*adjusted for dependency among 154 symptoms.
†B1 is constrained to be positive so its sampling distribution is skewed right, giving a standard error that is not entirely meaningful. It is better to use the standard error for ln(B1) to get confidence limits for ln(B1), and then exponentiate to get confidence limits for B1. For similar reasons, a z-score and p-value for H0: B1
= 0, do not make sense, since by definition B1 > 0. Values are provided based on ln(B1).
The regression equation to estimate the P(symptom resolution) is:
P(symptom resolution) = 1 / (1+exp(-(ln(P) – 1.510 + 0.795×AMB –
0.00308×Ts) / 0.478)), Eq. 22
where P is a real or computed input, AMB = 1 if ambulation took place during part of the altitude exposure, otherwise AMB = 0; and where Ts is the elapsed time at PB in min to onset of a DCS symptom. We consider Eq. 22 as a model since one source of P input comes from the TBDM even though Eq. 22 is simply a statistical regression equation optimized to empirical data.
Fig. 32 shows 4 curves from Eq. 22 for an ambulatory exposure where the subject reports a symptom at 60, 120, 180, or 240 min into the exposure. As the time to report a symptom increases the P(symptom resolution) at a particular P decreases.
Fig. 32. P(symptom resolution) for the ambulatory condition. The subject reports a symptom at a) 60 min, b) 120 min, c) 180 min, or d) 240 min into the exposure.
0 4 8 12 16 20 24 28 32 36 40
deltaP (psid)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (s y m pt om res o lu ti on)
a b
c d
Fig. 33 shows 4 curves from Eq. 22 for a nonambulatory exposure where the subject reports a symptom at 60, 120, 180, or 240 min into the exposure. As the time to report a symptom increases the P(symptom resolution) at a particular P decreases. Also, the
P(symptom resolution) is lower for the nonambulatory compared to the ambulatory condition at a given symptom onset time at a particular P.
Fig. 33. P(symptom resolution) for the nonambulatory condition. The subject reports a symptom at a) 60 min, b) 120 min, c) 180 min, or d) 240 min into the exposure.
We have no mechanistic explanation why the P(symptom resolution) for a given P and Ts is so much lower for the nonambulatory condition compared to the ambulatory condition.
However, a comparison of data in Table XIII does suggest why the regression performs as it does.
0 4 8 12 16 20 24 28 32 36 40
deltaP (psid)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (s y mp to m r e s o lu ti o n )
a b
c
d
Table XIII. Comparison of Ambulatory and Nonambulatory Symptom Data data ambulatory (n=100 symptoms) nonambulatory (n=54 symptoms) source historical testing (1983-1998) PRP testing (1999-2009) plus
historical AGRO testing
DCS cases 78 41
global DCS% 13% (78 / 591 exposures) 11% (41 / 378 exposures)
mean symptom time 142 ± 68 min 116 ± 41 min
Type I symptoms 93% (93 / 100 symptoms) 83% (45 / 54 symptoms) Type II symptoms 7% (7 / 100 symptoms) 17% (9 / 54 symptoms) GLO after symptom 38% (38 / 100 symptoms) 89% (48 / 54 symptoms) HBO after symptom 3% (3 / 100 symptoms) 31% (17 / 54 symptoms)
PRP – Prebreathe Reduction Program where exercise during PB was used to accelerate denitrogenation.
The global DCS incidence is about the same between the ambulatory (13%) and nonambulatory (11%) conditions, suggesting that the overall decompression stress is about equivalent between the conditions. However, of the 20 symptoms that were persistent or residual at site pressure, thus requiring subsequent HBO treatment, 17 were reported by 7 subjects tested in the nonambulatory condition, whereas only 3 were reported by 2 subjects that were
ambulatory. Considering that almost 2/3 of these symptoms (100/154) arose from testing of ambulatory subjects, it appears that symptoms arising from the nonambulatory condition would require greater P for resolution.
Fig. 34 shows the P(symptom resolution) for Ts = 120 min in the ambulatory (upper curve) and the nonambulatory (lower curve) condition. The 95% CLs, not accounting for dependency among the symptoms, show a greater range for the nonambulatory condition.
Fig. 34. Simulation with ambulatory (upper curve) and nonambulatory (lower curve) subject without accounting for dependency among symptoms, where Ts = 120 min. The figure
demonstrates the range of the 95% CLs without accounting for dependency among symptoms.
Finally, Fig. 35 shows the P(symptom resolution) for Ts = 120 min in the ambulatory (upper curve) and the nonambulatory (lower curve) condition. The 95% CLs, accounting for dependency among the symptoms, show a greater range for the nonambulatory condition when compared to the ambulatory condition and larger when compared to Fig. 34.
0 4 8 12 16 20 24 28 32 36 40
deltaP (psid)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (sym p to m r e so lu ti o n )
Fig. 35. Simulation with ambulatory (upper curve) and nonambulatory (lower curve) subject accounting for dependency among symptoms, where Ts = 120 min. The figure demonstrates the range of the 95% CLs after accounting for dependency among symptoms.
Simulations to Estimate P(symptom resolution)
Two simulations show the application of the treatment model (Eq. 22). Fig. 36 shows the time course of BGI growth and resolution calculated from Eq. 16 for a hypothetical treatment situation, in which a 120-min resting PB at 14.7 psia and a 6-min ascent to 4.3 psia on 100% O2
has reduced and continues to reduce PtisN2 (Eq. 17) through time. Pain occurs in an ankle at Ts = 60 min after the beginning of the ambulatory exposure (66 min from the start of ascent) with BGI = 15.0. A 30-min delay before repressurization then causes the BGI to increase to B1 = 21.8. Finally, the BGI reduces to B2a = 14.8 during a 15-min repressurization to 14.7 psia and continues to decrease to B2b = 11.2 during one hour of GLO breathing at 14.7 psia.
0 4 8 12 16 20 24 28 32 36 40
deltaP (psid)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (sym p to m r e so lu ti o n )
Fig. 36. Simulation of BGI growth at 4.3 psia and dissolution at 14.7 psia given a short PB with Ts = 60 min and 66 min from start of ascent.
In this example, the values of P needed to reduce the BGI from B1 to B2a, or from B1 to B2b may be obtained from Eq. 9 where V1 is the volume of a spherical bubble with radius R1 = 3
B1 m at the time just before repressurization interacting with a unit volume of tissue during the exposure at low pressure (P1 = 4.3 psia), and V2 is the new volume of a bubble with radius R2a = 3 BGIC mafter a change to a higher pressure (P2 = 14.7 psia) at the end of the
repressurization, or with radius R2b = 3 B2b m at the end of the subsequent GLO breathing.
Thus before repressurization, V1 = = 1,176,964.8 m3. Subsequently, V2 = = 370,255.0 m 3 at the end of repressurization or V2 = m 3= 159,167.1 m 3 after the 1-hr GLO treatment. Thus using Eq. 9 with P1 = 4.3 psia, the value of P needed to reduce the BGI from B1 to B2a (21.8 to 14.8) would be 9.37 psid and to reduce it from B1 all the way to B2b = 11.2 with repressurization followed by a 1-hr period of GLO would require a higher P to 27.5 psid.
Substituting these values of P into Eq. 22 with AMB = 1 and Ts = 60 min, we obtained
P(symptom resolution) = 0.94 (0.86 to 0.97) following the repressurization step to sea level and P(symptom resolution) = 0.99 (0.98 to 0.998) at the conclusion of the GLO breathing, at an