Clinical Science (1971) 40,175-191.
G A S - I N D U C E D OSMOSIS A S A F A C T O R I N F L U E N C I N G
T H E D I S T R I B U T I O N O F B O D Y WATER
B . A. H I L L S
Department of Surgery, Duke University Medical Center, Durham, North Carolina
(Received 15 March 1970)
SUMMARY
1. Two methods have been used to determine whether differences in gas concentrations between adjacent regions of tissue can induce osmosis.
2. In a steady-state experiment water has been shown to move in the direction of
increasing gas concentration across gross sections of excised tissues such as bladder
and peritoneum.
3. In a second experiment it was found that more water was retained in subcutaneous pockets of saline saturated with a soluble gas (nitrous oxide or ethylene)
than was retained in a control pocket saturated with nitrogen and simultaneously
monitored in the same rabbit.
4. A value of the reflexion coefficient for nitrous oxide has been estimated from
the results of the experiments with the gross tissue sections and shown to be compatible with those known for non-gaseous solutes by extrapolation with respect to
molecular size.
5. The significance of possible osmotic effects due to transient gas concentration
gradients are discussed in connection with dry joints, aseptic bone necrosis in caisson
workers and inert gas narcosis, the approach offering a quantitative correlation of
narcotic potency by a simple physical mechanism.
6. The steady-state gas concentration gradients which arise in tissue as a result of
metabolism are suggested as a third driving force in homeostasis but, unless larger
reflexion coefficients can be demonstrated, this effect would only appear to be
significant for inspired oxygen partial pressures appreciably greater than normal.
Recent theories of fluid homeostasis in tissue continue to be based essentially upon Starling’s
hypothesis in which the two major parameters determining water retention by the interstitium are the transcapillary hydrostatic pressure and the colloid osmotic pressure (Reeve &
Guyton, 1967). However, the delicate balance between these opposing forces could be inCorrespondence: Dr B. A. Hills, Department of Surgery, Duke University Medical Center, Durham, North
Carolina, U.S.A.
175
176
B. A . Hills
fluenced significantly if there is also an osmotic pressure across the capillary wall generated by
a gas concentration differential. The latter could arise by virtue of the permanent total gas
tension difference known to exist between arterial blood and interstitial fluid (Hills & LeMessurier, 1969), or as a temporary effect following a change in breathing mixture or pressure.
Transient gas osmotic pressures have been obtained in vitro by Kylstra, Longmuir & Grace
(1968) employing a synthetic membrane specifically formulated to be less permeable to the gas
used than to water. ,However, similar selectivity needs to be demonstrated by sections of tissue
before local gas concentration differentials can be considered seriously as a factor influencing
the distribution of body water. Even if gases can be shown to induce an osmotic movement of
water across gross tissue sections, it must then be tested in vivo before being invoked as a possible third driving force for transcapillary water exchange or cellular dehydration.
Hence at least two experiments have been considered necessary. The first has been designed
to detect any selectivity in passing gases and water displayed by gross tissue sections, and the
second to determine whether the effect is significant at the capillary level since the walls of
capillaries are generally regarded as particularly permeable to all molecules of low molecular
weight.
METHODS
Gas osmometer
In view of the serious implications of a permanent osmotic water shift arising from the
natural gas unsaturation of tissue, any evidence of gas osmosis would be more significant if
demonstrated under steady-state conditions.
This has been effected by maintaining a steady gas concentration gradient across the aqueous
system of an osmometer consisting of a membrane separating two identical chambers holding
the aqueous fluid. The unit is shown in Fig. 1 . The gas gradient was maintained by placing
a source of a very soluble gas, and another of a relatively insoluble gas, at opposite ends of the
aqueous system, i.e. in contact with aqueous fluid at the faces of each chamber remote from
those holding the membrane. The sources consisted of compartments containing oil through
which each pure gas was bubbled, at the same pressure, and allowed to escape to atmosphere.
Thus each oil compartment was a source for one gas and a sink for the other, so maintaining
a large steady-state gas concentration gradient across the aqueous fluid and membrane by
virtue of selecting gases of widely differing solubility in water. The use of two gases provided
a convenient hydrostatic balance between the ends of the system.
Direct oil-water phase contact was preserved, yet the dispersion of oil and gas bubbles into
the aqueous phase was prevented by means of Millipore filters (0-45 p pore diameter). These
filter papers served to locate the boundary geometrically and to retain each phase by capillarity
provided they were first wetted with the olive oil before the aqueous chambers were filled.
A more rapid pressure response could be obtained if the filter papers were prevented from
distending by means of wire screen supports-as shown in Fig. 1.
The oil, and all gases bubbled through it, were saturated with water to prevent its loss from
the aqueous solution via the oil. The aqueous fluid placed in the chambers adjacent to the
membrane was physiological saline. Care had to be taken in filling the chambers with this
solution to avoid trapping bubbles, since these could undergo differential expansion and contraction depending upon the direction of the gas concentration gradient. Any leakage from the
aqueous system could be detected as a total fall in the heights of the fluid columns on either
Gas-induced osmosis
177
side of the membrane. The osmotic pressure was read as the difference between the heights of
the saline columns (HI). The gas connections were then interchanged between oil compartments. Invariably this reversed the displacement of aqueous fluid and the new reading was
recorded (Hz). About 12 h were needed to obtain a steady reading after starting or reversing
the process.
The membrane used was a thin section of tissue (0.2-1.5 mm) supported between two films
of reinforced silicone film of 0.025 mm thickness for mechanical support. When the two silastic
'
wire screen
\ '
VERY SOLUBLE
GAS
INSOLUBLE
GAS
FIG. 1. An osmometer in which a steady-state gas concentration gradient is maintained across
a tissue section by bubbling a soluble and a relatively insoluble gas through well-stirred oil
compartments in contact with opposite ends of the aqueous system. The aqueous fluid is physiological saline whose final difference in levels (H) is the osmotic pressure.
films were used alone, no fluid displacement could be induced by any pair of gases, these
including N,, N,O, CzH4, and air. This indicated that the osmotic pressures recorded in other
runs could only be attributed to the biological material present.
Tissue sections selected for this work were taken from the bladders of freshly-killed dogs and
the visceral peritoneum of dogs and rabbits after careful removal of the adhering muscularis.
Subcutaneous fluid pockets
In order to determine whether gas-induced osmosis is another factor to be considered in
applying Starling's hypothesis to a tissue, it is necessary to maintain a gas concentration
differential across the wall of the capillary. Blood will tend to equilibrate with interstitium as it
178
B. A . Hills
approaches the venous end, so that it is necessary to re-establish the concentration differential
before that blood is returned to the arterial system. Since the lungs provide a particularly
convenient ‘sink’ for intravascular gas, it is simpler to locate the ‘source’ of gas extravascularly. Moreover, this has the advantage that the same ‘sink’ can then be used for several interstitial ‘sources’ within the same animal, so that it is now possible to allow for any other
physiological disturbances simply by comparing the water retention properties of two regions
which differ only in the solubility of the inert gas used in each. This has been effected by the
subcutaneous injection of 50 ml of saline, saturated with nitrous oxide, into the abdominal
region of one side of a lightly-anaesthetized rabbit followed by 50 ml of nitrous oxide gas via the
same needle and insertion. Within 1 min the same procedure was repeated in a contralateral
site, injecting 50 ml of nitrogen-saturated saline followed by 50 ml of nitrogen. The rabbit was
then left prone in a perfectly symmetrical posture and maintained in a light plane of anaesthesia
by means of pentobarbital solution (1-2 ml of 1% Nembutal) administered through a vein in
the ear.
Before quantities were removed to be saturated with either gas, the saline was coloured with
patent blue violet which is a dye of very high molecular weight and therefore unlikely to diffuse
across membranes. Change in the relative concentration of dye in the saline/gas pockets gives
a measure of differential water movement. Thus it provided a particularly convenient index of
any gas-induced osmosis since the concentration of patent blue violet proved easy to measure
photometrically. At least this can be claimed provided that the gases have no physiological
action of their own.
The only alternative explanation to gas-induced osmosis which could be conceived for any
differential water retention was one of differential vaso-activity induced by the two gases, since
nitrous oxide may act as a very mild vasodilator (Collins, 1952). To mask any such pharmacological effect, a very strong vasodilator (lidocaine hydrochloride) was added to the saline at
a molar concentration equal to that of nitrous oxide in water saturated at 37”, i.e. as 0.2 g
Xylocaine per litre of saline. After saturating 100 ml volumes of the saline, one with nitrogen
and the other with the more soluble gas, they were checked for equal optical density before
injection of 50 ml from each.
An hour after injection 0.3-0.5 ml of fluid was removed from each subcutaneous pocket,
diluted ten-fold with clear saline and then placed in a spectrophotometer (Coleman model 6A)
for estimation of colour density. Setting the instrument range from 100% for the initial saline/
dye solution, similarly diluted, to 0% for the same dilution of saline and Xylocaine, but omitting the dye, readings N1 and S1 were taken for fluid recovered from pockets saturated with
nitrogen and the more soluble gas respectively. These were all recorded for the wavelength of
light to which the patent blue violet proved most sensitive. However, a complete survey of the
visible spectrum of each sample was made. Any trace of red contamination was taken as an
indication of the presence of blood introduced by chance damage of a vessel by the hypodermic
needles required to inject saline and remove samples.
Two hours after injection further samples of 0.3-0.5ml of fluid were removed, one from each
pocket, and measured photometrically as described for the 1 h samples. These readings were
designated N2 and S2 for fluid from pockets containing nitrogen and the more soluble gas
respectively.
If the more soluble gas was first used on the left-hand side and nitrogen on the right, this
order was reversed the next time that animal was used. A series of six runs were also performed
179
Gas-induced osmosis
in which the Xylocaine was omitted from the injection fluid saturated with the more soluble
gas, yet retained in the other. Both nitrous oxide and ethylene were used as the more soluble
gas, nitrogen being the control gas in all runs.
RESULTS
Gas osmometer
It was found, in runs using gross tissue sections, that the saline level rose on the side nearest
to the source of the more soluble gas and fell on the other. Occasionally the rise was negligible
(one run in four giving a movement of less than 1 mm), but these membranes generally revealed
pin holes upon subsequent examination. Two osmometers were used, these differing in the
length of the aqueous system (2L in Fig. I), and hence in the gas concentration gradient. Typical
results are given in Table 1 .
TABLE
1. Values for the osmotic pressure induced by one steady-stategas concentrationgradient produced by
diffusing a soluble and a relatively insoluble gas in opposite directions across a section of various tissues (Fig. 1);
Hz is the value for the first reversal of gases, while HBis that for the second reversal, i.e. when the directions are
the same as that for HI
Run
Tissue
Animal
More
soluble
gas
Peritoneum
Bladder
Peritoneum
Peritoneum
Peritoneum
Bladder
Peritoneum
Peritoneum
Peritoneum
Osmotic pressures
(mmHzO)
Less
soluble
gas
L
(mm)
Hi
Hz
H3
8.5
17.4
12.2
7.6
6.8
106
8.1
22.9
26.2
8.0
14.2
7.6
7.2
6.1
9.9
6.8
19.9
25.5
7.2
10.0
4.9
42
-
4.8
8.2
-
15.9
15.9
15.9
15.9
15.9
15.9
15.9
6.4
6.4
Estimation of reflexion coefjicient
The van’t Hoff equation would predict that a liquid equilibrated with a gas of solubility a,
at a partial pressure p , would exert an osmotic pressure up when separated from the pure
liquid by a. perfectly semi-permeable membrane, where a has dimensions of volume of gas
(reduced to S.T.P.) per unit volume of solution per atmosphere, i.e. a is the Bunsen coefficient.
However, most membranes are ‘leaky’, the best index of this imperfection being Staverman’s
reflexion factor (0). The significance of this dimensionless coefficient is fully described by
Davson (1964) but, essentially, a varies from 0 for complete permeability to a value of 1 for
perfect semi-permeability corresponding to all solute molecules being reflected by the membrane at its interface with the solution. Thus the actual gas osmotic pressure (I&) should be
given by :
Ilg = aap
(1)
where II, is expressed in the same units as p .
180
B. A . Hills
In the experiment employing the gas osmometer, it is difficult to estimate how much of the
total gas concentration difference between 'the outer ends of the aqueous system (Ac,) fell
across the membrane (thickness t ) . However, since tissue is very unlikely to be more permeable
than water to the same gas, the concentration gradient (Act/f) across the tissue should not be
lower than the average gradient, viz. Aca/(2L+ t), where L is the length of each aqueous compartment (Fig. 1) while Act and Ac, are the concentration differentials across the tissue alone
and across the whole aqueous system. Thus the application of equation (1) gives:
IIs = o,.Acts and os.Ac,, = o,aSpt/(2L+t)
where
os.Acts20s.Ac,, for the more soluble gas
and
II,
where
on.Act,, 2 on.Ac,,, for nitrogen.
= tsn.Actn and on.Ac,, = ananpf/(2L+t)
Also the total concentration differential of each gas across the tissue cannot exceed that
across the whole aqueous system (Act< Ac,) when the application of equation (1) gives:
II, = oS.Actsand oS.Acas= usasp
<
where
os.Acts us.Acas for
and
II,
where
o,,.
Act, Si on.Ac,, for nitrogen.
=
the more soluble gas
on.Act, and o,.Ac,, = tsnanp
The net gas osmotic pressure is given by AII, = II, - II,, since the gradients of the two gases
are in opposite directions. Since IT, 2 II,, and p = 760 mmHg, the four above expressions may
be combined to give the following limits for AII,:
760t(aSas- o,u,)
(2L f )
+
< AII, <760(0,a, - ~.,CL,)
The solubility of nitrous oxide exceeds that of nitrogen by some 40-fold (as/an= 40.6)
while, on the basis of their molecular weights of 44 and 28 respectively, on should exceed o, by
a much lower factor-less than 2. Hence onancan be ignored relative to oSusin the above
expression for determining the limits of osin terms of the experimentally-measured parameter
(An,) as:
w+wn,>
AH,
,as/
(3)
13.6 x 760taS
13.6 x 760as
,
where AHg is expressed in mmH,O, 13.6 being the specific gravity of mercury. The approximate value o f t was 1-5mm and CI,= 0.567 for N,O at 20". For this gas the results in Table 2
give :
A n , = R , = 9.4 mmH,O for L = 15.9 mm
A n , = R, = 24.6 mmH,O for L = 6.4 mm.
Substitution of these values in equation (3) gives:
0.0356 2 as>,0.00160 for L = 15.9 mm
and
0.0401 >, o,>0.00420 for L
=
6.4 mm
181
Gas-induced osmosis
The similarity between values for the upper limit indicates that this is likely to be much
closer to the true value. Taking the mean of the above values for this upper limit:
aG0.0378for N,O
(4)
Subcutaneousj h i d pockets
A total of twenty-four runs have been completed using six rabbits, each weighing 1.5-2 kg.
The light absorption readings of the diluted samples from pockets saturated with nitrogen
(N1 and N2) and the more soluble gas (S1 and S2) taken after 1 h and 2 h respectively are
recorded in Table 2. Where spectral analysis has indicated blood contamination, that result
has been ignored.
In all runs except one (No. 8), the recovered samples tended to be more dilute than the
TABLE
2. The amount of light absorbed by patent blue violet in samples removed from contralateral pockets in
the same animal but saturated with differentgases-expressed as a percentage of the light absorbed in the fluid
before injection
Light absorption as % of injected value
Soluble gas
Run
Rabbit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17*
18*
19*
20
21*
22*
23*
24
Mean
Standard deviation
Gas
2h
l h
Side
Differences
0-E)
N1
s1
N2
s2
L
L
L
L
R
R
93
100
98
b
93
99
99
101
94
92
99
98
89
95
97
99
94
b
98
93
99
97
95
96
96
98
94
91
92
100
99
100
90
94
99
93
90
94
98
97
96
99
96
95
96
96
93
94
90
99
95
b
b
98
96
102
91
88
96
96
86
87
95
92
84
b
93
85
94
91
85
94
92
96
88
84
90
98
97
100
84
89
96
92
b
85
95
90
88
92
89
87
89
86
82
92
-3
2
4
-2
3
7
1
-1
0
1
4
-2
0
5
-1
1
-1
2
-2
0
-1
2
7
-1
0
4
2
0
2
-4
2
-2
3
1
2
2
4
-2
5
5
3
2
96.27
95.42
92.34
90.48
0.818
2.174
1.800
2.668
R
R
L
L
L
L
R
R
R
R
L
L
L
L
R
R
R
L
-
-
-
-
N1-Sl
-
-
NZS2
-
-
* Xylocaine added only to the pocket containing nitrogen-saturatedsaline. b indicatescontamination by blood.
182
B. A . Hills
injected fluid (N and S<lOO). This dilution tended to be greater in the pockets containing
fluid saturated with the more soluble gas than in the others, i.e. N1 >S1 and N2>S2. Thus
(N1 - Sl) and (N2- S2) provide convenient indices for comparing the water retention properties of the more soluble gas relative to nitrogen after I and 2 h of absorption respectively.
These differences are given in Table 2.
Statistical analysis
The results in Table 2, comparing the two pockets in each animal at the same time, are
ideally suited for analysis by the ‘paired t’ test, since this largely eliminated variation between
animals and between different runs with the same animal. A statistical survey of the data
shows:
1. That 1 h after injection there was greater water retention by the more soluble gas in
thirteen out of twenty-two runs and vice versa in seven, the significance just reaching the 90%
level according to the ‘paired t’ test (I = 1.71). However, this is not considered significant by
many statisticians (Halstead, 1966).
2. That 2 h after injection there was greater water retention by the more soluble gas in
twelve out of twenty runs and vice versa in five. The same statistical test now indicates that the
99% significance level is exceeded ( t = 2.86).
3. Further analyses of the data using x2 and t tests show no significant correlation:
(a) between animals,
(b) between left and right hand sides (L and R in Table 2),
(c) between N,O and C2H4as the more soluble gas,
(d) between runs in which Xylocaine was added to one pocket only or to both.
DISCUSSION
The results of the experiment using the osmometer would seem to leave little doubt that
differential concentrations of gases can induce osmosis across gross sections of such tissues as
bladder and peritoneum. It is difficult to see how the effect can be an artifact in view of the
reversal of water movement when the gases were switched and the care taken to remove all
bubbles from the aqueous chambers before each run.
A figure of about 0.0378 for the reflexion coefficient of nitrous oxide is consistent with the
range to be predicted by extrapolating from known values of non-volatile solutes such as
0-37 for sucrose and 0.20 for glucose on the popular basis of solute radius (Davson, 1964)
although higher than the value of 0.024 for urea. Rather than attempting to determine accurate
absolute values for B , it is felt that the gas osmometer experiment should be considered qualitatively as demonstrating that these values are significant and hence that water movement by
osmosis must at least be considered wherever there is an appreciable gas concentration
gradient across tissue.
If the synovium also displays this effect, then gas-induced osmosis can provide a simple
explanation for the ‘dry joints’ experienced by divers during compression and upon reaching
maximum pressure (Hamilton, Macinnis, Noble & Schreiner, 1966). The high differential
concentration of blood gas produced by sudden increase in alveolar pressure could easily
induce an osmotic efflux of water from the synovial cavity before such gradients could be dissipated by diffusion. Moreover this effect should then be greater for more rapid compression-
Gas-induced osmosis
183
which is in agreement with the recent Naval practice of slow compression for very deep dives
in order to avoid excessivejoint pains-to which Fenn (1969) refers as ‘hyperbaric arthralgia’.
While the foregoing evidence would seem to provide good reason to suspect that gases can
induce osmosis across gross sections of tissues, the second experiment would indicate that this
may also apply to the capillary wall and hence to fluid homeostasis and the general clinical
problem of oedema formation. In all except one run, there was a dilution of the indicatorpresumably by pericapillary filtrate which would then carry away the dye macromolecules via
the lymphatics. This is consistent with a lower light absorption in samples collected from the
same pocket after 2 h than after 1 h (Table 2). The tendency for dilution to be faster on the side
saturated with the more soluble gas would indicate a greater net driving force for outward
filtration on that side. This cannot be attributed to differential vaso-activity of the gases since
the addition of an equal molar quantity of a strong vasodilator (Xylocaine) to the nitrogen side
showed no detectable difference from other runs (Table 2).
However, the differential increase in the driving force for transcapillary filtration could be
provided by an osmotic pressure induced by the higher concentration of gas in the interstitium
over that in the capillary, blood of the same composition being supplied to both pockets. It is
difficult to invoke any other explanation since the pockets differed only in the gas saturating the
fluid in each, so that the ‘paired t’ test provides a particularly sensitive statistical test of the
significance of the data obtained. The fact that this exceeded the 99% probability level for the
longer injection period must add strong support for including gas-induced osmosis as an
additional factor to be considered in determining fluid homeostasis.
Fluid homeostasis
In applying Starling’s hypothesis, the net gas osmotic pressure across the wall of the
capillary (An,) must now be considered along with the net hydrostatic pressure difference
(AP)and the net colloid osmotic pressure (AH,) along its length, to give the net pressure ( F )
for the outward filtration of water as:
F = AP-AIIc+AII,
(5)
where AH, could assume negative values if the intravascular concentration of gas exceeds that
in the interstitium.
This has many clinical implications which may be classified into two groups corresponding
to the two principal means by which a gas concentration differential can occur in vivo, these
being :
1. transient gradients of inert gases induced by a sudden change in pressure or the composition of the breathing mixture, and
2. steady-state gradients arising in tissue by virtue of metabolism.
Transient gradients. For a rapid compression to 200 ft in the ocean while breathing air, equation (1) would predict a gas osmotic pressure of 60cr, mmHg where 0, can have any value
between 0 and 1. Making the gross extrapolation from the polar solutes, for which reflexion
coefficients are quoted above in gross tissue sections, to the non-polar N2molecule by using
the value of cr = 0,0378 for N20, then A n , would be of the order of 2-25 mmHg. Relative
to a colloid osmotic pressure of 25 mmHg this would tend to induce a maximum water influx
of 9% in the capillaries.
184
B. A . Hills
If A l l g is significant for such rapid compressions, then one would anticipate a change in
haematocrit with change of pressure. While no record could be found of haemodilution upon
compression, there is definite evidence of haemoconcentration upon decompression, the
experimental values (Cockett, Nakamura & Franks, 1965;Heimbecker, Lemire, Chen, Koven,
Leask & Drucker, 1968) varying from 35% to below the 9% value estimated above using the
N 2 0 value for u.
The transient movement of water induced by inert gases could occur in any tissue, but those
of immediate interest to the hyperbaric field are bone, nervous tissue and synovium. The latter
has already been discussed in connection with ‘dry joints’.
Bone poses a particularly interesting case in view of its rigid structure and the absence of any
known lymphatic system. Any tendency for water to accumulate would therefore become
manifest as a pressure change rather than as oedema, the system acting more like an osmometer even though the medulla is being continuously perfused with blood. Gas-induced
osmosis has therefore been postulated as an aetiologic agent in the development of aseptic bone
necrosis (Hills, 1970) by which this disease can be attributed to the compression phase of hyperbaric exposure rather than a feature of decompression sickness. This approach is supported by
recent measurements which show an appreciable fall of intramedullary pressure upon compression, bearing no significant relation to changes in vascular pressures simultaneously
monitored (Harrelson & Hills, 1970). Moreover similar changes can be induced by intravenous
injection of alcohol-a strong osmotic agent whose excessive imbibement has often been
associated with ‘idiopathic’ cases of aseptic bone necrosis (Kelly, 1968).
Cellular membranes are generally regarded as more selective than the capillary wall (Landis
& Pappenheimer, 1963), and should therefore give higher reflexion coefficients. Thus compression could cause an appreciable movement of water across the myelin membrane, so tending to
dehydrate nervous tissue. It is known that osmotic concentration by such agents as mannitol
and glucose increases the resting potential and so decreases the activity of many neurones
(Hughes & Kerkut, 1965; Kerkut, 1969). These changes are often preceded by a momentary
fall in potential (more positive phase). Hence gas-induced osmosis could be a factor contributing to inert gas narcosis which is known to be more pronounced for greater exposure, use of
a more soluble inert gas (Miller, Paton & Smith, 1967) and more rapid compression (Bean,
1950). Each of these features should lead to a greater osmotic pressure differential tending to
dehydrate neurones at the time of reaching maximum pressure. A faster rate of compression is
compatible with enhanced narcosis on the basis of permitting less time for dissipation of the
gas concentration gradient by diffusion.
It may be argued (Kety, 1951) that diffusion coefficients for gross tissue sections, e.g. those of
Krogh (1918), are too large and hence diffusion is too rapid to permit any significant extravascular gradient of gases to be established. However, this need not apply in cells. Much lower
cellular diffusion coefficients have been recorded for various polar solutes (Fenichel & Horowitz, 1963) and for inert gases (Hills, 1967).
However, at the maximum exposure pressure, gas concentration gradients must eventually be
reduced to zero with subsequent return of cell water to its original distribution. This is consistent with the known amelioration of mental and physical impairment experienced by an airbreathing diver remaining at the exposure pressure, the narcosis reaching a maximum about 2
min after arriving at a depth of 300 ft (Case & Haldane, 1941).
There are many neurological aspects of inert gas narcosis with which any new hypothesis
Gas-induced osmosis
185
needs to be compatible. These have been summarized by Smith (1969) who emphasizes the
‘non-specificity’ of the narcotic gases which behave as general anaesthetics; ‘acting in all
neural areas’. Moreover, there appears to be ‘no pattern of chemical structure associated with
their potency’ and ‘their wide range of size suggests that they act not at a particular receptor
site but in some region which behaves superficially,as a bulk phase’. This is totally compatible
with a mechanism for narcosis based upon the overall dehydration of the nervous system
induced by osmosis. Moreover, the occasional momentary fall in resting potential, mentioned
above for dehydration induced by mannitol, could account for the transient state of hyperexcitability through which some subjects pass in being anaesthetized by gases.
Moreover, if gas-induced osmosis were truly the initiating mechanism, equation (1) predicts
that the narcotic potency of each gas should be proportional to acr. In other words, the same
degree of narcosis should be induced in the same subject by the same displacement of water
caused by the same net gas osmotic pressure (lIg)-whichever inert gas is used. Interpreting cr in
terms of effective molecular size (see Appendix) since larger solute molecules are more likely to
be reflected by membranes, equation (1) would predict that:
(6)
av(l+p)P, = K
where K is a constant for a given subject, P,, is the inert gas partial pressure for equal narcosis,
v is the true molecular volume of the inert gas and p is the fractional increase in that volume
caused by hydration in those gases known to be associated with water molecules when in
aqueous solution. In fact hydrate formation per se has been postulated as a mechanism for
gaseous anaesthesia (Pauling, 1961). However, upon this basis alone, it is difficult to correlate
the differences in narcotic potency between the gases such as He, Ne, H, and N2 which are not
hydrated at body temperatures.
Equation (6) can be tested by taking values of P,, from a list of equivalent ‘anaesthetic pressures’ compiled by Miller et al. (1967). This has been done in Table 3 for the truly inert gases
including CF, and SF,, since these have proven anomalous to many hypotheses for gaseous
anaesthesia. Most approaches have been tested semi-quantitativelyby defining a relevant index
of narcosis whose values are then used to predict the order of potency of the various gases.
One of the most popular of these indices (Meyer, 1937) is the fat/oil solubility ratio (R)which is
also shown in Table 3. It is seen that the osmotic index av(1 +p), offers a better prediction of the
order of potency of the gases, the only defect being the inability to differentiate between A and
CF,. However, the osmotic approach also offers a full quantitative correlation of narcosis by
predicting the absolute value of P,,. In Table 3 values of the constant (K)for equal narcosis
have been calculated for each gas. The standard deviation for these values is only f 17% which
is well within the likely error for values of P,, and v. The greatest deviation is that for argon
which can be partially eliminated by using a quoted value for this gas of a = 0.026 (Roth,
1967) in place of a = 0.0293 in Table 3, when av(1 +p)P,, = 13.28 compared with an average
of 11.05.
While it would seem reasonable to offer gas-induced osmosis as a possible explanation for
the transient component of inert gas narcosis, its time dependence restricts extrapolation of this
hypothesis to gaseous anaesthesia-despite the compatibility with the central nature of the
action of those agents. On that basis, one would need to predict that a patient anaesthetized
with nitrous oxide alone would regain consciousness after an hour or two unless the dose were
continuously increased. This would be necessary in order to maintain gas gradients rather than
P
190
110
85
35
24
19
6.9
3.9
1.1
04095
0.0109
0.0190
0.0141
0.0293
04043
0.0045
04492
0.102
2.30
2.58
2.32
3.53
2.86
(3.66)
(4.59)
3.14
3.24
6.37
8.99
6.54
23.03
12.25
25.68
54.02
16,21
20.94
11.37
8.61
2.09
1 68
3.1 1
2 39
11.50
avPn
1.9
-0.2
-0.2
1.1
0
0
0
0
0
0.74
4.59
4.59
2.21
4.22
1.79
2.02
3.00
5.39
5.12
16.74
57.78
9.96
16.67
k 17%
11.50
10.78
10.56
11.37
14.97
11.68
9.39
9.98
12.48
Oil/water
solubility (equ. 6)
index av(l+B)P.
Standard error
0.061
0.098
0.124
0.33
0.62
0.62
1.69
2.56
11.3
Hydration Osmotic
coefficient index
log(Ph)
B
av(l+b)
Values a and R are taken from Bennett (1969), while values of P. and Phare taken from Miller ef al. (1967),Ph being the hydrate
dissociation pressure of the gas at 0". Values of d are from Weast (1969).
Gas
Equinarcotic
Bunsen Molecular Molecular
pressure coefficient diameter volume
P n
a
d
V
(mmHg) (water 37")
(A)
(A3)
TABLE
3. The experimental narcotic potency of nine inert non-polar gases compared with the oil/water solubility ratio ( R )and the
osmotic index [av(l +b)] together with a test of the constant K (equation 6) for equal narcosis
z
r4
3
b
b
187
Gas-induced osmosis
absolute concentrations and so prolong the water displacement. However, in cases where the
normal partial pressure of inspired oxygen has been maintained, and anaesthesia therefore
induced by hyperbaric exposure to nitrous oxide, human subjects with constant body N,O have
been found to recover consciousness completely (Smith, 1967). Since these observations would
provide good reason for extending the osmotic hypothesis for inert gas narcosis to include
gaseous anaesthesia, much effort has been expended in this laboratory towards repeating this
hyperbaric work with a view to varying the rate of change of inert gas at a constant tension of
inspired oxygen. However, the study has been abandoned on account of hypoxia arising from
respiratory complications in the rabbits and rats used, sudden exposure to 1.7 atmospheres
N,O causing an 80% death rate in rabbits from pulmonary oedema-discussed later as another
possible manifestation of gas-induced osmosis.
If equal water displacement implies equal anaesthesia, then ethylene should exert about the
same osmotic pressure as nitrous oxide, or even slightly higher according to the data of Miller
et al. (1967), despite its much lower water solubility (a five-fold smaller) and lower oil/water
solubility ratio. This is compatible with the conclusions from both of the experiments described
above in which no significant osmotic difference between N20and C,H,could be found in runs
using either the gas osmometer or the fluid pockets in viva.
However, much more experimental work is envisaged to determine the magnitude of the
transient component to anaesthesia, and any further correlation with gas-induced osmosis,
since this offers such a simple physical explanation for the narcotic action of gases such as
neon and argon which are so inert chemically.
Steady-state gradients. A further implication of gas osmosis is that which could be induced
by steady-state gradients of the gases involved in metabolism-notably 0,and CO,. It has
been shown that the interstitium remains permanently unsaturated with respect to total gas in
the external environment (Hills & LeMessurier, 1969), this difference or inherent unsaturatian
being a function of the pressure arld composition of the breathing mixture. Moreover, these
studies, and those analysing subcutaneous gas bubbles (van Liew, Bishop, Walder & Rahn,
1965), indicate that the interstitium remains essentially at the venous tensions of the inspired
gases at normal atmospheric pressure. Thus a net gas concentration gradient can arise, and be
maintained, across the arterial end of the capillary if total concentrations in arterial and venous
blood are not equal, i.e.
Allg
=
oo,.ao,(Pven,o, -Par,o,)
+oco,.aco,(Pven,co,
-Par,co,)
+ Ani
(7)
where the last term (Ani)is included to allow for the shift in ions (chloride and bicarbonate)
arising by virtue of the difference in gas concentrations. If ocand ob are the reflexion coefficients
of chloride and bicarbonate while Cven,c and Cven,b are the venous concentrations and
Car,c and Car,b are the arterial plasma concentrations of chloride and bicarbonate respectively
in mEq/l then A l l i is given by:
A l l i = 17*02[a,(Cven,c- Caw) + o,(Cven,b- Car,b)] mmHg
(8)
Substituting typical values given by Comroe (1965) of Pven,co, = 53.1, Par,co, = 49.0,
Pven,o, = 40, Par,oz = 100 mmHg, Cven,c = 26.98, Car,c = 25.38, Cven,b = 97.87 and
Car,b = 99.32 mmol/l, while ao, = 0-0240and aco, = 0-568 to give:
Allg = 2.33OC02 - 1.44a0, +27*23~,-24*68~~b
(9)
188
B. A . Hills
Since each 6 term can have any value between 0 and 1, An, can have any value between
29.56 and -26.12 mmHg. However, making the gross assumption that
6COZ N 60,21 6,N 6 b N 6
then Ang=3.446 mmHg.
If 6 were as small as the value of 0.0378 indicated for nitrous oxide from the first experiment,
then A r I , ~ 0 - 1 3mmHg indicating that the permanent gas concentration gradient would be
almost negligible relative to an oncotic pressure of 25 mmHg. However, one of the reflexion
coefficients in equation (9) could well be appreciably higher than 0.0378, when All, would be
significant in determining body water distribution under steady-state conditions.
Although the estimated values of 6 for gases would appear to give permanent values of
Allg which are barely significant at the capillary level, the direction of the force is interesting.
According to equation (9), Angis likely to make a positive contribution to F in equation (2).
However, the reverse should hold in the lung. Since pulmonary capillaries are perfused with
systemic venous blood, and exchange gases with alveoli which are at essentially arterial gas
tensions, the permanent gas osmotic pressure would help to retain water within the vascular
system. Elevation of the inspired oxygen partial pressure would tend to reduce, or even reverse,
this pull. Thus gas-induced osmosis could be implicated as a possible factor contributing to the
pulmonary oedema associated with oxygen toxicity in the lung.
While steady-state gradients arising by virtue of metabolism could be tending to influence
the distribution of water, the total driving force is still small relative to the colloid osmotic
pressure. At least, this is true unless reflexion coefficients for O2 and CO, prove to be higher
than those estimated for N,O in the gas osmometer experiment. However, even using these
values, the inert gases should exert an appreciable transient driving force during rapid compression to pressures normally experienced by divers and caisson workers, causing a temporary
displacement of body water which could be potentially harmful in several tissues.
APPENDIX
Reflexion coeficients
In the expression for the gas osmotic pressure (equation l), the parameter not known for
most gases is the reflexion coefficient. Most theories of membrane permeability are based upon
the concept of 'pores' into which the smaller solute molecules tend to pass more easily and are
thus transmitted more readily (Davson, 1964). Thus, other factors being equal, as might be
anticipated with inert gases, the larger the molecule the greater the likelihood that it will be
reflected by the same membrane, i.e.
(10)
(TGCV'
where v' is the effective molecular volume. However, in aqueous solution many solutes are
hydrated, this hydration increasing their true molecular volume (v) by a fraction p, such that
v' = v(l +fi) when equation (10) gives:
6 =
(1 1)
kv(l+fi)
where k is a proportionality constant.
We know that gases such as He, Ne, H, and N, are not hydrated at 37" when /3
=
0 for these
189
Gas-induced osmosis
gases. Hence it would seem particularly significant that avP, for these gases is almost constant-see Table 3. If it is now assumed that the deviation of avP, for other gases is due to
hydration, then the value of this hydration coefficient @) necessary for exact correlation with
the mean value of 11.05 for the 'anhydrous' gases can be determined as [(ll~OS/avP,)-l].
However, when these values determined from Table 1 are tabulated alongside known values
for the dissociation pressure (PJ of their hydrates at 0" (Miller et al., 1967), it can be seen that
there is a direct correlation (Table 4). This must add strong support to the concept that the
TABLE
4. Correlation of the dissociated pressure (Ph)of the
gas hydrate at 0"with the deviationin avP, from the average
value for the non-hydrated gases (Table 3)
Gas
avP.
11.05
--
A
Kr
Xe
CF4
SFcj
8-61
3.11
2.39
2.09
1.68
0.28
2.55
3.62
4.31
5.58
avP,
B
log ('h)
1 *9
1-1
0
-0 2
-0.2
(from equ. 12)
0.74
2-21
422
459
4.59
Values of /3 are calculated from P, according to equation
(6) taking K = 11.05.
deviations in avP, for A, CF,, SF6, Kr and Xe can be attributed to hydration. Moreover,
a regression line can be calculated from the data in Table 4 as:
j? = 4.22- 1.83 log(Ph)
(12)
This empirical expression can then be used to calculate j? for any gas-including those used
in determining the regression line. These theoretical values can then be used in Table 3 to
determine the osmotic index av(1 +p).
This use of experimental data to determine an empirical relationship (equation 12) from
which values of j? are then calculated and fed back into the analysis of the same data (Table 3)
does not really constitute circular reasoning. However, the extraction of the constants 4.22 and
1.83 for use in equation (12) does reduce the number of degrees of freedom of the analysis by
two. This has the significance equivalent to having tested only seven gases rather than nine in
Table 1 and finding them all to agree within a standard error of & 17%.
Alternatively, equations (2) and (12) can be combined to give:
aPJ5.22- 1.83 log(PJ1 = K-11.05
when it may be claimed that this empirical expression is found to correlate the narcotic potency
of nine inert non-polar gases with their physical properties by means of a parameter consistent
with gas-induced osmosis.
Molecular volumes
Molecular diameters could be found for all gases listed in Table 3 except CF, and SF6.
However, rough estimates sufficient for ascertaining the order of narcotic potency on the basis
of the osmotic index, can be determined from consideration of bond lengths.
190
B. A . Hills
The diameter (d,) of the unassociated SF, molecule should be given by:
d , %2(S-F)
+(F-F)
where S-F and F-F are the sulphur to fluorine and fluorine to fluorine inter-nuclear distances
for covalent bonding. Standard chemical tables (Weast, 1969) give: S-F = 1.585 8, and F-F =
1.42 A when d, = 4.59 A. The actual value is likely to be higher, which would improve the
correlation for this gas in Table 1.
The diameter (d2)of the unassociated CF, molecule should be given by:
d,
=
(C-F)Jw)+(F-F)
where C-F is the inter-nuclear distance of the carbon to fluorine bond and 0 is the bond
angle of the carbon tetrahedron. Standard chemical tables (Weast, 1969) give C-F = 1-36 A
and 0 = 110” when d2 = 3.66 A.
EQUATION 1
n
=
on’
(4
by definition, where II is the actual osmotic pressure, IT is the theoretical osmotic pressure for
the same solution separated from its solvent by a perfectly semi-permeable membrane, and o
is the reflexion coefficient.
A solution with a tension p (mmHg) of a gas with a Bunsen coefficient ci contains cip/760
ml of gas (S.T.P.) per ml of solution or 22.4mp/760 litres of gas (S.T.P.) for 22.4 litres of solution, i.e. cip/760 moles of gas per 22.4 litres of solution. But 1 mole in 22.4 litres gives II’ = 1
atmosphere = 760 mmHg. Hence cip/760 moles in 22.4 litres gives II’ = cip.
Hence
rI
= oap
(equation 1)
provided II and p are expressed in the same units (as detailed in paper).
REFERENCES
BEAN,J.W. (1950) Tensional changes of alveolar gas in reactions to rapid compression and decompression and
question of nitrogen narcosis. American Journal of Physiology, 161, 417425.
BENNEW,
P.B. (1969) Inert gas narcosis. The Physiology and Medicine of Diving (Ed. by P. B. Bennett and D. H.
Elliott), chap. 7. Bailliere, Tindall & Cassell, London.
J.B.S. (1941) Human physiology under high pressure. Journal of Hygiene, 41,225-249.
CASE,E.M. & HALDANE,
J.J. (1965) Recent findings in the pathogenesis of decompresCOCKEW,A.T.K., NAKAMURA,
R.M. & FRANKS,
sion sickness (dysbarism). Surgery, 58, 384-389.
COLLINS,
V.J. (1952) Principles and Practice of Anesthesiology, p. 273. Lea & Febiger, Philadelphia.
COMROE,
J.H. (1965) Physiology of Respiration, pp. 162 and 176. Year Book Publishers, Chicago.
DAVSON,
H. (1964) A Textbook of General Physiology, 3rd edn. Churchill, London.
FENICHEL,
I.R. & HOROWITZ,
S.B.(1963) The transport of nonelectrolytes as a diffusional process in cytoplasm.
Acta Physiologica Scandinavica, 60, suppl. 221.
FENN,W.O. (1969) The physiological effects of hydrostatic pressures. The Physiology and Medicine of Diving
(Ed. by P. B. Bennett and D. H. Elliott), chap. 3. Baillikre, Tindall & Cassell, London.
HALSTEAD,H.J. (1966) Introduction to Statistical Methods. Macmillan, Melbourne.
HAMILTON,
R.W., MACINNIS,
J.B., NOBLE,A.D. & SCHREINER,
H.R. (1966) Tech. Mem. B411, Ocean Systems
Inc., Tonawanda, New York.
Gas-induced osmosis
191
HARRELSON,
J.H. & HILLS,B.A. (1970) Changes in bone marrow pressure during hyperbaric exposure. Aerospace Medicine, 9, 1018-1021.
HEIMBECKER,
R.O., LEMIRE,
G., CHEN,C., KOVEN,
I., LEASK,D. & DRUCKER,
W.R. (1968) Role of gas embolism
in decompression sickness: a new look at ‘the bends’. Surgery, 64,264-272.
HILLS,B.A. (1967) Diffusion versus blood perfusion in limiting the rate of uptake of inert non-polar gases by
skeletal rabbit muscle. Clinical Science, 33, 67-86.
HILLS, B.A. (1970) Gas-induced osmosis as an aetiologic agent for gouty arthritis and aseptic bone necrosis
induced by exposure to compressed air. Review of Subaquatic Physiology and Hyperbaric Medicine, 2, 3-7.
HILLS,B.A. & LEMESSURIER,
D.H. (1969) Unsaturation in living tissue relative to the pressure and composition
of inhaled gas and its significance in decompression theory. Clinical Science, 36,185-196.
HUGHES,
G.M. & KERKUT,
G.A. (1965) Electrical activity in a slug ganglion in relation to the concentration of
Locke solution. Journal of Experimental Biology, 33,282.
KELLY,P.J. (1968) Anatomy, physiology, and the pathology of the blood supply of bones. Journal of Bone and
Joint Surgery, SOA, 766-783.
KERKUT,
G.A. (1969) The use of snail neurons in neurophysiological studies. Endeavour, 38,22-26.
K E n , S.S. (1951) Theory and applications of inert gas at lungs and tissues. Pharmacological Reviews, 3, 1-41.
KROGH,A. (1918) The rate of diffusion of gases through animal tissues with some remarks upon the coefficient
of invasion. Journal of Physiology, 52, 391.
I.S. & GRACE,M. (1968) Dysbarism: a study of gas osmosis. Science, 161,289.
KYLSTRA,
J.A., LONGMUIR,
LANDIS,
E. & PAPPENHEIMER,
J.R. (1963) Exchange ofsubstances through capillary walls. Handbook of Physiology,
Sect. 2: Respiration (Ed. by W. F. Hamilton and P. Dow), Vol. 2, chap. 29. American Physiological Society,
Washington.
MEYER,
K.H. (1937) Contributions to the theory of narcosis. Transactions of the Faraday Society, 33, 10621068.
MILLER,K.W., PATON,
W.D.M. & S-,
E.B. (1967) The anesthetic pressures of certain fluorine-containing
gases. British Journal of Anaesthesia, 39, 910-918.
PAULING,
L. (1961) A molecular theory of general anesthesia. Science, 134, 15-21.
REEVE,
E.B. & GWTON,A.C. (1967) Physical Bases of Circulatory Transport. Saunders, Philadelphia.
ROTH,E.M. (1967) Space-Cabin Atmospheres. 111. Physiological Factors of Inert Gases. N.A.S.A., Washington.
SMITH,
E.B. (1969) The role of exotic gases in the study of narcosis. The Physiology and Medicine of Diving (Ed.
by P.B. Bennett and D.H. Elliott). BailliBre, Tindall & Cassell, London.
SMITH,
W.D.A. (1967) Experiments demonstrating the uptake, distribution, and elimination of nitrous oxide in
the context of out-patient anaesthesia. British Journal of Anaesthesia, 39, 464-471.
P.D. & RAHN,
H. (1965) Effects of compression on composition and
VANLIEW,H.D., BISHOP,B., WALDER,
absorption of tissue gas pockets. Journal of Applied Physiology, 20,927-933.
WEAST,R.C. (1969) Handbook of Physics and Chemistry, 50th edn. Chemical Rubber Co., Cleveland.