fundamentals of decompression - umd

Fundamentals of DecompressionENAE 697 -Space Human Factors and Life Support

U N I V E R S I T Y O FMARYLAND

Fundamentals of Decompression

• History• Tissue models

– Haldane– Workman– Bühlmann

• Physics of bubbles• Spacecraft cabin atmospheres

© 2009 David L. Akin - All rights reservedhttp://spacecraft.ssl.umd.edu

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Caissons

• Pressurized chambers for digging tunnels and bridge foundations

• Late 1800’s - caisson workers exhibited severe symptoms– joint pain– arched back– blindness– death

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Brooklyn Bridge• Designed by John Roebling,

who died from tetanus contracted while surveying it

• Continued by son Washington Roebling, who came down with Caisson Disease in 1872

• Competed by wife Emily Warren Roebling

• 110 instances of caisson disease from 600 workers

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Decompression Sickness (DCS)

• 1872 - Dr. Alphonse Jaminet noted similarity between caisson disease and air embolisms

• Suggested procedural modifications– Slow compression and decompression– Limiting work to 4 hours, no more than 4 atm– Restricting to young, healthy workers

• 1908 - J.B.S. Haldane linked to dissolved gases in blood and published first decompression tables

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Supersaturation of Blood Gases

• Early observation that “factor of two” (50% drop in pressure) tended to be safe

• Definition of tissue ratio R as ratio between saturated pressure of gas compared to ambient pressure

• 50% drop in pressure corresponds to R=1.58(R values of ~1.6 considered to be “safe”)

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R =PN2

Pambient= 0.79 (nominal Earth value)



Tissue Models of Dissolved Gases

• Issue is dissolved inert gases (not involved in metabolic processes, like N2 or He)

• Diffusion rate is driven by the gradient of the partial pressure for the dissolved gas

where k=time constant for specific tissue (min-1)P refers to partial pressure of dissolved gas

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dPtissue(t)dt

= k [Palveoli(t)− Ptissue(t)]



Solution of Dissolved Gas Differential Eqn.

• Assume ambient pressure is piecewise constant (response to step input of ambient pressure)

• Result is the Haldane equation:

• Need to consider value of Palveoli

where Q=fraction of dissolved gas in atmosphere ΔPO2=change in ppO2 due to metabolism

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Ptissue(t) = Ptissue(0) + [Palveoli(0)− Ptissue(0)](1− e−kt

)

Palveoli =(

Pambient − PH2O +1−RQ

RQPCO2

)Q

Palveoli = (Pambient − PH2O − PCO2 + ∆PO2)Q



Linearly Varying Pressure Solution

• Assume R is the (constant) rate of change of pressure - solution of dissolved gases PDE is

• This is known as the Schreiner equation • For R=0 this simplifies to Haldane equation• Produces better time-varying solutions than

Haldane equation• Easily implements in computer models

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Pt(t) = Palv0 + R

(t− 1

k

)−

(Palv0 − Pt0 −

R

k

)e−kt



Tissue Saturation following Descent

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Tissue Saturation after Ascent

10



Effect of Multiple Tissue Times

11



Haldane Tissue Models

• Rate coefficient frequently given as time to evolve half of dissolved gases:

• Example: for 5-min tissue, k=0.1386 min-1

• Haldane suggested five tissue “compartments”: 5, 10, 20, 40, and 75 minutes

• Basis of U. S. Navy tables used through 1960’s• Three tissue model (5 and 10 min dropped) • 1950’s: Six tissue model (5, 10, 20, 40, 75, 120)

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T1/2 =ln (2)

kk =

ln (2)T1/2



Workman Tissue Models

• Dr./Capt. Robert D. Workman of Navy Experimental Diving Unit in 1960’s

• Added 160, 200, 240 min tissue groups• Recognized that each type of tissue has a

differing amount of overpressure it can tolerate, and this changes with depth

• Defined the overpressure limits as “M values”

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Workman M Values• Discovered linear relationship between partial

pressure where DCS occurs and depth

M=partial pressure limit (for each tissue compartment)M0=tissue limit at sea level (zero depth)ΔM=change of limit with depth (constant)

d=depth of dive

• Can use to calculate decompression stop depth

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M = M0 + ∆Md

dmin =Pt −M0

∆M



PADUA (Univ of Pennsylvania) Tissue ModelTissue T1/2 (minutes) M0 (bar)

1 5 3.0402 10 2.5543 20 2.0674 40 1.6115 80 1.5816 120 1.5507 160 1.5208 240 1.4909 320 1.490

10 480 1.459

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Bühlmann Tissue Models• Laboratory of Hyperbaric Physiology at

University Hospital, Zurich, Switzerland• Developed techniques for mixed-gas diving,

including switching gas mixtures during decompression

• Showed role of ambient pressure on decompression (diving at altitude)

• Independently developed M-values, based on absolute pressure rather than SL depth

• “Zurich” 12 and 16-tissue models widely used

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Bühlmann M-Value Models• Modifies Workman model by not assuming sea

level pressure at water’s surface

Pamb=pressure of breathing gasb=ratio of change in ambient pressure to change in tissue pressure limit (dimensionless)a=limiting tissue limit at zero absolute pressure

• ZH-L16 model values for a and b

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M =Pamb

b+ a

a = 2 T− 1

31/2 < bar > b = 1.005− T

− 12

1/2



Physics of Bubbles

• Pressure inside a bubble is balanced by exterior pressure and surface tension

where γ=surface tension in J/m2 or N/m (=0.073 for

water at 273°K)

• Dissolve gas partial pressure Pg=Pamb in equilibrium

• Gas pressure in bubble Pint>Pamb due to γ

• All bubbles will eventually diffuse and collapse

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Pinternal = Pambient + Psurface = Pambient +2γ

r



Critical Bubble Size

• Minimum bubble size is defined by point at which interior pressure Pint = gas pressure Pg

• r<rmin - interior gas diffuses into solution and bubble collapses

• r>rmin - bubble will grow • r=rmin - unstable equilibrium

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rmin =2γ

Pg − pambient



Bubble Formation and Growth

• In equilibrium, external pressure balanced by internal gas pressure and surface tension

• Surface tension forces inversely proportional to radius

20



“Clinical” Discussion of DCS

• Tissue models are predictive, not definitive• Every individual is different

– Overweight people more susceptible to DCS– Tables and models are predictive limits - there will be

“outliers” who develop DCS while adhering to tables

• Doppler velocimetry reveals prevalence of bubbles in bloodstream without presence of DCS symptoms - “asymptomatic DCS”

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Implications of DCS in Space Flight

• Drop from sea level pressure to ~4 psi, 100% O2 pressure– Equivalent to ascent from fully saturated 120 ft dive – Launch in early space flight– Extravehicular activity from shuttle or ISS

• To have “safe” (R=1.4) EVA from shuttle requires suit pressure of 8.2 psi

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R =PN2

Pamb=

14.7(0.78)4

= 2.87



Current Denitrogenation Approaches

• Depress to 10.2 psi for 12-24 hours prior to EVA– Full cabin depress in shuttle– “Campout” in air lock module of ISS

• Exercise while breathing 100% O2• In-suit decompression on 100% O2 (3.5-4 hours)

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Historical Data on Cabin Atmospheres

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from Scheuring et. al., “Risk Assessment of Physiological Effects of Atmospheric Composition and Pressure in Constellation Vehicles” 16th Annual Humans in Space, Beijing, China, May 2007



Spacecraft Atmosphere Design Space

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Effect of Pressure and %O2 on Flammability

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from Hirsch, Williams, and Beeson, “Pressure Effects on Oxygen Concentration Flammability Thresholds of Materials for Aerospace Applications” J. Testing and Evaluation, Oct. 2006



Atmosphere Design Space with Constraints

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Constellation Spacecraft Atmospheres

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fundamentals of decompression - umd

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