Varying Permeability Model

The Varying Permeability Model, Variable Permeability Model or VPM is an algorithm that is used to calculate the decompression stops needed for ambient pressure dive profiles using specified breathing gases. It was developed by D.E. Yount and others for use in professional diving and recreational diving. It was developed to model laboratory observations of bubble formation and growth in both inanimate and in vivo systems exposed to pressure.^[1] In 1986, this model was applied by researchers at the University of Hawaii to calculate diving decompression tables.^{[citation needed]}

The VPM presumes that microscopic bubble nuclei always exist in water and tissues that contain water. Any nuclei larger than a specific "critical" size, which is related to the maximum dive depth (exposure pressure), will grow upon decompression when the diver ascends. The VPM aims to minimize the total volume of these growing bubbles by keeping the external pressure large, and the inspired inert gas partial pressures low during decompression. The model depends on the assumptions that different sizes of bubbles exist within the body; that the larger bubbles require less reduction in pressure to begin to grow than smaller ones; and that fewer large bubbles exist than smaller ones. These are used to construct an algorithm that provides decompression schedules designed to allow the larger, growing bubbles to be eliminated before they can cause problems.^[2][3]

This section needs expansion with: describe model in more detail. You can help by adding to it. (October 2021)

This bibliography list was compiled by E.B. Maiken and E.C. Baker as reference material for the V-Planner web site in 2002.^[4]

• Yount, D.E.; Hoffman, D.C. (1984). Bachrach, Arthur J.; Matzen, M.M. (eds.). Decompression theory: A dynamic critical-volume hypothesis. Underwater physiology VIII: Proceedings of the eighth symposium on underwater physiology. Bethesda: Undersea and Hyperbaric Medical Society. pp. 131–146.</ref>
• Yount, D.E.; Hoffman, D.C. (1986). "On the use of a bubble formation model to calculate diving tables". Aviat Space Environ Med. 57 (2): 149–156. ISSN 0095-6562. PMID 3954703.
• Yount, D.E.; Hoffman, D.C. (1989). "On the use of a bubble formation model to calculate nitrogen and helium diving tables". In Paganelli, C.V.; Farhi, L.E. (eds.). Physiological functions in special environments. New York: Springer-Verlag. pp. 95–108.
• Yount, D.E.; Maiken, E.B.; Baker, E.C. (2000). Lang, M.A.; Lehner, C.E. (eds.). Implications of the Varying Permeability Model for Reverse Dive Profiles. Proceedings of the Reverse Dive Profiles Workshop. Washington, D.C.: Smithsonian Institution. pp. 29–61.

• D'Arrigo, J.S. (1978). "Improved method for studying the surface chemistry of bubble formation". Aviat Space Environ Med. 49 (2): 358–361. ISSN 0095-6562. PMID 637789.
• Kunkle, T.D. 1979. Bubble nucleation in supersaturated fluids. Univ. of Hawaii Sea Grant Technical Report UNIHI-SEAGRANT-TR-80-01. Pp. 108.
• Paganelli, C.V.; Strauss, R.H.; Yount, D.E. (1978). "Bubble formation within decompressed hen's eggs". Aviat Space Environ Med. 48 (1): 48–49. ISSN 0095-6562. PMID 831713.
• Strauss, R.H. (1974). "Bubble formation in gelatin: Implications for prevention of decompression sickness". Undersea Biomed. Res. 1 (2): 169–174. ISSN 0093-5387. OCLC 2068005. PMID 4469188. Archived from the original on April 15, 2013. Retrieved 2008-04-16.{{cite journal}}: CS1 maint: unfit URL (link)
• Strauss, R.H.; Kunkle, T.D. (1974). "Isobaric bubble growth: A consequence of altering atmospheric gas". Science. 186 (4162): 443–444. Bibcode:1974Sci...186..443S. doi:10.1126/science.186.4162.443. ISSN 0193-4511. OCLC 5206521. PMID 4413996. S2CID 32874911.
• Yount, D.E.; Kunkle, T.D. (1975). "Gas nucleation in the vicinity of solid hydrophobic spheres". Journal of Applied Physics. 46 (10): 4484–4486. Bibcode:1975JAP....46.4484Y. doi:10.1063/1.321381. ISSN 0021-8979. Archived from the original on 2013-02-24. Retrieved 2008-04-16.
• Yount, D.E.; Strauss, R.H. (1976). "Bubble formation in gelatin: A model for decompression sickness". Journal of Applied Physics. 47 (11): 5081–5089. Bibcode:1976JAP....47.5081Y. doi:10.1063/1.322469. ISSN 0021-8979. Archived from the original on 2013-02-23. Retrieved 2008-04-16.
• Yount, D.E.; Kunkle, T.D.; D'Arrigo, J.S.; Ingle, F.W.; Yeung, C.M.; Beckman, E.L. (1977). "Stabilization of gas cavitation nuclei by surface-active compounds". Aviat Space Environ Med. 48 (3): 185–191. ISSN 0095-6562. PMID 856151.
• Yount, D.E. (1979). "Skins of varying permeability: a stabilization mechanism for gas cavitation nuclei". J. Acoust. Soc. Am. 65 (6): 1429–1439. Bibcode:1979ASAJ...65.1429Y. doi:10.1121/1.382930. ISSN 1520-8524. S2CID 53315872.^{[permanent dead link‍]}
• Yount, D.E.; Yeung, C.M.; Ingle, F.W. (1979). "Determination of the radii of gas cavitation nuclei by filtering gelatin". J. Acoust. Soc. Am. 65 (6): 1440–1450. Bibcode:1979ASAJ...65.1440Y. doi:10.1121/1.382905. ISSN 1520-8524.^{[permanent dead link‍]}
• Yount, D.E. (1979). "Application of a bubble formation model to decompression sickness in rats and humans". Aviat Space Environ Med. 50 (1): 44–50. ISSN 0095-6562. PMID 217330.
• Yount, D.E. 1979. Multiple inert-gas bubble disease: a review of the theory. In: Lambertsen, C.J. and Bornmann, R.C. eds. Isobaric Inert Gas Counterdiffusion Workshop^[usurped]. Undersea Medical Society, Bethesda, 90-125.
• Yount, D.E.; Lally, D.A. (1980). "On the use of oxygen to facilitate decompression". Aviat Space Environ Med. 51 (6): 544–550. ISSN 0095-6562. PMID 6774706.
• Yount, D.E. (1981). "Application of a bubble formation model to decompression sickness in fingerling salmon". Undersea Biomed. Res. 8 (4): 199–208. ISSN 0093-5387. OCLC 2068005. PMID 7324253. Archived from the original on 2018-05-04. Retrieved 2008-04-16.{{cite journal}}: CS1 maint: unfit URL (link)
• Yount, D.E.; Yeung, C.M. (1981). "Bubble formation in supersaturated gelatin: a further investigation of gas cavitation nuclei". J. Acoust. Soc. Am. 69 (3): 702–708. Bibcode:1981ASAJ...69..702Y. doi:10.1121/1.385567. ISSN 1520-8524. S2CID 54050598.^{[permanent dead link‍]}
• Yount, D.E. (1982). "On the evolution, generation, and regeneration of gas cavitation nuclei". J. Acoust. Soc. Am. 71 (6): 1473–1481. Bibcode:1982ASAJ...71.1473Y. doi:10.1121/1.387845. ISSN 1520-8524. S2CID 53411356.^{[permanent dead link‍]}
• Yount, D.E.; Hoffman, D.C. (1983). Hoyt, J.W. (ed.). "On the use of a cavitation model to calculate diving tables". Cavitation and Multiphase Flow Forum 1983. New York: American Society of Mechanical Engineers: 65–68. OCLC 232584820.
• Yount, D.E. (1983). "A model for microbubble fission in surfactant solutions". Journal of Colloid and Interface Science. 91 (2): 349–360. Bibcode:1983JCIS...91..349Y. doi:10.1016/0021-9797(83)90347-8. ISSN 0021-9797.
• Yount, D.E.; Gillary, E.W.; Hoffman, D.C. (1984). "A microscopic investigation of bubble formation nuclei". J. Acoust. Soc. Am. 76 (5): 1511–1521. Bibcode:1984ASAJ...76.1511Y. doi:10.1121/1.391434. ISSN 1520-8524. S2CID 46764818.^{[permanent dead link‍]}
• Yount, D.E. (1997). "On the elastic properties of the interfaces that stabilize gas cavitation nuclei". Journal of Colloid and Interface Science. 193 (1): 50–59. Bibcode:1997JCIS..193...50Y. doi:10.1006/jcis.1997.5048. ISSN 0021-9797. PMID 9299088.

• V-Planner: VPM-B & VPM-B/E, VPM-B/FBO.^[4]
• MultiDeco: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-B, ZHL-C, GF, and GFS.^[5]
• Ultimate Planner: VPM-B, VPM-B/U, VPM-B (Dec-12), VPM-B/U (Dec-12), ZHL-B, ZHL-C, ZHL-D, GF and GF/U.^[6]
• DecoPlanner: VPM-B.^[7]
• HLPlanner: VPM-B.^[8]
• JDeco: VPM-B.^[9]
• PalmVPM: VPM.^[10]
• DivePlan: VPM.^[11]
• Baltic Deco Planner: VPM-B.^[12]
• Subsurface: VPM-B.^[13]

• V-Planner Live: VPM-B & VPM-B/E.^[14]
• MultiDeco-X1: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-C, GF, and GFS.^[15]
• MultiDeco-DR5: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-C, GF, and GFS.^[16]
• Shearwater Research Predator, Petrel, Perdix and NERD models: GF, VPM-B plus GFS.
• RATIO Computers: iX3M series and iDive (Tech and Reb) series VPM-B and ZHL16-B.^[17]
• TDC-3 with MultiDeco-TDC: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-C, GF, and GFS.^[18]
• HeinrichsWeikamp OSTC4: VPM-B

• Decompression (diving) – Pressure reduction and its effects during ascent from depth
• Decompression sickness – Disorder caused by dissolved gases forming bubbles in tissues
• Decompression theory – Theoretical modelling of decompression physiology
• Dive computer – Instrument to calculate decompression status in real time
• Physiology of decompression – The physiological basis for decompression theory and practice
• Reduced gradient bubble model – Decompression algorithm
• Bühlmann decompression algorithm – Mathematical model of tissue inert gas uptake and release with pressure change

• VPM web site
• VPM development time line