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On the use of a bubble formation model to calculate diving tables
Abstract
Previous decompression tables for humans were based upon unsupported assumptions because the underlying processes by which dissolved gas is liberated from blood and tissue were poorly understood. Some of those assumptions are now known to be wrong, and the recent formulation of a detailed mathematical model describing bubble nucleation has made it possible to calculate diving tables from established physical principles. To evaluate this approach, a comprehensive set of air diving tables has been developed and compared with those of the U.S. and British Navies. Conventional decompressions, altitude bends, no-stop thresholds, and saturation dives are all successfully described by one setting of four global nucleation parameters, which replace the U.S. Navy's matrices of M-values. Present air diving tables show great irregularity, even within sets created by the same authors. In contrast, this new approach is remarkably self-consistent, permitting accurate interpolation and extrapolation.
... The force across the gas-liquid interface is represented by the term 2γ /r and depends on the acting surface tension of the gas bubble [10,19]. M depicts the additional pressure exerted from tissue displacement. ...
... The second strategy intends to predict the number of bubbles excited into growth during decompression. Two common examples that are introduced in the following are the Varying Permeability Model (VPM) [19] and the Reduced Gradient Bubble Model (RGBM) [21]. ...
... The Varying Permeability Model (VPM) was first introduced by Yount and colleagues [19] and is based on studies of bubble formation performed in a laboratory setting [20]. Their research work focused on bubble kinetics and how it can be applied for safe decompression scheduling. ...
Decompression illness and decompression sickness are pathologies mostly associated with diving incidents, which result from excessive bubble formation from dissolved gas. Great efforts are undertaken to perform research to understand the pathology and fundamental mechanisms, which result from the dynamic effects of compression and decompression. In this chapter, the clinical manifestation of decompression illness including the impact on different physiological systems is presented. Principles in physics, chemistry and biology are investigated that build the base to understand the mechanisms of decompression and bubble kinetics. These principles are then used to derive algorithms and concepts to calculate decompression schedules, which aim to safely step the diver back to the surface. Different approaches are dissected for their general ideas and implementation.
... The VPM and RGBM models are both BM algorithms. The VPM [3] and RGBM [4] are BM algorithms and stage ascents by requiring that excited bubble volumes, ϕ , never exceed a limit point, called the phase limit, Φ on surfacing. Both GM and BM models assign tissue compartments, τ , which quantify dissolved gas buildup and elimination during a dive. ...
... Collapse time in the Rayleigh-Plesset picture is linear in initial bubble radius, r i and inversely proportional to the square root of the tension gradient, p, or the surface tension, γ. Taking all quantities as previously, with density, ρ=1.15 g/cm 3 , we find with surface tension suppressed, 3 2.91 10 ...
... A systematic theory of bubble broadening developed by Lifshitz et al. [15] (LSW) suggests in supersaturated and solid solutions that the distribution mean bubble radius, r m , evolves in time as, 3 3 ...
The question of bubble regeneration and broadening in the diver under compression-decompression is virtually unanswered and untractable. We take up these hypothetical
questions and suggest impacts on diver staging using well established and validated
decompression models (USN, ZHL, VPM, RGBM). These are estimates and have not been
verified nor tested in diver. Results are on the conservative side nonetheless and of interest to table designers, modelers, diving professionals, training agencies, doctors and
engineers.
... Decompression science and application to diving is an ongoing effort. The systematics of gas exchange [11,14,39,45,59,79], nucleation [3,4,14,29,31,42,71], bubble growth [7,11,28,66,71,90] and elimination [22,26,50,54,55], counterdiffusion [40,46,82,89], oxygen impact [34,51,52,72] and adaptation [12,13,30,36,41] upon diving decompression staging [15,30,39,44,57,64], and attendant altitude modifications [5,16,27,39,70,77] are so complicated that theories only reflect pieces of the puzzle. Computational algorithms, tables and manned testing are, however, requisite across a spectrum of activities. ...
... These approaches are used in decompression meters and dive planning software [82,86], as well as the USN linear-exponential model (LEM) already discussed. While never measured in the laboratory, the approach will always impart conservatism to any computational algorithm [85,88,89]. ...
... Only computer downloaded profiles with DCS outcomes are considered in this analysis. The models are the USN [85], ZHL16 [15], VPM [89] and RGBM [75]. The USN and ZHL16 models are dissolved gas models [1] that ultimately require decompression stops in the shallow zone to eliminate dissolved nitrogen and helium. ...
This monogram covers a body of biophysics, gas transport, bubble studies, data and attendant
models used in high pressure applications. It divides naturally into five Parts, namely;
Part 1: Fundamental Concepts and Relationships, Part 2: Biophysics and Models, Part 3:
Correlations and Validation, Part 4: Exposure Risk and Part 5: Applications and Exercises.
The biophysics of compression and decompression in the human body is extremely complex.
More needs be learned to safely and routinely stage divers and astronauts The physics, biology,
engineering, physiology, medicine and chemistry of diving center on pressure and pressure
changes. The average individual is subject to atmospheric pressure swings of 3% at sea level,
as much as 20% a mile in elevation, more at higher altitudes and all usually over time spans of
hours to days. Divers and Astronauts and their equipment can experience compressions and
decompressions orders of magnitude greater and within considerably shorter time scales. While
effects of pressure change are readily quantified in physics, chemistry and engineering applications,
the physiology, medicine, and biology of pressure changes in living systems are much
more complicated. Caution is needed in transposing biological principles from one pressure
range to another. Incomplete knowledge and biophysical complexities often prevent extensions
of even simple causal relationships in biological science. Gas exchange, bubble formation and
elimination and compression-decompression in blood and tissues in diving are governed by
many factors, such as diffusion, perfusion, phase separation and equilibration, nucleation and
cavitation, local fluid shifts and combinations thereof. Owing to the complexity of biological
systems, multiplicity of tissues and media, diversity of interfaces and boundary conditions
and plethora of bubble impacting physical and chemical mechanisms, it is difficult to solve
the compression-decompression problem in vivo. And equally difficult and elusive are direct
measurements of bubbles, bubble sites and effective transport properties of tissues and blood
in living human systems. Early decompression studies adopted the medical supersaturation
viewpoint. Closer looks at the physics of phase separation and bubbles in the mid-1970s,
and insights into gas transfer mechanisms, culminated in extended kinetics and dissolved-free
phase theories. In both cases, models are employed to stage diversand astronauts as safely as
possible to the surface. Optimally, these models ought be correlated with existing diving data
and linked to the most current biophysics. So, the monogram describes underlying biophysics,
connectivity to macroscopic models and correlation with real diving data, with correlations as
important as models. Applications to mixed gas, decompression, open circuit (OC) and rebreather
(RB) diving are linked to a correlated bubble model for comparisons and risk analyses.
Applications focus mainly on deep exposures where risks increase and statistical collections
and tabulations of data are very important
1
... A diving protocol is a combination of model, data and ascent staging procedure that can be safely used across commercial, sport, technical, research, and scientific underwater operations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Accordingly, this work analyzes four popular models against actual diver deep stop profile data and DCS outcomes. ...
... Only computer downloaded profiles with DCS outcomes are considered in this analysis. The models are the USN [20], ZHL16 [3], VPM [21], and RGBM [19]. The USN and ZHL16 models are dissolved gas models [1] that ultimately require decompression stops in the shallow zone to eliminate dissolved nitrogen and helium. ...
... As will be seen, the deep stop models (VPM, RGBM) correlate well with the LANL DB, while the shallow stop models (USN, ZHL16) do not. Turns out that both shallow and deep stops can be made at the same relative risk level, but deep stops usually admit shorter overall decompression times [5,12,13,19,21], an important aspect of operational diving when mission objectives are folded over diving requirements, especially diver safety. ...
Data correlations of computer, table, and software real world implementations of useful and popular diving models are warranted for surety, testing, reproducibilty, and safety. Model correlations are of broad interest across the diving community and the focus of this communication. Permissible supersaturation is a fundamental model element for correlation and we analyze four popular ones, namely the USN, ZHL16, VPM, RGBM model permissible supersaturations within model dynamical constraints. Correlations are obtained in statistical likelihood analysis from computer profile records with DCS outcomes in the Los Alamos National Laboratory Data Bank (LANL DB). Permissible supersaturations, limited by model staging constraints varying across depths, times, and gas mixtures, are quantified for the four models. Parameters and risk functions useful to estimate profile risk are also obtained. To correlate and fit data, a modified Weibull-Levenberg-Marquardt routine is employed across 2994 computer downloaded (only) profile records with 23 cases of DCS in nitrox, trimix, and heliox deep and decompression diving. The routine is useful for low probability (low−p) data usually encountered in the diving accident arena. Model agreement with data is χ2 significant as follows, using the logarithmic likelihood ratio of data set to fit set:
USN-(χ2=0.081)
ZHL16-(χ2=0.131)
VPM-(χ2=0.717)
RGBM-(χ2=0.861)
LANL DB computer profiles exhibit very low DCS prevalence and correlate well with the deep stop models, VPM and RGBM, and further manned testing is always welcome. This correlation suggests that dive computers, software and tables based on deep stop models like VPM and RGBM can safely be used by sport and technical divers. The shallow stop models, USN and ZHL, have, of course, been used safely in computers, tables, and software for decades while deep stop models are fairly new on the diving scene.
... There are several main algorithms used to create decompression profiles in use today. Generally, they can be divided into Haldane type models [1,2], which split body into tissue types referred to as "compartments" and establish decompression times for each tissue, and bubble models [3], which study the formation of the bubbles and create decompression profiles that minimise the number and size of the bubbles during the ascent. ...
... This problem has been noted many times previously and if bubbles are to be predicted then it is necessary to introduce some model of nucleation in order to get physically realistic predictions. One of the simplest model of nucleation is to assume that there is some mechanisms that prevents bubbles from completely collapsing [3]. This may be due to lipid layers on the interface that provide some mechanical strength (as outlined in figure 1) or due to small particles in the tissue around which the bubble can form. ...
... The meaning of R c (This figure came from a website Deep Ocean Diving's Diving Science: Decompression Theory -Bubble Models, although the same ideas are in[3]). ...
Executive Summary At present, no decompression algorithm is able to predict safe decom-pression for all dive scenarios. In practice, empirical adjustments are made by experienced organisations or divers in order to improve de-compression profiles for the range of depths and durations needed on any particular dive. Bubble formation and growth in the human body are the fundamental causes of decompression sickness, and it is believed that there is significant scope for incorporating better modelling of these processes into the design of decompression algorithms. VR Technology is a leading supplier of technical dive computers. The company is interested in expanding upon an existing algorithm (the Variable Gradient Model-VGM), which is used to design ascent pro-files/decompression schedules and thereby mitigate the risk of decom-pression sickness in divers. The Study Group took the approach of trying to extend the existing Haldane model to account more explicitly for the formation of bubbles. By extending the model to include bubble dynamics it was expected that some physical understanding could be gained for the existing modifications to some of the parameters. The modelling that occurred consisted of first looking at the Haldane model and then considering a single small isolated bubble in each of the compartments and interpreting the predictions of the model in terms of decompression profiles.
... The reduced gradient bubble model of Wienke [13] was developed in the late 90s for recreational and technical diving. Using equationsof-state (EOS) from lipid and aqueous substrates to parameterize the structure of bubble skins, the RGBM uses an exponential number distribution (decreasing with bubble radius) for bubble nuclei excited into growth by compression-decompression. That number is summed over the exposure profile in 10 fsw increments and allowed to expand or contract under pressure and temperature changes to yield a surfacing estimate of excited bubble volume. ...
... Gradient Factors -Gradient factors (GFs) are a spinoff of published RGBM reduction factors (RFs) for recreational diving [13]. They merely reduce dissolved gas limiters (M-Values) at depth thus producing deep stops on top of dissolved gas staging. ...
... Because they are based upon unsupported assumptions, alternative models using more physical principles have been developed. The Variable Permeability Model (VPM) [3], as well as the Reduced Gradient Bubble Model (RGBM) [4], take into account the dynamics of the gas phase. As neo-Haldanian models do not so, they can apply only to the simple enough situations from which they have been tuned, mostly dives that do not include too many decompression stops and that have simple profiles [5]. ...
... However, VPM and RGBM themselves rely on particular assumptions that could be discussed: In VPM, bubbles are supposed to be spherical. Wellknown in-vitro models of bubble nucleation are extrapolated to in-vivo situations [3,4,6]. Many models establish a duality between "safe" or "unsafe" desaturation situations, whereas the occurrence of decompression sickness is a probabilistic phenomenon as evoked for example in [7]. ...
... Collapse time in the Rayleigh-Plesset picture is linear in initial bubble radius, r i and inversely proportional to the square root of the tension gradient, p ∆ , or the surface tension, γ . Taking all quantities as previously, with density, ρ = 1.15g/cm 3 , we find with surface tension suppressed, 3 2.91 10 sec ...
... Larger ice crystals grow at the expense of smaller ones within the ice cream creating a coarser surface texture. A systematic theory of bubble broadening developed by Lifshitz, Slyozov and Wagner 10 (LSW) suggests that in supersaturated and solid solutions the distribution mean bubble radius, m r , evolves in time as, 3 3 ...
The question of bubble broadening (Ostwald ripening) in the diver under compression-decompression is virtually unanswered and untractable. Effects have not been measured nor quantified to date and remain unlikely in the near future. We take up this question and suggest hypothetical impacts on diver staging using available data and recent experimental results in the laboratory. A well known and safe bubble model, RGBM, provides a framework to estimate hypothetical effects in mixed gas diving on open circuit (OC) and rebreather (RB) systems. These are estimates and are neither
verified nor tested in divers. However the projections are conservative, increasing decompression time and shortening no decompression time limits (NDL), so that implementation in diver staging protocols, software, dive computers and dive tables is patently safe and of interest to modelers, table designers, training agencies, dive tenders, engineers, doctors, dive computer vendors and related professionals. Experiments impacting broadening are briefly detailed. Particular are the broadening studies in hydrocarbon and glycerol substrates. Features of bubble models affected by broadening are quantified within the RGBM framework. Comparative results are given with and without broadening. Broadening times can range from hours to days. Corresponding broadening estimates ofdecreases in NDLs and increases in decompression times range 2\% to 8\% for nominal (recreational) exposures and 10\% to 18\% for extreme diving and extended (technical) exposures. Overall effects are small to moderate
within existing data and recreational to technical diving protocols but diver staging effects of broadening increase with depth and exposure time. Beyond 8 hrs broadening time scales effects are insignificant.
This is a first time ever estimate of hypothetical impacts of bubble broadening on diver staging protocols
... The VPM and RGBM models are both BM algorithms. The VPM [3] and RGBM [4] are BM algorithms and stage ascents by requiring that excited bubble volumes, φ, never exceed a limit point, called the phase limit, Φ, on surfacing. Both GM and BM models assign tissue compartments, τ, which quantify dissolved gas buildup and elimination during a dive. ...
... 1. Varying Permeability Model (Yount 1986) The tissue compartments in the Yount VPM for nitrogen consist of the set, τ N 2 = (1, 2, 5, 10, 20, 40, 80, 120, 160, 240, 320, 400, 480, 560, 720) min (17) with the helium compartments scaling, ...
The question of bubble regeneration and broadening (Ostwald ripening) in the diver under compression-decompression is virtually unanswered and untractable. Effects in vivo have not been measured nor quantified to date and remain unlikely in the near future. We take up this question and suggest hypothetical impacts on diver staging using available data and recent experimental results in the laboratory. Four well known and widely used diver staging models, USN, ZHL, VPM and RGBM, provide a framework to estimate hypothetical effects in mixed gas diving on open circuit (OC) and rebreather (RB) systems. These are estimates and are neither verified nor tested in divers. However the projections are conservative, increasing decompression time and shortening no decompression time limits (NDL), so that their implementation in diver staging protocols, software, dive computers and dive tables is patently safe and of interest to modelers, table designers, training agencies, dive tenders, engineers, doctors, dive computer vendors and related professionals. Experiments impacting broadening and regneration are briefly detailed. Particular are the regeneration and broadening studies in gel, blood, agar, water and fluorocarbon substrates. Features of diving models (USN, ZHL, VPM, RGBM) affected by bubble regeneration and broadening are quantified within model frameworks. Comparative results are given with and without regeneration and broadening. Regeneration and broadening times can range from hours to days. Corresponding decreases in NDLs and increases in decompression times range 2% to 8% for nominal (recreational) exposures and 10% to 16% for extreme diving and extended (technical) exposures. Overall effects are thus small to moderate but diver staging effects will increase with decreasing regeneration time scales and increase with increasing broadening time scales for given depth, breathing mixture and bottom time. Effects will always increase with depth. Regeneration effects and broadening effects for time scales beyond 8 hrs are relatively small overall in this hypothetical study within the USN ZHL, VPM and RGBM frameworks. Hopefully real experiments measuring bubble regeneration and broadening in the body will pin these issues down in the future. Standard (SI) and English units are employed. By convention, by usage or for ease, some nonstandard units are employed. Pressure and depth are both measured in feet-of-seawater (f sw) and meters-of-seawater (msw) with 1 atm = 33 f sw = 10 msw to good approximation. Also used for scale lengths of bubbles are micron with 1 micron = 10 −6 m. Acronyms are employed herein. They are standard: ANDI: Association of Nitrox Diving Instructors. BM: bubble phase model dividing the body into tissue compartments with halftimes that are coupled to inert gas diffusion across bubble film surfaces of exponential size distribution constrained in cumulative growth by a volume limit point. bubble broadening: noted laboratory effect that small bubbles increase and large bubbles decrease in number in liquid and solid systems due to concentration gradients that drive material from smaller bubbles to larger bubbles over time spans of hours to days. bubble regeneration: noted laboratory effect that pressurized distributions of bubbles in aqueous systems return to their original non-pressurized distributions in time spans of hours to days. CCR: closed circuit rebreather, a special RB system that allows the diver to fix the oxygen partial pressure in the breathing loop (setpoint).
... Application and use is growing, particularly in the technical diving sector, over the past 20-25 years with new computers implementing bubble models. In particular, the VPM[16] and RGBM[17] models are noteworthy and used extensively within recreational and technical diving sectors and follow:Varying permeability model[16]: The tissue compartments in the Yount VPM for nitrogen consist of the set, ...
... Application and use is growing, particularly in the technical diving sector, over the past 20-25 years with new computers implementing bubble models. In particular, the VPM[16] and RGBM[17] models are noteworthy and used extensively within recreational and technical diving sectors and follow:Varying permeability model[16]: The tissue compartments in the Yount VPM for nitrogen consist of the set, ...
Dive computers and diveware are important tools and staging devices across sport, technical, commercial
military, scientific, exploration, and research diving sectors. They are supplanting traditional dive tables and
their use is growing as diving activities grow. While important diving data and staging parameters are displayed
throughout the dive, DCS risk associated with arbitrary ascents to depths above the diver and surfacing risks
are not yet encoded into underwater devices and diveware and that is the focus here. Risk estimators are
needed for diver safety and sensible dive planning, We define and discuss end of dive (EOD) and on the fly
(OTF) exponential risk functions for both dissolved gas and bubble models using profile data correlated with
the LANL Data Bank, a collection of computers downloaded mixed gas, decompression profiles across OC
and RB diving. Risk estimates are based on profile supersaturations in excess of permissible supersaturations
which is a standard metric. Comparative results are given for both nonstop and decompression diving on OC
and RB systems. Computer implementation is easily accomplished with existing dive computers and diveware
platforms. Techniques are underscored and results discussed. References detail background information
and work extends earlier published analyses for end of dive risk estimation.
... Application and use is growing, particularly in the technical diving sector over the past 20-25 years with new computers implementing bubble models. In particular, the VPM [16] and RGBM [17] models are noteworthy and used extensively within recreational and technical dive computers as detailed in the following. An early forerunner of BM algorithms, the Hills thermodynamic model (TM), is also described in for completeness. ...
... It also generates deep stops but dive computer encoding is very limited in application. 1. Varying Permeability Model ( Yount 1986) The tissue compartments in the Yount VPM for nitrogen consist of the set, τ N 2 = (1, 2, 5, 10, 20, 40, 80, 120, 160, 240, 320, 400, 480, 560, 720) min with the helium compartments scaling, ...
... The variable permeability model (VPM) incorporated size distribution of bubbles formed after decompression of gelatin. In order to slow down diffusion to fit the rate of development of DCI, it was assumed that bubbles have a skin with varying gas permeability (Yount, 1979;Yount and Hoffman, 1986;Yount et al., 2000;Kuch et al., 2011). Wienke (1990Wienke ( , 2009, in his reduced gradient bubble model, assumed exponential size distribution of gas micronuclei enveloped in surfactants to enable them to achieve stability. ...
... Previous models of decompression presented investigators with difficulty when it came to matching the time required for bubble expansion by diffusion (a short process) with the development of DCI (a prolonged process). To overcome this problem, some investigators suggested an artificially low diffusion constant (Hugon, 2014), while others suggested a bubble skin as a barrier to diffusion (Yount, 1979;Yount and Hoffman, 1986;Yount et al., 2000;Kuch et al., 2011) or an envelope of surfactants (Wienke, 1990(Wienke, , 2009. A bi-phasic mechanism of bubble expansion, initiation (Figure 10) followed by diffusiondriven growth, against the background of the AHS, makes bubble expansion compatible with the development of DCI. ...
Decompression illness (DCI) occurs following a reduction in ambient pressure. Decompression bubbles can expand and develop only from pre-existing gas micronuclei. The different hypotheses hitherto proposed regarding the nucleation and stabilization of gas micronuclei have never been validated. It is known that nanobubbles form spontaneously when a smooth hydrophobic surface is submerged in water containing dissolved gas. These nanobubbles may be the long sought-after gas micronuclei underlying decompression bubbles and DCI. We exposed hydrophobic and hydrophilic silicon wafers under water to hyperbaric pressure. After decompression, bubbles appeared on the hydrophobic but not the hydrophilic wafers. In a further series of experiments, we placed large ovine blood vessels in a cooled high pressure chamber at 1,000 kPa for about 20 h. Bubbles evolved at definite spots in all the types of blood vessels. These bubble-producing spots stained positive for lipids, and were henceforth termed “active hydrophobic spots” (AHS). The lung surfactant dipalmitoylphosphatidylcholine (DPPC), was found both in the plasma of the sheep and at the AHS. Bubbles detached from the blood vessel in pulsatile flow after reaching a mean diameter of ~1.0 mm. Bubble expansion was bi-phasic—a slow initiation phase which peaked 45 min after decompression, followed by fast diffusion-controlled growth. Many features of decompression from diving correlate with this finding of AHS on the blood vessels. (1) Variability between bubblers and non-bubblers. (2) An age-related effect and adaptation. (3) The increased risk of DCI on a second dive. (4) Symptoms of neurologic decompression sickness. (5) Preconditioning before a dive. (6) A bi-phasic mechanism of bubble expansion. (7) Increased bubble formation with depth. (8) Endothelial injury. (9) The presence of endothelial microparticles. Finally, constant contact between nanobubbles and plasma may result in distortion of proteins and their transformation into autoantigens.
... p new ss will be a more aggressive decompression causing bubbles of a smaller r 0 to be excited r new 0 . This process is done iteratively until the volume V max differs from V crit by 64 Chapter 2. The use of in vitro models in DCS a tolerated amount [161]. ...
... This led to the development of the critical volume criterion [161] as well as the inclusion of a Boyle's law contribution to the bubble growth [162]. This updated VPM, (VPM-B) produced total decompression times more in keeping with tables calculated from the LE algorithm but with a shift towards deep stops [14]. ...
For over 200 years, the formation of bubbles in the body as a result of ambient pres- sure changes has been linked to decompression sickness (DCS). The mechanisms by which bubbles may lead to DCS are poorly understood, despite this long history of re- search. Mathematical modelling has played a key role in DCS prevention through the development of dive computer algorithms. Algorithms which incorporate mechanistic bubble models must make assumptions about a selected bubble property being statisti- cally related to the incidence of DCS. This poses a problem for the validation of such algorithms. Given the uncertain relationship between the mechanistic model output and the symptoms of DCS, direct bubble observation is required to validate the mechanistic portion of the model; such measurements, however, are not currently possible in vivo. The use of biomimetic in vitro models provides a new research avenue to investigate the causal mechanism as well address the validation problem currently faced. In the work described in this thesis an in vitro matrix model (collagen type I gel) was used to validate and further develop a 3D computational model of extravascular bubble dynamics. The collagen gels together with a microscope compatible pressure chamber provided the means to directly measure bubble formation and dynamics within the gels during decompression profiles. The effect of material and dive parameter vari- ations on bubble growth was first investigated and validated. Bubble-bubble interaction and coalescence were then analysed. Both the computational and experimental results of these analyses indicated that a model of bubble nucleation would be essential to model bubble dynamics accurately. The possible nature and distribution of nucleation sites was investigated. Options for incorporation of the nucleation findings are anal- ysed. Finally the influence of live cells bubble dynamics through oxygen consumption and the effect bubble proximity has on cell viability were investigated.
... p new ss will be a more aggressive decompression causing bubbles of a smaller r 0 to be excited r new 0 . This process is done iteratively until the volume V max differs from V crit by 64 Chapter 2. The use of in vitro models in DCS a tolerated amount [161]. ...
... This led to the development of the critical volume criterion [161] as well as the inclusion of a Boyle's law contribution to the bubble growth [162]. This updated VPM, (VPM-B) produced total decompression times more in keeping with tables calculated from the LE algorithm but with a shift towards deep stops [14]. ...
For over 200 years, the formation of bubbles in the body as a result of ambient pres- sure changes has been linked to decompression sickness (DCS). The mechanisms by which bubbles may lead to DCS are poorly understood, despite this long history of re- search. Mathematical modelling has played a key role in DCS prevention through the development of dive computer algorithms. Algorithms which incorporate mechanistic bubble models must make assumptions about a selected bubble property being statisti- cally related to the incidence of DCS. This poses a problem for the validation of such algorithms. Given the uncertain relationship between the mechanistic model output and the symptoms of DCS, direct bubble observation is required to validate the mechanistic portion of the model; such measurements, however, are not currently possible in vivo. The use of biomimetic in vitro models provides a new research avenue to investigate the causal mechanism as well address the validation problem currently faced. In the work described in this thesis an in vitro matrix model (collagen type I gel) was used to validate and further develop a 3D computational model of extravascular bubble dynamics. The collagen gels together with a microscope compatible pressure chamber provided the means to directly measure bubble formation and dynamics within the gels during decompression profiles. The effect of material and dive parameter vari- ations on bubble growth was first investigated and validated. Bubble-bubble interaction and coalescence were then analysed. Both the computational and experimental results of these analyses indicated that a model of bubble nucleation would be essential to model bubble dynamics accurately. The possible nature and distribution of nucleation sites was investigated. Options for incorporation of the nucleation findings are anal- ysed. Finally the influence of live cells bubble dynamics through oxygen consumption and the effect bubble proximity has on cell viability were investigated.
... The reduced gradient bubble model of Wienke [13] was developed in the late 90s for recreational and technical diving. Using equationsof-state (EOS) from lipid and aqueous substrates to parameterize the structure of bubble skins, the RGBM uses an exponential number distribution (decreasing with bubble radius) for bubble nuclei excited into growth by compression-decompression. That number is summed over the exposure profile in 10 fsw increments and allowed to expand or contract under pressure and temperature changes to yield a surfacing estimate of excited bubble volume. ...
... Gradient Factors -Gradient factors (GFs) are a spinoff of published RGBM reduction factors (RFs) for recreational diving [13]. They merely reduce dissolved gas limiters (M-Values) at depth thus producing deep stops on top of dissolved gas staging. ...
This short article deals with useful and modern bubble models used to stage divers to the surface and correlations, if and when they exist, with actual data, usually decompression sickness (DCS) outcomes across a limited spectrum of exposures. Many of the early (wet) tests were carried out by world Navies, later by hyperbaric chamber testing and today also by statistical inference from downloaded computer profiles. All have contributed to correlation of models and data but in varying degrees as the scope of mixed gas, open circuit (OC) and rebreather (RB), nonstop to saturation and sea level to altitude diving is immense. No amount of wet or chamber testing will ever cover the ground here, but there is considerable hope and potential for downloaded computer profile data coupled to DCS outcomes to provide necessary correlations across the varied activities of modern diving.
... For decades, there has been an ongoing debate about how ambient pressure reduction should be conducted in nonsaturation dives [4], i.e., whether the reduction of the ambient pressure should start earlier or later in the decompression phase. Dissolved gas models, based on John S. Haldane's tables [1] and later developed by many others, were, over time, partially replaced by decompression algorithms based on the control of bubble formation and growth, including, among others, the varying permeability model developed by Yount [5], causing the speed in ambient pressure reduction, to start earlier in the decompression phase of the dive, i.e., requiring divers to start decompression stops deeper in the water column. ...
Background: The present study was designed to observe if different decompression profiles, calculated as a function of tissue supersaturation during ascent, would result in significantly different outcomes, measured through different physiological stress indicators, even in the absence of symptoms of decompression sickness. Aim: The aim of this study was to evaluate if simulated decompression profiles would affect the immune system, oxidative stress indicators, and heart rate variability. Methods: A total of 23 volunteers participated in two different experimental protocols in a dry hyperbaric chamber. These simulated dives comprised two different compression–decompression arrangements with the same maximum pressure and duration but different decompression profiles. Results: The shallow decompression profile with shorter deeper stops and longer shallow stops presented an increase in the standard deviation of the normal-to-normal R-R interval (a wide indicator of overall variability); the deep decompression profile with longer deeper stops and shorter shallow stops did not exhibit such increase. The shallow decompression profile resulted in an increase in neutrophil count and its microparticles (MPs), but no changes were observed for platelet count and its MPs, as well as for endothelial-derived MPs. In contrast, the deep decompression profile resulted in no changes in neutrophil count and its MPs, but a decrease in platelet count along with an increase in MPs from both platelets and endothelial cells. The observed difference might be related to different levels of decompression-related activation of immune system responses and oxidative processes triggered by different levels of inert gas supersaturation upon surfacing. Conclusion: From previous results and literature data, we present a tentative schematic of how the velocity of ascent would trigger (or not) pro-inflammatory and immune system responses that could ultimately lead to the development of decompression sickness. Relevance for patients: Increasing safety in exposure to hyperbaric environments and subsequent decompression by evaluating individual physiological responses to the process.
... The elastic skin, composed of surface active molecules surrounding the gas bubble, formed by adsorption onto the surface, gradually thickens as the bubble decreases in size until it becomes sufficiently rigid to inhibit any fiirther shrinkage of the bubble, thereby providing the compression strength necessary to resist collapse and gas loss into the liquid, thus stabilizing the bubble. This model for stabilizing gas nuclei was further developed and modified by Yount [93,94], who used light and electron microscopy to investigate bubble formation, and was able to provide evidence for spherical gas microbubbles. The varying-permeability membranes are usually gas permeable, but when subjected to large compressions, exceeding ~ 8 atm, they become effectively impermeable. ...
p>Reducing the size of offshore separator vessels can result in large economic and safety advantages, in terms of space saving, mobility and installation costs. Yet the lack of knowledge and understanding regarding the rapid evolution of gas following a sudden reduction in pressure, has so far hampered any significant size reduction in surface separating facilities. Following a review into the needs of the offshore oil and gas industry, and a review of the literature concerning the behaviour of gases in liquids, a fully instrumented thermodynamically enclosed rig facility was designed to study the non steady-state conditions created during, and immediately after, the rapid depressurization of a gas-saturated liquid. The mechanisms of gas evolution and the processes controlling the rate of gas evolution were investigated using techniques predominantly experimental in nature. The test conditions, in what is essentially a pressure vessel, included initial saturation pressures up to 30 bara, liquid temperatures up to 60oC and salinities up to full saturation. The range of gases, CO2, N2, O2, Ar and CH4, were investigated in water, brine (NaCl) solutions, two distillate oils, kerosene and gas oil and Statfjord crude, under controlled conditions. Owing to their industrial significance, exploratory tests were carried out using mixed gas compositions of N2 and CO2, and oil/water mixes.
Video evidence of events during depressurization and subsequent recovery was recorded and correlated with the pVT data. Gas evolution and hence pressure recovery to equilibrium occurred predominantly by bubbling, although pressure recovery by molecular diffusion was apparent over the latter stages of the approach to equilibrium for all gases. Owing to the dissociation reaction of CO2 in water, a more complex gas evolution pattern and a slower rate of approach to equilibrium, by ~2 orders of magnitude, was observed with CO2 in water compared to the other gases in water. In addition, the extent of dissociation of CO2 in brine, compared with that in tap water, was found to significantly influence the rate of gas evolution. In kerosene, the behaviour of CO2 was found to be similar to that of the other gases tested, where equilibrium was generally reached within seconds of depressurization. The main factors which were found to significantly increase the rate of gas evolution included the initial liquid temperature, fluid agitation and the addition of solid nuclei, in the form of 5 μ m uni-sized silica flour particles. The rate of gas evolution was not found to be significantly influenced by the purity of the water.</p
... exp 6 aggressive, similar to RGBM: TTS = 22 min details: pls. cf. the next 2 slidesLegend: TTS: time-to-surface, i.e.: (bottom depth/ascent rate) + sum of all stop times VPM: Varying Permeability Model, Ref.[3] RGBM: Reduced Gradient Bubble Model, Ref.[4] ...
Adaption of a COMEX procedure for recreational bounce dives on air:
a COMEX decompression procedure, once developped for deep experimental and saturation dives with Heliox is adapted for the use in the deep diving range for recreational & technical bounce dives on regular breathing air.
As well a comparison is done between different staging protocols and decompression
procedures, for. eg. from the United States Navy and the Buehlmann SAT tables.
... In conclusion, some of the currently used algorithms for the construction of decompression tables, such as the varying permeability model, based as it is on the theoretical considerations of Yount and Hoffman (1986), are founded on the size distribution of microbubbles in gelatin. Others, such as the reduced gradient bubble model (Wienke, 1990), have developed theories of an exponential distribution of gas micronuclei. ...
We found that lung surfactant leaks into the bloodstream, settling on the luminal aspect of blood vessels to create active hydrophobic spots (AHS). Nanobubbles formed by dissolved gas at these AHS are most probably the precursors of gas micronuclei and decompression bubbles. Sheep blood vessels stretched on microscope slides, and exposed under saline to hyperbaric pressure, were photographed following decompression. Photographs of an AHS from a pulmonary vein, containing large numbers of bubbles, were selected in 1‐min sequences over a period of 7 min, starting 18 min after decompression from 1,013 kPa. This showed bubble detachment, coalescence and expansion, as well as competition for dissolved gas between bubbles. There was greater expansion of peripheral than of central bubbles. We suggest that the dynamics of decompression bubbles on the surface of the blood vessel may be the closest approximation to true decompression physiology, and as such can be used to assess and calibrate models of decompression bubbles. We further discuss the implications for bubble size in the venous circulation. Bubble formation on luminal aspect of blood vessels are the best experimental model for decompression bubbles, their interactions and dynamics.
... With GFs you can get almost anything for stops and nothing about GFs has ever been correlated and validated in the same manner as VPM and RGBM have been correlated and published. See References for details of VPM and RGBM published model correlations and validation [44,35,14,45]. And see comparisons of USN and ZHL correlations just for completeness [37]. ...
The question of deep and shallow decompression stops is interesting and fraught with controversy in diving circles and operations, training, exploration and scientific endeavors. Plus fraught with some misunderstanding which is understandable as the issues are complex. We accordingly detail a short history of deep and shallow stops, physical aspects, staging differences, diving tests, models, data correlations, data banks, diver statistics and DCS outcomes for diving amplification. Pros and cons of deep stop and shallow stop staging are presented. Misinformation is corrected. Training Agency Standards regarding deep and shallow stops are included. A tabulation of well known and popular dive computers and software algorithms is given. From diving data, tests, DCS outcomes, data banks and field usage, we conclude that both deep stops and shallow stops are safely employed in recreational and technical diving today. For diver safety this is important.
... With GFs you can get almost anything for stops and nothing about GFs has ever been correlated and validated in the same manner as VPM and RGBM have been correlated and published. See References for details of VPM and RGBM published model correlations and validation (Yount and Hoffman, 1986;O'Leary, 2016, 2008;Wienke, 2015). And see comparisons of USN and ZHL correlations just for completeness (Wienke and O'Leary, 2018). ...
The question of deep and shallow decompression stops is interesting and fraught with controversy in diving circles and operations, training, exploration and scientific endeavors. Plus fraught with some misunderstanding which is understandable as the issues are complex. We accordingly detail a short history of deep and shallow stops, physical aspects, staging differences, diving tests, models, data correlations, data banks, diver statistics and DCS outcomes for diving amplification. Pros and cons of deep stop and shallow stop staging are presented. Misinformation is corrected. Training Agency Standards regarding deep and shallow stops are included. A tabulation of well known and popular dive computers and software algorithms is given. From diving data, tests, DCS outcomes, data banks and field usage, we conclude that both deep stops and shallow stops are safely employed in recreational and technical diving today. For diver safety that is important.
... Maximum bubble grades were noted and the Kisman integrated severity scores (KISS) (Jankowski et al., 1997) were calculated for each subject following each treatment. Although an indirect relationship, the higher the bubble load, the more likely DCS is to occur (Francis and Mitchell, 2003), and large numbers of bubbles over a protracted period indicate a high free-gas load so increasing the risk of clinical symptoms (Spencer and Johanson, 1974;Yount and Hoffman, 1986). Therefore, maximum grades are useful to illustrate the highest number of VGE and to infer some idea of DCS risk to the individual at a particular point in time. ...
Human extravehicular activity (EVA) is essential to space exploration and involves risk of decompression sickness (DCS). On Earth, the effect of microgravity on physiological systems is simulated in an experimental model where subjects are confined to a 6° head-down bed rest (HDBR). This model was used to investigate various resting and exercise regimen on the formation of venous gas emboli (VGE), an indicator of decompression stress, post-hyperbaric exposure. Eight healthy male subjects participating in a bed rest regimen also took part in this study, which incorporated five different hyperbaric exposure (HE) interventions made before, during and after the HDBR. Interventions i–iv were all made with the subjects lying in 6° HD position. They included (C1) resting control, (C2) knee-bend exercise immediately prior to HE, (T1) HE during the fifth week of the 35-day HDBR period, (C3) supine cycling exercise during the HE. In intervention (C4), subjects remained upright and ambulatory. The HE protocol followed the Royal Navy Table 11 with 100 min spent at 18 m (280 kPa), with decompression stops at 6 m for 5 min, and at 3 m for 15 min. Post-HE, regular precordial Doppler audio measurements were made to evaluate any VGE produced post-dive. VGE were graded according to the Kisman Masurel scale. The number of bubbles produced was low in comparison to previous studies using this profile [Kisman integrated severity score (KISS) ranging from 0–1], and may be because subjects were young, and lay supine during both the HE and the 2 h measurement period post-HE for interventions i–iv. However, the HE during the end of HDBR produced significantly higher maximum bubble grades and KISS score than the supine control conditions (p < 0.01). In contrast to the protective effect of pre-dive exercise on bubble production, a prolonged period of bed rest prior to a HE appears to promote the formation of post-decompression VGE. This is in contrast to the absence of DCS observed during EVA. Whether this is due to a difference between hypo- and hyperbaric decompression stress, or that the HDBR model is a not a good model for decompression sensitivity during microgravity conditions will have to be elucidated in future studies.
... However, as demonstrated by Herzfeld and Fox, for a bubble to form spontaneously in a pure solution with dissolved gas, a supersaturation greater than 10.0MPa is required, which corresponds to a water depth of 900 m [11]. The bubble nucleation theory also predicts that the gas supersaturation required for nucleating a bubble in pure solutions is significantly greater than that which could be achieved in a conventional diving exposure [12][13][14]. Hypotheses to explain this discrepancy have been mainly focused on the existence of pre-formed gaseous micronuclei [15] that are stabilized by surfactants or amphiphilic organic compounds [16,17], or more recently the existence of nanobubbles inspired by the recently found surface nanobubbles on hydrophobic surfaces [18,19]. At present, however, they all remain undetectable experimentally. ...
Decompression sickness (also known as diver's sickness) is a disease that arises from the formation of a bubble inside the body caused by rapid decompression from high atmospheric pressures. However, the nature of pre-existing micronuclei that are proposed for interpreting the formation and growth of the bubble, as well as their very existence, is still highly controversial. In this work, atomistic molecular dynamics simulations are employed to investigate the nucleation of gas bubbles under the condition of nitrogen supersaturation, in the presence of a lipid bilayer and lipid micelle representing other macromolecules with a smaller hydrophobic region. Our simulation results demonstrate that by crossing a small energy barrier, excess nitrogen molecules can enter the lipid bilayer nearly spontaneously, for which the hydrophobic core serves as a potential well for gas enrichment. At a rather low nitrogen supersaturation, gas molecules in the membrane are dispersed in the hydrophobic region of the bilayer, with a slight increase in membrane thickness. But as the level of gas supersaturation reaches a threshold, the accumulation of N2 molecules in the bilayer center causes the two leaflets to be decoupled and the formation of nanobubbles. Therefore, we propose a nucleation mechanism for bubble formation in a supersaturated solution of inert gas: a cell membrane acts as a potential well for gas enrichment, being an ideal location for forming nanobubbles that induce membrane damage at a high level of gas supersaturation. As opposed to previous models, the new mechanism involves forming gas nuclei in a very low-tension hydrophobic environment, and thus a rather low energy barrier is required and pre-existing bubble micronuclei are not needed.
... An approach that has produced a large proportion of quantitative data suitable for computational model validation is in vitro models. Yount and colleagues [24][25][26][27] made extensive use of gelatin models to investigate bubble nucleation and used their data to develop and validate the varying permeability model (VPM) -a commercial diving algorithm. Van Liew et al. [28] used bubbles in saline to compare bubble growth to computational models. ...
The growth of bubbles within the body is widely believed to be the cause of decompression sickness (DCS). Dive computer algorithms that aim to prevent DCS by mathematically modelling bubble dynamics and tissue gas kinetics are challenging to validate. This is due to lack of understanding regarding the mechanism(s) leading from bubble formation to DCS. In this work, a biomimetic in vitro tissue phantom and a three-dimensional computational model, comprising a hyperelastic strain-energy density function to model tissue elasticity, were combined to investigate key areas of bubble dynamics. A sensitivity analysis indicated that the diffusion coefficient was the most influential material parameter. Comparison of computational and experimental data revealed the bubble surface's diffusion coefficient to be 30 times smaller than that in the bulk tissue and dependent on the bubble's surface area. The initial size, size distribution and proximity of bubbles within the tissue phantom were also shown to influence their subsequent dynamics highlighting the importance of modelling bubble nucleation and bubble-bubble interactions in order to develop more accurate dive algorithms.
... Application and use is growing, particularly in the technical diving sector, over the past 20-25 years with new computers implementing bubble models. In particular, the VPM [16] and RGBM [17] models are noteworthy and used extensively within recreational and technical diving sectors. They also follow: ...
Dive computers and diveware are important underwater tools and staging devices across sport, technical, commercial , military, scientific, exploration and research diving sectors. They are supplanting traditional dive tables and their use is growing as decompression activities grow. While important computer parameters are displayed thoughout a dive, DCS risk associated with surfacing and arbitrary ascents to depths above the diver are not yet encoded into underwater devices and diveware and that is the focus here. Risk estimation is needed for diver safety and sensible dive planning. We discuss (two) basic biophysical models, oxygen toxicity and then methodology for risk estimators that can be employed in present generation dive computers and dive planning software for end of dive (EOD) and on the fly (OTF) risk at any point on a dive. Exponential risk functions are defined for dissolved gas and bubble models using profile data correlated with the LANL Data Bank, a collection of computer downloaded mixed gas decompression profile with DCS outcomes across OC and RB diving. Risk functions are based on profile supersaturations in excess over permiss-ble supersaturations which are a standard metric. Comparative results and applications are given for both nonstop and deep decompression diving on OC and RB systems. Computer implementation is easily accomplished within existing dive computers and diveware platforms. Techniques are underscored and results are discussed. References detail background information and analyses and work extends earlier published analyses for EOD risk estimation. It is hoped that this methodology is useful, well defined and pertinent for the dive computer and dive software industry. Animal Disclaimer-Humans and animals were not used for testing in this paper. Certainly animals and humans were employed in cited References. DEFINITIONS AND ACRONYMS Standard (SI) and English units are employed. By convention, by usage or for ease, some nonstandard units are employed. Pressure and depth are both measured in feet of sea water (f sw) and meters of sea water (msw), with 1 atm = 33 f sw = 10 msw to good approximation. Acronyms are used herein. They are standard throughout the dive community with definitions:
... Application and use is growing, particularly in the technical diving sector, over the past 20-25 years with new computers implementing bubble models. In particular, the VPM [16] and RGBM [17] models are noteworthy and used extensively within recreational and technical diving sectors. They also follow: ...
Dive computers and diveware are important underwater tools and staging devices across sport, technical, commercial , military, scientific, exploration and research diving sectors. They are supplanting traditional dive tables and their use is growing as decompression activities grow. While important computer parameters are displayed thoughout a dive, risk associated with surfacing and arbitrary ascents to depths above the diver are not yet encoded into underwater devices and divewear and that is the focus here. Risk estimation is needed for diver safety and sensible dive planning. We discuss (two) basic biophysical models, oxygen toxicity and then methodology for risk estimators that can be employed in present generation dive computers and dive planning software for end of dive (EOD) and on the fly (OTF) risk at any point on a dive. Exponential risk functions are defined for dissolved gas and bubble models using profile data correlated with the LANL Data Bank, a collection of computer downloaded mixed gas decompression profile with DCS outcomes across OC and RB diving. Risk functions are based on profile supersaturations in excess over permiss-ble supersaturations which are a standard metric. Comparative results and applications are given for both nonstop and deep decompression diving on OC and RB systems. Computer implementation is easily accomplished within existing dive computers and diveware platforms. Techniques are underscored and results are discussed. References detail background information and analyses and work extends earlier published analyses for EOD risk estimation. It is hoped that this methodology is useful, well defined and pertinent for the dive computer and dive software industry. Standard (SI) and English units are employed. By convention, by usage or for ease, some nonstandard units are employed. Pressure and depth are both measured in feet of sea water (f sw) and meters of sea water (msw), with 1 atm = 33 f sw = 10 msw to good approximation. Acronyms are used herein. They are standard throughout the dive community with definitions:
... Currently this estimation is simply the partial pressure of the respiration gas mixture. A far more robust estimation can be obtained by implementing the Varying Permeability Model (VPM) [12]. VPM is used by deep sea divers to calculate safe decompression plans, with nitrogen partial pressure a key parameter that is calculated. ...
... The numerous models developed are principally empirical and rather than physiological, and so they are safe only in a ranges as a function of the depth and the time. The increase or decrease of the pressure gradient mainly depends on two criteria: super-saturation or the gaseous oversaturation coefficients [16], and the growth and develop of gaseous bubbles in the organism [17]. The evolution of the bubbles generated in the tissues in the ascent, from positions hyperbaric with air has been deduce a from theorical models and clinical observations [18, , 19]. ...
We have studied decompression processes when pressure changes that take place, in blood and tissues using a technical numerical based in electrical analogy of the parameters that involved in the problem. The particular problem analyzed is the behavior dynamics of the extravascular bubbles formed in the intercellular cavities of a hypothetical tissue undergoing decompression. Numerical solutions are given for a system of equations to simulate gas exchanges of bubbles after decompression, with particular attention paid to the effect of bubble size, nitrogen tension, nitrogen diffusivity in the intercellular fluid and in the tissue cell layer in a radial direction, nitrogen solubility, ambient pressure and specific blood flow through the tissue over the different molar diffusion fluxes of nitrogen per time unit (through the bubble surface, between the intercellular fluid layer and blood and between the intercellular fluid layer and the tissue cell layer). The system of nonlinear equations is solved using the Network Simulation Method, where the electric analogy is applied to convert these equations into a network-electrical model, and a computer code (electric circuit simulator, Pspice). In this paper, numerical results new (together to a network model improved with interdisciplinary electrical analogies) are provided.
Decompression illness is a collective term for two maladies (decompression sickness [DCS] and arterial gas embolism [AGE]) that may arise during or after surfacing from compressed gas diving. Bubbles are the presumed primary vector of injury in both disorders, but the respective sources of bubbles are distinct. In DCS bubbles form primarily from inert gas that becomes dissolved in tissues over the course of a compressed gas dive. During and after ascent (‘decompression’), if the pressure of this dissolved gas exceeds ambient pressure small bubbles may form in the extravascular space or in tissue blood vessels, thereafter passing into the venous circulation. In AGE, if compressed gas is trapped in the lungs during ascent, pulmonary barotrauma may introduce bubbles directly into the pulmonary veins and thence to the systemic arterial circulation. In both settings, bubbles may provoke ischaemic, inflammatory, and mechanical injury to tissues and their associated microcirculation. While AGE typically presents with stroke-like manifestations referrable to cerebral involvement, DCS can affect many organs including the brain, spinal cord, inner ear, musculoskeletal tissue, cardiopulmonary system and skin, and potential symptoms are protean in both nature and severity. This comprehensive overview addresses the pathophysiology, manifestations, prevention and treatment of both disorders.
This article is a further one in an unintended series concerning the design of diving technology [1,2,3]. It contains answers to questions raised by readers upon reading previous articles and by users of the systems described therein by way of example. The articles also refer to the discussion held at the annual NATO Working Group meeting on the various types of decompression presented by the Polish side [4,5,6,7]. The previous articles were linked to the acceptance of the results of the project No. DOB-BIO8/О9/О1/2016 carried out under the contract with the NCBiR National Centre for Research and Development entitled “Decompression schedules for MCM/EOD II diving” carried out in 2016-2021. The current article is linked to the new project No. DOBBIO-12-03-001-2022 implemented under the contract with the NCBiR entitled: “The effects of combat effort and air transport on the safety of combat divers in the execution of underwater combat operations,” scheduled for 2023-2025.
Scientific diving (SD) is defined as any diving activity that applies scientific procedures to produce subsidies for studies and technical works in underwater environments. The first report of an underwater scientific study in Brazil dates to the 19th century, in the Abrolhos reefs. Currently, in Brazil, scientific diving has been performed in various areas, from shallow coastal regions to remote and sometimes hard-to-reach places, such as oceanic islands, flooded caves, and icy areas like Antarctica. However, the regulation of SD in Brazil still lacks more concrete actions towards an effective and efficient self-regulation that offers physical safety to practitioners and institutional safeguards for organizations that use it in their research projects. Thus, this article aims to contribute to a better understanding of this critical issue in Brazil and to serve as a reference and incentive for the training of professionals and the development of these activities in the country. It includes: 1) a historical review of SD; 2) a diagnosis of the training and application of SD in Brazil; 3) the evolution of marine sciences in Brazil from the perspective of SD; 4) a review of the use of environmental assessment and underwater conservation techniques in oceans and internal waters; 5) an analysis of the evolution of scientific diver training in Brazil, including a diagnosis on training; 6) the history and updates of the rules, regulations, and safety of SD. Given all the potential of diving combined with specific techniques for research, monitoring, and marine and limnic science in Brazil, we aim to understand the evolution of scientific diving teaching and to outline perspectives in the country, as it is crucial for the training of qualified scientists capable of performing these underwater tasks. Finally, we present future plans for the development of this activity in Brazil from the point of view of research and the labor market.
Introduction:
Increased concentrations of tau protein are associated with medical conditions involving the central nervous system, such as Alzheimer's disease, traumatic brain injury and hypoxia. Diving, by way of an elevated ambient pressure, can affect the nervous system, however it is not known whether it causes a rise in tau protein levels in serum. A prospective observational pilot study was performed to investigate changes in tau protein concentrations in serum after diving and also determine their relationship, if any, to the amount of inert gas bubbling in the venous blood.
Methods:
Subjects were 10 navy divers performing one or two dives per day, increasing in depth, over four days. Maximum dive depths ranged from 52-90 metres' sea water (msw). Air or trimix (nitrogen/oxygen/helium) was used as the breathing gas and the oxygen partial pressure did not exceed 160 kPa. Blood samples taken before the first and after the last dives were analyzed. Divers were monitored for the presence of venous gas emboli (VGE) at 10 to15 minute intervals for up to 120 minutes using precordial Doppler ultrasound.
Results:
Median tau protein before diving was 0.200 pg·mL⁻¹ (range 0.100 to 1.10 pg·mL⁻¹) and after diving was 0.450 pg·mL⁻¹ (range 0.100 to 1.20 pg·mL⁻¹; P = 0.016). Glial fibrillary acidic protein and neurofilament light protein concentrations analyzed in the same assay did not change after diving. No correlation was found between serum tau protein concentration and the amount of VGE.
Conclusion:
Repeated diving to between 52-90 msw is associated with a statistically significant increase in serum tau protein concentration, which could indicate neuronal stress.
Dissolved gas models (GM) focus on controlling and eliminating tissue dissolved gas by bringing the diver as close to the surface as possible. Bubble phase models (BM) focus on controlling hypothetical bubble growth and coupled dissolved gas by staging the diver deeper before surfacing. The former gives rise to shallow decompression stops while the latter requires deep decompression stops in the popular lingo these days. As models go both are fairly primitive only addressing the coarser dynamics of dissolved gas buildup and bubble growth in tissues and blood. Obviously, their use and implementation is limited, but purposeful and useful when correlated with available data and implemented in dive computers.
A potpourri of diving software packages (diveware) available on the market are described briefly. They are chosen because of their widespread use, utility, historical perspectives and diver popularity. New ones are coming online every day. They are popularly categorized as dissolved gas, dissolved gas with GFs, pseudo-bubble and bubble models. Dissolved gas, dissolved gas with GFs and pseudo-bubble models are collectively termed neo-Haldane models. In neo-Haldane models, M-values and Z-values are reduced compared to the original USN and ZHL compilations. The RGBM and VPM are the only true bubble models of interest and commercially available in diveware and computers.
Bubble birth, growth, evolution, destruction and elimination in the body of human divers are central issues in safe diver staging protocols from exposures at depth. Today, despite incredible technological advances in medical and physiological science, we really know very little about bubbles in vivo and their complex behavior under pressure and environmental changes. Measuring bubbles and their properties in vivo by invasive means often destroys or changes what is being measured. Measuring with non-invasive techniques is very limited. Doppler scoring of moving body bubbles is only able to count numbers. Experiments using materials with properties similar to blood and tissue can be useful as a starting point for simulating bubble behavior but of course blood and tissue are metabolic and perfused adding additional complexity and unknowns to coupled modeling and simulation. In this vein, therefore, we investigate bubble data and experiments in the laboratory to make some hypothetical estimates of possible impacts of bubble regeneration and broadening on diver staging regimens. A working framework for implementation of bubble regeneration and broadening is detailed for dive computers and diveware.
Testing and validation of GM models has been a successful medical exercise for many years dating back to the 1900s and certainly could fill a book. Some are recounted here and more can be found elsewhere. BM models are newer and do not enjoy the testing history of GM models. Apart from computer profile correlations some wet and dry tests have transpired. For BM computers these are important benchmarks. We start at the beginning in first recounting early deep stop testing by Haldane and the deep stop hook-or-crook protocols of Australian and Hawaiian pearl divers and fishermen. And then work thru recent tests and data.
To validate computer models, diving data is necessary. In the past, data consisted mostly of scattered open ocean and dry chamber tests of specific dive schedules. In such instances, the business of correlating model and diving data was only scratched. Today, profile collection across diving sectors is proceeding more rapidly. Notable are the efforts of Divers Alert Network (DAN) and Los Alamos National Laboratory (LANL). DAN USA is collecting profiles in an effort called Project Dive Exploration (PDE) and DAN Europe has a parallel effort called Diving Safety Laboratory (DSL). The focus has been recreational dive profiles for air and nitrox. The LANL Data Bank collects profiles from technical diving operations on mixed gases for deep and decompression diving on OC and RB systems. Both have uncovered interesting trends in diving and have been used for meaningful statistical correlations of diving models.
Risk estimation on the fly (OTF) or end of dive (EOD) is not yet implemented in dive computers nor planning software. The following suggests appropriate methodology for implementation of both. As dive computers working in the recreational (air and nitrox) depth regime, d < 130 fsw roughly, use GM models for speed and simplicity and dive computers working in the technical (mixed gases and decompression) depth regime, d > 130 fsw, employ BM models, we will define GM risk functions in comparative applications for shallow recreational diving, d < 130 fsw, and BM risk functions in comparative applications for deep and decompression technical diving, d > 130 fsw.
Much like functional hook-or-crook approaches of Australian pearl divers, ad hoc diving protocols on top of existing procedures have surfaced in the last 20 years or so. To date, none of the ad hoc protocols have been tested nor correlated with actual data. Anecdotally, these procedures seem to work though, at least reports contraindicating their usage are not generally recorded. That is certainly good. Just briefly, some important ones are mentioned. The technical diving community has been the primary pusher of many of these protocols. In varying degrees they have been embedded into both GM and BM dive computers.
The French physician Paul Bert (1833–1886) recognized the problem of accidents during and after decompression and therefore recommended a slow ascent. John Scott Haldane developed dive tables for the US Navy in 1908. Fundamentals of his research are incorporated in today’s dive tables. His calculations included exponential saturation and desaturation, five different body compartments, gradual decompression in 3-m intervals and the concept of maximum supersaturation with the so-called Haldane factor [7]. He postulated that the partial pressure of inert gases in all tissues should not exceed twofold (2:1) of the ambient pressure during the ascent to avoid decompression accidents. In other words, a direct reduction to an ambient pressure from a twofold overpressure is regarded not to cause any DCS symptoms. For example, a direct ascent from 10 m after a saturation dive without deco stop is supposed to be safe. However, Workman corrected the value later to 1.58:1, considering only partial pressures of inert gases, primarily nitrogen. Haldane assumed that the main factor of a decompression accident during rapid ascents is caused by fast compartments. He postulated that slow compartments are responsible for decompression accidents during slow ascents and decompression stops. He established the basic principle of compartment saturation and desaturation based on tissue perfusion. He set the ascent rate initially to 18 m/min than later to 9 m/min.
The Ostwald ripening phenomenon for gas bubbles in a liquid consists mainly in gas transfer from smaller bubbles to larger bubbles. An experiment was carried out in which the Ostwald ripening for air bubbles, in a liquid fluid with some rheological parameters of the human blood, is reproduced. There it has been measured time evolution of bubbles mean radius, number of bubbles and radius size distribution. One of the main results shows that, while the number of bubbles decreases in time the bubbles mean radius increases, therefore smaller bubbles disappear whereas the, potentially dangerous for the diver, larger bubbles grow up. Consequently, it is presumed that such a bubble broadening effect could contribute, even minimally, to decompression illness: decompression sickness and arterial gas embolism. This conjecture is reinforced by the preliminary results of Ostwald broadening to RGBM (Reduced Gradient Bubble Model) decompression schedules for a closed circuit rebreather (CCR) dive to 420fsw (128m) with 21/79 Heliox gas mixture.
The Ostwald ripening phenomenon for gas bubbles in a liquid consists mainly in gas transfer from smaller bubbles to larger bubbles. An experiment was carried out in which the Ostwald ripening for air bubbles, in a liquid fluid with some rheological parameters of the human blood, is reproduced. There it has been measured time evolution of bubbles mean radius, number of bubbles and radius size distribution. One of the main results shows that, while the number of bubbles decreases in time the bubbles mean radius increases, therefore smaller bubbles disappear whereas the, potentially dangerous for the diver, larger bubbles grow up. Consequently, it is presumed that such a bubble broadening effect could contribute, even minimally, to decompression illness: decompression sickness and arterial gas embolism. This conjecture is reinforced by the preliminary results of Ostwald broadening to RGBM (Reduced Gradient Bubble Model) decompression schedules for a closed circuit rebreather (CCR) dive to 420fsw (128m) with 21/79 Heliox gas mixture.
A short treatise on modern dive computers for the computer scientist, mathematician,
doctor, physiologist, engineer, commercial and technical diver, dive computer manufacturer, table designer, dive instructor, surface tender, military diver, statistician, physicist, recreational diver, biologist. lawyer and any interested individual in the many
aspects of modern dive computers, operations, models, correlations, data banks, risk
analyses, wet and dry tests, ad hoc protocols, training agency and computer vendor
algorithm implementations and the related interplay for safe and sanel computer diving.
The vast majority of recreational dives are performed by divers using single cylinders of compressed air and open-circuit breathing systems, typically to a maximum depth of 40 m of seawater (msw). More extreme dives (in terms of depth and duration) are performed by a small subgroup of recreational divers who refer to their activity as ‘technical diving’. Technical divers substitute helium for nitrogen in gas mixes for deep diving to reduce the narcotic effect of nitrogen respired at high partial pressures and to reduce the density of the gas. These mixes also contain less oxygen than air in order to manage the risk of cerebral oxygen toxicity. Adequate gas supplies for long dives are carried in multiple cylinders, or divers may utilise ‘rebreather’ devices that recycle expired gas through a carbon dioxide (CO2) absorbent and which include a system for maintaining a safe inspired pressure of oxygen (PO2) as oxygen is consumed. These devices are complex and error-prone, and there is some evidence for relatively high accident rates in their use. Using these techniques, compressed gas dives between 40 and 100 msw are now relatively ‘routine’, and more extreme dives to depths in excess of 300 msw have been completed. A challenge of deep technical diving is the effect on respiratory physiology. There are multiple factors (including increased density of the respired gas) that increase the work of breathing during deep dives. This, in turn, may cause significant perturbation of normal respiratory control. In particular, there is a tendency for divers to hypoventilate and retain CO2 which can produce a number of dangerous secondary effects. Another significant challenge is uncertainty over the optimal protocol for decompression from deep dives. Technical divers utilise progressively more oxygen-rich breathing mixes during ascent in order to accelerate inert gas elimination, but there is uncertainty over how to plan the duration and depths of the ‘decompression stops’ that are completed during the ascent to allow time for this elimination to occur.
Decompression sickness is caused by a reduction in ambient pressure which results in supersaturation and the formation of gas bubbles in blood or tissue. This well-known disease syndrome, often called “the bends,” is associated with such modern-day activities as deep-sea diving, working in pressurized tunnels and caissons, flying at high altitudes in unpressurized aircraft, and flying EVA excursions from spacecraft. A striking feature is that almost any body part, organ, or fluid can be affected, including skin, muscle, brain and nervous tissue, the vitreous humor of the eye, tendon sheath, and bone. Medical signs and symptoms range from itching and mild tingling sensations to crippling bone necrosis, permanent paralysis, and death.
Saturation decompression is a physiological process of transition from one steady state, full saturation with inert gas at pressure, to another one: standard conditions at surface. It is defined by the borderline condition for time spent at a particular depth (pressure) and inert gas in the breathing mixture (nitrogen, helium). It is a delicate and long lasting process during which single milliliters of inert gas are eliminated every minute, and any disturbance can lead to the creation of gas bubbles leading to decompression sickness (DCS). Most operational procedures rely on experimentally found parameters describing a continuous slow decompression rate. In Poland, the system for programming of continuous decompression after saturation with compressed air and nitrox has been developed as based on the concept of the Extended Oxygen Window (EOW). EOW mainly depends on the physiology of the metabolic oxygen window-also called inherent unsaturation or partial pressure vacancy-but also on metabolism of carbon dioxide, the existence of water vapor, as well as tissue tension. Initially, ambient pressure can be reduced at a higher rate allowing the elimination of inert gas from faster compartments using the EOW concept, and maximum outflow of nitrogen. Then, keeping a driving force for long decompression not exceeding the EOW allows optimal elimination of nitrogen from the limiting compartment with half-time of 360 min. The model has been theoretically verified through its application for estimation of risk of decompression sickness in published systems of air and nitrox saturation decompressions, where DCS cases were observed. Clear dose-reaction relation exists, and this confirms that any supersaturation over the EOW creates a risk for DCS. Using the concept of the EOW, 76 man-decompressions were conducted after air and nitrox saturations in depth range between 18 and 45 meters with no single case of DCS. In summary, the EOW concept describes physiology of decompression after saturation with nitrogen-based breathing mixtures.
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