Expansion of air bubbles in aqueous solutions of nitrous oxide or xenon

G. Lockwood

Department of Anaesthesia, Hammersmith Hospital, Ducane Road, London W12 0HS, UK

Accepted for publication: March 25, 2002


    Abstract
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix
 References
 
Background. Anaesthesia using xenon may be contraindicated in some situations because of its diffusion into intravascular bubbles. The expansion of air bubbles in water equilibrated with either nitrous oxide or xenon was studied.

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 20–23 µl) and 30 µl (range 27–34 µl) in water equilibrated with xenon and nitrous oxide, respectively. Half of the expansion took place in the first 20 s (15–45 s) for xenon and in the first 5 s (5–10 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: 282–6

Keywords: anaesthetics gases, xenon; anaesthetics gases, nitrous oxide; blood, intravascular bubbles


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix
 References
 
As an anaesthetic, xenon has several desirable pharmacological and pharmacokinetic properties but because it has to be used in a high concentration it may, like nitrous oxide, have adverse effects from diffusion into closed spaces and bubbles within the blood stream. Recent work has shown that xenon diffuses into the gut more slowly than does nitrous oxide,1 2 but in this situation mass transfer may not be limited by diffusion from blood to the cavity but rather by the rate of carriage of gas in blood to the mucosa. The lower blood solubility of xenon compared with nitrous oxide would then affect its slower diffusion into the gut. By contrast, an intravascular bubble has, prima facie, an almost limitless source of gas from the surrounding blood and it is possible that xenon would diffuse into bubbles as quickly as nitrous oxide does. These in vitro experiments compare the potential for xenon and nitrous oxide to expand bubbles.


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix
 References
 
Distilled water was equilibrated with either nitrous oxide or xenon in a closed tonometer.3 The equilibration took place at ambient pressure in a water bath at 37 or 20°C. Headspace gas was sampled and analysed in a gas chromatograph (HP6800, Hewlett Packard) using a hydrogen carrier gas flow of 30 ml min–1 through a 3 m Poroplot megabore column maintained at 30°C, and a thermal conductivity detector. After sampling gas from the headspace, a sample of water was transferred into a 5 ml vial containing a stirring magnet using a needle and syringe (Fig. 1). The vial cap, which included a teflon-faced rubber septum, was applied carefully to leave no bubble within the vial. The vial was placed in a small, insulated waterbath placed on top of a magnetic stirrer and maintained within 0.4°C of the temperature of equilibration. The central section of a polyethylene manometer tube was fixed horizontally to a flat surface on a level with the top of the vial, with the female end angled vertically and the male end free. The tube was flushed with methanol stained with a blue dye from the elevated female end and allowed to drain through a 23-gauge needle attached to the other end.



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Fig 1 The experimental arrangement. A 5 ml vial containing a magnetic stirrer is filled with water equilibrated with a test gas and placed in a water bath on a magnetic stirrer (not shown). The septum in the cap is punctured by a needle connected to a polyethylene tube holding a horizontal methanol column, dyed blue for convenience. When an air bubble is injected through the septum the change in volume of the bubble is measured by marking at frequent intervals the position of the meniscus (enlarged inset) as water is displaced into the tubing.

 
When the trailing meniscus of the methanol was in the horizontal section of the tubing, the needle was pushed through the vial cap. The position of the meniscus was observed to confirm that it was stationary. A 10 µl bubble of air was injected from a gas-tight syringe (Scientific Glass Engineering, Melbourne, Australia) through the cap, and the position of the meniscus marked by hand every 5 s for 30 s, every 15 s for a further 1 min, then every 30 s until 3 min had elapsed. The initial displacement caused by the bubble was measured by injecting known volumes of air from the syringe into a vial prepared in the same way, but filled with water that had been equilibrated with air at room temperature. This procedure produced a stable displacement of the meniscus.

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 Kruskal–Wallis 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.


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix
 References
 
The anaesthetic gas concentrations in the tonometer ranged from 37 to 81% with no significant differences between xenon and nitrous oxide or between temperatures, although there was a trend towards greater concentrations in the xenon groups. Nine paired samples of water and headspace gas drawn from the tonometer showed that equilibration had been achieved. Loss of anaesthetic during the experiments was modest in the nine paired samples—the greatest difference between the tension in vials after bubble expansion and its tonometer tension was 5 vol%.

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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Fig 2 Experimental results.

 

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Table 1 Experimental results
 

    Discussion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix
 References
 
When an air bubble is present in a liquid equilibrated with nitrous oxide, nitrous oxide will diffuse into the bubble, but simultaneously nitrogen will be diffusing out. The evolution of the bubble will be determined by the interplay between these dynamic processes. Clearly, the diffusion coefficients of the two gases studied here will ultimately be involved in the differences between their effects on bubbles, and in this respect xenon should be slower because its atom is so heavy. However, if diffusion were the whole story then air would diffuse out of the bubble more rapidly than either anaesthetic could diffuse in and the bubbles would collapse. Solubility is also important because a buffer zone of partly equilibrated liquid will be created around the bubble, reducing the local concentration gradients that drive the diffusion process. The relative importance of diffusivity and solubility of the gases in the liquid is not obvious a priori, and although the larger size of the xenon atom and its lower solubility in water should reduce its potential to enlarge bubbles when compared with nitrous oxide, we cannot make a quantitative statement. Furthermore, the influence of these factors may be negligible in comparison with the gas tension gradient driving the process. The present study was designed to address this uncertainty.

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 experiments—that air bubbles expand more slowly in xenon solutions than in nitrous oxide solutions—does 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.


    Appendix
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix
 References
 
Direct comparison of the raw results of the experiments is difficult for a number of reasons. (i) The tension of anaesthetic in the tonometer cannot be controlled exactly and so the tensions of nitrous oxide and xenon can only be approximately the same. (ii) Although turbulent flow caused by the magnetic stirrer was intended to minimize local depletion of dissolved gas around the injected bubble, migration of dissolved gas into the bubble inevitably depleted the total amount remaining in solution and therefore reduced the tension of anaesthetic in the water around the bubble. The different solubilities of nitrous oxide and xenon in water means that the depletion would affect the xenon results more. (iii) Inspection of duplicate results suggested that rapid injection of the bubble into the vial was associated with significant variability in the injected volume, i.e. the volumes of the ‘10 µl’ bubbles were only nominally 10 µl. A mathematical model was therefore developed to describe the dynamics of the bubbles based on the following assumptions.

A1: the gas tensions in the water and the bubble are both homogeneous.

A2: rate of transfer of gas across the gas–liquid 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 {sigma} 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 {lambda}x. Subsequently, using A1, the anaesthetic tension within the bubble is given by Ax/V and the tension within the vial by (Ax0Ax)/Vw{lambda}x. The difference between these is denoted {Delta}x. The amount of air in the system A0air is the sum of the amount injected, V0, and the amount dissolved in water, (1–Tx0)Vw{lambda}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, {Delta}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, Runge–Kutta 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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Table 2 Physical constants. Water:gas solubility coefficient of air, {lambda}air, of xenon, {lambda}Xe, or of nitrous oxide, {lambda}N2O; vapour pressure of water, Pwater; surface tension, {sigma}
 
Given the number of variable parameters, it is not surprising that the model generally fitted the data well. At both temperatures, comparisons were made between kx for xenon and for nitrous oxide using the Mann–Whitney test. Similar comparisons were made between the set of values for kair derived from the xenon experiments and those derived from the nitrous oxide experiments (there should be no difference). Results are shown in Figure 3. Mean initial bubble volume was 9.8 µl (SD 1.3 µl). Differences between kx for xenon and nitrous oxide were significant at 20°C (P<0.01) and at 37°C (P<0.001). The difference between the kair values derived from the nitrous oxide or the xenon experiments was not significant at 20°C but was at 37°C (P<0.01), suggesting that the model is not a complete representation of the physical processes involved.



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Fig 3 The values for the parameter, k, derived from the individual experiments. Nitrous oxide, closed circles; xenon, closed triangles; nitrogen calculated from experiments with nitrous oxide, open circles, or xenon, open triangles. Triangles are offset to the right for clarity.

 

    Acknowledgements
 
The gas chromatograph used in this study was made available by a grant from the Association of Anaesthetists of Great Britain and Ireland. The xenon was kindly supplied by Professor M. Maze, Imperial College School of Medicine, UK.


    References
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix
 References
 
1 Reinelt HR, Schirmer U, Marx T, Topalidis P, Schmidt M. Diffusion of xenon and nitrous oxide into bowel. Anesthesiology 2000; 94: 475–7[ISI]

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: 512–3[ISI][Medline]

3 Smith MA, Sapsed-Byrne SM, Lockwood GG. A new method for measurement of anaesthetic partial pressure. Br J Anaesth 1997; 78: 449–52[Abstract/Free Full Text]

4 Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical Recipes in Pascal: the Art of Scientific Computing. Cambridge: Cambridge University Press, 1989; 602–24

5 Nelder JA, Mead R. A simplex method for function minimisation. Comp J 1965; 7: 308–13





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