Parameter estimation of the copernicus decompression model with venous gas emboli in human divers
- 184 Downloads
Decompression Sickness (DCS) may occur when divers decompress from a hyperbaric environment. To prevent this, decompression procedures are used to get safely back to the surface. The models whose procedures are calculated from, are traditionally validated using clinical symptoms as an endpoint. However, DCS is an uncommon phenomenon and the wide variation in individual response to decompression stress is poorly understood. And generally, using clinical examination alone for validation is disadvantageous from a modeling perspective. Currently, the only objective and quantitative measure of decompression stress is Venous Gas Emboli (VGE), measured by either ultrasonic imaging or Doppler. VGE has been shown to be statistically correlated with DCS, and is now widely used in science to evaluate decompression stress from a dive. Until recently no mathematical model has existed to predict VGE from a dive, which motivated the development of the Copernicus model. The present article compiles a selection experimental dives and field data containing computer recorded depth profiles associated with ultrasound measurements of VGE. It describes a parameter estimation problem to fit the model with these data. A total of 185 square bounce dives from DCIEM, Canada, 188 recreational dives with a mix of single, repetitive and multi-day exposures from DAN USA and 84 experimentally designed decompression dives from Split Croatia were used, giving a total of 457 dives. Five selected parameters in the Copernicus bubble model were assigned for estimation and a non-linear optimization problem was formalized with a weighted least square cost function. A bias factor to the DCIEM chamber dives was also included. A Quasi-Newton algorithm (BFGS) from the TOMLAB numerical package solved the problem which was proved to be convex. With the parameter set presented in this article, Copernicus can be implemented in any programming language to estimate VGE from an air dive.
KeywordsDiving Vascular bubbles Nonlinear optimization Ultrasound Decompression sickness
This study has been supported by UWATEC AG, Switzerland and by the Norwegian Petroleum Directorate, Norsk Hydro, Esso Norge and Statoil under the “dive contingency contract” (no 4600002328) with Norwegian Underwater Intervention (NUI). Thanks to R. Y. Nishi for providing the data set from DCIEM on the square profile dives.
- 2.Brubakk AO, Eftedal OS (1999) Evaluation of reverse dive profiles. In: Lang MA, Lehner CE (eds) Reverse dive profiles workshop. Smithsonian Institution, Washington, DC, pp 111–121Google Scholar
- 3.Bühlmann AA (1984) Decompression–decompression sickness. Springer-Verlag, Berlin, New YorkGoogle Scholar
- 8.Eftedal O, Brubakk AO (1991) A method for detecting intravascular gas bubbles using 2d ultrasonic scanning and computer-based image processing. In: Michalodimitrakis E (ed) Proceedings of the XVII annual meeting EUBS. EUBS, Heraklion, Crete, pp. 311–316Google Scholar
- 13.Gernhardt ML (1991) Developement and evaluation of a decompression stress index based on tissue bubble dynamics. Ph.D. thesis, University of PennsylvaniaGoogle Scholar
- 16.Gutvik CR, Møllerløkken A, Brubakk AO (2007) Difference in bubble formation using deep stops is depend on bottom time. Eur J Underw Hyperb Med 8(3):42Google Scholar
- 17.Hemingway R, Baker EC (1984) V-planner, V3.81. http://www.v-planner.co.
- 18.Hofwegen K, Fjelsten P (2007) GAP-software, V2.3. http://www.gap-software.co.
- 19.Holmström K (1999) The TOMLAB optimization environment in Matlab. Adv Model Optim 1(1):47–69Google Scholar
- 21.Kisman KE, Masurel G, LaGrue D (1978) Evaluation de la qualite d’une decompression basee sur la detection ultrasonore de bulles. Med Aéro Spat Med Sub Hyp XVII:293–97Google Scholar
- 24.Maton A, Hopkins J, McLaughlin CW, Johnson S, Warner MQ, LaHart D, Wright JD (1993) Human biology and health. Prentice Hall, Englewood Cliffs, New JerseyGoogle Scholar
- 25.McArdle WD, Katch FI, Katch VL (2000) Essentials of exercise physiology, 2nd edn. Lippincott Williams and Wilkins, PhiladelphiaGoogle Scholar
- 26.Naval Sea Systems Command (2007) U.S. navy diving manual, 5th edn. AquaPress Publishing, PhiladelphiaGoogle Scholar
- 27.Nishi RY, Brubakk AO, Eftedal O (2003) Bubble detection. In: Brubakk AO, Neuman TS (eds) Bennett and Elliot‘s physiology and medicine of diving, 5th edn., Chap. 10.3. Saunders, London, pp 501–529Google Scholar
- 28.Sawatzky KD (1991) The relationship between intravascular doppler-detected gas bubbles and decompression sickness after bounce diving in humans. Master’s thesis, York University, Toronto, OntarioGoogle Scholar