Half time (physics)

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Half time is the time taken by a quantity to reach one half of its extremal value, where the rate of change is proportional to the difference between the present value and the extremal value (i.e. in exponential decay processes). It is synonymous with half-life, but used in slightly different contexts.

Contents

The diagram shows the increase in the quantity (red) in response to a step-change in the motive force that changes it (blue). The time-axis is in multiples of the half time. It can be seen that the quantity increases to one-half of its final value after one half time, to three-quarters after two half times, to seven-eighths after three half times, and so on.

The relationship between the quantity (Q) and time (t) is described by the mathematical formula:

where Qf is the extremal value and λ is a constant, approximately equal to 0.69 divided by the half time – more precisely: loge(2) / (half time).

Where the quantity decreases in response to a step-decrease in the motive force that changes it, the curve is mirrored in the time-axis and may be referred to as exponential decay.

The concept of half time is used in diving physiology where body tissues take up and release inert gases (usually nitrogen) following changes in depth. Different tissue types have different half times for a given inert gas, and modelling the uptake and release of gases by the tissues is important to avoid decompression sickness.

Examples

See also

Related Research Articles

<span class="mw-page-title-main">Decompression sickness</span> Disorder caused by dissolved gases forming bubbles in tissues

Decompression sickness is a medical condition caused by dissolved gases emerging from solution as bubbles inside the body tissues during decompression. DCS most commonly occurs during or soon after a decompression ascent from underwater diving, but can also result from other causes of depressurisation, such as emerging from a caisson, decompression from saturation, flying in an unpressurised aircraft at high altitude, and extravehicular activity from spacecraft. DCS and arterial gas embolism are collectively referred to as decompression illness.

<span class="mw-page-title-main">Dive computer</span> Instrument to calculate decompression status in real time

A dive computer, personal decompression computer or decompression meter is a device used by an underwater diver to measure the elapsed time and depth during a dive and use this data to calculate and display an ascent profile which, according to the programmed decompression algorithm, will give a low risk of decompression sickness.

Decompression Illness (DCI) comprises two different conditions caused by rapid decompression of the body. These conditions present similar symptoms and require the same initial first aid. Scuba divers are trained to ascend slowly from depth to avoid DCI. Although the incidence is relatively rare, the consequences can be serious and potentially fatal, especially if untreated.

The reduced gradient bubble model(RGBM) is an algorithm developed by Bruce Wienke for calculating decompression stops needed for a particular dive profile. It is related to the Varying Permeability Model. but is conceptually different in that it rejects the gel-bubble model of the varying permeability model.

The Bühlmann decompression set of parameters is an Haldanian mathematical model (algorithm) of the way in which inert gases enter and leave the human body as the ambient pressure changes. Versions are used to create Bühlmann decompression tables and in personal dive computers to compute no-decompression limits and decompression schedules for dives in real-time. These decompression tables allow divers to plan the depth and duration for dives and the required decompression stops.

<span class="mw-page-title-main">Dive profile</span> Divers pressure exposure over the time of a dive

A dive profile is a description of a diver's pressure exposure over time. It may be as simple as just a depth and time pair, as in: "sixty for twenty," or as complex as a second by second graphical representation of depth and time recorded by a personal dive computer. Several common types of dive profile are specifically named, and these may be characteristic of the purpose of the dive. For example, a working dive at a limited location will often follow a constant depth (square) profile, and a recreational dive is likely to follow a multilevel profile, as the divers start deep and work their way up a reef to get the most out of the available breathing gas. The names are usually descriptive of the graphic appearance.

The Thalmann Algorithm is a deterministic decompression model originally designed in 1980 to produce a decompression schedule for divers using the US Navy Mk15 rebreather. It was developed by Capt. Edward D. Thalmann, MD, USN, who did research into decompression theory at the Naval Medical Research Institute, Navy Experimental Diving Unit, State University of New York at Buffalo, and Duke University. The algorithm forms the basis for the current US Navy mixed gas and standard air dive tables. The decompression model is also referred to as the Linear–Exponential model or the Exponential–Linear model.

Albert Alois Bühlmann was a Swiss physician who was principally responsible for a number of important contributions to decompression science at the Laboratory of Hyperbaric Physiology at the University Hospital in Zürich, Switzerland. His impact on diving ranged from complex commercial and military diving to the occasional recreational diver. He is held in high regard for his professional ethics and attention to his research subjects.

<span class="mw-page-title-main">Decompression (diving)</span> Pressure reduction and its effects during ascent from depth

The decompression of a diver is the reduction in ambient pressure experienced during ascent from depth. It is also the process of elimination of dissolved inert gases from the diver's body which accumulate during ascent, largely during pauses in the ascent known as decompression stops, and after surfacing, until the gas concentrations reach equilibrium. Divers breathing gas at ambient pressure need to ascend at a rate determined by their exposure to pressure and the breathing gas in use. A diver who only breathes gas at atmospheric pressure when free-diving or snorkelling will not usually need to decompress, Divers using an atmospheric diving suit do not need to decompress as they are never exposed to high ambient pressure.

<span class="mw-page-title-main">Decompression practice</span> Techniques and procedures for safe decompression of divers

To prevent or minimize decompression sickness, divers must properly plan and monitor decompression. Divers follow a decompression model to safely allow the release of excess inert gases dissolved in their body tissues, which accommodated as a result of breathing at ambient pressures greater than surface atmospheric pressure. Decompression models take into account variables such as depth and time of dive, breathing gasses, altitude, and equipment to develop appropriate procedures for safe ascent.

<span class="mw-page-title-main">History of decompression research and development</span> Chronological list of notable events in the history of diving decompression.

Decompression in the context of diving derives from the reduction in ambient pressure experienced by the diver during the ascent at the end of a dive or hyperbaric exposure and refers to both the reduction in pressure and the process of allowing dissolved inert gases to be eliminated from the tissues during this reduction in pressure.

<span class="mw-page-title-main">Decompression theory</span> Theoretical modelling of decompression physiology

Decompression theory is the study and modelling of the transfer of the inert gas component of breathing gases from the gas in the lungs to the tissues and back during exposure to variations in ambient pressure. In the case of underwater diving and compressed air work, this mostly involves ambient pressures greater than the local surface pressure, but astronauts, high altitude mountaineers, and travellers in aircraft which are not pressurised to sea level pressure, are generally exposed to ambient pressures less than standard sea level atmospheric pressure. In all cases, the symptoms caused by decompression occur during or within a relatively short period of hours, or occasionally days, after a significant pressure reduction.

<span class="mw-page-title-main">Pyle stop</span> Type of short deep decompression stops in addition to the standard profile

A Pyle stop is a type of short, optional deep decompression stop performed by scuba divers at depths well below the first decompression stop mandated by a conventional dissolved phase decompression algorithm, such as the US Navy or Bühlmann decompression algorithms. They were named after Richard Pyle, an American ichthyologist from Hawaii, who found that they prevented his post-dive fatigue symptoms after deep dives to collect fish specimens.

<span class="mw-page-title-main">Haldane's decompression model</span> Decompression model developed by John Scott Haldane

Haldane's decompression model is a mathematical model for decompression to sea level atmospheric pressure of divers breathing compressed air at ambient pressure that was proposed in 1908 by the Scottish physiologist, John Scott Haldane, who was also famous for intrepid self-experimentation.

<span class="mw-page-title-main">Decompression equipment</span> Equipment used by divers to facilitate decompression

There are several categories of decompression equipment used to help divers decompress, which is the process required to allow divers to return to the surface safely after spending time underwater at higher ambient pressures.

Brian Andrew Hills, born 19 March 1934 in Cardiff, Wales, died 13 January 2006 in Brisbane, Queensland, was a physiologist who worked on decompression theory.

<span class="mw-page-title-main">Thermodynamic model of decompression</span> Early model in which decompression is controlled by volume of gas bubbles forming in tissues

The thermodynamic model was one of the first decompression models in which decompression is controlled by the volume of gas bubbles coming out of solution. In this model, pain only DCS is modelled by a single tissue which is diffusion-limited for gas uptake and bubble-formation during decompression causes "phase equilibration" of partial pressures between dissolved and free gases. The driving mechanism for gas elimination in this tissue is inherent unsaturation, also called partial pressure vacancy or the oxygen window, where oxygen metabolised is replaced by more soluble carbon dioxide. This model was used to explain the effectiveness of the Torres Straits Island pearl divers empirically developed decompression schedules, which used deeper decompression stops and less overall decompression time than the current naval decompression schedules. This trend to deeper decompression stops has become a feature of more recent decompression models.

<span class="mw-page-title-main">Physiology of decompression</span> The physiological basis for decompression theory and practice

The physiology of decompression is the aspect of physiology which is affected by exposure to large changes in ambient pressure, and involves a complex interaction of gas solubility, partial pressures and concentration gradients, diffusion, bulk transport and bubble mechanics in living tissues. Gas is breathed at ambient pressure, and some of this gas dissolves into the blood and other fluids. Inert gas continues to be taken up until the gas dissolved in the tissues is in a state of equilibrium with the gas in the lungs,, or the ambient pressure is reduced until the inert gases dissolved in the tissues are at a higher concentration than the equilibrium state, and start diffusing out again.

Inner ear decompression sickness, (IEDCS) or audiovestibular decompression sickness is a medical condition of the inner ear caused by the formation of gas bubbles in the tissues or blood vessels of the inner ear. Generally referred to as a form of decompression sickness, it can also occur at constant pressure due to inert gas counterdiffusion effects.

The US Navy has used several decompression models from which their published decompression tables and authorized diving computer algorithms have been derived. The original C&R tables used a classic multiple independent parallel compartment model based on the work of J.S.Haldane in England in the early 20th century, using a critical ratio exponential ingassing and outgassing model. Later they were modified by O.D. Yarborough and published in 1937. A version developed by Des Granges was published in 1956. Further developments by M.W. Goodman and Robert D. Workman using a critical supersaturation approach to incorporate M-values, and expressed as an algorithm suitable for programming were published in 1965, and later again a significantly different model, the VVAL 18 exponential/linear model was developed by Edward D. Thalmann, using an exponential ingassing model and a combined exponential and linear outgassing model, which was further developed by Gerth and Doolette and published in Revision 6 of the US Navy Diving Manual as the 2008 tables.

References

  1. Tikuisis, Peter; Gerth, Wayne A (2003). "10.1: Decompression Theory". In Brubakk, Alf O; Neuman, Tom S (eds.). Bennett and Elliott's physiology and medicine of diving, 5th Revised edition. United States: Saunders Ltd. p. 439. ISBN   0-7020-2571-2. OCLC   51607923.
  2. Boycott A. E., Damant G. C. C., Haldane John Scott (1908). "Prevention of compressed air illness". Journal of Hygiene. 8 (3): 342–443. doi:10.1017/S0022172400003399. PMC   2167126 . PMID   20474365. Archived from the original on 2011-03-24. Retrieved 2009-06-15.{{cite journal}}: CS1 maint: multiple names: authors list (link) CS1 maint: unfit URL (link)
  3. Lippmann, John; Mitchell, Simon J (October 2005). "15". Deeper into Diving (2 ed.). Victoria, Australia: J.L. Publications. p. 215. ISBN   0-9752290-1-X. OCLC   66524750.
  4. des Granges, M (1957). "Standard Air Decompression Table". United States Navy Experimental Diving Unit Technical Report. NEDU-RR-5-57. Archived from the original on April 15, 2013. Retrieved 2009-06-15.{{cite journal}}: CS1 maint: unfit URL (link)
  5. Lippmann, John; Mitchell, Simon (October 2005). "17". Deeper into Diving (2 ed.). Victoria, Australia: J.L. Publications. p. 226. ISBN   0-9752290-1-X. OCLC   66524750.
  6. Bühlmann, Albert A. (1984). Decompression-Decompression Sickness. Berlin New York: Springer-Verlag. ISBN   0-387-13308-9.