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Underwater decompression meters or computers sense a diver's changes of depth in real-time and calculate a decompression schedule for the individual diver's exposure. Currently available devices compare calculated nitrogen tissue tensions to a set of stored 'safe' constants. No explicit quantitative connection between these rules and the risk of decompression sickness has been established. Well calibrated probabilistic models, even though computationally more intense, can be used to specify decompression procedures tailored to control the risk of decompression sickness. Probabilistic models allow conscious choice of the degree of 'safety' or acceptable risk. Previously, the choice required searching up to tens of thousands of possibilities for any given dive. That method cannot be employed in real time without a very fast computer. We describe a quicker search method that depends upon a 'recent optimal' solution so that it can be implemented in real time. The real time algorithm compared favorably with decompression schedules obtained by extensive searches. Timing requirements for updating calculations (important for hardware specification) depends on how fast the 'recent optimal' answer changes. Risk management for repetitive diving is described in terms of conditional probability. The algorithm can be used to permit the acceptable risk level to vary during real time as the dive severity increases, and to include multiple breathing gases.

Content uploaded by Paul K Weathersby

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All content in this area was uploaded by Paul K Weathersby on Mar 06, 2015

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... The maximum likelihood approach with the above general expression had been used to optimise many DCS models, with the main variation being the chosen form of the hazard function. In collaboration with Thalmann, Weathersby et al. used a large dataset of over 8000 dives was used to calibrate the LE model and optimise parameters [153,154,3]. The hazard function was of the form: ...

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 maximum likelihood approach with the above general expression had been used to optimise many DCS models, with the main variation being the chosen form of the hazard function. In collaboration with Thalmann, Weathersby et al. used a large dataset of over 8000 dives was used to calibrate the LE model and optimise parameters [153,154,3]. The hazard function was of the form: ...

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.

... This model was successfully validated in a prospective dive trial (5,6), and then recalibrated by adding this validation trial data to the original data set. A PC-based dive planner using the final model, USN93, was developed and approved for use by Naval Special Warfare (NSW) personnel (7,8). This experience established a novel methodology wherein an initial model, based on existing data, provided the basis for a dive trial, and the final model then incorporated the results of that trial to fine tune model performance for the eventual application. ...

... For dives with longer bottom times the resulting decompression proved unworkably long. The only way to keep the decompression times within operational feasibility was to allow the target risk to assume a higher value for the longer dives, making them riskier (Survanshi et al 1996(Survanshi et al , 1997. ...

... [41] The linear-exponential model was used in an algorithm that allows real time calculation of the decompression profile with inputs of acceptable probability of DCS and the pressure/time profile of the dive. [51] The algorithm was tested in a validation trial of more than 700 multilevel dives. [52] It was then used to develop a set of multilevel decompression tables that were consistent with the dive computer algorithm. ...

Decompression sickness is a complex phenomenon involving gas exchange, bubble dynamics and tissue response. Relatively simple deterministic compartmental models using empirically derived parameters have been the mainstay of the practice for preventing decompression sickness since the early 1900s. Decades of research have improved our understanding of decompression physiology, and the insights incorporated in decompression models have allowed people to dive deeper into the ocean. However, these efforts have not yet, and are unlikely in the near future, to result in a 'universal' deterministic model that can predict when decompression sickness will occur. Divers using current recreational dive computers need to be aware of their limitations. Probabilistic models based on the estimation of parameters using modern statistical methods from large databases of dives offer a new approach and can provide a means of standardisation of deterministic models. Future improvements in decompression practice will depend on continued improvement in understanding the kinetics and dynamics of gas exchange, bubble evolution and tissue response, and the incorporation of this knowledge in risk models whose parameters can be estimated from large databases of human and animal data.

... There may be some leeway in the particular pattern of times at stops: Survanshi and coworkers state that with certain probabilistic models, many different stop-time combinations having the same TDT result in the same probability of DCS. 19 THE COMPENDIUM Table 1 lists the18 files in the U.S. Navy Decompression Database that contributed single-level, nonrepetitive air-breathing dives for our analysis. Each of the 18 files is based on a particular published report and is reviewed in a summary Navy report.1 4 The entries in the source files provide information about 1-86 persons who followed a particular dive profile. ...

We compare outcomes of experimental air dives with prescriptions for ascent given by various air decompression tables. Among experimental dives compiled in the U.S. Navy Decompression Database, many profiles that resulted in decompression sickness (DCS) have longer total decompression times (TDTs, defined as times spent at decompression stops plus time to travel from depth to the surface) than profiles prescribed by the U.S. Navy table; thus, the divers developed DCS despite spending more time at stops than the table requires. The same is true to a lesser extent for the table used by the Canadian forces. A few DCS cases occurred in profiles having longer TDTs than those of the VVal-18 table and a table prepared at the University of Pennsylvania. The TDTs for 2.2% risk according to the probabilistic NMRI'98 Model are often far longer than TDTs of experimental dives that resulted in DCS. This analysis dramatizes the large differences among alternative decompression instructions and illustrates how the U.S. Navy table provides too little time at stops when bottom times are long.

Decompression sickness (DCS) is a disease known to be related to inert gas bubble formation originating from gases dissolved in body tissues. Probabilistic DCS models, which employ survival and hazard functions, are optimized by fitting model parameters to experimental dive data. In the work reported here, I develop methods to find the survival function gain parameter analytically, thus removing it from the fitting process. I show that the number of iterations required for model optimization is significantly reduced. The analytic gain method substantially improves the condition number of the Hessian matrix which reduces the model confidence intervals by more than an order of magnitude.

This first-ever validation trial of a probabilistic decompression algorithm was conducted from 1991-92. A real time computer algorithm updated subjects' optimal decompression schedule within a numerical specification of the acceptable risk of decompression sickness (DCS). Long dives (majority over 6 hours) were chosen for testing because of operational needs and under-representation in the calibration data set: long repetitive air dives and multi-level dives - with air throughout, or with 0.7 ATA O2 during shallow transits or during the final decompression. Non-acclimatized divers wearing wet suits were immersed, chilled, and performed moderate exercise on the bottom but rested during decompression. A total of 730 dives resulted in 36 DCS cases, and another 20 cases with marginal symptoms. A subset (158 dives) were performed with the Combat Swimmer Multi-level Dive procedure, demonstrating greater safety when shallow transits were taken at 15 than at 30 feet of seawater. Overall the model was a predictive success: on none of the profiles were observed DCS incidence outside statistical uncertainty, and optimal model parameters were not greatly changed by the addition of the trial data. The real time algorithm is reliable enough for general Navy use.

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