B.R. Wienke

Reduced gradient bubble model

An approach to decompression modeling, the reduced gradient bubble model (RGBM), is developed from the critical phase hypothesis. The phase limit is introduced, extended, and applied within bubble-nucleation theory proposed by Yount. Much is different in the RGBM algorithm, on both theoretical and applied sides, with a focus on permissible bubble excesses rather than just dissolved gas buildup, something of a departure from traditional models. Overall, the approach is conservative, with changes in parameter settings affording flexibility. Marginal profiles permitted by tables and meters are restricted by the bubble algorithm. Highlighted features of the conservative algorithm include: (1) reduced no-stop time limits from the varying-permeability model (VPM); (2) short safety stops (or shallow swimming ascents) in the 10-20 feet of sea water (fsw) zone; (3) ascent and descent rates of 60 fsw/min, or slower; (4) restricted repetitive exposures, particularly beyond 100 fsw, based on reduced permissible bubble excess; (5) restricted spike (shallow-to-deep) exposures based on excitation of additional micronuclei; (6) restricted multi-day activity based on regeneration of micronuclei; (7) consistent treatment of altitude diving within model framework; (8) algorithm linked to bubble-nucleation theory and experiment. Coupled to medical reports about the long term effects of breathing pressurized gases and shortcomings in dissolved gas models, conservative modeling seems prudent.

Diving decompression models and bubble metrics: Modern computer syntheses

A quantitative summary of computer models in diving applications is presented, underscoring dual phase dynamics and quantifying metrics in tissue and blood. Algorithms covered include the multitissue, diffusion, split phase gradient, linear-exponential, asymmetric tissue, thermodynamic, varying permeability, reduced gradient bubble, tissue bubble diffusion, and linear-exponential phase models. Defining relationships are listed, and diver staging regimens are underscored. Implementations, diving sectors, and correlations are indicated for models with a history of widespread acceptance, utilization, and safe application across recreational, scientific, military, research, and technical communities. Presently, all models are incomplete, but many (included above) are useful, having resulted in diving tables, underwater meters, and dive planning software. Those herein employ varying degrees of calibration and data tuning. We discuss bubble metrics in tissue and blood as a backdrop against computer models. The past 15 years, or so, have witnessed changes and additions to diving protocols and table procedures, such as shorter nonstop time limits, slower ascent rates, shallow safety stops, ascending repetitive profiles, deep decompression stops, helium based breathing mixtures, permissible reverse profiles, multilevel techniques, both faster and slower controlling repetitive tissue halftimes, smaller critical tensions, longer flying-after-diving surface intervals, and others. Stimulated by Doppler and imaging technology, table and decompression meter development, theory, statistics, chamber and animal testing, or safer diving consensus, these modifications affect a gamut of activity, spanning bounce to decompression, single to multiday, and air to mixed gas diving. As it turns out, there is growing support for many protocols on operational, experimental, and theoretical grounds, with bubble models addressing many concerns on plausible bases, but with further testing or profile data analyses requisite.

Numerical phase algorithm for decompression computers and application

Present generation decompression computers employ a simplified algorithm, limiting dissolved gas build-up in tissue and blood according to a method proposed by Haldane 80 years ago. Such a model works well for single dives, but is usually liberal and theoretically incomplete for multiple exposures within 24 hr spans. Using the critical phase hypothesis in a bubble model, we have extended the classical model of Haldane to multi-exposures. This model is discussed, and a decomputer algorithm described for multi-diving. The focus is permissible bubble excess, not just dissolved gas per se, with phase constraints affecting all tissues, fast and slow, and requiring a systematic lowering of repetitive tissue tensions. Deep repetitive and shallow multi-day exposures are impacted most by the procedure. Within nucleation theory deeper-than-first dives are also treated. A set of multi-diving fractions, xi, accounting for micronuclei excitation and regeneration, reduced bubble elimination in repetitive activity, and coupled effects on tissue tension, are proposed, with xi representing a set of multiplicative factors (less than one) applied to critical tissue tensions for multi-exposures. These factors affect repetitive activity over short time spans, deeper-than-previous and continuous multi-day activities, compared to standard computer software, and are easily encoded into existing decompression meters, potentially extending their range and flexibility over exposure regimes.

Computer validation and statistical correlations of a modern decompression diving algorithm

A diving algorithm is a safe combination of model and data to efficiently stage diver ascents following arbitrary underwater exposures. To that end, we detail a modern one, the LANL reduced gradient bubble model (RGBM), dynamical principles, and correlations with the LANL Data Bank data. Table, profile, and meter fit and risk parameters are obtained in statistical likelihood analysis from decompression exposure data. The RGBM algorithm enjoys extensive and utilitarian application in mixed gas diving, both in recreational and technical sectors, and forms the bases for released tables, software, and decompression meters used by scientific, commercial, and research divers. The LANL Data Bank is described, and the methods used to deduce risk are detailed. Risk functions for dissolved gas and bubbles are summarized. Parameters that can be used to estimate profile risk are tallied. To fit data, a modified Levenberg-Marquardt routine is employed. The LANL Data Bank presently contains 2879 profiles with 20 cases of DCS across nitrox, trimix, and heliox deep and decompression diving. This work establishes needed correlation between global mixed gas diving, specific bubble model, and deep stop data. Our objective is operational diving, not clinical science. The fit of bubble model to deep stop data is chi squared significant to 93%, using the logarithmic likelihood ratio of null set (actual set) to fit set. The RGBM algorithm is thus validated within the LANL Data Bank. Extensive and safe utilization of the model reported in field user statistics for tables, meters, and software also suggests real world validation, that is, one without noted nor reported DCS spikes in the field.

Computational decompression models

Early computational models for decompression are based on supersaturation assumptions for dissolved gases. Such models, and our understanding of decompression biophysics, have been extended in the past 20 years by analyses of phase separation of gases. Generally termed thermodynamic decompression (or phase equilibration), these studies postulate a continuous exchange of inert gas between tissues and nucleation sites (gas micropockets), consistent with many commonplace phenomena. Postulates lead to decompression schedules and transfer mechanisms that differ from their earlier predecessors. The precise physical and computational bases supporting both viewpoints are described and contrasted.

MODELING DISSOLVED AND FREE PHASE GAS DYNAMICS UNDER DECOMPRESSION

Dissolved and free gases do not behave the same way in tissue under pressure, and their interaction is complex. Differences are highlighted, particularly with respect to time scales, gradients and transport. Impacts of free phases on diving are described, contrasting increased off-gassing pressures, slower ascent rates, safety stops and reduced repetitive exposures as consistent practical measures within Haldane models (limited supersaturation) which can be played off against buildup of dissolved gas. Simple computations illustrate the points.

Bubble number saturation curve and asymptotics of hypobaric and hyperbaric exposures

Within bubble number limits of the varying permeability and reduced gradient bubble models, it is shown that a linear form of the saturation curve for hyperbaric exposures and a nearly constant decompression ratio for hypobaric exposures are simultaneously recovered from the phase volume constraint. Both limits are maintained within a single bubble number saturation curve. A bubble term, varying exponentially with inverse pressure, provides closure. Two constants describe the saturation curve, both linked to seed numbers. Limits of other decompression models are also discussed and contrasted for completeness. It is suggested that the bubble number saturation curve thus provides a consistent link between hypobaric and hyperbaric data, a link not established by earlier decompression models.

The performance of asynchronous iteration schemes applied to the linearized Boltzmann transport equation

Abstract We present a summary of numerical experiments that explore the effects of asynchronous (chaotic) iteration schemes for solutions of the Boltzmann transport equation. Our experiments are performed on both common and distributed memory parallel processing systems. Two chaotic and one deterministic schemes are developed directly from a computational algorithm known as discrete ordinates that uses iterative techniques in solving the linearized Boltzmann particle transport equation. From an analysis based on the performance of these schemes on various parallel architectures, a third chaotic scheme is developed that executes faster in either parallel or sequential modes. The behavior of these methods, both deterministic and chaotic, will be examined for the Denelcor HEP, the Encore Multimax, and the Intel iPSC hypercube.

Equivalent multi-tissue and thermodynamic decompression algorithms.

Multi-tissue and thermodynamic decompression algorithms are described and a computational equivalence is established between the two approaches. Eigenvalues and weighted eigenfunctions of the Fick-Fourier equation effectively define response functions from which Haldane half-lives can be extracted from arbitrary exposures, operationally bridging the two approaches. Decompression criteria for the algorithms are also described and coupled. Comparisons of similarities and differences of approaches are given from both theoretical and applied viewpoints. A seven-parameter set, spanning both models, forms the basis of analysis. We find that representative thermodynamic parameters in a perfusion-diffusion model effectively recover Haldane half-lives in a bootstrap and that critical parameters overlap, though ranges differ in the two cases.

SNEX: Semianalytic solution of the one-dimensional discrete ordinates transport equation with diamond differenced angular fluxes

SNEX fournit une solution numerique aux equations a ordonnees discretes monoenergetiques dans les applications de transport de particules chargees et neutres, de plasma, en hydrodynamique, en transfert radiatif