Department of Anaesthesia, Hammersmith Hospital, Ducane Road, London W12 0HS, UK
Accepted for publication: March 25, 2002
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Abstract |
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Methods. Equilibrated water was transferred to a stirred vial, closed except for a long, narrow-bore tube. Injection of an air bubble caused displacement of water along the tube, allowing expansion of the bubble to be charted on a linear scale.
Results. At 20°C, bubbles expanded from 10 µl to a median volume of 23 µl (range 2023 µl) and 30 µl (range 2734 µl) in water equilibrated with xenon and nitrous oxide, respectively. Half of the expansion took place in the first 20 s (1545 s) for xenon and in the first 5 s (510 s) for nitrous oxide. At 37°C the expansion was less with both gases, but the relative differences were maintained between them.
Conclusion. Xenon anaesthesia may be less likely to aggravate injury from intravascular bubbles than anaesthesia with nitrous oxide.
Br J Anaesth 2002; 89: 2826
Keywords: anaesthetics gases, xenon; anaesthetics gases, nitrous oxide; blood, intravascular bubbles
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Introduction |
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Methods |
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During the experiments, water samples were frequently drawn from the tonometer and from bubble vials after equilibration. The tension of xenon or nitrous oxide was measured by repeated headspace analysis.3
The KruskalWallis test (Arcus QuickStat 1.0, Research Solutions, Cambridge, UK) was used to compare the final bubble volumes and to compare the time taken to expand to half that amount.
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Results |
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The meniscus moved a mean of 37.4 (SD 1.2) mm after injection of a 10 µl bubble into air-equilibrated water. The timecourses of individual experiments are shown in Figure 2 and detailed results appear in Table 1. At 3 min, the bubble sizes in the four groups were significantly different (overall, P<0.001). At each temperature the difference between anaesthetics was very significant (P<0.0001), and the difference between temperatures was also significant for each anaesthetic (P<0.01). The median time taken to expand to 50% of their final volume increase was also significantly different between groups (overall, P<0.001; difference between anaesthetics at both temperatures, P<0.0001), i.e. bubbles expanded more rapidly in water equilibrated with nitrous oxide than in water equilibrated with xenon.
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Discussion |
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The number of experiments undertaken was small but the results are unambiguous with no overlap between the bubble dynamics observed in the two anaesthetic solutions. There is no evidence of systematic bias to explain this difference: the tonometer concentrations tended to be greater in the xenon experiments, and loss of either gas during the experiments was minimal. The solutions were stirred briskly to minimize local depletion of gas, which might have delayed diffusion of the less soluble gas into the bubble. Gross mixing, demonstrated by spread of dye within the vial, appeared to be instantaneous and it was found that the stirring rate did not affect the outcome of the experiments unless it was very slow (data not shown).
Although the growth of bubbles in water is not of great interest to anaesthetists, the expansion of bubbles in blood is an important concern; nitrous oxide should be avoided immediately before and during cardiopulmonary bypass for this reason. The experiments described above involve significant spillage of the test liquid when the vials are sealed without air bubbles, so the risk of contamination from blood spills needed to be balanced against the risk of extrapolating from results in water to results in blood. The solubilities of the two gases in blood at body temperature lie within the range of solubilities in water at 20 and 37°C as studied here, and the rate of diffusion is normally assumed to be the same in blood and water. The effect of surface tension is small in bubbles of the size studied, so the difference between blood and water is negligible in this respect. The greater viscosity of blood would increase any buffer zone, which might further accentuate the differences found between nitrous oxide and xenon. Finally, stirring the vials could cause haemolysis and affect the similarity between in vitro and in vivo conditions. There is no reason to suppose that the main result of these experimentsthat air bubbles expand more slowly in xenon solutions than in nitrous oxide solutionsdoes not hold in blood.
Both the rate of increase and the final size of the bubbles are lower with xenon compared with nitrous oxide. These results, coupled with the smaller expansion at the higher temperature, support the idea that gas solubility is the critical factor in bubble expansion. This study suggests that xenon anaesthesia could cause less injury from intravascular bubbles than anaesthesia with nitrous oxide. Nonetheless, this risk remains and must be balanced carefully against benefits of xenon before it can be used for patients at risk, such as those undergoing cardiopulmonary bypass or who have been diving recently.
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Appendix |
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A1: the gas tensions in the water and the bubble are both homogeneous.
A2: rate of transfer of gas across the gasliquid interface was proportional to the difference in gas tension in the water and the bubble, and proportional to the area of the bubble surface.
A3: the bubble was spherical.
A4: the pressure within the bubble was determined by atmospheric pressure and surface tension only.
Three differential equations describing interdependent variables were developed and integrated simultaneously. These were Ax, the amount of anaesthetic gas in the bubble at ambient temperature and pressure; Aair, the amount of air in the bubble at ambient temperature and pressure; V, the volume of the bubble from which we can calculate the surface area, S, and radius, r. Using A3, the pressure within the bubble with respect to ambient pressure is, P, given by
where is the surface tension of water. The hydrostatic pressure in these experiments should be an order of magnitude less than that due to surface tension and is ignored. The amount of anaesthetic in the system is initially Ax0 and it is all in the water. It is given by the product of the initial anaesthetic tension Tx0, the volume of water Vw in the vial and the solubility coefficient
x. Subsequently, using A1, the anaesthetic tension within the bubble is given by Ax/V and the tension within the vial by (Ax0Ax)/Vw
x. The difference between these is denoted
x. The amount of air in the system A0air is the sum of the amount injected, V0, and the amount dissolved in water, (1Tx0)Vw
air. (For these purposes, the solubility of air is taken to be the solubility of nitrogen.) The air tension in the bubble, in the water and the difference between them,
air, are calculated in the same way as for the anaesthetic. It is assumed that the gas in the bubble is saturated instantly. Assumption A2 can be represented formally by:
k has units of amount of gas per unit of force per unit of time. Similarly,
If, for convenience, the amount of gas is measured as volume at experimental temperature and room pressure, then the total amount of gas and vapour is given by PV. The rate of change of this quantity is the sum of the rates of change of anaesthetic, air and water vapour.
Note that if the saturated vapour pressure of water at the experimental temperature is Pwater then
Also, from equation (1) and A3
The left hand side of equation (4) can now be expanded
The identities in equations (2), (3), (5) and (6) allow equation (4) to be solved explicitly for dV/dt. After rearranging we obtain
For any experiment, the initial tension of gas in the water is known from analysis of the tonometer headspace and the unknowns are the initial size of the bubble and the constants of proportionality, k, for the rate of transfer of air out of the bubble and of the test gas into the bubble. Given values of Tx0, V0, kx and kair, and using standard values of the physical constants (Table 2), equations (2), (3) and (7) can be integrated simultaneously by a fourth order, RungeKutta numerical technique.4 Starting with the measured Tx0 and arbitrary values for V0, kx and kair, the squares of the differences between the model and measured data were summed. The values of V0, kx and kair were modified using a downhill simplex iterative technique5 to produce the best fit (in the least-squares sense) of the model to the data.
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Acknowledgements |
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References |
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2 Reinelt H, Marx T, Schirmer U, Luederwald S, Topalidis P, Schmidt M. Diffusion of xenon and nitrous oxide into the bowel during mechanical ileus. Anesthesiology 2002; 96: 5123[ISI][Medline]
3 Smith MA, Sapsed-Byrne SM, Lockwood GG. A new method for measurement of anaesthetic partial pressure. Br J Anaesth 1997; 78: 44952
4 Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical Recipes in Pascal: the Art of Scientific Computing. Cambridge: Cambridge University Press, 1989; 60224
5 Nelder JA, Mead R. A simplex method for function minimisation. Comp J 1965; 7: 30813