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How To Calculate the Risk Of Pulmonary Oxygen Toxicity

Most tech divers track their oxygen exposure on big and or long dives via computer using methods, such as REPEX OTUs, developed in the 1980s. The consensus among researchers, however, is that these methods aren’t accurate. Enter retired Israeli hyperbaric physiologist, Ran Arieli, who offers a new data-driven method for computing your risk of pulmonary oxygen toxicity.



By Ran Arieli
Header image by Sean Romanowski

Hyperbaric oxygen (HBO) is an intrinsic facet of diving. However the risk of pulmonary oxygen toxicity (POT) has become a prominent issue due to the expansion of diving techniques, which include oxygen-enriched gas mixtures and technical diving. But there is still no satisfactory, practicable method of calculating the cumulative risk of oxygen toxicity during an HBO exposure. 

The concept of the Unit Pulmonary Toxic Dose (UPTD), which is based on a modification of the rectangular hyperbola, was proposed in response to a request for oxygen exposure limits based on a very small amount of research data: a point at 4 bar and the absence of known injury at 0.5 bar (Lambertsen, personal communication). However, this was merely descriptive, and not based on any physical-chemical-physiological mechanism. The NOAA REPEX method, originally developed by R.W.”Bill” Hamilton in the 1980s, is based on a simple linear assumption without sufficient research validation. It is well accepted that both of these methods are inaccurate.

Because any chemical reaction, including the production of reactive oxygen species (ROS) and reactive nitrogen species (RNS), can be described by a polynomic expression, we chose the power law approach. Having incomplete knowledge of the reaction, we assumed that the rate of development of oxygen toxicity is related to the highest power of the PO2. When the various oxygen toxicity parameters such as a decrease in lung capacity, reduced hypoxic ventilatory drive, changes in skin conduction, or increased thickness of the alveolar wall, among others, are modeled as a function of exposure time, the result can best be expressed as a quadratic equation.

The rate of production of hydrogen peroxide (a precursor of ROS and RNS) is also related to the square of time, which can explain this time relationship. The power equation was shown to have good predictive capability.1,2  

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Deriving The Power Equation

From the above considerations, it follows that the development of oxygen toxicity should be related to the square of the exposure time (t) and to some power of PO2 (PO2c).

Initially, we derived the power equation for the loss of vital capacity (VC), with the addition of a parameter to adjust for the units:

%ΔVC = 0.0082 × t2 × (PO2)4.57                       

The predictive capacity of the power equation compared with the UPTD concept is shown in the following figure. At a PO2 above 1 bar, the UPTD concept fails.

Figure 1. Prediction by two models of the reduction in vital capacity of the lung at four oxygen pressures as a function of time: the NMRI modified pulmonary toxicity dose (blue lines), and our POT index (red lines).

It has been found that the recovery of VC (at a PO2 < 0.48 bar) has the form of an exponential expression, where the time constant increases linearly with the oxygen pressure of the previous exposure, as seen in the following figure. 

Figure 2. Time constant (τ) for the recovery of human VC as a function of pre-recovery PO2 exposure. The line represents the linear regression solution.

It was demonstrated that the pulmonary pathology is different at high and low PO2, that is, they represent distinct pathologies. With exposure to an increased PO2, central (cerebral) effects on the lung are greater than the local pulmonary effects of HBO. Thus, exponential recovery of pulmonary oxygen toxicity took the form:

ΔVCtr% = ΔVCe% × e – [- 0.42 + 0.384 × (PO2)ex] × tr

where tr is the recovery time in hours, ΔVCtr is the value after the recovery time, ΔVCe is the value following the previous hyperbaric oxygen exposure, and (PO2)ex is the previous exposure to hyperbaric oxygen in bar. The rate of recovery depends on the PO2 which caused the insult, and occurs with exposure to a PO2 > 1.1 bar.

A recently published study proposed other parameters to replace the changes in VC as an indicator of POT: incidence of symptoms (inspiratory burning, cough, chest tightness and dyspnea) and a change in pulmonary physiological parameters (FVC, FEV25-75 , FEV1  and DLCO). Because the units of the POT index [t2 × (PO2)4.57] are squared for time and the powered PO2, this index can also accommodate estimates which employ the other parameters. The incidence of POT in 16 different HBO exposures conducted at the U.S. Navy Experimental Diving Unit (NEDU) is plotted in the next figure as a function of the calculated POT index.

Figure 3. Incidence of POT plotted as a function of the POT index calculated for each of the 16 different exposures. The regression line is also shown.

Thus, the POT index can be used to predict the incidence of POT:

Incidence (%) = 1.85 + 0.171 × POT index   (1)                   


For the accumulation of toxicity at a PO2 above 0.6 bar use Eq. 2:

For a number of periods (n) of continuous hyperoxic exposure, each for a different length of time and at a different PO2, the calculation should take the form of Eq. 3.

During recovery at oxygen pressures below 0.50 bar, Eq. 4 is used.

POT index trPOT indexe  × e – [- 0.42 + 0.384 × (PO2)ex] × tr  (4)

where tr is the recovery time in hours, POT indextr  is the value after the recovery time, POT indexe is the value following the previous hyperbaric oxygen exposure, and (PO2)ex is the PO2 in the previous exposure in bar.

When there is a recovery period in between the hyperoxic exposures, the POT index at the end of recovery should be calculated from Eq. 4. The time required to obtain the same POT index for the next PO2 (PO2nx) in the following hyperoxic exposure will then be derived by rearranging Eq. 2 thus:

t* = [POT index / (PO2nx)4.57)]0.5. (5)

This calculated time t* should be added to the time of the coming hyperoxic period, as if the whole exposure started at this PO2. Thus:

POT index = (t*+tnx)2 × (PO2nx)4.57 (6)

The U.S. Navy recommends oxygen exposure limits that will result in a 2% change in VC, the maximum permissible exposure being expected to produce a 10% decrease. Thus, inserting ΔVC = 2% or ΔVC = 10% into the power equation will set the PO2 and time limits. For these two values of ΔVC, the POT index should not exceed 244 and 1,220, respectively, both at a constant pressure and for a complex exposure. We propose that the POT index be used to replace the UPTD or REPEX methods. 

In summary, one may either employ the POT index limits of 244 (mild) to 1220 (exceptional), or determine the appropriate chosen risk from the incidence equation: Incidence (%) = 1.85 + 0.171 × POT index

“In summary, one may either employ the POT index limits of 244 (mild) to 1220 (exceptional), or determine the appropriate chosen risk from the incidence equation: Incidence (%) = 1.85 + 0.171 × POT index.”

Saturation Dives

Ed. note: Saturation diving has become a main modality for commercial diving (see: “Anatomy Of A Commercial Mixed Gas Dive”). Though it is not directly relevant for technical dives, it is remarkable that Arieli’s model spans the gamut from bounce dives to saturation. Mind those PO2s!

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In principle, no threshold was incorporated in the power expression, which operates when ROS and RNS production overpowers the antioxidant activity that induces recovery. It was suggested that in prolonged exposures with a relatively low PO2, for example in saturation diving with a PO2 of 0.45–0.6 bar, a recovery process for POT accompanies the development of toxicity to attenuate but not entirely eliminate the toxic outcome.3

In one report of an experimental chamber saturation dive lasting 261 hours with a PO2 of 0.5‒0.6 bar, 2 of the 8 subjects (25%) developed POT. The POT index for 25% amounts to 136 (from Eq. 1). To adjust for these two opposing effects of cumulative toxicity and the recovery process, the following equation may be used:

POT index = t2 × PO24.57 × e-0.0135 × t (7)                                       

where t is the exposure time to a toxic level of hyperoxia in h. 

Figure 4. POT index calculated for the 261 hr. exposure to a PO2 of 0.55 bar for both cumulative toxicity and recovery which take place throughout the exposure (Eq. 7). The POT index reaches 136 at the end of the exposure, which is consistent with a POT incidence of 25%. 

Evidently, eight dives are an insufficient sample. However, after the publication of reference #3, I obtained a further set of eight saturation dives. These divers dived for 4 days at a PO2 of 0.6 bar. Half of them suffered POT. The calculated percentage using Eq. 7 and Eq. 1 yielded 43.6% – rather close to the 50%. I would therefore recommend the use of Eq. 7 and Eq. 1 for long saturation dives with a PO2 close to the lower range of toxicity and above 0.48 bar.


1. Arieli R, Yalov A, Goldenshluger A. Modeling pulmonary and CNS O2 toxicity and estimation of parameters for humans. J Appl Physiol. 2002;92:248‒56. doi: 10.1152/japplphysiol.00434.2001. PMID: 11744667.

2. Arieli R. Calculated risk of pulmonary and central nervous system oxygen toxicity: a toxicity index derived from the power equation. Diving Hyperb Med. 49: 154-160, 2019. doi: 10.28920/dhm49.3.154-160. PMID: 31523789

3. Arieli R. Pulmonary oxygen toxicity in saturation dives with PO2 close to the lower end of the toxic range – a quantitative approach. Respir Physiol Neurobiol 268: 103243, 2019. doi: 10.1016/j.resp.2019.05.017. PMID: 31158523.

Dive Deeper:

Note that respiratory physiologist Barbara Shykoff, US Navy Experimental Diving Unit (NEDU), has also developed a model for estimating risk of pulmonary toxicity (2018): Calculator For Estimating The Risk of Pulmonary Toxicity 

Shearwater Research: Why UPTD Calculations Should Not Be Used by Barbara Shykoff, 2017

Shearwater Research: Oxygen Toxicity Calculations by Erik C. Baker (2012). Explains earlier UPTD and REPEX calculations.

Tolerating Oxygen Exposure by RW Bill Hamilton, 1997

RW Bill Hamilton’s Original REPEX paper: Tolerating Exposure To High Oxygen Levels: Repex And Other Methods by RW Hamilton, 1989

An early 1985 review of the UPTD Model: Predicting Pulmonary O2 Toxicity: A New Look at the Unit Pulmonary Toxicity Dose by AL Harabin, L.D. Homer, PK Weathersby and ET Flynn 

Ed. note: We plan to run an article discussing and comparing these various methods for calculating the risk of pulmonary oxygen toxicity in a coming issue of InDepth, including some practical tips for calculating the risks of your own dives.

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Dr. Arieli is the retired Head of the Hyperbaric Physiology Research Unit at the Israel Naval Medical Institute. He obtained his Ph.D. from Tel-Aviv University, completing a post-doctorate at Buffalo, The State University of New York.  He lectured in respiration physiology at the Technion Faculty of Medicine in Haifa. His main topics of research are respiratory physiology, integrative physiology, oxygen toxicity, and decompression physiology. Dr. Arieli has investigated the environmental factors which affect oxygen toxicity, proposing algorithms for the prediction of pulmonary and central nervous system oxygen toxicity. In his research into decompression physiology, Dr. Arieli has presented a new mechanism underlying bubble formation on decompression. Dr. Arieli has published 128 research papers, and continues to pursue his research at the Israel Naval Medical Institute in Haifa and the Western Galilee Medical Center in Nahariya, Israel.

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Hyperbaric Chambers Are Turning Away Divers. Will There Be One Nearby When You Need It?

Unfortunately, it’s hard to make a business case for treating divers versus wound and burn care victims. As a result, many hyperbaric chambers no longer treat divers, leaving fewer facilities available for divers in need and increasing their post-dive time to treatment. InDEPTH editor Ashley Stewart reports on this growing crisis in the US and what can be done!




By Ashley Stewart

The hyperbaric chamber at the University of California San Diego. Photo courtesy of Sherri Ferguson

Steven Wells was diving on the scuttled wreck of the USS Oriskany off the coast of Florida in 2016 when a problem with his buoyancy compensator caused a rapid ascent to the surface.

Wells’ dive buddies followed the emergency action plan for the Oriskany listed on the Florida Fish and Wildlife Conservation Commission’s website at the time and brought Wells straight to Naval Air Station Pensacola, the nearest facility with a hyperbaric chamber. The facility turned him away because there was no one there to run it.

Wells was taken 30 minutes away to Baptist Hospital, which also has a chamber capable of treating his injuries, but the hospital had years earlier decided only to use it for wound care. Doctors there decided Wells would be taken by ambulance more than an hour away to Mobile, Alabama, the nearest facility that accepts divers.

By the time Wells arrived at the only chamber that would help him, it was too late.

Steven Wells

“I got a call from the hospital saying, ‘Your husband is on life support. You need to get here now,’” Rachel Wells said of her late-husband of more than 23 years. 

Julio Garcia — the program director of Springhill Medical Center’s wound care and hyperbaric facility where Steven Wells was to be treated — told InDEPTH that while no one can be certain how sooner treatment would have affected the outcome of Wells’ case, it would have given him the best chance for a full recovery.

Each year in the US, there are about 400 serious cases of decompression illness (DCI) — a category including both arterial gas embolism and decompression sickness — in divers, according to one 2020 paper. The Divers Alert Network (DAN) hotline dealt with 587 cases annually over the past five years.

The availability of hyperbaric chambers to treat decompression illness is something many divers take for granted. We try to avoid dive-related injuries through training, but expect treatment to be available when we need it. 

The reality — as Steven and Rachel Wells tragically learned — is that only a minority of divers are close to care for diving-related injuries, according to medical professionals in the field. The estimates vary, but it’s generally believed there are about 1,500 hyperbaric medicine facilities in the US and only 67 are currently treating diving accidents, according to DAN.

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The estimates vary, but it’s generally believed there are about 1,500 hyperbaric medicine facilities in the US and only 67 are currently treating diving accidents, according to DAN.

“The problem is only getting worse, not better,” Garcia, the Springhill Medical Center program director, said. Garcia has been sounding the alarm about this problem for more than a decade. His hospital takes patients from as far away as Florida cave country and treated 20 DCI cases in 2022. Those patients had an average transportation time of 11.5 hours, according to an InDEPTH analysis of Garcia’s records.

Florida stands out because it’s a popular diving destination, DAN Research Director Frauke Tillmans said, but the situation is not much better across the US. Many of the 1,500 hyperbaric medicine facilities, like Pensacola’s Baptist Hospital, have transitioned to treating wound care only for economic reasons. Emergency hyperbaric services are expensive to train and staff, and come with increased liability.

Patient briefing before treatment at the Environmental Medicine and Physiology Unit at Simon Fraser University. 

Time to treatment can be important in DCI cases

Time is of the essence when treating DCI. Divers Alert Network Director of Medical Services Camilo Saraiva told InDEPTH time to treatment is a “pivotal determinant” when it comes to outcomes for DCI patients. “Swift intervention significantly influences the effectiveness of therapeutic recompression,” Saraiva said.

Decompression sickness, for example, results from rapid changes in pressure and can form gas bubbles in body tissues. Initiating recompression therapy minimizes bubble size and number, Saraiva said, enhancing their elimination and reducing the risk of further vascular obstruction and tissue damage.

“The timely provision of hyperbaric oxygen therapy not only aids in bubble resolution but also mitigates the potential for neurological deficits and other severe complications, highlighting the critical role of early treatment in optimizing outcomes for DCI patients,” Saraiva said.

The 2018 paper “In water-recompression” stated delays to recompression in military and experimental diving are typically less than two hours and more than 90% of cases are completely resolved during the first treatment.

Frank K. Butler and Richard E. Moon, hyperbaric medicine experts, wrote in a 2020 letter to the Undersea and Hyperbaric Medicine journal editors suggesting a minority of patients who need life-saving hyperbaric oxygen treatment (HBO2) are close to a major hospital with a 24-hour emergency hyperbaric facility.

Julio Garcia’s log on patient time to treatment at Springhill Medical Center. Click to enlarge

“Despite the urgent need for treatment, most hyperbaric chambers will decline to accept emergent patients at present,” Butler and Moon wrote. “Patients may eventually receive HBO2 but after a significant delay and a transfer of several hundred miles. Many never receive indicated HBO2, often resulting in poorer patient outcomes.”

Patients who are delayed treatment, they wrote, face the possibility in some cases of “death, permanent neurological damage, permanent loss of vision, or loss of an extremity, most of which would have been readily preventable had emergent HBO2 been administered.”

Why fewer chambers treat dive injuries

As recently as two decades ago, according to Butler and Moon, the majority of hyperbaric treatment facilities were available 24/7 to treat emergency patients. The percentage of those facilities now treating emergency patients is unclear, but it’s universally agreed the number has fallen significantly.

The reasons for the loss of emergency HBO2 facilities, Butler and Moon suggest, include “a better economic return when chambers focus on wound care patients as opposed to emergencies; the greater legal liability involved with treating high-acuity emergency patients; and the increased training and staffing requirements that would be required to manage critically ill patients — especially diving injuries and iatrogenic gas embolism patients.”

A letter from an administrator at Baptist Hospital — which sent Steve Wells to Springhill Medical Center — viewed by InDEPTH shows the hospital discontinued hyperbaric emergency services in December 2010, citing lack of staffing for specialty trained hyperbaric physicians who can provide 24-hour patient care. Baptist has yet to respond to InDEPTH’s request for comment.

Julio R. Garcia at Springhill Medical Center Hyperbaric Center

There’s also the issue of pay. Garcia, the Springhill program director, said the current rate of pay for doctors who administer hyperbaric treatments regardless of length is around $150. A typical hyperbaric treatment for other conditions is about two hours. Diving treatments are usually six or seven, he said. “What doctor wants to get paid $150 to be up all night for seven hours, at that point making less than the technician?” Garcia said. “The fix is that healthcare payers need to pay more for the supervision of the treatment for diving injuries. Make it something that’s worth a doctor’s time besides the goodness of their hearts.”

Silence from lawmakers

Medical and diving organizations in 2020 sent a letter to the House and Senate, federal government agencies, governors of Florida and California, and the American Hospital Association expressing concerns about the lack of availability of chambers to treat diving injuries.

“There are approximately three million recreational scuba divers in the US,” the letter stated. “In the unlikely event that they suffer a diving-related injury, they trust that the US medical system will provide state-of-the-art care for their injuries, but the steadily- decreasing number of hyperbaric treatment facilities in the US willing to treat them emergently for decompression sickness or arterial gas embolism often places them at much greater risk than they realize.”

Garcia has on his own contacted lawmakers, reporters, medical systems — even private space companies like SpaceX because his facility is also the only one nearby treating altitude decompression sickness from space and air travel.

Little has changed, Garcia said.

Garcia showed InDEPTH a 2014 letter from a Defense Health Agency director who said, while there are three Undersea and Hyperbaric Medicine Society-accredited clinic hyperbaric medicine facilities and two additional facilities that can treat civilian emergencies, they are not staffed 24/7 and not designed for patients with other medical illnesses. Garcia at the time requested the creation of a federal grant to support the expansion of 24/7 hyperbaric services, but the director said that was outside of the agencies’ purview. 

The hyperbaric chamber at the University of California San Diego. Photo courtesy of Sherri Ferguson

Two years after this exchange, Steven Wells was taken to and turned away from one of these facilities — the NAS Pensacola, listed on the Florida Fish and Wildlife Conservation Commission’s (FWC) emergency action plan at the time. 

The Florida Fish and Wildlife Conservation Commission website now shows a map of the nearly 4,000 artificial reefs across Florida’s 1,350 miles of coastline. Two chambers, one in Mobile, Alabama, and one is Orlando, cover 500 of those miles densely packed with dive locations, according to Garcia.

The FWC website now shows a map of the nearly 4,000 artificial reefs across Florida’s 1,350 miles of coastline. Two chambers, one in Mobile, Alabama, and one is Orlando, cover 500 of those miles densely packed with dive locations, according to Garcia. A report from the University of West Florida estimated the sinking of the Oriskany, scuttled in 2006, generated nearly $4 million for Pensacola and Escambia County in the next year alone.

So many reefs, so few chambers! FWC map screenshot

An FWC spokesperson said the agency provides diver safety reminders and recommended actions on its website “as a courtesy” and is not intended for emergency response. FWC and Visit Florida did not respond to inquiries about how much Florida’s government spends on advertising the artificial reefs and other diving activities, or whether any effort to expand the availability of hyperbaric facilities to treat the divers who show up as a result.

“My question is what is my husband’s life worth compared to your chambers,” Rachel Wells, Steven Wells’ widow said. “Why did he have to die?”


DIVER: A Crisis in Emergency Chamber Availability by Dan Orr (April 2022)

Divenewswire: A Crisis Lurking Below the Surface Emergency Hyperbaric Treatment Availability by Dan Orr (August 2021)

Undersea and Hyperbaric Medicine (2020): Emergency hyperbaric oxygen therapy: A service in need of resuscitation – an open letter by Frank K. Butler, MD, and Richard E. Moon, MD

White paper: Access to emergent hyperbaric oxygen (HBO2) therapy: an urgent problem in health care delivery in the United States (2020)

InDEPTH: A New Look at In-Water Recompression (IWR) (2019) by Reilly Fogarty

Diving and Hyperbaric medicine (2018): In-water Recompression, Doolette DJ and Mitchell SJ 

aquaCORPS (1993): In-Water recompression As An Emergency Field Treatment for Decompression Illness by Richard L. Pyle and David A. Youngblood

InDepth Managing Editor Ashley Stewart is a Seattle-based journalist and tech diver. Ashley started diving with Global Underwater Explorers and writing for InDepth in 2021. She is a GUE Tech 2 and CCR1 diver and on her way to becoming an instructor. In her day job, Ashley is an investigative journalist reporting on technology companies. She can be reached at:

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