INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION APPENDIX REFERENCES

ASTRONAUTS PERFORMING EXTRAVEHICULAR activities (EVAs), when exposed to a reduced absolute pressure in their space suits, may experience decompression illness (DCI) (6-8). The primary cause of DCI is the formation and growth of gas bubbles within tissues evolving from excess dissolved gases (7, 8). It has been suggested that metabolic gases make up significant fractions of the gas in bubbles during altitude decompression (11, 41). In tissues supersaturated with an inert gas, typically N₂, in the presence of O₂ (30, 45), CO₂, and water vapor, de novo bubbles are generated from primordial gaseous entities, "gas micronuclei." The initial explosive bubble growth involves the surrounding tissue (11, 40) and may recruit all dissolved gases. To reduce bubble formation and growth, a denitrogenation or N₂ "washout" procedure consisting of prebreathing a hyperoxic mixture is performed before ascent to a constant working altitude pressure. We refer to the overall sequence of O₂ prebreathe, ascent, and time at altitude as a "decompression profile." When referring to the actual process of pressure reduction, however, we use the simpler term "decompression." Bubbles may form, grow, and decay during the sojourn at altitude, usually disappearing on recompression to sea level.

It has become increasingly apparent that skeletal muscle exercise, regardless of when it is performed, influences the onset of DCI (20, 48). A possible explanation is that exercise may create gas micronuclei (44). In particular, high-intensity exercise before decompression may create gas micronuclei (19), which increase the risk of DCI. Also, mechanical movement of body structures may cause cavitation (19) and increase the production of bubbles after decompression (20). Although exercise may accelerate N₂ elimination, it does not invariably precipitate bubble formation (20) and, therefore, may even induce a protection against DCI. Experimental results from Webb et al. (48) indicated that moderate exercise performed during the O₂-prebreathe period enhanced the tissue N₂ washout and reduced the incidence of DCI. Here, we develop a bubble formation-and-growth model (FGM) to answer the following questions. First, how do exercise-induced mechanisms impact formation and growth of gas bubbles? Second, are these mechanisms competing, and if so how? In the accompanying study (11a), the FGM will be validated in a survival analysis to predict the incidence of DCI in the National Aeronautics and Space Administration Altitude Experimental Data Set.

A bubble is defined as a volume of gas in a tissue that follows the phenomenological laws of ideal gases, diffusion and surface tension (40). Bubble growth is controlled by the classical laws of motion: the pressure of the gas provides the driving force to expand the bubble, while the inertia and elastic recoil of the tissue, together with the interfacial tension of the bubble wall, provide resistance to expansion (40). The actual work to change the bubble volume is accomplished solely by pressure gradients of gases across the interface between the bubble and surrounding tissue (21). During breathing of pure O₂ after decompression, the N₂ pressure gradient is directed from the tissue to the alveolus. Although this pressure gradient creates a flux that tends to remove N₂ from the vicinity of the tissue bubble, N₂ still diffuses into the bubble, which enlarges (40). In our hypotheses, the relevant system in which thermodynamic forces act consists of two distinct spatial and functional subsystems. First, there is a microsystem consisting of tissue volume containing the bubble, its boundary layer, and a tissue shell. This microsystem then interacts with a macrosystem as the alveolus-arterial blood-tissue shell-venous blood serial cascade of structural or functional barriers. We then developed the FGM to explain how bubble growth is influenced by exercise-induced changes in the O₂ physiological resistances in series in both systems.

Because bona fide bubbles appear to form randomly (47, 50), we hypothesized that their spatial and temporal distributions in small units of tissue volume follow a Poisson process. Informally, the Poisson process asserts that the event of bubble formation occurs independently through time in any of a large number of small units of tissue volume, but with a small probability in any given unit at a given time (32, 38). This process is characterized by parameters that may depend on the type, intensity, duration, and chronology of exercise. At working altitude pressure, the total volume of all bubbles in tissue is propagated in time through the growth-and-decay mechanism, which applies independently for each bubble relative to its time of formation.

We demonstrated the potential mechanisms of exercise by applying the FGM in simulations to calculate total bubble volume for several variations of decompression procedures typical of actual EVAs. These variations were primarily characterized by differences in O₂ consumption, blood flow, and bubble formation rates (Poisson process). The results of our simulations suggested that exercise-induced elevation of O₂ consumption at altitude facilitated the persistence of bubbles in tissues, whereas exercise-enhanced perfusion tended to suppress 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.

Glossary

(A-a)PO2(t)	Alveolar-arterial PO2 difference, Pa
Ab(t)	Surface area of the bubble at time t, m2
	Parameter of the Poisson process, dimensionless
(a-)PO2(t)	Arterial-venous PO2 difference, 8,000 Pa (~60 mmHg) at rest
	Parameter of the Poisson process, dimensionless
Di	Diffusivity of the ith gas species in the tissue, m2/min
	Thickness of the diffusion barrier (protein layer), 2 × 106 m
FIO2	Fraction of O2 in the inspired medium, dimensionless
h	Constant of proportionality = 2, dimensionless
JN	Net flux of all gas species across the boundary layer, mol · m2 · min1
Ji	Molar flux of the ith gas species across the boundary layer, mol · m2 · min1
k1	Tissue gas exchange rate constant for washin and washout of N2, min1
k2	Tissue gas exchange rate constant for washin and washout of O2, min1
Mb(t)	Number of gas moles in the bubble, mol
mCO2(t)	Number of dissolved moles of CO2 in the tissue, mol
mH2O(t)	Number of moles of water vapor from the tissue shell, mol
m(t)	Mean of the Poisson process, dimensionless
Mti(t)	Number of gas moles in the tissue shell, mol
	Tissue elastic recoil from Ref. 14, 3.7 × 103 Pa (= 3.7 × 104 dyn/cm2)
N(t)	Total number of bubbles in the n tissue units, dimensionless
Ni(t)	Number of bubbles formed in the ith unit at time t, dimensionless
	Constant of proportionality estimated from Table 2, 0.87, dimensionless
P	Ambient pressure, Pa
Pad,O2(t)	Partial tension of O2 fraction dissolved in the arterial blood, Pa
PAi(t)	Alveolar partial pressure of gas i, Pa
Pai(t)	Arterial tension of gas i, Pa
PaHb O2(t)	Partial tension of O2 fraction bound to Hb, Pa
Pb,i	Partial pressure of the ith gas in the bubble, Pa
Pb,mg(t)	Pressure of metabolic gases in the bubble, Pa
PIi(t)	Partial pressure of gas i in inspired breathing medium, Pa
Ptii	Tissue tension of the ith gas, Pa
Pi(t)	Tension of gas i in the mixed venous blood, Pa
PO2	Tension drop of dissolved tissue O2 due to O2 consumption, Pa
PO2	Mixed venous PO2, Pa
Pw(t)	O2 window, Pa
O2(t)	Arterial partial tension of dissolved O2 that is not utilized in tissue metabolism, Pa
O2(t)	Overall O2 pressure gradient in the macro- and microsystem, Pa
1(t)	Sum of pressures due to surface tension and tissue elastic recoil, Pa
ti(t)	Blood flow in the tissue shell, m3/min
R	Universal gas constant, N · m · mol1 · K1
R	Respiratory exchange ratio: 0.7-1.12, 0.82 at rest, dimensionless
Rb(t)	Radius of a bubble at time t, m
b(t)	Mean radius of bubbles from the entire region at time t, m
b,max	Maximum mean radius of bubbles from n units at time t, m
Rq	Circulatory convective resistance, Pa · l1 · min
sb,i	Solubility of the ith gas in the blood, ml · ml1 · 100 Pa1
sti,i	Solubility of the ith gas in the tissue, ml · ml1 · 100 Pa1
	Surface tension of the tissue from Refs. 13 and 14, 102 N/m (= 10 dyn/cm)
T	Temperature, Kelvin
T	Total time of exposure to altitude, min
t	Time of interest measured from first pressure change (prebreathe), min
talt	Time of exposure to altitude immediately after decompression, min
tb ij	Time of onset of the jth generated bubble in the ith unit of tissue volume measured from talt (talt = 0), min
t1/2,N2	Half time for tissue washin and washout of N2, min
t1/2,O2	Half time for tissue washin and washout of O2, min
Vb(t)	Volume of the bubble at time t, m3
Vb·(t)	Volume of bubbles in the tissue region, m3
Vb · max	Maximum volume of bubbles in the tissue region, m3
v(t)	Intensity of the Poisson process, bubbles formed/min
tiO2(t)	O2 uptake in the tissue shell, m3/min
Vti(t)	Volume of the tissue shell at time t, m3
Vtot(t)	Volume of the tissue element at time t, m3
Vtu	Volume of the tissue unit (realized as a cube), m3
xi	Molar fraction of the ith gas species, dimensionless

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION APPENDIX REFERENCES

Growth-and-Decay Model for a Single Bubble

Macro- and microsystems of gas exchange. We define a tissue element to be a small spherical unit of tissue containing the bubble (Fig. 1A), where significant gas exchanges take place (4, 40). We assumed that every tissue element contains a single bubble and that the ratio of the volume of the tissue element (V_tot) to the bubble volume (V_b) is constant. The part of the tissue element that does not include the bubble per se will be referred to as the homogeneous tissue shell. We proceed to derive a differential equation relating the bubble radius (R_b), and hence V_b, to physical and physiological parameters obtainable from the characteristics of the decompression profile.

View larger version (64K): [in this window] [in a new window]   Fig. 1.   A: views of the microsystem for 2 bubble sizes. The bubble is coated with a thin adsorbed protein layer, which is a barrier for the diffusion of gases into and out of the bubble. The spherical tissue shell surrounding the coated bubble of volume Vtot is proportional to the bubble volume (Vb) and continually redefined as the bubble grows or decays (Vtot = hVb). We assume that h = 2. B: periphery of spherical tissue element (part of the macrosystem) envelops the microsystem, an imaginary smaller and inner spherical volume without any real interface. The microsystem contains the bubble and the surrounding tissue shell, which is sufficiently small so that any gas moles entering or leaving the tissue shell are also involved in exchanges across the bubble diffusion barrier. Movement of gas is illustrated by arrows. Direction of gas fluxes during the initial explosive bubble growth phase is shown; later during decay, flux directions of certain gas species may be reversed. Sign (+ or ) of gas flux is obtained according to the rule described in METHODS. C: pressure gradients and structural and functional barriers. Six O2 physiological resistances in series modify the O2 pressure gradient to the bubble (Eq. 9). In the case of N2, only 2 functional barriers, the tissue dissolution and elimination, are critical (Eq. 7). Because we simulate submaximal levels of exercise, the total content of CO2 increase in the tissue should not exceed the removal capacity by blood flow. Therefore, we derived our equations for a constant PCO2 in tissue of 6.13 kPa (46 mmHg). D: tissue region is made up of n identical and homogeneous volumes, the units of tissue volume. Four of these units are pictured by cubes that contain bubbles. In each unit of tissue volume, bubbles of different age and size follow a Poisson distribution. Mean for the Poisson distribution is 6.

Diffusion of gases across the diffusion barrier in the microsystem. The volumes of gases are expressed under standard body conditions of temperature, ambient pressure, and saturated with water vapor (BTPS). In a three-dimensional coordinate system, the molar flux of the ith permeating ideal gas species (J_i) obeys Fick's first phenomenological law of diffusion (4, 14, 17, 18, 33, 39, 43) and can then be estimated by J_i = (P/RT)D_ix_i, where P is the ambient pressure, R is the universal gas constant, T is the temperature in degrees Kelvin, D_i is the diffusion coefficient, and x_i is the molar fraction gradient of the ith gas in the macrosystem. For air breathing, gas exchange dynamics involve four relevant species: CO₂, N₂, O₂, and H₂O (i = 1, ... ,4). In the macrosystem, x_i is defined along a direct path to the center of the bubble, where the inward direction is negative and outward is positive. Resulting fluxes have signs in accordance with the "macrosystem" rule (inward = negative; outward = positive). In the microsystem, we establish that a flux is positive if it has the same direction as in the macrosystem (opposite direction = negative). Therefore, the CO₂ and N₂ fluxes are negative (Fig. 1B). The net flux (28) (J_N) into or out of the bubble is expressed as follows

(1)

Applying Henry's law to the dissolved tissue gases surrounding the bubble and using the ideal gas equations for gas pressures inside the bubble (14), J_N(t) can be approximately expressed in terms of partial pressures of the ith gas as a function of time. As reported previously (14, 28), the net flux is thus expressed as follows

(2)

where s_ti,i is the solubility of the ith gas species in the tissue element,  is the thickness of the diffusion barrier, and Pti_i(t) and P_b,i(t) are the partial tissue tension and pressure within the bubble of the ith gas, respectively. When referring to a specific gas species, we use the convention of replacing the subscript i by the gas name (e.g., s_ti,N2 instead of s_ti,i). Time is expressed in minutes and measured from the start of the prebreathe period to the end of the exposure to altitude. The prebreathe period begins at time t = t₀ = 0, when partial pressures of gases in the breathing medium start to change from the equilibrium of standard atmospheric conditions. Arrival at working altitude pressure (end of depressurization), occurs at time t = t_alt.

Moles of gas within the tissue shell and in the bubble. To evaluate the net flux (Eq. 2), we next calculate the number of moles of each gas crossing the diffusion barrier. Suppose a particular bubble forms at t_b > t_alt. For t > t_b, let M_ti(t) be the total number of moles of gas in the tissue shell. From Henry's law (14), we have

(3)

where m_CO2(t) and m_H2O(t) are the number of moles of dissolved CO₂ and water vapor, respectively, Vti(t) is the tissue shell volume pertaining to the bubble at time t [which has been in existence for (t  t_b) min], and _O2(t) is the O₂ overall pressure difference between the macro- and the microsystem. Using the equation of state of an ideal gas (14), we estimate the number of moles in the bubble

(4)

where V_b(t) is the volume of the bubble at time t.

Estimation of the bubble radius. From the law of conservation of mass (21, 28), the number of moles diffusing into and out of the bubble per minute is

(5)

for t > t_b, where A_b(t) is the surface area of the bubble and _ti(t) and _b(t) are gas mole uptake into and out of the tissue shell (microsystem) and into and out of the bubble, respectively. (We use the convention that the overdot denotes differentiation with respect to time.) By definition of the microsystem, we assume Vti to be proportional to V_b (h = Vti/V_b1) and h to be sufficiently small so that any gases entering or leaving the tissue shell are being involved in exchanges across the diffusion barrier of the microsystem. Finally, for t > t_b, Eq. 5 can be rewritten in terms of the bubble radius R_b(t)

(6)

where L(t) and K(t) are quantities derived in the APPENDIX. For a given decompression profile, values of K(t), L(t), and J_N(t) may be obtained as a function of time through measurements of inspired pressure and fraction of gases. Details of the calculation of (t) and (t) are given in the APPENDIX. Equation 6 has no analytic solution for R_b(t) and must be solved numerically.

Gas transport in the macrosystem: estimation of pressures and/or tensions. To obtain L(t) and K(t) in Eq. 6, it is first necessary to estimate the pressure gradients in the macrosystem. These may be calculated from values of the absolute pressure and inspired fractions of N₂ and O₂ and expired CO₂ in the breathing medium for each phase of our decompression profiles. In addition, within the macrosystem, we consider partial pressures of each gas: inside the alveolus [PA(t)], inside the pulmonary capillary [Pa(t)], and in the mixed venous blood [P(t)]. For all gases, we assume P(t) = Pti(t).

N₂ tissue tension. On the downstream side of the macrosystem flow, we estimated Pti_N2 for t > t_alt using the classical exponential equation (8, 11, 14). Using this method, we computed Pti_N2 by increments at fixed times t₁, t₂, ... ,t_n, where t_n1 = t_alt and t_n = t. The incremental expression for Pti_N2 is given by

(7)

where Pa_N2 is the N₂ arterial tension derived from the alveolar gas equations and partial pressures (11, 42) and k₁ is the tissue gas exchange rate constant for N₂.

O₂ transport. On the upstream side of the macrosystem flow portrayed in Fig. 1B, O₂ is driven through a series of interfaces (12) into the tissue element, where it is dissolved. To correctly model the flow, it is necessary to estimate pressure differences across various encountered interfaces as follows (Fig. 1C). First, because of the alveolar membrane, there is an alveolar-arterial pressure difference [(A-a)PO₂(t)], which tends to increase with PI_O2(t) (5, 15, 37). On the basis of our own measured values of PI_O2(t), we estimated (A-a)PO₂(t) with an algorithm that uses values given by Clark and Lambertsen (5). We then obtained Pa_O2(t) by subtraction from PA_O2(t). Second, the O₂ transfer to the capillaries occurs when O₂ is transported in physical solution or bound to Hb. Above the threshold Pa_O2(t) of 13.33 kPa (100 Torr, 1 kPa = 7.50062 Torr), the O₂ saturation is assumed to be 100% and the unbound O₂ remains in physical solution. In terms of tension, the arterial O₂ tension is made up of two components, the O₂ dissolved fraction [Pa_d,O2(t)] and the Hb-bound O₂ [Pa_Hb O2(t)]. We used an algorithm derived from the O₂ dissociation curve (29, 35, 36) to estimate Pa_Hb O2(t) as a function of Pa_O2(t). Third, the O₂ supply to the mitochondria results in the withdrawal of O₂ from further utilization in the O₂ transport process across the bubble boundary layer. Di Prampero and Ferretti (9, 10) derived a relationship between the O₂ tissue consumption [ti_O2(t)] and the arteriovenous O₂ difference [(a-)PO₂(t)]. The relationship is ti_O2(t) = [(a-)PO₂(t)]/R_q = P_O2(t)/R_q, where R_q is the circulatory convective resistance and P_O2 is the tension drop of dissolved tissue O₂ due to O₂ consumption. Finally, O₂ supplied to the tissue element can potentially participate in bubble gas exchanges of the microsystem. Thus the tension of the dissolved O₂ that is applied to the microsystem at time t [_O2(t)] can be written in the form

(8)

Dissolution of O₂ in the tissue element follows Henry's law and is described by an exponential relation similar to Eq. 7. As was the case for N₂, _O2(t), the overall O₂ pressure gradient in the macro- and microsystem that applies from the alveolus to the tissue element can be expressed incrementally at fixed times t₁, t₂,... ,t_n  t, so that

(9)

where k₂ is the tissue gas exchange rate constant for O₂. Indeed, metabolism lowers the O₂ tension in the tissue element below Pa_O2, creating a phenomenon known as the "O₂ window" or "inherent unsaturation" (11, 16, 23, 34, 42). The sum of partial tensions of the dissolved gases in the tissues is usually less than atmospheric pressure. The O₂ window [P_w(t)] is calculated by subtracting the sum of pressures of all dissolved gases to the ambient pressure and can be written using _O2(t) so that P_w(t) = _O2(t) + {P(1  FI_O2)  [Pti_N2(t) + Pti_CO2(t) + Pti_H2O(t)]}. Equations 7 and 9 are then used in the APPENDIX to calculate L(t) and K(t).

Number and onset times of bubbles in tissue. Yount (50) proposed a stochastic model for accretion and deletion of skin molecules that leads to an exponential distribution for the number of micronuclei. Here, we consider a stochastic model of bubble formation in which micronuclei evolve into bubbles at random times after decompression following a Poisson process. Consider a tissue region divided into n units of tissue that are identical in makeup and perfusion (40). Each tissue unit is independent, and there is no diffusion from one unit to another. All tissue units are the same size, and units are evenly distributed in space. In contrast, bubbles in one unit are of different age and size. Schematically, the units are illustrated as cubes of constant volume V_tu in Fig. 1D. For a total time at altitude of T minutes, N_i(t) (i = 1, ... , n), the number of bubbles formed in the ith unit of tissue volume up to time t (in minutes, 0 < t  T) is assumed to follow a nonhomogeneous Poisson process (32, 38) with intensity v(t), v(t) = e^t. The parameters  and  are driven by the decompression procedure and the level of exercise or rest. For a given procedure,  also serves as a scaling factor, being proportional to V_tu. The decreasing exponential form of v(t) reflects the rapidly decreasing propensity to form bubbles as exposure time increases (6, 22).

(10)

Mean bubble radius and total volume of bubbles. The mean bubble radius for the given region of tissue at time t can be written as

(11)

where N(t) = _i=1^IN_i(t) and R_b,ij(t) is the radius of the jth bubble in the ith tissue unit. By convention, we take R_b,ij(t) = 0 if the bubble has not formed by time t. Under the additional assumption that bubbles form and grow independently over the n tissue units, N(t) is also a Poisson process (32, 38). If the region is homogeneous in the sense that all the Poisson processes N_i(t) have identical values of  and , then the mean of N(t) is simply (n/)(1  e^t). With the assumption of spherical bubbles, the total volume of bubbles in the region of tissue at time t is

(12)

Experimental Design

For each profile type, various simulations of bubble formation and growth were analyzed to examine the effect of exercise on _b(t) and V_b·(t). For simulations A9-A11 (Table 1), we modified values of P_O2 while keeping all other parameters fixed to isolate the effect of ti_O2. These higher values are representative of heavier exercise workloads required to perform EVA tasks during some orbital missions. For simulations A7 and A8,  was increased by a factor of 3 to emulate the effect of an increased rate of bubble formation, but with physiological parameters remaining at no-exercise levels. This would be the case if mechanical motion takes place without significant additional O₂ consumption. It has been conjectured that mechanical motion of tissues may cause cavitation (19) and increase the bubble formation rate (20). For simulations involving profiles A, C, and D, the parameter  was chosen to make the expected number of bubbles per tissue unit ( /) equal to 6.0 over 50 tissue units.

For the case of exercise at altitude (simulations B1-B14), we investigated the effect of bubble formation rate on maximum bubble volume. This rate was again controlled by varying . During this exercise, more units of tissue would be recruited for bubble formation; therefore, we increased n, the number of tissue units, to 100. Also, the density of bubbles per tissue unit would be expected to be greater than at rest; hence, we changed  so that the mean number of bubbles per unit was 25.

Simulation Process

View larger version (20K): [in this window] [in a new window]   Fig. 2.   Simulation flow chart.

From the Poisson distribution with mean m(t) (Eq. 10), we generated N_i(T), the total number of bubbles formed over a decompression period of T minutes. Values of  and  defining m(t) are given in Table 1. Methodology for generating random numbers from the Poisson distribution is well known (32). Next, we used a property of Poisson processes (32) that relates the conditional distribution of event times to the mean, when the total number of events is known. This enabled us to generate random bubble creation times t_b,ij [j = 1, ... , N_i(T); see APPENDIX].

For each creation time, Eq. 6 was constructed using Eqs. 1-5 and A1-A13, where t_b in the APPENDIX is replaced by t_b,ij, i.e., onset time of the jth bubble in the ith unit of tissue volume. Numerical solutions R_b,ij(t) for R_b(t) in Eq. 6 were then found for each simulated bubble radius at 10-min intervals using Mathematica software version 3.0.1 (49). Solution of Eq. 6 proved difficult. In general, a combination of nonstiff Adams or stiff Gear, Fehlberg order 4-5, or Runge Kutta methods for nonstiff equations was required to achieve convergence. The Gel'fand-Lokutsiyevski chasing method was used for solving the boundary value problem. Processing of 300 bubbles took ~2 min to run on a 300-mHz personal computer with 64 MB of random access memory. Finally, the R_b,ij(t) was used in Eqs. 11 and 12 to calculate _b(t) and V_b·(t).

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION APPENDIX REFERENCES

Effects of O₂ Consumption on Bubble Dynamics

View larger version (19K): [in this window] [in a new window]   Fig. 3.   Simulations of b in various conditions. Time is measured from the start of prebreathe period and the elapsed time until altitude exposure begins at 216 min. Some bubbles start to grow on arrival at altitude. A: simulations of decompression profile A under 4 levels of O2 consumption, i.e., PO2 at 8 kPa (A1), 12 kPa (A9), 18 kPa (A10), and 20 kPa (A11); as tiO2 (and PO2) increases, bubbles decay less rapidly. B: effect of the O2 window. At an altitude exposure of 60 kPa (D1, FIO2 = 1), a large O2 window suppresses bubble growth. Two realizations (A1 and A3) of profile A (no exercise) show very little difference in b; variance due to the Poisson process is minimal and does not significantly impact interpretation of the results. See Glossary for definition of abbreviations.

Exercise Decreases the Mean Bubble Radius

Hills and LeMessurier (16) reported that, after 15 min of exposure of rabbits to an hyperoxic medium, the O₂ window was large. Here, we agree that only a small amount of O₂ would dissolve in the tissue during this time interval. However, during several hours of hyperoxic O₂ prebreathe/altitude exposure, greater amounts of O₂ would dissolve in tissues, thereby eventually reducing the O₂ window. According to Lambertsen et al. (23), other mechanisms such as hypercapnic vasodilatation may also facilitate the O₂ transfer to the tissue, which in turn accelerates the window reduction. Lambertsen et al. also showed in humans, that arterial hypercapnia, a highly potent vasodilator of cerebral blood vessels, in conjunction with breathing for 15 min at 3.5 atm (fraction of CO₂ in the inspired medium = 0.02, FI_O2 = 0.98) induced a significant elevation of P_O2 (146 kPa) in internal jugular venous blood samples, as compared with breathing without hypercapnia (FI_O2 = 1, P_O2 = 10.13 kPa). In both cases Pa_O2 = 266 kPa; however, hypercapnia via cerebral vasodilatation reduced the O₂ window in very limited time.

Observations in pigs breathing hyperoxic mixtures showed that the bubble incidence in the pulmonary artery was reduced as Pa_O2 increased (34). Here, for pure O₂ breathing, we illustrate how P = PI_O2 affects _b(t) through change in Pa_O2. Figure 3B shows _b(t) for the case of no exercise at two different altitudes: P = 30 kPa (simulation A1) and P = 60 kPa (simulation D1). At 60 kPa, the larger value of Pa_O2 induces a significant reduction in _b,max. Therefore, we postulate that the O₂ window inhibits bubble enlargement at the beginning of the altitude exposure. Later, because of increased perfusion, the higher O₂ flow to tissues augments the amount of dissolved O₂ in the unit of tissue volume. This, in turn, decreases the O₂ window, thus tending to slow the rate of bubble decay. However, the greater amounts of physically dissolved O₂ facilitate increased O₂ exchange within the microsystem. According to Van Liew and Burkard (41), many short O₂ transients would permeate rapidly in the bubble, resulting finally in a marked decay rate of bubble radii.

Figure 4 compares _b,max for decompression profiles whose physiological parameters (P_O2, R, t_1/2,N2 and t_1/2,O2) have the characteristics of no exercise, moderate exercise at altitude, and heavy exercise during prebreathe, but where  is held fixed. First, we compared the effect of exercise when  is set to the resting value of 0.014 (simulations A1, B1, and C1). Then a similar comparison was made for  = 0.017 (simulations A2, B2, and C2). For both values of , we observed that _b,max dropped by ~64%, (from 34.1 to 12.4 µm for  = 0.014 and from 44.5 to 16.2 µm for  = 0.017). When the effect of heavy exercise during prebreathe was compared with the case where there is no exercise, the drop was more dramatic, i.e., ~83% for both values of . Results of these simulations illustrate how an augmentation of blood flow, which decreases t_1/2,N2 and t_1/2,O2, is paralleled by a reduction of bubble radius regardless of the intensity of the Poisson process and the level of ti_O2.

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Maximum bubble growth in various conditions of rest and exercise. Simulations of no exercise (A1, A2, A7, and A8), exercise at altitude (B1 and B2), and heavy exercise during prebreathe (C1 and C2) are shown.

Also, with an acceleration of the nucleation process ( increased from 0.014 to 0.017), the increase in _b,max was much more pronounced for the no-exercise case than for the case of exercise at altitude. However, the relative increase was about the same (30%), and for the prebreathe case the relative change appeared less (~20%). This is probably because, regardless of the nucleation rate, only small amounts of dissolved N₂ remain to be available for bubble growth after the start of decompression.

For profile A, we investigated the effect of increasing  from its resting value of 0.014 to large values reflecting intense bubble formation with physiological parameters remaining fixed (P_O2 = 8 kPa, R = 0.82, t_1/2,N2 = 360 min and t_1/2,O2 = 313.2 min). We observed that in simulations A1, A2, A7, and A8, _b,max increased from 34.1 to 49.8 µm as  increased from 0.014 to 0.051 (Fig. 4). As  increases, early formation of bubbles before N₂ supersaturation drops, leading to larger radii than the resting case (simulation A1). The pattern of increase was nonlinear, tending toward a plateau for large values of . This is because, no matter how early the bubble is formed, for a fixed N₂ pressure gradient, the amount of N₂ available for diffusion into a bubble is limited.

Does Exercise at Altitude Increase the Volume of Tissue Bubbles?

View larger version (17K): [in this window] [in a new window]   Fig. 5.   A: effect of exercise at altitude on total volume of bubbles. A5, no exercise; B5, exercise at altitude. To achieve the same Vb · max as at rest [N(t) = 274],  had to be increased by a factor of ~2.5 (from 0.014 to 0.38), resulting in ~9.5 times as many bubbles as with exercise at altitude [N(t) = 2,612]. For B5, a relatively large number of smaller bubbles formed earlier; for A5, larger bubbles were formed, but mostly at later times. Therefore, Vb · max for A5 was shifted to the right. B: limitation of the maximal bubble volume produced in the tissue region. In simulations B3-B14, we calculated Vb · max for profile B (exercise at altitude), with  ranging from 0.036 to 1.5. Vb · max increases rapidly as a function of  when  is small and reaches a plateau of ~0.1 mm3 for  > 0.3.  had to be increased by a factor of ~11.7 ( = 0.2) in simulation B12 to achieve the same Vb · max as in simulation A6 ( = 0.017).

As demonstrated in Fig. 4, exercise-enhanced blood flow reduces _b,max and, therefore, V_{b · max} for a fixed number of bubbles formed. In this case, the only way V_{b · max} could be increased is through a more intense generation of bubbles. In simulations B3-B14, we calculated V_{b · max} for simulation B (exercise at altitude), with  ranging from 0.036 to 1.5. In Fig. 5B, V_{b · max} increases rapidly as a function of  when  is small and reaches a plateau of ~0.1 mm³ for  > 0.3. The reason is that, similar to the no-exercise case, the N₂ pressure gradient limits the supply of N₂ available for bubble growth in the tissue region.

Stability

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Review of Assumptions

Perspectives