A new biophysical decompression model for estimating the risk of articular bends during and after decompression

Abstract

The biophysical models that intend to predict the risk of decompression sickness after a change of pressure are not numerous. Few approaches focus in particular on joints as target tissues, with the aim to describe properly the mechanisms inducing pain. Nevertheless, for this type of decompression incidents, called articular bends, no model proved to fit the empirical results for a broad range of exposures and decompression procedures. We present here an original biophysical decompression model for describing the occurrence of articular bends. A target joint is broken down into two parts that exchange inert gases with the blood by perfusion and with each other by diffusion over distances of a few millimetres. This diffusion pathway allows the slow amplification of microbubbles growing during and after decompression, consistent with the possible delayed occurrence of bends. The diffusion coefficients introduced into this model are larger than those introduced into most modern decompression models. Their value remains physical (#10(-9)m(2)/s). Inert gas exchanges and the formation, amplification and resorption of microbubbles during and after decompression were simulated. We used a critical gas volume criterion for predicting the occurrence of bends. A risk database extracted from COMEX experience and other published studies were used for the correlation of model parameters not known a priori. We considered a large range of exposure, and the commonly used inert gases nitrogen and helium. This correlation phase identified the worst biophysical conformations most likely to lead to the formation, in tissues such as tendons, of a large number of microbubbles recruited from pre-existing gas nuclei during decompression. The risk of bends occurrence was found to be linked to the total separated gas volume generated during and after decompression. A clamping phenomenon occurs soon after the start of decompression, greatly slowing the gas exchanges controlled especially by the oxygen window. This model, which reproduces many empirical findings, may be considered both descriptive and predictive.

A combined three-dimensional in vitro–in silico approach to modelling bubble dynamics in decompression sickness

“…denser tissue will contain larger bubbles that persist for a longer time; tissues with lower surface tension will contain bubbles with a larger radius; finally, more lipid rich tissues (higher solubility coefficient) will also tend to contain larger bubbles. Support for these conclusions is found widely in the modelling literature [34,40,47,48] and to a certain degree in the experimental literature [22,28,49]. However, for the majority of data from in vivo experiments, it is difficult or even impossible to separate the individual effects of material parameters from each other and also from those of perfusion.…”

Quantification of cell-bubble interactions in a 3D engineered tissue phantom

“…That no significant change in the plateau radii or half lives of the bubbles could be measured with varying cellular density (p = 0.23 and p = 0.99 respectively), highlights the importance of competition for dissolved gas as a mechanism to regulate bubble dynamics. Such interactions are considered only in small number of DCS bubble models 38, 70–72 . In addition, widely used dive algorithms do not vary the magnitude of the oxygen windows in different tissue compartments 38, 71, 73 , however, as shown here, this may have a significant impact on the bubble density and hence bubble dynamics of different tissues.…”

“…Such interactions are considered only in small number of DCS bubble models 38, 70–72 . In addition, widely used dive algorithms do not vary the magnitude of the oxygen windows in different tissue compartments 38, 71, 73 , however, as shown here, this may have a significant impact on the bubble density and hence bubble dynamics of different tissues. This is an effect that could be easily incorporated into current dive algorithms by use of Michaelis-Menten kinetics or by simply varying the fixed oxygen window size parameter for different tissue compartments.…”

“…In addition, as the amount of dissolved nitrogen does not change but the tissue tension decreases, the effect increases the pp N 2 thereby increasing the gradient for nitrogen to diffuse out of any bubbles present 36 . Although all tissues in the body metabolise oxygen at different rates, the custom in dive algorithms is to have a single fixed value, implemented by grouping O 2 and CO 2 into a single fixed pressure contribution–the fixed metabolic gases 37, 38 . In other fields of research oxygen metabolism is more explicitly modelled by, Michaelis-Menten kinetics.where E is the enzyme, S is the substrate, P the product and k denotes a rate constant.…”