters, even if it comes at the cost of increasing the number or parameters than can be derived through isolated in-vitro experiments (with surely simplistic assumptions when it comes to how those experimental outcomes transfer to a diver's body).

Of course this only works if the model dynamics themselves are close enough to the actual physiological processes. The further away a model gets from modelling real DCS risk dynamics, the more it will need to rely on fitted parameters in order to produce good results within the range of profiles that were covered in the training data (and results will start getting increasingly unreliable when extrapolating outside of the training set - different profiles, different gases etc.).

I believe I once suggested to you a "hybrid" approach, where an in-vitro / assumed value range could be used as a probabilistic prior within the optimization, while allowing some degree of data fitting to still occur in these parameters. This would potentially help decrease over-fitting, and increase the likelihood that the resulting model will extrapolate well to profiles outside of the training data set.

Anyway, happy to hear that the Navy is still pursuing multiple approaches! Looking forward to see what the future brings in deco model research. I'm still hopeful that we will eventually get to a place where the theoretical appeal of a physics-inspired model and empirical results from dive trials will once again match up.