Dissolved and Free Phase Gas Dynamics

Dissolved and Free Phase Gas Dynamics

BY DR. JOHNNY E. BRIAN, JR.

Photo by David Rhea

The idea that decompression stops deeper in the water column can allow for more efficient inert gas removal seems very counter intuitive. Traditional Haldane-based decompression theory emphasizes the need to move as shallow as possible to maximize gas removal from tissue. Haldane-based models assume that all gas remains in dissolved phase, where the gradient for inert gas removal is the partial pressure of the inert gas in the tissue (determined by the breathing mix and the time/depth profile) and the partial pressure of inert gas in blood (determined by the breathing mix and the current depth). In a dissolved gas model, formation of bubbles is assumed to indicate a violation of allowed supersaturation ratios. Today we know that bubbles are very common, and that phase transition (gas moving from dissolved phase to free phase in bubbles) should be considered in decompression theory. The gradients for gas movement are very different once gas leaves the dissolved phase and enters the free phase, which leads to the need for stops much deeper than predicted based on dissolved gas theory.

LeMessurier and Hills were the first to propose that free phase gas elimination might be an important component of decompression (LeMessurier and Hills, 1965). They based their theory on observations of Japanese shellfish divers who made repetitive dives to 200-300 FSW, and developed decompression procedures without knowledge of pre-existing theory. The divers used decompression stops that were much deeper than any tables in use at the time (1965), and the divers would surface directly from 30 to 40 FSW. The explanation that LeMessurier and Hills developed for why such decompression procedures worked was that gas was being removed from bubbles, and if the bubbles were efficiently eliminated, the need for the shallow stops was greatly reduced or eliminated.

DISSOLVED PHASE GAS DYNAMICS
When gas remains in the dissolved phase, tissue offgassing is controlled by the dissolved gas partial pressure difference between the tissue and blood. The amount of dissolved gas in tissue or blood is expressed as a "partial pressure" value in units of pressure (mmHg, FSW, etc.). This terminology is somewhat unfortunate, as it can mislead divers to think that gas in solution exerts pressure as does gas in cylinders. This is not true, as gas that is dissolved in liquid (tissue or blood) is dissolved as salt dissolves in water, and does not exert a pneumatic "pressure." Partial pressure of a gas in liquid means that to dissolve a given amount of a gas in a liquid will require exposure of the liquid to a specific pressure of the gas in the gas phase. The amount of gas that dissolves in the liquid depends on the intrinsic properties of the gas and the liquid (i.e., how soluble the gas is in the liquid) as well as the temperature. For example, if we expose one liter of water at 37°C (body temperature) to 1 ATA of nitrogen, 14.4 milliliters of nitrogen will dissolve in the water. The dissolved nitrogen would also be described as having a partial pressure of 1 ATA, which is one way of expressing the amount of nitrogen dissolved in the water. Movement of dissolved gas is driven by diffusion, and not the pressure gradients that we are familiar with that drive bulk gas flow, as in fill whips and cylinders. Diffusion is the random movements of atoms and molecules, and transfer of a species from one place to another is driven by the probability that more molecules will move from an area of higher concentration to an area of lower concentration than visa versa. It is the movement of independent gas molecules during diffusion that causes gas transfer, rather than the bulk movement of many gas molecules driven by pressure differentials.

Following any given dive, the amount of gas (partial pressure) dissolved in a tissue is determined by the tissue half-time, the concentration of inert gas in the breathing mix and the depth/time profile. The gradient for dissolved gas to move out of the tissue is determined by the partial pressure of inert gas in the tissue and the partial pressure of the inert gas in blood. The partial pressure of the inert gas in blood is determined by the partial pressure of the inert gas in the breathing mix and the current depth (ambient pressure). Because depth controls the partial pressure of inert gas in blood, depth controls the gradient for dissolved gas to move from tissue to blood. Haldane's theory was to reduce depth to a minimum to maximize the gradient between tissue and blood short of bubble formation. Gas dissolved in solution is not governed by the pressure-volume gas law for gas in free phase. Dissolved gas can exist at less than ambient pressure (undersaturation) or greater than ambient pressure (supersaturation). Haldane's theory evolved to the M-values developed by Workman which define the dissolved gas supersaturation allowed for each of the tissue half-times (Workman, 1965).

[See the attached file at the bottom of the page for figures for this article.]

Figure 1A shows an example of dissolved gas gradients after a dive to 132 FSW on air where there has been saturation of a tissue with nitrogen. The line depicted with squares is the nitrogen partial pressure gradient between a tissue saturated with the nitrogen fraction in air at 132 FSW and nitrogen in blood during ascent to the surface while breathing air. As a diver ascends in the water column, the gradient becomes larger as the partial pressure of nitrogen in the lung is reduced, which reduces the partial pressure of nitrogen in blood. Nitrogen partial pressure in blood is determined by the fraction of nitrogen in the breathing mix and ambient pressure. If the diver continues to breath air to the surface, the only factor that decreases the amount of dissolved nitrogen in blood is the reduction of ambient pressure. This is the basis for dissolved gas models where the underlying idea is to maximize the dissolved gas partial pressure differential between tissue and blood by maximizing the pressure reduction.

BUBBLE PHASE GAS DYNAMICS
When gas moves from the dissolved phase into the gas phase (phase change), gradients for gas movement become quite different. Unlike dissolved gas, gas partial pressure in bubbles is governed by ambient pressure. Because bubbles can expand and contract, they will change size as ambient pressure is altered, which also alters the partial pressure of the gases in the bubble. The movement of gas from the bubble into the dissolved phase is determined by the partial pressure of the gas in the bubble and the partial pressure of the gas in the surrounding tissue (remember, the surrounding tissue could be blood). During ascent to the surface, a bubble will expand, reducing the pressure in the bubble, which also reduces the nitrogen partial pressure in the bubble. Bubbles exist at somewhat above ambient pressure because of the surface tension of the bubble. Hills derived the formula for the gradient between a bubble and surrounding tissue (in mmHg pressure) (Hills, 1970):

where X is the fraction of inert gas in the breathing mix. Similar analysis of gradients can be found in the work of Van Liew and Wienke (Van Liew et al., 1965; Wienke, 1987). The line depicted with circles in Figure 1A is the gradient for gas absorption from a bubble that forms on ascent to the surface. If the diver were to ascend from the bottom at 132 FSW and stop at 99 FSW (80% of the maximum pressure absolute), the gradient from a bubble would be approximately equal to the dissolved gas gradient, shown by the line with squares (24-26 FSW). As the diver ascends from 99 FSW to a shallower depth, however, the gradients diverge with the gradient between the bubble and tissue being reduced as the bubble expands during ascent to the surface. The bubble expands as ambient pressure is reduced, also reducing the partial pressure of gases in the bubble.

The line depicted with triangles in Figure 1A is the oxygen window, which is formed by the metabolic consumption of dissolved oxygen that is incompletely replaced by carbon dioxide. Because more oxygen is transported in the dissolved phase as depth increases, the oxygen window also increases. The gradient for inert gas absorption from a bubble parallels the oxygen window (Figure 1A), because the oxygen window is the primary determinant of the nitrogen gradient between the bubble and tissue. A bubble gradient equation derived by Van Liew better illustrates the importance of the oxygen window in determining the absorption of inert gas from a bubble (Van Liew et al., 1965). The partial pressures of nitrogen inside of a bubble can be defined by subtraction of all of the gas partial pressures other than nitrogen from ambient pressure:

It is assumed that the tissue and bubble partial pressures are in equilibrium for oxygen, carbon dioxide and water. In a similar fashion, the pressure of nitrogen in the arterial blood is defined by:

With the gradient between bubble and blood as:

Which reduces to:

This is the equation for the oxygen window. Values and gradient calculations from the above Hills and Van Liew formulas can be found in Table

The oxygen window determines the gradient for nitrogen across the bubble because the window determines the amount of nitrogen in blood - i.e., the larger the window, the less nitrogen there will be in blood and the larger the gradient will be from bubble to tissue. The bubble must exist at ambient pressure, and the additional partial pressure not occupied by oxygen, carbon dioxide or water vapor inside of a bubble, is composed of nitrogen. Because tissue partial pressure of oxygen is significantly below the partial pressure of oxygen in arterial blood, this means that the nitrogen partial pressure inside of a bubble will always be greater than nitrogen partial pressure in tissue by the value of the oxygen window - i.e., the space in the bubble not occupied by oxygen will be filled with nitrogen. As the oxygen window increases or decreases, so will the nitrogen gradient between the bubble and tissue.

Figure 1B shows the same gradients as 1A, but instead of breathing air to the surface, in this example the diver switches to 40% nitrox at 99 FSW. The oxygen window, shown by the line with triangles, increases at 99 FSW due to the gas switch, and then declines as ambient pressure is reduced. Both the dissolved gas gradient (squares) and the bubble gradient (circles) are shifted upward by the increase in the oxygen window.

One factor that may not be fully evident in calculation of inert gas gradients from bubbles to tissue is that the tissue surrounding a bubble cannot exist in a state of supersaturation as with dissolved gases. When a bubble forms, dissolved gas in supersaturation will move from the dissolved phase into the bubble. The dissolved gas gradients presented in Figures 1A and 1B are large because of the assumption that the tissue remains supersaturated with the nitrogen fraction of air at 132 FSW. The gradients for free phase gas (bubbles) are based on the tissue surrounding the bubble having a dissolved nitrogen fraction determined by the inspired fraction of nitrogen and the current ambient pressure. Thus, the partial pressure of nitrogen in the bubble and the surrounding tissue is reduced during ascent to the surface. Any nitrogen present in the tissue above ambient pressure (supersaturation) simply moves into the bubble, and the bubble expands.

Figure 2A. Bubble and tissue gas partial pressures during air breathing at 99 FSW.

Figure 2A shows gas partial pressures in a tissue with a bubble and the surrounding tissue saturated with air at 99 FSW. This example ignores the increase in pressure inside of the bubble due to surface tension for simplicity. The nitrogen partial pressure in the bubble (125.8 FSW) exceeds the nitrogen partial pressure in the surrounding tissue (102.6 FSW) by 23.2 FSW. The oxygen window is the difference between the oxygen partial pressure in arterial blood (25.2 FSW) and the oxygen partial pressure in tissue (2.2 FSW), or 23 FSW, equal to the gradient for nitrogen from bubble to tissue. In Figure 2B, the oxygen window is increased by breathing 40% oxygen at 99 FSW. By increasing the partial pressure of oxygen in arterial blood, there will be less nitrogen in arterial blood, and less nitrogen in tissue. However, the oxygen in tissue changes only slightly, so that the amount of nitrogen in the bubble is unchanged, leading to a larger gradient for nitrogen from the bubble to tissue.

Inspection of Figures 1A and 1B should emphasize why increasing the oxygen window is important for both removal of dissolved and free phase inert gas during decompression. The above examples were applied to nitrogen-based dives for simplicity of presentation, but are equally applicable for other inert gases and combinations of inert gases.

References
1. LeMessurier, D.H. and Hills, B.A. Decompression sickness: a thermodynamic approach arising from a study of Torres Strait diving techniques. Hvalradet Skrifter. 48:54-84, 1965.

2. Workman, R.D. Calculation of decompression schedules for nitrogen-oxygen and helium-oxygen dives. Research report 6-65, Washington, DC: US Navy Experimental Diving Unit, 1965.

3. Hills, B.A. Limited supersaturation versus phase equilibration in predicting the occurrence of decompression sickness. Clinical Science. 38:251-267, 1970.

4. Van Liew, H.D., Bishop, B., Walder, D.P., and Rahn, H. Effects of compression on composition and absorption of tissue gas pockets. Journal of Applied Physiology. 20: 927-933, 1965.

5. Wienke, B.R. Computational decompression models. International Journal of Bio-Medical Computing. 21: 205-211, 1987.

Dr. Johnny E. Brian, Jr., is an associate professor of anesthesiology at the University of Iowa Hospitals and Clinics. He earned an M.D. degree and completed anesthesiology training at the University of Arkansas, followed by a post-doctoral fellowship in basic science research at Johns Hopkins University. In addition to clinical patient care, Dr. Brian directs an NIH-funded research laboratory that focuses on cerebral vascular physiology. Current research investigates oxygen-mediated regulation of cerebral blood flow as well as inflammatory-mediated alteration of gene expression that leads to subsequent alterations of cerebral vascular regulation. More information can be found at: http://www.anesth.uiowa.edu/cv.asp?ID=7.