Capítulo 3 3 Análisis y diseño del sistema
4.3. Diagrama de componentes
Paul Bert’s hypothesis that bubbles caused DCS was central to Haldane’s theory, and he argued that DCS would not occur if bubbles could be avoided.3,5 Having noted that caisson workers were free from DCS if they decompressed to 1 ata from not more than 2 ata, he proposed that decompression would be bubble-free so long as the differ-ence between the dissolved nitrogen tension in tissue and the absolute pressure, the supersaturation, did not exceed a critical value. Haldane expressed supersaturation as the ratio of tissue nitrogen tension to ab-solute pressure and claimed that bubble-free decompression was possible as long as the supersaturation ratio did not exceed 2:1. He tested this hypothesis by exposing goats to high pressure followed by immediate decom-pression to a lower pressure. Within biologic variability, he convinced himself that decom-pression was safe from 2 to 1 atm, from 4 to 2 atm, and from 6 to 3 atm (Fig. 4–1).
53
Haldane had been impressed by the strong effect that dive duration had on DCS risk.
Alexander Lambert, a famous Siebe-Gorman diver, had safely salvaged £70,000 in gold from the wreck of the Alfonso during 33 dives at 162 fsw (48.6 msw) with bottom times of 25 min,3,8but on extending his dive to 45 min, he experienced paralysis from which he never fully recovered. According to the current U.S.
Navy tables,9Lambert’s 25 min dives needed 30 min of decompression while the 45 min dive needed 100 min of decompression.
Haldane thought that Lambert’s short dives were safe because he had absorbed insufficient nitrogen to exceed the 2:1 super-saturation ratio at which bubbles would form. This suggested to him that a diver would absorb nitrogen progressively while at depth as the circulation carried dissolved nitrogen from lungs to tissue, and he rea-soned theoretically that nitrogen was absorbed rapidly at the start of a dive but more slowly as the tissue nitrogen tension approached the alveolar partial pressure.
When these were equal, the diver was said
to be saturated with nitrogen at his current pressure.
Because diffusion distances between tissue capillaries are very small, Haldane thought that arterial nitrogen would diffuse into and completely equilibrate with nitro-gen in tissue and venous blood. Today, such tissue is described as well-stirred or perfusion-limited (Fig. 4–2, inset), with effec-tively instantaneous diffusion of nitrogen between blood and tissue.10Blood flow is the sole determinant of inert gas exchange in a perfusion-limited tissue. Without formal mathematics, Haldane showed that perfusion-limited tissue could be characterized by a half-time that defined the tissue’s rate of sat-uration (or desatsat-uration) such that the dif-ference between the arterial tension and the tissue (or venous) nitrogen tension was reduced by half with each passing half-time (see Fig. 4–2). Thus, a tissue would be 50%
saturated (or desaturated) in one half-time, 75% saturated in two half-times, 87.5% satu-rated in three half-times, and so on until sat-uration or desatsat-uration was effectively complete (98%) after about six half-times.
6 5 4 3 2 1 0
2
4
6
Sea level 2/1 = 2
4/2 = 2
6/3 = 2
2
3
Time Absolute pressure (ata) 1
Figure 4–1. Derivation of Haldane’s 2:1
supersaturation ratio rule. Goats were exposed for 4 hrs at various pressures before ascent to a lower pressure. Decompression sickness did not occur if the initial pressure was less than two times the final pressure.
well-stirred tissue 100
80 60 40 20
00 1 2
Time (tissue half-times)
% Saturation
3 4
93.75%
87.5%
75.5%
50% Arterial blood
Venous blood
Figure 4–2.Absorption of nitrogen as a function of time as measured in tissue half-times. The half-time defines the rate of nitrogen exchange in well-stirred tissue (see inset).
The Mathematics of Nitrogen Exchange in Perfusion-Limited Tissue.
In describing nitrogen exchange in perfusion-limited tissue, the venous (PvN2) and tissues (PtN2) nitrogen tensions are assumed equal to represent rapid diffusion between closely spaced capillaries. A mass balance for nitrogen is given by
(N2)stored= (N2)in– (N2)out
The mass balance is illustrated in Figure 4–3 in which nitrogen enters with the arterial blood at a tension equal to the alveolar nitrogen partial pressure (PAN2) and leaves with the venous blood where αb and αtare the nitrogen solubilities in blood and tissue, Q is blood flow and Vt is the tissue volume. In this example, PaN2 is assumed to change instantaneously to a constant value, Pa, at a time, t, equal to zero.
Haldane postulated that the tissues of the body have different perfusion rates that he represented by half-times of 5, 10, 20, 40, and 75 min (Fig. 4–4, inset). Tissues with shorter half-times saturated (or desaturated) faster than those with longer half-times (see Fig. 4–4). The longest tissue half-time deter-mined the exposure for which the entire body reached equilibrium (saturated) with atmospheric nitrogen after a change in pressure.
The behavior of Haldane’s five-tissue model is illustrated in Figure 4–5 for a 4 min dive on air to 168 fsw (50.4 msw), with descent and ascent at 5 fsw/min.3To simplify his calculations, Haldane assumed air to be
100% nitrogen. Tissue with a 5 min half-time is nearly saturated by the end of the bottom time and begins to desaturate immediately on ascent. Slower tissues continue to absorb nitrogen during initial ascent.
These ideas led Haldane to conclude that the accepted method of slow linear ascent was both unsafe and unnecessarily long. He called his alternative method stage decom-pression in which a rapid initial ascent at 30 fsw/min (9 msw/min) was followed by increasingly longer stages or stops as the diver approached the surface. Figure 4–6 compares stage decompression with uniform ascent at 3.5 fsw/min for a 16 min dive to 168 fsw (50.4 msw). Nitrogen exchange in The Mathematics of Nitrogen Exchange in Perfusion-Limited Tissue—cont’d.
The rate of change of PtN2defines the rate at which nitrogen is stored in the tissue.
Thus,
αt*Vt*dPt/dt = αb*Q.
*PaN2– αb*Q.
*PVN2 dPt/dt + k*Pt= k*Pa
k = αb*Q. /αt*Vt The solution to Equation 4–1 is
Pt(t) = Pa*[1 – exp(–k*t)] + P0*exp(–k*t) where P0is the initial N2tension and the tissue half-time is
T1/2= 0.693/k = 0.693/(ab*Q. /at*Vt)
Pt(t) in Equation 4–2 is the sum of the decay in the initial nitrogen tension and the response to a step change in PAN2as illustrated in Figure 4–3.
(4-1)
(4-2) and
where
αt
Vt
PtN2
αb
Q PaN2
⭈ αb
Q PvN2
⭈
t
Pa*(1 – e–k*t)
P0* e–k*t Pa
P0 PtN2(t) = P0* e–k*t+ Pa*(1 – e–k*t) t1/2 = 0.693 αtVt k
αbQ⭈ k =
Figure 4–3.The mathematics of nitrogen exchange in a well-stirred tissue (see text).
tissue with a 20 min half-time is shown for both methods of ascent. (The other tissues are omitted for clarity.) With stage decom-pression, rapid initial ascent avoids the addi-tional nitrogen uptake that occurs with slow linear ascent. The stages were chosen so that
the 2:1 pressure ratio was never exceeded in any tissue. Stage decompression allowed the diver to surface with a 2:1 pressure ratio in a 20 min tissue, whereas with linear ascent, the pressure ratio was 3:1.
Haldane published two tables of stage decompression schedules.3,5 The first was for short dives as deep as 204 fsw (62.5 msw) with decompression times of up to 30 min.
This table proved very successful for the short, deep dives that were typical for the unpredictable waters of the British Isles and virtually eliminated DCS, but with experi-ence, the deeper decompression stages were judged to be unnecessary. This is illus-trated in Figure 4–8A for a 40 min dive to 100 fsw (30 msw) with decompression according to the Haldane and U.S. Navy schedules.9 The first stop of the Haldane schedule is at 30 fsw (9 msw), whereas that of the U.S. Navy schedule is at 10 fsw (3 msw). The total stop times are 15 min for the U.S. Navy schedule and 30 min for the Haldane schedule.
Time (min) 5
Lung min 10 min
20 min
40 min
75 min
5 min
10 min
20 min 40 min
75 min 100
80 60 40 20
00 10 20 30 40 50 60 70
% Saturation
Figure 4–4.Nitrogen exchange in the human body as defined by Haldane’s five parallel well-stirred tissues (see inset). Tissue half-times are indicated in minutes.
5 fpm
5 fpm 168 fsw for 4 min
5 min 10 min
20 min
40 min 75 min
0 20 40 60 80
Time (min)
Figure 4–5. Nitrogen uptake and elimination from the five Haldane tissues during a 4-min dive to 168 fsw (51.4 msw). Ascent and descent are at 5 fsw/min.
What Îs the Half-time of the Slowest Tissue in the Body?
If tissues are 98% saturated (equilibrated with alveolar nitrogen) in six half-times, a 5 min tissue is nearly saturated in 30 min and 75 min tissue is nearly saturated in 7.5 hrs. The slowest tissue used to calculate the U.S. Navy dive tables was 120 min, and these tables consider a diver to be “clean” (free of excess nitrogen) at 12 hrs after a previous dive11,12. As 24–48 hrs is believed to be long enough to saturate the body with inert gas during a saturation dive (Chapter 6), this would imply that the slowest tissue half-times are on the order of 240–480 min. Thus, Neo-Haldanian decompression theories with tissue half-times as long as 1,440 min13would not appear to represent perfusion-limited inert gas exchange and may suggest other physiologic mechanisms.
6 5 4 3 2 1
0 20 40
Time (min)
60
Depth (fsw)
Nitrogen partial pressure (atm)
3.5 fpm 168 fsw for 16 min
30 fpm
20 min tissue
150
100
50 33 0 2:1 ratio
Figure 4–6. Comparison of slow uniform ascent and stage decompression. The nitrogen tension in the tissue with the 20-min half-time is higher after uniform ascent than after stage decompression.
Haldane’s second table was for dives with bottom times longer than 1 hour and with more than 30 min of decompression.
Figure 4–8B shows the Haldane and U.S. Navy schedules for a 120 min dive at 100 fsw (30 msw). The first Haldane stop is at 40 fsw
(12 msw), whereas the first U.S. Navy stop is at 30 fsw (9 msw). The Haldane schedule is 81 min long, whereas the U.S. Navy schedule is 131 min long. The decompression sche-dules of Haldane’s second table proved too short to prevent DCS.
Linear Ascent and Stage Decompression a Century Later.
A modern experiment by Broome in 1996 appears consistent with Haldane’s stage decompression theory14. Broome dived two groups of 20 pigs to 200 fsw (60 msw) for 25 min (Figure 4–7). One group decompressed at a linear ascent rate of 20 fsw/min (6 msw/min) while the other group ascended in two phases, at 60 fsw/min (18 msw/min) until reaching 110 fsw (33 msw) and at 12.9 fsw/min (4 msw/min) to the surface. Both groups reached the surface in 10 min, but with uniform ascent, the DCS incidence was 55%
while with the bi-phasic ascent, the incidence was 25%. The difference was nearly significant at p=0.053. These results (Figure 4–7) are consistent with the Haldane theory illustrated in Figure 4–6.
200
150
100
50
0
0 5 10 15
Time (min)
30 25 20
Depth (fsw) 25% DCS
in 20 pigs
55% DCS in 20 pigs 60 fpm
110 fsw
12.9 fpm 20 fpm
Figure 4–7. A comparison of the DCS incidences in pigs for uniform ascent at 20 fsw/min (fpm) with biphasic ascent at 60 fsw/min to 110 fsw (33 msw) and 12.9 fsw/min to sea level.
0 min 15 30
10 fsw USN
Haldane 30 fsw
100 fsw for 40 min
0 min 81 131
40 fsw USN
Haldane 30 fsw
100 fsw for 120 min
A B
Figure 4–8.A. A decompression schedule from Haldane’s first table5. Schedules from this table have deeper first stops and more decompression time than corresponding U.S. Navy schedule9. B. A decompression schedule from Haldane’s second table. Schedules from this table have deeper first stops but less decompression than corresponding U.S. Navy schedules.