The Impact of Weighting Marginal DCS Events as Non-Events, Pharmacokinetic Gas Content Models, and Optimal Decompression Schedule Calculation

Abstract

Decompression sickness (DCS) in man is a condition associated with reduction in ambient pressure. These reductions may result from a return to normobaric pressure from hyperbaric pressure, or an ascent to hypobaric pressure. Previous approaches to mitigate the risk of DCS have been based on both deterministic and probabilistic decompression algorithms. Deterministic decompression algorithms generate ascent schedules with binary outcomes. Following the prescribed ascent schedule should prevent the onset of DCS. Failure to comply with the prescribed schedule should make the onset of DCS an inevitable outcome. However, in practice DCS may occur in individuals that follow deterministic decompression schedules precisely and may not occur in individuals that fail to comply with these schedules. Probabilistic algorithms do not provide a decompression schedule with a binary outcome, instead they generate a schedule associated with a target probability of DCS occurring.In this work, several aspects of probabilistic algorithms are investigated using the techniques of survival analysis and numerical optimization. All work was completed using computer software coded in the C# programming language. Model optimization and evaluation techniques described below were completed using U.S. Navy standard dive data sets. These dive data sets consist of time series recordings of pressure, inspired gas, DCS outcome, last known time at which test subjects were healthy, and time at which DCS symptoms were definitely present if applicable. This data did not require institutional review board approval for use and has been previously described in the literature.Models investigated were evaluated with their optimized parameters using statistical tests to determine how well they described both the training data and data not included in the training set. Statistical techniques used to evaluate the models included the Akaike information criterion (AIC), Pearson Х2 test, and occurrence density functions. AIC had to be used as the models examined during this work were often not nested within each other. When models were nested, the log likelihood difference test was used to compare the candidate models. In addition to these rigorous statistical tests, graphs were frequently used to present qualitative information about the underlying models and/or data.There is no diagnostic test for DCS, and as such, the outcome of an exposure is not always clear. Test subjects may experience transient symptoms of DCS which spontaneously resolve prior to recompression treatment. These mild events which spontaneously resolve are termed marginal DCS events. During optimization, marginal DCS events are typically assigned a fractional weight of either 0.5 or 0.1 with a full DCS event being weighed as 1.0 and a non-event as 0.0. Previous work has shown that the overall quality of model fit to the data can be improved by assigning a weight of 0.0 to marginal DCS events during optimization. In this work the U.S. Navy LE1 and LEM models were re-optimized against the BIG292 and NMRI98 data sets with marginal DCS events weighted as 0.0. Features were added incrementally to the EE1 model until LE1 or LEM were formed to evaluate if the features were still statistically justified. All features were found to be statistically relevant; these features were a linear gas washout and a threshold term in the case of LE1 and linear gas washout, a threshold term, and the inclusion of oxygen as a participating gas in the case of LEM. Further, the addition of these features enabled both models to more accurately predict the observed incidences and times of occurrence of DCS for the profiles in their training sets. Prior to re-optimization, LE1 had incorrectly ascribed the risk of marginal DCS events entirely to bounce dives. LEM gave undue weight to saturation dives in the training set due to the bulk of marginal events occurring during saturation dive exposures, despite saturation dives only comprising 14.4% of the data. It is concluded that marginal DCS events should not be assigned a fractional weight, but should be accommodated by another mechanism in the model optimization process.Pharmacokinetic gas content models have been shown to well describe gas uptake and washout in the skeletal muscle and cerebral tissue of sheep. These models differ from the EE1, LE1, and LEM models in that they feature multi-exponential kinetics. The multi-exponential kinetics arise from using a series of compartments coupled by either perfusion or diffusion in lieu of a collection of parallel independent perfusion limited compartments. Eleven models incorporating coupled compartments were investigated in this work along with one model that consisted of a single perfusion-limited compartment. Six of the models had been previously investigated using sheep and five were novel.No pharmacokinetic gas content model described the overall NMRI98 data better than the LEM model by weighted AIC index. However, several data subsets including single air, repetitive and multilevel air, and oxygen decompression dives were better described by pharmacokinetic gas content models than either LEM or the single perfusion limited compartment. A single perfusion limited compartment outperformed both LEM and all of the pharmacokinetic gas content models for saturation exposures. No one model being the best descriptor of all dive data types indicates that multiple compartment structures are needed to best describe the data. The four best performing pharmacokinetic gas content models; Central Serial Two Tissue (CS2T/CS2T_3) and Perfusion Diffusion Base (PDB/PDB_10); were augmented with the incorporation of oxygen as a participating gas. Oxygen was incorporated by the addition of a sink term to the differential equations describing oxygen uptake and washout. A sink term was used to allow for oxygen to be scaled in future work with the addition of exercise information. Unlike a model based on a collection of parallel uncoupled compartments (LEM), none of the pharmacokinetic gas content models were improved by the addition of oxygen as a participating gas. This suggests that the benefit from including oxygen as a participating gas is a function of the underlying model structure and not the data.Combining multiple pharmacokinetic gas content models was also explored in this work. The combinations of CS2T3_PLB, PDB_PLB, CS2T3_PDB, and PDBX2 were all tested. PLB stands for perfusion limited base model (the single perfusion limited compartment used above) and PDBX2 is two copies of the PDB model in parallel. Notionally, using a collection of pharmacokinetic gas content models in parallel should allow for one compartment (PLB) to describe the saturation dive data and another collection of compartments such as CS2T_3 to describe the rest of the data. In practice this did not happen, each of the models combined optimized to each bear a fraction of the risk for all dives. Pharmacokinetic gas content models consisting of a collection of different parallel compartment structures did not better describe the data than LEM. The final problem considered in this work is the problem of calculating an ascent path to end a hyperbaric exposure with the shortest possible ascent time and without exceeding a specified target risk (probability of DCS occurring). Current methods for solving this problem are based upon searching through hundreds to thousands of possible schedules until an acceptable solution is found. However, it is possible to directly calculate the shortest ascent path which does not exceed the target risk. The necessary calculations to determine the shortest path within a target risk are described. However, this path is not necessarily unique and further work will be needed prior to this work becoming a complete solution to the ascent search problem.This work provides significant advances to probabilistic algorithms for mitigating the risk of DCS during diving. The LE1 and LEM models were re-optimized with marginal DCS events weighted as non-events. Re-optimization resulted in more accurate prediction of risk by the models when compared to their respective training data. Pharmacokinetic gas content models were investigated in depth and they were found to be good predictors for air diving and oxygen decompression diving. The need for oxygen as a participating gas was ruled out for pharmacokinetic gas content models. Combinations of multiple pharmacokinetic gas content models were found to not optimize well when naively combined, suggesting a need for a more complex likelihood function. Finally, an outline for directly calculating the optimal ascent path for a given hyperbaric exposure as part of a probabilistic decompression algorithm was provided. Together this work provides a significant step toward probabilistic decompression algorithms being a viable replacement for deterministic decompression algorithms in all underwater operations.