1. Decompression Model for Divers Jean-Pierre O’Brien (UCL) 22 nd November 2010

2. Aims Improve VR Technology’s current decompression algorithm particularly in the deep diving (>80m) regime Develop a coupled bubble-tissue model to improve understanding of the processes as well as providing validation for current practices

3. Recreational Diving Recreational diving is normally no-stop ie. there is no need to decompress to return to the surface

4. Technical Diving Technical divers go beyond the recreational limits by diving deeper and staying longer Decompression in stages is required to return to the surface, often using different gas mixes

5. Why Decompress? It was first noted by Boyle in 1670 that bubbles could form in living tissue under pressure changes Bringing caisson workers constructing the Brooklyn Bridge up slowly reduced their propensity to fall ill Hence it has been surmised that excessive numbers or size of bubbles leads to Decompression Sickness aka the Bends aka Caisson’s Disease

6. Cause of Bubbles Breathing compressed air at pressure causes inert gases to dissolve into tissues On return to the surface, dissolved gas diffuses out of tissues Any gas coming out of solution can cause bubble formation Nanofibre Nascent bubble

7. Modelling Decompression: Haldane Model Divide body into tissue types called compartments Characterise each compartment by the time it takes for it to become half saturated, called its half time Rate of change of partial pressure is proportional to the difference in partial pressures between gas in the lungs and gas dissolved in the tissue/compartment

8. Haldane / Bühlmann limits There exists a partial pressure limit, M, that each compartment can tolerate before signs of DCS appear where: M is the partial pressure limit for a compartment 1/b is the increase of the limit per unit ambient pressure a is the theoretical value at 0 bar Values for a and b are derived experimentally

9. Problems Different dive scenarios can still lead to DCS if using the same dive coefficients This ‘sledgehammer’ approach does not address the appearance of bubbles The a and/or b Bühlmann coefficients must be altered depending on the dive scenario

10. Variable Gradient Model (VGM ® ) Alter b coefficients depending on depth and time Make fast compartments less tolerant at greater depth and time, whereas slower compartments become more tolerant

11. VGM2 Old VGM algorithm led to unrealistic decompression times during long, deep dives Rewrite algorithm in terms of tanh functions for smoother transitions

12. The Bubble Problem

13. New Bubble Approach Model a block of tissue and bubble growth within Growth of one bubble can affect the growth of neighbouring bubbles by “consuming” nearby gas Following the growth of bubbles and attempting to cap their size below some critical value that represents the onset of DCS, it is hoped this model will be more realistic Agreement with the algorithms currently employed by VR Technology will provide validation

14. The Set-Up c – concentration D – diffusion coefficient P a – breathing gas partial pressure 1,…,N – bubble number 1 2 3 N PaPa PaPa PaPa PaPa

15. Governing Equations Henry’s Law Ideal Gas Law Diffusive Flux in/out of bubble Diffusion Equation c - concentration k – Henry’s constant P – pressure V – volume m – mass of gas α := BT/M B – universal gas constant T – temperature (K) M – molar mass of gas D – diffusion coefficient r – radial coordinate R – bubble radius P b – pressure inside bubble P amb – ambient pressure σ – surface tension λ – tissue modulus of tissue elasticity Interior Bubble Pressure

16. Method Randomly distribute N microbubble nuclei in the tissue Prescribe a decompression and gas mix profile and record the evolution of bubble size Problem is solved using finite difference numerical method Repeat for a number of decompression profiles and gas mixes of varying riskiness

17. Bubble Results

18. Normal Deco – 10 bubbles 45m for 25 min Max bubble radius = 8.0μm

19. Bubble Evolution

20. Normal Deep Dive - OC 120m for 20 minutes Max bubble radius = 19.0 μm Large bubble growth

21. Bubble Evolution Bubbles near centre persist for longer – they ‘feed’ each other

22. Conclusions The most important factor on bubble growth is the ascent Aggressive profiles lead to larger bubbles However the longer deco time allows these bubbles to dissolve to the extent that bubbles are smaller on exit than in conservative dives Does this mean that the danger of aggressive profiles lies in slightly larger bubbles or bubble formation outside of tissues? Gas changes do not have sudden substantial effects on bubble growth. Rich O 2 mixes do increase rate of dissolution

23. Haldane Model v. Bubble Models Haldane model encourages divers to ascend as much as possible to increase the partial pressure gradient between tissues and the arteries in order to increase rate of offgassing Bubble models attempt to limit the volume of gas in free phase by making deeper stops in order to limit bubble growth Variable Gradient Model successfully mimics behaviour of bubble models whilst allowing significant user customisability in a wide range of dive regimes

24. Further work Bubble-tissue model –Alter parameters for diffusion, D, and Henry’s Constant, k, for different types of tissue –Alter size of tissue –Alter boundary conditions to take into account gas loading in tissue from other parts of the body Implementation –Currently developing and testing VGM2 for use in a commercially available product

25. Acknowledgements Thanks to the following for their help throughout the internship: Nick Bushell (VR Technology) Dr Nick Ovenden (UCL) Dr Eleanor Stride (UCL) Dr David Leppinen (University of Birmingham) Vera Hazelwood (KTN)