Computing the Probability of DCS

[Mike Boswell]

I downloaded and read DAN’s 2008 Annual Diving Report. On Page 37 the report describes a dive made by a 37 year old male to a depth of 141 fsw with a rapid ascent and a missed 5-minute decompression stop. The diver was put on oxygen for 30 minutes on the boat, and did not suffer any symptoms. The report goes on to say:

“The conditional probability for DCS (Pdcs) for this dive was 1.03%. Pdcs estimates the likelihood that DCS will occur given the time-depth profile of the previous profile including the residual effects of all prior exposures to depth since the last 12 hour surface interval.”

As an engineer, I am intrigued by the math aspect of this, and I wonder if anyone can answer some questions:

1. How is this DCS probability Pdcs calculated? Is there a formula for this?

2. By how much did the administration of oxygen reduce Pdcs?

3. What is the accepted maximum Pdcs for recreational divers?

 

[Dr Deco]

Hi Mike:

​

You certainly have sent in a very interesting question, some aspects of which I will address here.


1. How is this DCS probability [Pdcs] calculated? Is there a formula for this?

The calculation is made based on calculated gas loading in the body using a Haldane model [i.e., compartments and halftimes]. These loads are compared to other dives in a large DAN data base that was collected over a couple of decades. The gas loads are tracked over a period of twelve hours to account for multiple dive scenarios. There is not, to my knowledge, a single formula that will give the result.

The calculation must compare "like-to-like" for the system to yield a reasonable answer. Thus, recreational divers perform short dives with little to no in-water decompression. Commercial divers with heavy equipment, surface-supplied air, and lengthy in-water decompression would need a different data base. This is understandable.

There is no direct allowance made for physical activity that would influence tissue micronuclei formation. [This is somewhat addressed when considering recreational diving, since it has several elements of similarity. There does not exist at present any method of allowing for musculoskeletal activity when the dives are so varied.] Because of several variables, a DCS percentage expressed to three significant figures is somewhat wishful thinking, but is here to distinguish 1% from 1.5% or 2%. Drs Dick Vann and Wayne Gerth [PhDs associated with DAN] refer to these as variables imponderables.

2. By how much did the administration of oxygen reduce Pdcs?

The DCS reduction is based on the tissue gas loads and these will be reduced by the addition of oxygen. This is assuming that all of the nitrogen is dissolved and not in bubbles as free gas. Again, the latter is an imponderable. Again, we do not really have three-figure accuracy here.

I can only say that oxygen gave the improvement they indicated; I am not able to perform the calculations myself.


3. What is the accepted maximum Pdcs for recreational divers?

It is zero. Experience dictates, however, that such is not strictly possible since some gas loading will produce DCS problems. Acceptable loads are balance between efficiency and safety. Clearly, some supersaturation gas loads are possible, since people ascend to altitude in airplanes everyday without DCS occurring.

Therefore, DCS from gas loading [as contrasted with AGE, for example] will probably never get lower than 1% in a printed table. Fortunately, in the real world, DCS in recreational divers is much less than 1%.

 

[gcbryan]

I read some figures (in one on Weinke's papers I believe) that suggested that there was a 1.7% chance (of DSC) on air at 100 fsw using a NDL of 20 minutes, 1% using 8 minutes and 5% using 45 minutes or something like that.

This was derived from some study. He also goes on to point out that DAN says that the real world reported numbers are a degree of magnitude lower than that but in a comparative sense it's still interesting as far as the relative numbers.

 

[Mr Carcharodon]

The 1.7% value is fairly consistent with the value reported by Workman for the Navy dive tables which used similar limits. But the incidence rate is going to depend on how DCS is defined.
Can anyone offer how DCS was defined for these studies?

It seems DCS can be anything from a "high" ultrasound bubble count, niggles, paralysis or death. But by lumping all of those together some of the significance of the term is lost.

 

[Dr Deco]

It is true that there is not a standard definition for DCS. However, it is never just the presence of Doppler-detectable bubbles. Some differences are clear:

[1] In the laboratory, subjects are very often given a test of pressure to confirm a diagnosis. This is not done in the field by recreational divers.

[2] Test subjects have little activity to mask mild DCS pain. In the field, DCS rates can be less because activity will divert attention from mild cases.

[3] Recreational divers under estimate DCS compared to laboratory subjects since novice SCUBA divers often believe - erroneously - that DCS will be very intense and painful. Laboratory subjects are coached to mention even very mild discomfort.

[4] Death is rarely an endpoint in SCUBA diving DCS. Curiously, death is the endpoint in most laboratory studies involving rats. While I have argued against this for decades, rat studies persist. It is death-as-an-endpoint that gave us so much bad work resulting in biochemical causes - and treatments for - decompression sickness.

 

[Gene_Hobbs]

There is an entire series of technical reports published by the US Navy how how this is done (They are also in our suggested reading list). I have not had time to scan the final numbered report (XII) yet so let me know if you get ready for it and I'll find it again. The final reports listed here are the data sets used. There is plenty more available if you want more but these should get you started. Enjoy!!

Statistically Based Decompression Tables. I. Analysis of Standard Air Dives: 1950-1970.
RRR ID: 3402

Statistically Based Decompression Tables. II. Equal Risk Air Diving Decompression Schedules.
RRR ID: 3403

Statistically Based Decompression Tables. 3. Comparative Risk Using U.S. Navy, British, and Canadian Standard Air Schedules.
RRR ID: 3404

Statistically Based Decompression Tables IV: Extension to Air and N2-02 Saturation Decompression.
RRR ID: 3405

Statistically Based Decompression Tables 5: Haldane-Vann Models for Air Diving.
RRR ID: 3406

Statistically-Based Decompression Tables. 6. Repeat Dives on Oxygen/ Nitrogen Mixes.
RRR ID: 3407

Statistically Based Decompression Tables. 7. Selection and Treatment of Primary Air and N2 - O2 Data.
RRR ID: 3408

Statistically Based Decompression Tables 8: Linear-Exponential Kinetics.
RRR ID: 3409

Statistically Based Decompression Tables IX: Probabilistic Models of the Role of Oxygen in Human Decompression Sickness.
RRR ID: 3410

Statistically Based Decompression Tables X: Real-Time Decompression Algorithm Using a Probabilistic Model.
RRR ID: 3411

Statistically Based Decompression Tables XI: Manned Validation of the LE Probabilistic Model for Air and Nitrogen-Oxygen Diving.
RRR ID: 3412

The Dive Profiles and Manifestations of Decompression Sickness Cases After Air and Nitrogen-Oxygen Dives. Volume 1: Data Set Summaries, Manifestation Descriptions, and Key Files.
RRR ID: 4975

The Dive Profiles and Manifestations of Decompression Sickness Cases After Air and Nitrogen-Oxygen Dives. Volume 2. Complete Profiles and Graphic Representations for DCS Events.
RRR ID: 4976

 

[Dr Deco]

Many thanks, Gene. [I do not notice any of Dr Wayne Gerth's work in the compilation, however.]

 

[Gene_Hobbs]

[I do not notice any of Dr Wayne Gerth's work in the compilation, however.]

Thanks for noticing... Since Keith has given me a hard time about this as well, I guess I should get on that. I am still waiting on Wayne to finish writing a few tech reports though. NAVSEA is just not giving them a break but they do owe all of us several reports including the summary of the new table development and the deep stops work.

One that I need to add soon is:
Gerth, WA, Vann, RD. Development of Iso-DCS Risk Air and Nitrox Decompression Tables Using Statistical Bubble Dynamics Models. NOAA, Office of Undersea Research, 1996; Final Report. RRR ID: 4602