Modelling and Measurement of Bubbles in Decompression Sickness Michael Chappell St. Hugh’s and Linacre Colleges Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy University of Oxford Trinity Term 2006 Supervised by Dr. Stephen Payne Modelling and Measurement of Bubbles in Decompression Sickness Michael Chappell St. Hugh’s and Linacre Colleges Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy Trinity term 2006 Abstract Decompression Sickness (DCS), also known as ‘the bends’, is a recognised problem for SCUBA divers and is a danger for anyone undertaking decompression. The condition arises because gas which has collected in solution in the body is released in the form of bubbles when the ambient pressure falls. Bubbles can form throughout the body, causing a wide range of symptoms, and have been observed both stationary in various body tissues and moving in the blood. Although bubbles are known to be the cause of DCS, their production and behaviour is still not well understood. In this work the problem of bubble formation is examined in two complementary ways: firstly by automating the predominant method for the measurement of bubbles in the blood. A bubble detection algorithm is derived which offers quantitative information about the occurrence of individual bubbles in the blood based on Doppler ultrasonic measurements. However, since only limited information about bubbles can be extracted by such a technique, mathematical modelling is then used to describe the formation of bubbles in the body. A model is presented for the growth of bubbles in the vasculature from crevice shaped nuclei. Since the precise form of vasculature nuclei is not known, the effect of nucleus geometry on bubble behaviour is explored. The behaviour of a bubble which breaks away from the nucleation site is also examined and finally the relationship between bubbles forming in the blood and those forming stationary in the tissue is modelled. The combination of quantitative measurements and physiological models as presented in this work offers a complete approach to the investigation of bubble formation in the body. Ultimately it offers a novel approach to the understanding and prevention of DCS. 1 Dedicated to Leslie Charles Chappell 1919-2004 ‘Grampi’ You see, at just the right time, when we were still powerless, Christ died for the ungodly. Very rarely will anyone die for a righteous man, though for a good man someone might possibly dare to die. But God demonstrates his own love for us in this: While we were still sinners, Christ died for us. Romans 5 v6-8 2 Acknowledgements Give thanks to the LORD, for he is good; his love endures forever. Psalm 118 v1. Of all the (many) pages of this work this is probably one of the hardest but one of the most satisfying: here finally I can give credit to all those without whom the last 3 years would not have been possible. I am eternally indebted to my wife, Becca, for a great deal of love, support and patience. I have far too much to thank her for than I could possibly fit here. I am also greatly indebted to Stephen Payne, who has guided me carefully and efficiently through this whole process. I have learnt a great deal from him both at undergraduate and post-graduate level, for which I am very thankful. I hope that, as his first student, I might have taught him one or two things about supervising post-graduates for the benefit of all who follow after me. I cannot omit to thank my parents who have been exceptionally supportive, always very excited about the next adventure I was about to embark upon and very understanding with my lack of a ‘real’ job. Alongside them there is a much wider family who have all had their effect on who I am today and what under, God’s sovereignty, I have achieved. This includes, in more recent times, Andrew and Sandra, who have the great honour of being Becca’s parents (hence I have much to thank them for). I must also thank Steve Collins, who when confronted with a reply to the question “are you considering doing a doctorate next year” of “only if someone pays for me to go diving”, took me seriously and helped me find a topic (although no-one ever did pay for my diving). I am also very grateful to Steve Daniels who provided very useful insight into the subject of bubbles in the body and a pile of literature I would never have found elsewhere. I am also thankful to the many people I have met at the UHMS and EUBS meeting who have been very welcoming and helpful including Alf Brubakk, Ron Nishi, Hugh Van Liew, David Doolette and Johnny Conkin. And finally thanks to all those around me day-by-day who provided much needed diversions and conversation. Alongside a large number of students from Univ. and Corpus to whom, perhaps, I have passed on some knowledge. 3 Contents 1. Introduction ............................................................................................................................. 8 2. Literature review ................................................................................................................... 12 2.1 Introduction................................................................................................................................... 12 2.2 Bubble detection............................................................................................................................ 12 2.2.1 Principles of Ultrasonic bubble detection ................................................................................. 12 2.2.2 Doppler ultrasonography .......................................................................................................... 14 2.2.3 Ultrasound imaging................................................................................................................... 23 2.2.4 Application of bubble grades for DCS assessment.................................................................... 25 2.2.5 Bubble detection conclusions .................................................................................................... 28 2.3 Bubble modelling .......................................................................................................................... 28 2.3.1 Gas exchange modelling............................................................................................................ 29 2.3.2 The Laplace equation ................................................................................................................ 35 2.3.3 Nucleation.................................................................................................................................. 37 2.3.4 Spherical bubble models............................................................................................................ 41 2.3.5 Crevice bubble models............................................................................................................... 45 2.3.6 Nucleation sites in the body....................................................................................................... 47 2.3.7 Bubble theory conclusions......................................................................................................... 48 2.4 Conclusions................................................................................................................................... 49 3. An algorithm for the detection of bubbles........................................................................... 50 3.1 Introduction................................................................................................................................... 50 3.2 Doppler ultrasound data ................................................................................................................ 51 3.3 Bubble detection algorithm ........................................................................................................... 52 3.3.1 Empirical Mode Decomposition................................................................................................ 52 3.3.2 Peak detection ........................................................................................................................... 55 3.3.3 Detection of heart beats............................................................................................................. 57 3.3.4 Detection of features.................................................................................................................. 59 3.3.5 Classification of features........................................................................................................... 61 3.4 Results........................................................................................................................................... 62 3.5 Discussion ..................................................................................................................................... 66 3.6 Validation considerations.............................................................................................................. 67 3.7 Summary and Conclusions............................................................................................................ 76 4 4. Crevice model theory............................................................................................................. 77 4.1 Introduction................................................................................................................................... 77 4.2 Crevice geometry