A model for influence of exercise on formation and growth of tissue bubbles during altitude decompression.

In response to exercise performed before or after altitude decompression, physiological changes are suspected to affect the formation and growth of decompression bubbles. We hypothesized that the work to change the size of a bubble is done by gas pressure gradients in a macro- and microsystem of thermodynamic forces and that the number of bubbles formed through time follows a Poisson process. We modeled the influence of tissue O(2) consumption on bubble dynamics in the O(2) transport system in series against resistances, from the alveolus to the microsystem containing the bubble and its surrounding tissue shell. Realistic simulations of experimental decompression procedures typical of actual extravehicular activities were obtained. Results suggest that exercise-induced elevation of O(2) consumption at altitude leads to bubble persistence in tissues. At the same time, exercise-enhanced perfusion leads to an overall suppression of bubble growth. The total volume of bubbles would be reduced unless increased tissue motion simultaneously raises the rate of bubble formation through cavitation processes, thus maintaining or increasing total bubble volume, despite the exercise.

Predicting time to decompression illness during exercise at altitude, based on formation and growth of bubbles.

For altitude decompressions, we hypothesized that reported onset times of limb decompression illness (DCI) pain symptoms follow a probability distribution related to total bubble volume [V(b.)(t)] as a function of time. Furthermore, we hypothesized that the probability of ever experiencing DCI during a decompression is associated with the cumulative volume of bubbles formed. To test these hypotheses, we first used our previously developed formation-and-growth model (Am J Physiol Regulatory Integrative Comp Physiol 279: R2304-R2316, 2000) to simulate Vb.(t) for 20 decompression profiles in which 334 human subjects performed moderate repetitive skeletal muscle exercise (827 kJ/h) in an altitude chamber. Using survival analysis, we determined that, for a controlled condition of exercise, the fraction of the subject population susceptible to DCI can be approximately expressed as a power function of the formation-and-growth model-predicted cumulative volume of bubbles throughout the altitude exposure. Furthermore, for this fraction, the probability density distribution of DCI onset times is approximately equal to the ratio of the time course of formation-and growth-modeled total bubble volume to the predicted cumulative volume.

Role of metabolic gases in bubble formation during hypobaric exposures.

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 N2 in tissues may facilitate the initial explosive bubble-growth phase.

Evolved gas, pain, the power law, and probability of hypobaric decompression sickness.

The intensity of a pain-only decompression sickness (DCS) symptom with respect to time at altitude increases, peaks, and then declines in some cases. A similar pattern is also seen in a graph of the probability density function [f(t)] for DCS. The f(t) is the proportion of DCS per unit time with respect to time at altitude. The integration of f(t) with respect to time provides the cumulative probability of DCS [P(DCS)]. We suspect that the perceived intensity of pain with a given stimulus intensity is related to the P(DCS); it may be related to the intensity of the stimulus to a power (alpha). Our stimuli are defined as pressure ratio [PR = (phi P1N2/ P2)-11] or pressure difference [delta P = phi P1N2-P2], where phi P1N2 is the N2 partial pressure calculated in the 360 min half-time (t1/2) compartment or t1/2 is estimated with other parameters and P2 is ambient pressure after the ascent. Both stimuli represent a potential released volume of gas. We tested the null hypothesis that alpha > 1 was no better than alpha = 1 in PR alpha and delta P alpha in a log logistic survival analysis of 1085 exposures in hypobaric chambers. The log likelihood number increased from -1198 for alpha = 0 for the null model to -724 for PR alpha when alpha = 3.52 with a 42 min t1/2 and -714 for delta P alpha when alpha = 8.44 with a 91 min t1/2. We conclude that the improvement in our expressions for decompression dose with alpha > 1 is not by random chance and that alpha may link the physics of gas evolution to the biology of pain perception. Because of our empirical approach, we do not exclude other possible interpretations.

Information about venous gas emboli improves prediction of hypobaric decompression sickness.

HYPOTHESIS: Information about venous gas emboli (VGE) detected in the pulmonary artery such as the occurrence of VGE, Grade of VGE, the time when VGE first appear, and the time course of the Grade or occurrence of VGE, could be used to better assess the probability of decompression sickness [P(DCS)] in any hypobaric decompression. We hypothesized that these data would improve the estimate of P(DCS) since objective measurements of the decompression stress are available for the individual. METHODS: A binary correlation and survival analysis approach were used on information from 1,322 hypobaric chamber exposures to establish the relationships between VGE and DCS. RESULTS: Based on the correlation analysis, the absence of VGE is highly correlated with the absence of a DCS symptom, as evident from a negative predictive value of 0.98. However, the presence of VGE in the pulmonary artery is not highly correlated with a subsequent DCS symptom, as evident from a positive predictive value of 0.39 for Grades III and IV VGE. The correlation results suggest the presence of VGE in the pulmonary artery is a necessary, but not sufficient, condition for DCS. Based on the survival analysis, the log logistic survival model, a one-variable model with two parameters gave a log likelihood (LL) of -757. This model was expanded to include seven additional variables, including four about VGE, and the nine-parameter model gave a better LL of -481. CONCLUSION: Information about VGE plus other variables known to influence DCS is useful to better assess the P(DCS) for hypobaric decompressions.

Relationship of the time course of venous gas bubbles to altitude decompression illness.

The correlation is low between the occurrence of gas bubbles in the pulmonary artery, called venous gas emboli (VGE), and subsequent decompression illness (DCI). The correlation improves when a "grade" of VGE is considered; a zero to four categorical classification based on the intensity and duration of the VGE signal from a Doppler bubble detector. Additional insight about DCI might come from an analysis of the time course of the occurrence of VGE. Using the NASA Hypobaric Decompression Sickness Databank, we compared the time course of the VGE outcome between 322 subjects who exercised and 133 Doppler technicians who did not exercise to evaluate the role of physical activity on the VGE outcome and incidence of DCI. We also compared 61 subjects with VGE and DCI with 110 subjects with VGE but without DCI to identify unique characteristics about the time course of the VGE outcome to try to discriminate between DCI and no-DCI cases. The VGE outcome as a function of time showed a characteristic short lag, rapid response, and gradual recovery phase that was related to physical activity at altitude and the presence or absence of DCI. The average time for DCI symptoms in a limb occurred just before the time of the highest fraction of VGE in the pulmonary artery. It is likely, but not certain, that an individual will report a DCI symptom if VGE are detected early in the altitude exposure, the intensity or grade of VGE rapidly increases from a limb region, and the intensity or grade of VGE remains high.

A probabilistic model of hypobaric decompression sickness based on 66 chamber tests.

One consequence of the NASA tissue ratio (TR) model is that calculated probability of decompression sickness [P(DCS)] is constant in tests at different ambient pressures so long as the ratio of P1N2 to P2 is the same in each test; P1N2 is N2 pressure in the 360 minute half-time compartment, and P2 is ambient pressure after decompression. We test the hypothesis that constant P(DCS) is better described by TRs that decrease as P2 decreases. Data were from 66 NASA and USAF hypobaric chamber tests resulting in 211 cases of DCS in 1075 exposures. The response variable was presence or absence of DCS while at P2. Explanatory variables were P1N2, P2, exercise at P2, (yes or no), time to DCS (failure time), and time to end of test in those without DCS (censored time). Probability models were fitted using techniques from survival analysis. The log likelihood for the two parameter log logistic survival model was -846 with only failure and censored times, -801 when TR [P1N2/P2] plus exercise were added, and -663 when modified TR [(((P1N2+cl)/P2)-1)c2] plus exercise were added, where c1 and c2 are fitted parameters in the five parameter model. Constant P(DCS) was better described by TRs that decrease as P2 decreases; a conclusion supported by additional empirical observations, and bubble growth models that are independent of DCS data. Exercise increased the P(DCS) at P2. As a description of decompression "dose", the modified TR was superior to TR over a wider range of experimental conditions.