High oxygen partial pressure in tissue delivered by stabilized microbubbles. Theory.
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Animals↗
Biomedical subjects
H D Van Liew
Publications and source records attributed to H D Van Liew.
Stabilized bubbles in the body: pressure-radius relationships and the limits to stabilization.
We previously outlined the fundamental principles that govern behavior of stabilized bubbles, such as the microbubbles being put forward as ultrasound contrast agents. Our present goals are to develop the idea that there are limits to the stabilization and to provide a conceptual framework for comparison of bubbles stabilized by different mechanisms. Gases diffuse in or out of stabilized bubbles in a limited and reversible manner in response to changes in the environment, but strong growth influences will cause the bubbles to cross a threshold into uncontrolled growth. Also, bubbles stabilized by mechanical structures will be destroyed if outside influences bring them below a critical small size. The in vivo behavior of different kinds of stabilized bubbles can be compared by using plots of bubble radius as a function of forces that affect diffusion of gases in or out of the bubble. The two ends of the plot are the limits for unstabilized growth and destruction; these and the curve's slope predict the bubble's practical usefulness for ultrasonic imaging or O2 carriage to tissues.
Excipients↗
Relationship of oxygen content to PO2 for stabilized bubbles in the circulation: theory.
Stabilized bubbles can pass through capillary beds, recirculate for a few minutes or hours, and carry O2 from the lungs to the tissues. Here, we develop the theory for the O2 content-PO2 relationship of bubbles and the alterations of the bubbles that are coupled to the O2 transport. We provide examples for bubbles stabilized by a slowly permeating gas; bubbles stabilized by mechanical structures may behave similarly. Because there are two mechanisms for O2 unloading (lowering of PO2 and shrinkage), the bubbles release a large fraction of their O2 content at high PO2; when pure O2 is breathed, one-half of the content of a 3-microns-radius bubble is released before PO2 falls to 500 Torr. The possibility that stabilized bubbles could become a clinical tool for therapeutic transport of O2 raises many issues to be investigated. The highunloading PO2 offers opportunities for delivering O2 by diffusion to poorly perfused regions of the tissue but also presents a hazard of O2 toxicity to perfused tissue.
Air Pressure↗
Breathing a mixture of inert gases: disproportionate diffusion into decompression bubbles.
To study the consequences of diving with gas mixtures, we simulated growth of decompression bubbles using an equation system that accounts for major determinants of bubble behavior. When breathing a mixture, bubbles are smaller than expected from linear interpolation between bubbles with either of the unmixed component gases because of disproportionate diffusion effects: a) When few bubbles form, the inert gas that permeates fastest becomes over-represented, relative to the breathing gas, inside bubbles during growth; this slows further entrance of the fast gas and enhances entrance of the slower gas. b) With N2-He mixtures and few bubbles, the over-represented gas is He in aqueous tissue, but is N2 in lipid tissue. c) When many bubbles form, the over-represented gas is the one with higher tissue solubility. Our simulations indicate that the smallest bubbles always occur with breathing of one of the component gases, but which gas that is depends on whether the tissue is lipid or aqueous and whether few or many bubbles form.
Absorption↗
Testing of hypotheses about altitude decompression sickness by statistical analyses.
This communication extends a statistical analysis of forced-descent decompression sickness at altitude in exercising subjects (J Appl Physiol 1994; 76:2726-2734) with a data subset having an additional explanatory variable, rate of ascent. The original explanatory variables for risk-function analysis were environmental pressure of the altitude, duration of exposure, and duration of pure-O2 breathing before exposure; the best fit was consistent with the idea that instantaneous risk increases linearly as altitude exposure continues. Use of the new explanatory variable improved the fit of the smaller data subset, as indicated by log likelihood. Also, with ascent rate accounted for, replacement of the term for linear accrual of instantaneous risk by a term for rise and then decay made a highly significant improvement upon the original model (log likelihood increased by 37 log units). The authors conclude that a more representative data set and removal of the variability attributable to ascent rate allowed the rise-and-decay mechanism, which is expected from theory and observations, to become manifest.
Altitude↗
Bubbles in circulating blood: stabilization and simulations of cyclic changes of size and content.
Surface tension, blood pressure, and inherent unsaturation due to O2 metabolism promote diffusion of gases out of bubbles in the bloodstream. We review the mechanisms that can overcome the absorptive tendencies so small spherical bubbles can persist. One general type of stabilizer is a mechanical structure at the gas-liquid interface that can support a negative pressure so that gases inside can be in diffusion equilibrium with their counterparts outside; one possibility for mechanical stabilizers are surfactant films. We show that a slowly permeating gas is analogous to a mechanical stabilizer; it allows equilibration of other gases inside-to-outside by diluting the gases inside. By using numerically solved equations based on physics of diffusion, we demonstrate how nonrigid stabilized bubbles change size as they move through the circulatory system. In small pulmonary vessels, the bubbles enlarge because blood pressure is low, there is no inherent unsaturation, and O2 and N2 diffuse from lung gas into the bubble; these gases diffuse out again in the systemic circulation.
Absorption↗
Effects of physical properties of the breathing gas on decompression-sickness bubbles.
To explore the relative dangers of different inert gases, we developed mathematical relationships concerned with bubble growth, using equations that separate gas properties from other variables. Predictions for saturation exposures were as follows. 1) Peak volume of a bubble is proportional to solubility in tissue when bubble density is high and to the 3/2 power of the ratio of the permeation coefficient to the partition coefficient when density is low. 2) Bubble duration is inversely proportional to the partition coefficient for the inert gas. 3). Sizes and durations of bubbles for one inert gas relative to another depend on whether the tissue is aqueous or lipid but are independent of the magnitude of the decompression and tissue half time. 4). He should give smaller bubbles than N2, except in aqueous tissue with low bubble density; our prediction correlates qualitatively with relative dangers observed with animals but seems to overestimate the safety afforded by He. Numerical simulations illustrate how nonsaturation dives are less predictable because more variables are involved.
Decompression Sickness↗
Simulation of gas bubbles in hypobaric decompressions: roles of O2, CO2, and H2O.
UNLABELLED: To gain insight into the special features of bubbles that may form in aviators and astronauts, we simulated the growth and decay of bubbles in two hypobaric decompressions and a hyperbaric one, all with the same tissue ratio (TR), where TR is defined as tissue PN2 before decompression divided by barometric pressure after. We used an equation system which is solved by numerical methods and accounts for simultaneous diffusion of any number of gases as well as other major determinants of bubble growth and absorption. We also considered two extremes of the number of bubbles which form per unit of tissue. RESULTS: A) Because physiological mechanisms keep the partial pressures of the "metabolic" gases (O2, CO2, and H2O) nearly constant over a range of hypobaric pressures, their fractions in bubbles are inversely proportional to pressure and their large volumes at low pressure add to bubble size. B) In addition, the large fractions facilitate the entry of N2 into bubbles, and when bubble density is low, enhance an autocatalytic feedback on bubble growth due to increasing surface area. C) The TR is not closely related to bubble size; that is when two different decompressions have the same TR, metabolic gases cause bubbles to grow larger at lower hypobaric pressures. We conclude that the constancy of partial pressures of metabolic gases, unimportant in hyperbaric decompressions, affects bubble size in hypobaric decompressions in inverse relation to the exposure pressure.
Aerospace Medicine↗
Simulation of exchanges of multiple gases in bubbles in the body.
This communication introduces a system of equations, for numerical solution, which simulates the generation, growth, and decay of bubbles. The system is an advance over previous works because it allows for simultaneous diffusion of any number of gases. Our purpose for developing the system is to gain insight into the bubbles that occur in the body in decompression sickness (DCS). We validate the calculation system by matching observed data of DCS bubbles and of large subcutaneous gas pockets in rats. We demonstrate how a temporary supersaturation and bubble formation can occur without change of ambient pressure when there is a change in the inert gas being breathed. With exposures to hypobaric environments, such as when astronauts work in space, simulations show that O2, CO2, and water vapor add appreciably to volume of bubbles and affect the diffusion of inert gas.
Atmospheric Pressure↗
Probabilistic model of altitude decompression sickness based on mechanistic premises.
To develop a predictive equation and to test ideas about the mechanisms involved in hypobaric decompression sickness, we performed statistical analyses on published results of 7,023 exercising O2-breathing men subjected to one-step decompressions in altitude chambers. The dependent variable was signs or symptoms so severe that the person's trial was terminated (forced descent). The three independent variables were 1) duration of 100% O2 breathing at ground level (prebreathing), 2) atmospheric pressure after ascent, and 3) exposure duration. The best model, chosen from trial-and-error combinations of premises about bubble behavior, indicates that decompression sickness outcome depends on 1) prebreathing time, but with an unexpectedly long washout half time for N2; 2) time at altitude, as if bubbles grow; and 3) the estimated difference, raised to the fifth power, between the partial pressure of N2 in tissue before and that in bubbles after decompression, perhaps an index of the number of bubbles generated. We expect the model to provide accurate predictions for decompressions matching those of the bulk of the data; the mechanistic cues should be considered hypotheses for further investigation.
Altitude Sickness↗
Oxygen transport to tissue by persistent bubbles: theory and simulations.
Persistent gas bubbles able to traverse capillaries can be prepared from a slowly permeating gas or with a mechanical structure surrounding a gas phase. If they are permeable to gases, such bubbles will carry O2 from the lungs to the tissues via the blood stream. Using a mathematical model based on physical laws, we present simulations of the behavior of bubbles stabilized by a slowly permeating gas (gas X). We show that the bubble persists longer if the tissue and venous blood contain N2 to dilute gas X and slow its outward diffusion. A 6-microns -diam bubble carries 0.11 pl of O2 during the breathing of pure O2, so 4.6 x 10(8) bubbles/ml in the blood will supply a normal arteriovenous difference. In conditions used for hyperbaric O2 therapy, a bubble carries approximately 0.26 pl of O2. Stabilized bubbles have the potential to transport O2 efficiently; they release O2 to tissue at high PO2 and require injection of only small amounts of a foreign substance.
Air↗
Density of decompression bubbles and competition for gas among bubbles, tissue, and blood.
We used numerical solutions of a system of equations to simulate gas exchanges of bubbles after a decompression, with particular attention to the effect of number of bubble formation sites per unit of tissue. If many bubbles grow, they deplete the excess dissolved gas in the tissue. The consequences are as follows: 1) the many individual bubbles do not become as large as they would if fewer were competing for gas; 2) more gas is evolved when there are many sites; 3) the bubbles are absorbed sooner than the bigger bubbles that grow with few sites; 4) after diffusion into many bubbles causes N2 partial pressure in the tissue to fall immediately to a low level, N2 partial pressure in the tissue and the exiting blood remain "clamped" to this low level because dissolved N2 removed by blood is replenished by diffusion out of the bubbles; and 5) as long as many bubbles persist, the long-term removal of inert gas from the total system (tissue plus bubbles) follows a straight-line time course rather than an exponential course.
Air Pressure↗
The oxygen window and decompression bubbles: estimates and significance.
The "oxygen window" causes a partial pressure difference of inert gas between the inside and outside of decompression bubbles. Estimates of Po2 and Pco2 in tissue are necessary for O2 window calculations and any calculations about growth or decay of decompression sickness bubbles, but the estimates involve many uncertainties. Using simplifying assumptions, we estimated the O2 window over a broad range of environments for tissues having a wide range of O2 extractions. The results were as follows: a) the window increases with ambient pressure, but levels off at very high pressure; b) the window is only 1 or 2 kPa for air breathing at extreme altitudes, and 200 kPa or more in hyperbaric environments; c) when O2 is breathed instead of air, the window is as much as 50 times larger at altitude but only about 10 times larger in hyperbaric environments; d) changes in bubble size due to the window decrease as barometric pressure increases; and e) there are seven additional factors which may supplement or oppose the action of the oxygen window.
Altitude↗
Failure of the straight-line DCS boundary when extrapolated to the hypobaric realm.
The lowest pressure (P2) to which a diver can ascend without developing decompression sickness (DCS) after becoming equilibrated at some higher pressure (P1) is described by a straight line with a negative y-intercept. We tested whether extrapolation of such a line also predicts safe decompression to altitude. We substituted tissue nitrogen pressure (P1N2) calculated for a compartment with a 360-min half-time for P1 values; this allows data from hypobaric exposures to be plotted on a P2 vs. P1N2 graph, even if the subject breathes oxygen before ascent. In literature sources, we found 40 reports of human exposures in hypobaric chambers that fell in the region of a P2 vs. P1N2 plot where the extrapolation from hyperbaric data predicted that the decompression should be free of DCS. Of 4,576 exposures, 785 persons suffered decompression sickness (17%), indicating that extrapolation of the diver line to altitude is not valid. Over the pressure range spanned by human hypobaric exposures and hyperbaric air exposures, the best separation between no DCS and DCS on a P2 vs. P1N2 plot seems to be a curve which approximates a straight line in the hyperbaric region but bends toward the origin in the hypobaric region.
Altitude↗
A computerized databank of decompression sickness incidence in altitude chambers.
This report describes a hypobaric decompression sickness databank (HDSD) for use with personal computers. The databank consolidates some of the decompression sickness (DCS) information that has accumulated from altitude chamber tests from 1942 to the present. The information was transcribed to a data collection form, screened for accuracy and duplication, and then added to the databank through a computer keyboard. The databank consists of two files; 63 fields contain details of the test conditions in the altitude chamber, the outcome of the test in terms of DCS and venous gas emboli, the physical characteristics of the group of subjects who underwent the test, and the denitrogenation procedures prior to decompression. The HDSD currently contains 378 records that represent 130,012 altitude exposures from 80 sources: scientific journal articles, government and contractor reports, and chapters from books.
Atmosphere Exposure Chambers↗
Simulation of the dynamics of decompression sickness bubbles and the generation of new bubbles.
This communication introduces a system of equations for simulating the dynamics of growth and decay of decompression bubbles. The equations are solved by a numerical method and account for gas diffusion, the action of surface tension, tissue N2 washout by blood, and the rate of ascent from depth. The simulations demonstrate how inward diffusion of N2 can generate a persistent gas bubble from a nucleation process or a nucleus (these are provisionally defined as entities that can give rise to a small bubble of a certain size); an explosive positive-feedback loop is set off as the enlarging radius decreases the pressure due to surface tension. Generation of persistent bubbles is most likely during ascent from depth when PN2 inside any gas phase is decreasing rapidly and PN2 outside is still high before appreciable tissue washout has occurred. The "susceptibility" for the generation of a persistent bubble at any time can be defined as the reciprocal of the difference, at that time, between partial pressure of the nitrogen in tissue and in a spherical bubble of the size that is characteristic of the nucleation process or nucleus; susceptibility is less when ascent is slow because PN2 in bubbles stays high while washout removes N2 from the tissue.
Atmospheric Pressure↗
An initiation into teaching for graduate students.
The Physiology Department at State University of New York at Buffalo offers a one-credit course that is intended to improve communication skills and to foster a problem-solving approach to the teaching/learning process. In the course, students practice lecturing, prepare examination questions, and participate in discussions of various teaching problems.
Communication↗
Display of the alveolar plateau of single-breath tests in "dilution index" format.
In 1949, Fowler (J. Appl. Physiol. 2: 283-299) advocated calculation of a "dilution index" from data of the alveolar plateau of single-breath tests; the calculation provides an estimate of the dilution of resident gas in the lung that gave rise to the observed concentrations. In this communication, we show that the calculation can be applied to conventional single-breath tests where O2 is inhaled by air-breathing persons, and we illustrate the principle with vital capacity breaths of a mixture that contained a low concentration of neon. The dilution was approximately 3:1 in young subjects (20-30 yr), as if a vital capacity of 6 liters were mixed with a residual volume of 2 liters. The dilution was less, 2:1, in older subjects (56 yr) and tended to become as low as 1:1 during emptying of the closing volume. In addition to being more informative, the dilution index format allows common sense comparison of alveolar plateau levels and slopes when single-breath tests are done by various methods.
Adult↗