Michael R. Powell

A Mathematical Model of Diffusion-Limited Gas Bubble Dynamics in Tissue with Varying Diffusion Region Thickness

The three-region model of gas bubble dynamics consists of a bubble and a well-stirred tissue region with an intervening unperfused diffusion region previously assumed to have constant thickness and uniform gas diffusivity. As a result, the diffusion region gas content remains unchanged as its volume increases with bubble growth, causing dissolved gas in the region to violate Henrys law. Earlier work also neglected the relationship between the varying diffusion region volume and the fixed total tissue volume. The present work corrects these theoretical inconsistencies by postulating a difference in gas diffusivity between an infinitesimally thin layer at the bubble surface and the remainder of the diffusion region, thus allowing both thickness and gas content of the diffusion region to vary during bubble evolution. The corrected model can yield bubble lifetimes considerably longer than those yielded by earlier three-region models, and meets a need for theoretically consistent but relatively simple bubble dynamics models for use in studies of decompression sickness (DCS) in human subjects.

Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue

AbstractModels of gas bubble dynamics employed in probabilistic analyses of decompression sickness incidence in man must be theoretically consistent and simple, if they are to yield useful results without requiring excessive computations. They are generally formulated in terms of ordinary differential equations that describe diffusion-limited gas exchange between a gas bubble and the extravascular tissue surrounding it. In our previous model (Ann. Biomed. Eng. 30: 232–246, 2002), we showed that with appropriate representation of sink pressures to account for gas loss or gain due to heterogeneous blood perfusion in the unstirred diffusion region around the bubble, diffusion-limited bubble growth in a tissue of finite volume can be simulated without postulating a boundary layer across which gas flux is discontinuous. However, interactions between two or more bubbles caused by competition for available gas cannot be considered in this model, because the diffusion region has a fixed volume with zero gas flux at its outer boundary. The present work extends the previous model to accommodate interactions among multiple bubbles by allowing the diffusion region volume of each bubble to vary during bubble evolution. For given decompression and tissue volume, bubble growth is sustained only if the bubble number density is below a certain maximum.

Mathematical model of diffusion-limited gas bubble dynamics in unstirred tissue with finite volume

AbstractModels of gas bubble dynamics for studying decompression sickness have been developed by considering the bubble to be immersed in an extravascular tissue with diffusion-limited gas exchange between the bubble and the surrounding unstirred tissue. In previous versions of this two-region model, the tissue volume must be theoretically infinite, which renders the model inapplicable to analysis of bubble growth in a finite-sized tissue. We herein present a new two-region model that is applicable to problems involving finite tissue volumes. By introducing radial deviations to gas tension in the diffusion region surrounding the bubble, the concentration gradient can be zero at a finite distance from the bubble, thus limiting the tissue volume that participates in bubble–tissue gas exchange. It is shown that these deviations account for the effects of heterogeneous perfusion on gas bubble dynamics, and are required for the tissue volume to be finite. The bubble growth results from a difference between the bubble gas pressure and an average gas tension in the surrounding diffusion region that explicitly depends on gas uptake and release by the bubble. For any given decompression, the diffusion region volume must stay above a certain minimum in order to sustain bubble growth.

A photograph-based study of the incidence of fatal truck underride crashes in Indiana

Photographs were used to estimate the incidence of fatal crashes in which passenger vehicles underrode the fronts, sides and rears of large trucks in Indiana during 1993. The photographs were obtained for 98 of the 107 eligible fatal crashes between large trucks and passenger vehicles in 1993. A protocol was developed to judge the presence and extent of underride, the presence of intrusion into the passenger vehicle compartment, and the likelihood of death or serious injury if underride had been prevented. The incidence of fatal underride was compared with the incidence reported in the Fatality Analysis Reporting System (FARS), a census of fatal crashes on public roads in the U.S.A. For the same 107 fatal large truck-passenger vehicle crashes, the incidence of underride reported in FARS was much lower than in the photograph-based study: 6 versus 63%. Photographs contain details absent from police reports, the primary data source for FARS, and thus enable more complete identification of underride crashes. Preventing underride would have substantially reduced the likelihood of death or serious injury in ca 20% of the underride crashes.

Incidence of large truck-passenger vehicle underride crashes in Fatal Accident Reporting System and National Accident Sampling System

Between 1988 and 1993, the Fatal Accident Reporting System (FARS) coded 4 percent of all fatal large truck–passenger vehicle crashes as involving underrides (portion of passenger vehicle slides under a large truck) or overrides (truck rides over another vehicle). In contrast, the National Accident Sampling System Crashworthiness Data System (NASS/CDS) coded 27 percent of a sample of 275 fatal large truck–passenger vehicle crashes as underrides during the same years. Seven percent of these 275 fatal crashes are identified as underrides in FARS. The discrepancy between FARS and NASS coding becomes more pronounced when underrides involving sides of passenger vehicles or trucks are considered. The reason for this discrepancy is that NASS/CDS did not code underrides involving side impacts, but FARS did. When underrides involving side impacts were added, the total percentage of underrides in NASS/CDS rose from 27 percent to 50 percent of fatal truck-car crashes. The most likely explanations for the lower incidence of underride coding in FARS are that (a) the greater amounts of information available to NASS/CDS analysts enable more complete identification of underrides, (b) FARS analysts sometimes may not recognize that an underride has occurred, and (c) underride was not a separate FARS variable before 1994. On the basis of NASS/CDS data, an estimated 1,108 fatal underride crashes occurred each year between 1988 and 1993 [95 percent confidence interval (CI) = 735, 1482]. Of these 1,108 underrides, 634 involved the front (CI = 328, 942), 248 involved the rear (CI = 137, 360), and 226 involved the sides (CI = 110, 341) of large trucks.

LEADING EDGE DEPLOYMENT SPEED OF PRODUCTION AIR BAGS

Air bags have proven to be effective in preventing deaths and serious injuries; however, in some instances when an occupant contacts an air bag while it is still deploying, injuries may result from this contact. most of these are minor injuries, such as skin abrasions, which are believed to be caused by the contact pressure created by the deploying air bag surface. To assess the relative potential of different air bag designs to cause skin abrasions, a series of static deployment tests was conducted to measure the leading-edge speed of driver-side air bags from several 1993 model cars. Results indicate that air bags exhibit a wide range of leading-edge speeds and that, in some cases, maximum leading-edge speed is a highly variable characteristic among air bags from the same model car. Maximum leading edge speeds ranged from 171 to 328 km/h. Comparison of speed profiles to an approximate abrasion reference value showed that many of the tested air bags are traveling at a speed great enough to cause abrasions as far away as 286 mm from the steering wheel; however, some air bags never reached this reference speed.

Early stopping of aerospace medical trials : application of sequential principles

A two‐period, crossover trial was conducted in the hypobaric chamber on human subjects to compare the influence of inflight exercise (experimental) and restricted activity (control) on altitude decompression sickness (DCS) during simulated extravehicular activities. Out of 39 pairs (total of 78 exposures), 4 cases of DCS occurred under control and 5 occurred under experimental conditions. Analysis of the crossover results showed that the P values for differences in DCS occurrence was 0.56. Under these circumstances, it was necessary to decide whether additional information would be obtained by accruing more subjects. This problem was examined by using a skew sequential design in which the “stopping rule” was based on an alpha of 0.05 (one‐sided) and power of 80%. The result of this analysis was in favor of the null hypothesis, and the trial was terminated. The authors recommend the use of similar stopping rules in aerospace trials to optimize sample size without compromising statistical validity.