Abstract
Our hypothesis is that metabolic gases play a role in the initial explosive growth phase of bubble formation during hypobaric exposures. Models that account for optimal internal tensions of dissolved gases to predict the probability of occurrence of venous gas emboli were statistically fitted to 426 hypobaric exposures from National Aeronautics and Space Administration tests. The presence of venous gas emboli in the pulmonary artery was detected with an ultrasound Doppler detector. The model fit and parameter estimation were done by using the statistical method of maximum likelihood. The analysis results were as follows. 1) For the model without an input of noninert dissolved gas tissue tension, the log likelihood (in absolute value) was 255.01. 2) When an additional parameter was added to the model to account for the dissolved noninert gas tissue tension, the log likelihood was 251.70. The significance of the additional parameter was established based on the likelihood ratio test (P < 0.012). 3) The parameter estimate for the dissolved noninert gas tissue tension participating in bubble formation was 19.1 kPa (143 mmHg). 4) The additional gas tissue tension, supposedly due to noninert gases, did not show an exponential decay as a function of time during denitrogenation, but it remained constant.5) The positive sign for this parameter term in the model is characteristic of an outward radial pressure of gases in the bubble. This analysis suggests that dissolved gases other than N_{2}in tissues may facilitate the initial explosive bubblegrowth phase.
 bubble growth
 Doppler ultrasound
 inert and noninert dissolved gases
 tissue ratio
 logistic model
 log likelihood
 gas kinetics
reduction in ambient pressure is experienced by divers, aviators, and astronauts. The Shuttle and the Russian Space Station Mir atmospheres are at a pressure of 101.3 kPa, but astronauts or cosmonauts are exposed to a reduced absolute pressure in the space suit when they are performing extravehicular activity (EVA). Decompression may lead to the formation and growth of gas bubbles within tissues (3,4, 16), with a resultant risk of decompression illness (DCI). In humans, the composition of gas bubbles in tissues is not amenable to direct experimental verification. Furthermore, analysis of intravascular bubbles does not provide information about the fractions of dissolved gas in tissues participating in bubble formation (8). O_{2} and CO_{2} rapidly permeate in and out of the bubbles, compared with N_{2} (13). After sufficient time, the gas in bubbles presumably equilibrates with metabolic levels of O_{2} and CO_{2} in mixed venous blood or tissue, and with the body saturation level for water vapor pressure (8, 13). In contrast to hyperbaric decompressions, metabolic gases form a large fraction of the gas in bubbles during hypobaric decompressions (15). Moreover, theoretical simulations utilizing a system of mathematical equations (13) suggested a significant role for metabolic gases in bubbles during hypobaric decompressions.
Our hypothesis is that metabolic gases are involved in the initial growth phase of bubbles. An analysis is made by using experimental results from human exposures conducted in altitude chambers that simulate EVA procedures. Oftentimes, venous gas emboli (VGE) can be detected in the venous blood flow (7, 9) when a Doppler ultrasound bubble detector is used. Bubbles spawned in capillaries of tissues were mobilized into the venous return by flexing the limb during the period of bubble monitoring. Models that account for the tensions of dissolved gases in tissues and predict VGE incidence were statistically fitted to the data. We evaluated whether the incorporation of an additional mechanistic parameter into a model produced a better fit to the observed response. The model with the best fit to the data is assumed to support the more realistic hypothesis.
METHODS
Glossary
 Fi_{O2}
 Fraction of inspired O_{2}, dimensionless
 Fi_{N2}
 Fraction of inspired N_{2}, dimensionless
 i
 Subscript for the ith record (426 records)
 L
 Likelihood function, dimensionless
 LL
 Natural logarithm of the likelihood function, dimensionless
 Pa_{CO2}
 Alveolar CO_{2} partial pressure of 5.33 kPa (40 mmHg)
 Pa_{H2}_{O}
 Alveolar H_{2}O pressure of 6.27 kPa (47 mmHg)
 Pa_{N2}
 Alveolar N_{2} partial pressure, kPa
 Pa_{N2}
 Arterial N_{2} tension, kPa
 Pa_{O2}
 Alveolar O_{2} partial pressure, kPa
 Pb
 Total absolute pressure of the breathing medium; pressure at altitude, kPa
 P_{other}
 Additional dissolved gas tissue tension, kPa
 P
 Probability of occurrence of VGE, dimensionless
 Pti_{N2}(0)
 Initial N_{2} tissue tension just before the procedure of interest, kPa
 Pti_{N2}(t)
 Dissolved N_{2} tissue tension at a time t; estimated dissolved N_{2} tissue tension at the end of denitrogenation, kPa
 R
 Respiratory exchange ratio,V˙co_{2}/V˙o_{2}, dimensionless
 t_{1/2}
 Tissue half time for washin and washout of N_{2}, min
 t
 Time of interest, usually the end of the O_{2}prebreathing, min
 V˙co_{2}
 Amount of CO_{2} eliminated, l/min
 V˙o_{2}
 Rate of O_{2} uptake, l/min
 y_{i}
 VGE outcome, 1 if VGE occurred, or 0 if none, dimensionless
Estimation of Dissolved N_{2} Tension in Tissues
The Pa
_{N2} determines the Pa_{N2}, and this in turn defines the dissolved N_{2} tension in the tissues. The denitrogenation, or N_{2} “washout” during the prebreathe procedure, consists of breathing an O_{2}enriched breathing medium (2); this can be pure O_{2} or an O_{2}N_{2} mixture with different inspired fractions of O_{2} and N_{2}, denoted by Fi
_{O2} and Fi
_{N2}, respectively. The Pa
_{O2} is calculated by using the alveolar gas equation (10). The Pa
_{N2} equals the total ambient pressure Pb of the breathing medium minus Pa
_{CO2}, Pa
_{O2}, and Pa
_{H2}
_{O}. In accordance with Dalton’s law, the Pa
_{N2} can be expressed as follows
Assuming a perfusionlimited system (24), an approximation of the N_{2} partial tension of dissolved inert gas in the tissue during any N_{2} partial pressure change in the breathing medium is provided by the classic exponential model
NASA Hypobaric Data Set
Subjects.
There were 164 volunteers (37 women and 127 men), who participated in 426 hypobaric exposures at the Johnson Space Center between 1982 and 1990. The average age was 31.38 ± 7.2 yr. Their individual characteristics were representative of the astronaut population. Women were included during the latter part of these studies. All were required to pass the United States Air Force Class III Flight Physical examination. The subjects signed an informed consent and were free to withdraw from the tests at any time.
Test procedures for simulated EVAs.
The chamber tests were not all the same, since 1) denitrogenation periods varied; 2) the breathing gas during the denitrogenation was 100% O_{2} at 101.3 kPa [14.7 lb./in.^{2} absolute (psia)]; 3) however, some tests used a staged decompression, a prolonged stay at an atmosphere of 70.3 kPa (10.2 psia) enriched with O_{2} and with a reduced N_{2} partial pressure (26% O_{2}74% N_{2}), as part of the denitrogenation process; 4) at altitude, after the final decompression, the breathing gas was 100% O_{2} or O_{2}N_{2} mixtures; 5) the pressure at altitude ranged from 29.64 kPa (4.3 psia) to 44.80 kPa (6.5 psia); and 6) the time at altitude varied from 3 to 6 h. In all these tests, no exercise was performed during the O_{2}prebreathe, and subjects were reclined or seated. Each subject was exposed to a particular denitrogenation and decompression profile; several of the same profiles constituted a test. Twenty tests were conducted. When test groups were separated with respect to gender, the total number of groups was 23. A low level of exercise during the simulated EVA involving upper limbs with an average metabolic rate of 837 kJ/h (200 kcal/h) was performed.
Dependent variable.
VGE in the pulmonary artery were detected with a Doppler ultrasound bubble detector in the precordial position at ∼15min intervals throughout the exposure. The bubbles were mobilized by flexing the joints and straining the muscle groups of a limb (1) at the time of bubble monitoring. It is assumed that we measure the “limb bubbleformation tendency” before the time of monitoring. We code the presence of VGE in the pulmonary artery as 1, or 0 if no bubbles were detected.
Independent variable.
We define a dose for the decompression (2, 14) as tissue ratio (TR), which is the ratio of the calculated dissolved N_{2} tissue tension for a given tissue to the ambient pressure
Statistical Analysis
Logistic regression model.
The probability of VGE occurrence is modeled as a function of the decompression dose, TR or TR′. An appropriate statistical model for the probability of occurrence of an event is often assumed to be logistic (6). In terms of a function of dose, the probabilityP of occurrence of VGE is defined by the logistic regression equation, namely
Maximumlikelihood method.
Maximumlikelihood estimation is the preferred technique (3, 4, 11, 14,20, 22) to estimate unknown parameters in a model so that the probability function is maximized. Given a set of data, the likelihood function L is defined as the product of the probability densities for the subjects’ outcomes
The tissue half time was estimated as part of the model by a trialanderror method (3, 14) with the use of systat. The trialanderror method is comparable with a fully computerized fitting process. A spectrum of half times from 240 to 700 min was tested initially at ∼20 to 50min intervals, and then the half times were progressively decreased to 1min intervals as the model approached the best fit to the data.
Test of statistical hypotheses.
The likelihood ratio test statistic (14, 20) is used to assess whether additional parameters added to a model improve the goodness of fit. The degrees of freedom of a test statistic are equal to the number of parameters estimated in a full model minus the number of parameters in a hypothesized model. The likelihood ratio test statistic is transformed, from a ratio to a difference, by taking twice the difference between the two corresponding LL values. The transformed statistic follows a χ^{2} distribution. Finally, a χ^{2} table is entered with the calculated likelihood ratio and the difference in degrees of freedom between the two models to determine the appropriate P value.
RESULTS
Table 1 lists the family of models tested, the fitted parameters in each model, and the LL value obtained in each case. The threeparameter model with only N_{2}dissolved tissue tension in the expression of dose defined by Eq.3 (P_{other} = 0), resulted in an LL value of 255.01. The ability to describe the response variable improved by accounting for an additional dissolved gas tissue tension other than N_{2} in the dose expression of Eq. 4. The fourparameter model (P_{other} ≠ 0) returned anLL of 251.70, the best LL value that we encountered, indicating that it has the best fit to the data. A decrease of 3.31LL units by the addition of P_{other} in dose is statistically significant at P = 0.012 under the likelihood ratio test. We also define an upper and lower boundary of theLL value (14, 20) to further evaluate the goodness of fit of our best model. The hypothesis that dose of decompression is not useful in predicting VGE defines the “null” model; it is considered as an upper boundary. This is a constantprobability model with one scaling parameter that is estimated by the odds ratio of cases with VGE vs. no VGE. This model returned a value of 290.46 for LL, which significantly differs from all the other models tested. The LLvalue of 240.08 corresponded to the lowboundary case of the “discontinuous” model, which consisted of separate null models for the 23 groups of data. This discontinuous model, of course, is too data specific to be effective for prediction beyond the range of observations utilized. The discontinuous model and the fourparameter model are, however, not statistically different, since the likelihood ratio test based on the 19 degrees of freedom for the χ^{2}statistics yielded a P value >0.50.
Table 2 lists information for the best fit fourparameter model shown in Table 1. The estimated value for P_{other} was 19.1 kPa (143 mmHg). The asymptotic SE for P_{other} was 4.64, which is small, relative to the parameter estimate. The asymptotic correlation matrix in Table3 indicates that P_{other} was poorly correlated with b _{0}; therefore, it merits retaining P_{other} in the model (12). However, P_{other} was significantly correlated withb _{1}, implying that a change in P_{other}would have caused large changes in b _{1}. The estimates of b _{0} and b _{1} were several times larger than their SE values, thus indicating their significance in the model. The t _{1/2} had a value of 329 min.
Because t _{1/2} was estimated from trialanderror modification of potential models, the study of these models allows further insight into relations between t _{1/2} and P_{other}. Close inspection of Fig.1 shows that the distribution of isopressure isopleths (LL vs. t _{1/2}, at six different values of P_{other}) follows a specific pattern. The parabolic shape of these isopleths is a property of the maximum likelihood optimization. As P_{other} increases in value, the isopleth becomes steeper. The minimum on the isopleth corresponds to the best fit of this model with the data. The intercept of the 19.1 isopleth with the 329min t _{1/2} corresponds to the best fit model. On the other hand, the t _{1/2}estimate for the threeparameter model located at the minimum of the 0 kPa isopleth has a value of 420 min. Figure 1 also shows that our best fit model is robust, since slight variations of P_{other}, e.g., within 2 kPa of 19.1 kPa, hardly affect the LL value. Furthermore, variations of P_{other} within the range of the SE (4.64 kPa) do not significantly affect the estimated model.
Another approach to making comparison between models is the graphic illustration of goodness of fit as shown in Figs. 2 and3. Each circle represents a group of subjects, and the size of a circle is proportional to the corresponding group size; there were 23 groups. For a given group, the value on the yaxis is the observed incidence of VGE in this group. The sigmoidal curves show the predicted probability of VGE by two different models: the best fit fourparameter model (Fig. 2) and a threeparameter model (Fig. 3). The models were fitted using a NASA data set consisting of 426 individual observations, as described earlier. The position of all the circles around the curve provides a visual impression of the fit; circles close to the sigmoidal curve indicate a better fit of the model to the data. However, this goodness of fit criterion based on the examination of group incidence is limited because of the lack of reliability of the visual interpretation of observed incidences. Because the model fit takes into account the size of groups of data as weight for each group of subjects, the model represents the larger groups of subjects better than it does the smaller groups. Overall, the best fit model (Fig. 2) does not seem to over or underpredict the incidence of VGE, except for a few small groups of subjects. In contrast, Fig. 3 depicts a poor fit for the threeparameter model with a 240mint _{1/2}, since it did over and underestimate the VGE incidence even in larger groups of subjects, and circles are dispersed away from the model curve. Although the model fit is weighted according to the size of subject groups, Fig. 3 shows that a model with an inappropriate t _{1/2} and absence of P_{other} fails to accurately predict the observed incidence, even in the case of larger groups of subjects.
Because Pa _{N2} (or Pa_{N2}) was estimated by using Eq. 1, it was appropriate to determine whether variations in the respiratory exchange ratio R affect the predictability of the model. We added R as an additional parameter to the fourparameter model and evaluated the model for values of R between 0.70 and 1.0. The ability to describe the response variable is not affected by including R as a parameter. The model is robust, since variations of R between 0.70 and 1.00 do not influence the LL value (251.70). Clearly, variations in R and, therefore, small changes in dissolved N_{2} tissue fraction have no influence on the model.
DISCUSSION
Presence of Bubbles
We considered only the existence of bubbles and their relationship to pressures of dissolved gases in the model. The model determines the probability of bubble formation on the basis of total tension of dissolved gases in tissue before decompression. However, the accuracy of the Doppler detection is limited. Precordial Doppler detection reflects the quantity of bubbles, but we do not know how to evaluate the sensitivity of the device. Stationary bubbles spawned in the microcirculation cannot be detected by Dopplershift ultrasonography (7) but may be detectable when dislodged by flexing the limb at the time of Doppler detection (1). A freegas phase, which is static or of small volume (7) and outside of the limit of sensitivity of the ultrasonic device, can give rise to false negatives (that is, no bubbles are detected, although they are present).
Mechanistic Hypotheses
Tissues with higher dissolved N_{2} gas tissue tension than ambient pressure facilitate bubble formation (5, 12). The generation of bubbles from “gas micronuclei” through “nucleation processes” (9, 16) is then followed by an initial explosive bubblegrowth phase (12) during the supersaturation. However, our results indicate that dissolved N_{2} may not be the only gas to initiate this explosive bubblegrowth phase. This explosive growth involves the immediate surroundings of the bubble and may recruit other dissolved gases in the tissue, e.g., CO_{2}, O_{2}, water vapor, and even argon (1 kPa). The accelerated log logistic survival model predicted that DCI (and presumably bubbles) may occur when the altitude pressure is ∼20 kPa, even though estimated N_{2} pressure was zero in the 360min compartment (3); therefore, this finding suggests a metabolic gas participation in bubble formation. After complete washout of dissolved N_{2} in a tissue, the dissolved metabolic gases in the tissue would evolve from solution as ambient pressure approaches a vacuum (3).
The initial explosivegrowth phase precipitates a series of events. Bubble size is inversely proportional to surface tension pressure, and the driving force for diffusion of gas into a bubble increases as surface tension pressure diminishes (12). Nitrogen tension in the tissue becomes a driving force for diffusion, causing N_{2} to diffuse from tissue to nascent bubble. Once molecules of N_{2}are captured inside the newly generated bubble, they are involved in the N_{2} partial pressure of the bubble as an outward radial pressure. In contrast, pressure due to surface tension is an inward radial pressure that tends to reduce the bubble volume. Thus, in modeling bubble growth, the surface tension pressure should be subtracted from N_{2} dissolved tissue tension. Similarly, tissue elastic recoil is also an inward radial pressure as well as O_{2} ambient pressure; both quantities should then be subtracted from the N_{2} dissolved tissue tension.
Underlying mechanisms of bubble growth suggest that surface tension pressure and tissue elastic recoil are not involved in P_{other}. If P_{other} is not due to inward radial elastic forces, it should then be caused by gas(es) in physical solution in the tissue before the initial explosivegrowth phase. The positive sign of P_{other} unmasks the contribution of an outward radial pressure due to this (these) dissolved gas(es).
Assuming that P_{other} is due to gas(es) previously dissolved in tissues, it is questionable whether the tissue gas(es) tension could follow various distributions with time. Indeed, an alternative to the singleexponential tissuegas exchange for N_{2} and to the constant secondterm P_{other} of Eq. 4 has to be examined. The number of plausible tissue types considered in the analysis may, in fact, be more than one (18). It has been shown (in dogs) that tissue isobaric gas exchange for ^{133}Xe (21) is better described by two or three exponential processes in series. The exponentialseries analysis (18) assigns one exponential term ort _{1/2} for inertgas washout for each tissue present in the expression of dose. These models were applied to predict probability of DCI in diving (11, 22), and it was found that the prediction of DCI incidence was similar for both the series and parallel arrangement of tissues (11). It is questionable how a detailed description of the tissue gas exchange for N_{2} including another exponential term in lieu of P_{other} in Eq. 4 would predict the VGE outcome in the NASA hypobaric exposures. Therefore, we tested (although analysis is not shown) an expression of dose derived from a doubleexponential gas exchange in a single tissue or a monoexponential gas exchange in a parallel arrangement of two tissues, each tissue with a different exponential term (22). This dose was then used in the logistic model. The addition of more parameters in the model even further reduced the goodness of fit. In contrast to some DCI data from hyperbaric exposures (11, 22), a monoexponential gas exchange in a single tissue for N_{2}, as described in our analysis, better fitted the data of hypobaric exposures than a complex gasexchange kinetics with two exponential terms. The rationale behind these observations is that P_{other} is not an additional pressure due to N_{2}, which would be disregarded by the Pti_{N2}(t) term of Eq. 4, and that noninert gas(es) would assist N_{2} during the initial explosive bubblegrowth phase.
Clearly, two types of tissue gas exchange appear in the expression for dose, TR′, in the best fit fourparameter model. Our best predictor for the total driving tension of the tissue ratio is made up of two pressure terms, each with a different relation to time. The two types of tissue gas exchange were 1) an elimination of dissolved N_{2} exponentially related with time, as described by others (5, 18); and 2) a gas tension in terms of P_{other}, which remains constant, presumably due to metabolic gases. Among all dissolved gases in tissues, this exponential elimination appears to be a characteristic of N_{2} tissue gas exchange.
The aforementioned mechanistic premises allow further insight into properties of P_{other} in bubble formation. However, no direct measurement could verify any postulate about P_{other}. Our statistical analysis shows a correlation between P_{other}and the model parameter b _{1}, and thus a decrease in the LL value may be due to an improvement in the model caused by the addition of P_{other} in determining dose.
It is also unclear whether the magnitude for P_{other}obtained in this analysis is a coincidence. The value of 143 mmHg (19.1 kPa) is approximately the tension (btps) of metabolic gases in tissue or in mixed venous blood. This finding suggests that nearly all the dissolved gas, other than the N_{2} that remains in physical solution in the tissue, has also been utilized to separate the gas phase.
The dissolved tissue tension of all gases involved in the bubble growth, or driving tension, warrants a brief description. Figure4 shows two doseresponse curves of the best fit fourparameter model corresponding to the two altitude pressures of 30 and 45 kPa, respectively. As a result of a complete denitrogenation [Pti_{N2}(t) = 0], the driving tension still available is ∼19.1 kPa; P_{other}, presumably because of metabolic gases, remains constant, whereas the dissolved N_{2} tissue tension in the expression of dose depends on the denitrogenation procedure. In contrast, without preliminary denitrogenation, and according to our analysis, the total driving tension that can potentially generate bubbles in tissues is 93.3 kPa; it is calculated by subtracting the arteriovenous O_{2} difference (8 kPa) from the standard pressure (101.3 kPa). The pressure difference of 8 kPa is due to a phenomenon known as the “oxygen window” (15) because metabolism lowers partial O_{2} tension in tissues below the value in arterial blood. The 95% confidence intervals were computed based on the propagation of error formula (14). It is seen that the confidence intervals are narrower in the case of 30 kPa than in the case of 45 kPa. The confidence interval provides a range for the parametric values, but it does not establish the accuracy of the estimate. Furthermore, the larger the sample size, the narrower the confidence intervals (3).
Fractions of Gases
The transfer of gases into nascent bubbles is related to their pressures in tissues at the end of the denitrogenation. The washout of dissolved N_{2} in tissue depends on the denitrogenation; when excess of dissolved N_{2} is removed from the tissue, metabolic gases fraction is obliged to be larger in nascent bubbles (13). The fraction of presumed metabolic gases was calculated for each of the 20 procedures as the ratio of the parameter estimate of P_{other} (equal to 19.1 kPa) to the estimated N_{2}dissolved tissue tension at the end of denitrogenation given by Eq.2. The fractiongenerating bubbles (for R = 0.82) ranged from 21 to 44%, whereas the balance N_{2} fraction ranged from 56 to 79%. The latter estimation applies to the initial explosive bubblegrowth phase; to estimate the fraction of metabolic gases that diffuse in and out of the bubble, after this initial phase, it is appropriate to use mathematical simulations of gas bubbles (13). Furthermore, during the slower bubble growth, simulations showed that the metabolic gases made up even larger fractions of the bubble because of transients for CO_{2} and O_{2} (13).
The mechanistic role of metabolic gases in bubble formation appears to be inversely proportional to the excess of dissolved N_{2} in tissue; comparison of hypobaric and hyperbaric exposures indicates significant difference. The P_{other} value derived from these NASA hypobaric decompressions is higher than values from direct measurements in diving experiments with guinea pigs breathing air or gas mixtures (8); metabolic gases fraction in bubbles was ∼10%, with the balance of 90% due to inert gas. In human dives, there is a slight chance that O_{2} could be 40% as effective as N_{2}in producing a risk of DCI (19). In hyperbaric conditions, dissolved N_{2} tissue tensions and fractions are large, whereas metabolic tissue tensions and fractions remain constant. Therefore, the fraction of inert gas that is likely to participate in the bubbleformation process should be greater in hyperbaric decompression than in hypobaric decompression. Moreover, a detailed model of tissue gas exchange considered in terms of either a series or parallel arrangement of tissues may provide a better fit to the data from diving exposures.
Conclusions
Our statistical analysis of empirical data suggests a significant role of gases other than N_{2} in bubble formation. First, the additional parameter of tension P_{other} is attributed to gases that are in physical solution in tissue at the end of the denitrogenation. Second, this tension of dissolved gases remains constant throughout the denitrogenation, whereas N_{2} tissue exchange follows an elimination that exponentially decreases with time. An exponential distribution in lieu of the P_{other} term used in Eq. 4 would have impaired the model prediction. Finally, third, the internal pressure exerted by gases other than N_{2}becomes an outward radial pressure of gas(es) in the bubble during the initial explosivegrowth phase. It appears that metabolic gases may assist the initial explosive bubblegrowth phase, as shown by our analysis.
Acknowledgments
P. P. Foster performed this research at National Aeronautics and Space Administration (NASA) Johnson Space Center as an External Postdoctoral Fellow of European Space Agency (8–10 rue MarioNikis, 75738 Paris cedex 15; associated with Laboratoire de Physiologie de l’Environnement, Faculté de Médecine Lyon GrangeBlanche, 8 Ave. Rockefeller, 69373 Lyon cédex 08, France) and as a visiting scientist through the Universities Space Research Association, Division of Space Life Sciences, 3600 Bay Area Blvd., Houston, TX 77058. Research of R. S. Chhikara was partially supported under NASA Grant NAG9802.
Footnotes

Address for reprint requests: P. P. Foster, Life Sciences Research Laboratories, Environmental Physiology Laboratory (SD3), NASALyndon B. Johnson Space Center, Houston, TX 77058.
 Copyright © 1998 the American Physiological Society