N M Gürmen | PubMed Health

PubMed2001

Simulation of dynamic bubble spectra in tissues.

Decompression sickness (DCS) is the result of bubble formation in the body due to excessive/rapid reduction in the ambient pressure. Existing models relate the decompression stress either to the inert gas load or to the size of a single bubble in a tissue compartment. This paper presents a model that uses the gas exchange equations combined with bubble dissolution physics and population balance equations to produce a new mathematical framework for DCS modeling. This framework, the population balance model for decompression sickness (PBMDS), simulates the number of bubbles with their corresponding size distributions in a compartmental tissue array. The model has a modular structure that enables one to explore different modeling results with respect to key aspects of DCS, such as gas exchange, nucleation, and surface tension. The paper's goal is to present the derivation of PBMDS in detail, however, three simple application case studies are provided. The aim of these case studies is to suggest that PBMDS supplies additional information on bubble distribution while supporting the results from current practice.

Computer Simulation↗

PubMed2000

Computation of decompression tables using continuous compartment half-lives.

There is no consensus on the number of compartments and the half-lives (T1/2) used in the calculation of inert gas exchange and decompression sickness (DCS) boundary in existing dive tables and decompression computers. We propose the use of a continuous variable for the tissue half-lives, allowing the simulation of an infinite number of compartments and reducing the discrepancy between different algorithms to a single DCS boundary expression. Our computational method is based on the premise that M-values can be expressed in terms of T1/2 and ambient pressure (D). We combined the surfaces defined by M(D,T1/2) and tissue tension H(t,T1/2) to plan decompression. The efficiency and applicability of the method is investigated with four different DCS boundaries. The first two utilize the M-value relations proposed by Bühlmann and Wienke to derive no-D limits for sea level. The third boundary is defined by a surface fitted to the empirical M-values of US Navy, Bühlmann tables, US Air Force, and our altitude diving data. This expression was used to design the decompression procedure for a multilevel dive at 11,429-ft altitude and was used in six man dives in the Kaçkar Mountains, Turkey. Although precordial bubbles were observed in two dives, there were no cases of DCS. The fourth DCS boundary is constructed with the addition of a constraint that forces calculated M-values to stay below the available M-values. This constraint aims the highest degree of "conservatism". As an application of the new boundary, the method is used to derive decompression stop diving schedules for 11,429-ft altitude. The concept of continuous tissue half-lives is applicable to different types of gas exchange and DCS boundary functions or to a combination of different models with a desired level of conservatism. It has proved to be a useful tool in planning decompression for undocumented modes of diving such as decompression stop diving or multilevel diving at altitude. The algorithm can easily be incorporated into dive computers.

Algorithms↗