Relationship between two different functions derived from diffusion-based decompression theory

Hempleman's diffusion-based decompression theory yields two different functions; one is expressed by a simple root function and the other by a complex series function. Although both functions predict the same rate of gas uptake for relatively short exposure times, no clear mathematical explanation has been published that describes the relationship between the two functions. We clarified that (1) the root function is the solution of the one-dimensional diffusion equation for a semi-infinite slab, (2) the series function is an applicable solution for a finite slab thickness, (3) the parameter values of the root function can be used to determine the parameter values of the series function, and (4) the predictions of gas kinetics from both functions agree until an adequate amount of diffusing inert gas reaches the boundary at the opposite end of the finite slab. The last point allows the use of the simpler root function for predicting short no-stop decompression limits. Experience dictates that the inert gas accumulation for a 22 min at 100 feet of seawater (fsw) dive is considered safe for no-stop decompression. Although the constraint, Depth square root of Bottom Time = 100 square root of 22, has been applied as an index to determine either the safe depth or bottom time (given the other) for no-stop decompression, it should not be applied more broadly to dives requiring decompression stops.

Selection of military survival gears using thermal manikin and computer survival model data

This study presents a practical example of the selection of protective equipment for 12-h cold survival on land and at sea using computer model and manikin data. The thermal immersion manikin was exposed to 19 realistic survival scenarios to estimate the thermal resistance of different survival systems. The computer survival model used specific environmental limits and anthropometric data from the target population in addition to the estimated manikin thermal resistance values to generate survival times. The results showed that the required 12-h survival time criteria were met for all dry land scenarios (> 2 Clo), but not for wet land or water scenarios ( < 1 Clo). Those data provided the basis for the selection of survival equipment and the development of survival strategies for aircrew.

Effect of caffeine on target detection and rifle marksmanship

Thirteen healthy and rifle-trained male military reservists performed shooting sessions on two separate occasions 1 h following the ingestion of placebo or 300 mg of caffeine. Shooting included both friend-foe (FF) and vigilance (VIG) tasks, and were performed in the following order: two FF sequences (4 min each), four VIG sequences (30 min each), and two additional FF sequences. The shooting sessions lasted approximately 2.5 h under outdoor conditions (air temperature range from - 3 to 14 degrees C) and were held 48 h apart in a counter-balanced order. Performance measures during the shooting session included engagement time, friend-foe discrimination, and marksmanship accuracy and precision. Assessments of thermal comfort, tiredness, and debilitating symptoms preceded and followed the shooting session, while a self-assessment on performance was administered post-shooting only. Blood was sampled immediately prior to the beginning of the shooting session and was used to determine plasma caffeine, cortisol, and testosterone levels. Engagement times were faster and certain measures of accuracy and precision were impaired during the later FF and VIG sequences. However, caffeine ingestion had no affect upon any of the marksmanship measures, although it did alleviate cold stress and tiredness. That caffeine ingestion did not affect target detection and rifle marksmanship is a finding that differs from other studies, and is explained by a beneficial arousal caused by the mild level of cold stress experienced by the participants.

Shivering endurance and fatigue during cold water immersion in humans

An important component of survival time during cold exposure is shivering endurance. Nine male and three female healthy and fit subjects [mean (SD) age 24.8 (6.3) years, body mass 71.7 (13.2) kg, height 1.75 (0.10) m, body fat 22.7 (7.4)%] were immersed to the upper chest level in cold water for periods ranging from 105 to 388 min on two occasions to test a prediction of shivering endurance. The water was cooled from 20 to 8 degrees C during the first 15 min of immersion and subsequently rewarmed (<20 degrees C) to elicit a near constant submaximal shivering response. The data were divided according to moderate (M) and high (H) levels of shivering intensity. Respective mean total immersion times were 250 (75) and 199 (80) min ( P=0.086) at different average shivering intensities of 61 (10) and 69 (8)% relative to maximal shivering ( P<0.001). Blood plasma glucose concentration increased during the immersion [from 3.44 (0.54) pre- to 3.94 (0.60) mmol x l(-1) post-immersion ( P=0.037)] and levels were higher during M ( P=0.012). When compared to a model prediction of shivering endurance, shivering activity continued well beyond the predicted endurance times in 18 out of the 24 trials. The average rates of oxygen consumption over the entire immersion period were lower ( P=0.002) during M [0.93 (0.20) l x min(-1)] compared to H [1.05 (0.21) l x min(-1)), and while these rates did not change during the last 90 min of immersion, there was an increase in fat oxidation. There were no trial differences in the average esophageal (T(es)) and mean skin temperatures during the entire immersion period (36.0 and 18.0 degrees C, respectively), yet T(es) decreased ( P=0.003) approximately 0.4 degrees C during the last 90 min of immersion. When the shivering intensity was normalized to account for this decrease, a significant downward trend of approximately 17% x h(-1) in the normalized shivering intensity was found after the predicted end of shivering endurance. These results suggest that shivering drive, and not shivering intensity per se, decreased during the latter stages of the immersion. Underlying mechanisms such as fatigue and habituation for this diminishing cold sensitivity are discussed.

On the likelihood of decompression sickness during H(2) biochemical decompression in pigs

A probabilistic model was used to predict decompression sickness (DCS) outcome in pigs during exposures to hyperbaric H(2) to quantify the effects of H(2) biochemical decompression, a process in which metabolism of H(2) by intestinal microbes facilitates decompression. The data set included 109 exposures to 22-26 atm, ca. 88% H(2), 9% He, 2% O(2), 1% N(2), for 0.5-24 h. Single exponential kinetics described the tissue partial pressures (Ptis) of H(2) and He at time t: Ptis = integral (Pamb - Ptis). tau(-1) dt, where Pamb is ambient pressure and tau is a time constant. The probability of DCS [P(DCS)] was predicted from the risk function: P(DCS) = 1 - e(-r), where r = integral (Ptis(H(2)) + Ptis(He) - Thr - Pamb). Pamb(-1) dt, and Thr is a threshold parameter. Inclusion of a parameter (A) to estimate the effect of H(2) metabolism on P(DCS): Ptis(H(2)) = integral (Pamb - A - Ptis(H(2))). tau(-1) dt, significantly improved the prediction of P(DCS). Thus lower P(DCS) was predicted by microbial H(2) metabolism during H(2) biochemical decompression.

Human body surface area: measurement and prediction using three dimensional body scans

The development of three dimensional laser scanning technology and sophisticated graphics editing software have allowed an alternative and potentially more accurate determination of body surface area (BSA). Raw whole-body scans of 641 adults (395 men and 246 women) were obtained from the anthropometric data base of the Civilian American and European Surface Anthropometry Resource project. Following surface restoration of the scans (i.e. patching and smoothing), BSA was calculated. A representative subset of the entire sample population involving 12 men and 12 women (G24) was selected for detailed measurements of hand surface area (SAhand) and ratios of surface area to volume (SA/VOL) of various body segments. Regression equations involving wrist circumference and arm length were used to predict SAhand of the remaining population. The overall [mean (SD)] of BSA were 2.03 (0.19) and 1.73 (0.19) m2 for men and women, respectively. Various prediction equations were tested and although most predicted the measured BSA reasonably closely, residual analysis revealed an overprediction with increasing body size in most cases. Separate non-linear regressions for each sex yielded the following best-fit equations (with root mean square errors of about 1.3%): BSA (cm2) = 128.1 x m0.44 x h0.60 for men and BSA = 147.4 x m0.47 x h0.55 for women, where m, body mass, is in kilograms and h, height, is in centimetres. The SA/VOL ratios of the various body segments were higher for the women compared to the men of G24, significantly for the head plus neck (by 7%), torso (19%), upper arms (15%), forearms (20%), hands (18%), and feet (11%). The SA/VOL for both sexes ranged from approximately 12.m-1 for the pelvic region to 104-123.m-1 for the hands, and shape differences were a factor for the torso and lower leg.

Measurement and prediction of peak shivering intensity in humans

Prediction equations of shivering metabolism are critical to the development of models of thermoregulation during cold exposure. Although the intensity of maximal shivering has not yet been predicted, a peak shivering metabolic rate (Shivpeak) of five times the resting metabolic rate has been reported. A group of 15 subjects (including 4 women) [mean age 24.7 (SD 6) years, mean body mass 72.1 (SD 12) kg, mean height 1.76 (SD 0.1) m, mean body fat 22.3 (SD 7)% and mean maximal oxygen uptake (VO2max) 53.2 (SD 9) ml O2.kg-1.min-1] participated in the present study to measure and predict Shivpeak. The subjects were initially immersed in water at 8 degrees C for up to 70 min. Water temperature was then gradually increased at 0.8 degree C.min-1 to a value of 20 degrees C, which it was expected would increase shivering heat production based on the knowledge that peripheral cold receptors fire maximally at approximately this temperature. This, in combination with the relatively low core temperature at the time this water temperature was reached, was hypothesized would stimulate Shivpeak. Prior to warming the water from 8 to 20 degrees C, the oxygen consumption was 15.1 (SD 5.5) ml.kg-1.min-1 at core temperatures of approximately 35 degrees C. After the water temperature had risen to 20 degrees C, the observed Shivpeak was 22.1 (SD 4.2) ml O2.kg-1.min-1 at core and mean skin temperatures of 35.2 (SD 0.9) and 22.1 (SD 2.2) degrees C, respectively. The Shivpeak corresponded to 4.9 (SD 0.8) times the resting metabolism and 41.7 (SD 5.1)% of VO2max. The best fit equation predicting Shivpeak was Shivpeak (ml O2.kg-1.min-1) = 30.5 + 0.348 x VO2max (ml O2.kg-1.min-1) - 0.909 x body mass index (kg.m-2) - 0.233 x age (years); (P = 0.0001; r2 = 0.872).

Calorimetry and respirometry in guinea pigs in hydrox and heliox at 10-60 atm

We used direct calorimetry and respirometry to measure the total rate of heat loss (Qsigma) and of oxygen consumption (VO2) in guinea pigs in 1-atm (0.1 MPa) air and at 10-60 atm in either heliox (98% He, 2% O2) or hydrox (98% H2, 2% O2). Our objective was to determine if the physiological responses to these two gas mixtures were different and, if so, whether the differences were attributable to the thermal characteristics of the gases alone or were confounded by additional mechanisms. At 10-40 atm, Qsigma and VO2 were not significantly different in the two gas mixtures, whereas at 60 atm, Qsigma and VO2 were significantly higher in heliox than in hydrox. The VO2/Qsigma ratio suggested that the animals were not in thermal equilibrium in hyperbaria. Based solely on the differing thermal properties of the gas mixtures, a mathematical model predicted a Qsigma that was higher in hydrox than in heliox at all pressures. Two plausible explanations are suggested: one is an adaptive lowering of the surface temperature as a physiological response of the animal to the thermally more stressful hydrox environment, and the other is related to the narcotic suppression of the animal's activity by hydrox.

Comparison of thermoregulatory responses between men and women immersed in cold water

Eleven women (age = 24.4 +/- 6.3 yr, mass = 65.0 +/- 7.8 kg, height = 167 +/- 8 cm, body fatness = 22.4 +/- 5.9%, mean +/- SD) were immersed to neck level in 18 degrees C water for up to 90 min for comparison of their thermal responses with those of men (n = 14) in a previous similarly conducted protocol. Metabolic rate increased about three times resting levels in men and women, whereas the rate of rectal temperature cooling (DeltaT(re)/Deltat) in women (0.47 degrees C/h) was about one-half that in men. With use of all data, DeltaT(re)/Deltat correlates with the ratio of body surface area to size and the metabolic rate of shivering correlates inversely to the square root of body fatness. No significant gender differences in total metabolic heat production normalized for body mass or surface area were found among subjects who completed 90 min of immersion (9 women and 7 men). Nor was there a gender difference in the overall percent contribution ( approximately 60%) of fat oxidation to total heat production. Blood concentrations of free fatty acids, glycerol, beta-hydroxybutyrate, and lactate increased significantly during the 90-min immersion, whereas muscle glycogen sampled from the right quadriceps femoris vastus lateralis decreased (free fatty acids, glycerol, and beta-hydroxybutyrate were higher in women). When the subjects were subgrouped according to similar body fatness and 60 min of immersion (6 women and 5 men), no significant gender differences emerged in DeltaT(re)/Deltat, energy metabolism, and percent fat oxidation. These findings suggest that no gender adjustments are necessary for prediction models of cold response if body fatness and the ratio of body surface area to size are taken into account and that a potential gender advantage with regard to carbohydrate sparing during cold water immersion is not supported.

Physiological responses of exercised-fatigued individuals exposed to wet-cold conditions

Thirteen healthy and fit men [age = 27 +/- 8 (SD) yr, height = 177 +/- 5 cm, mass = 75 +/- 7 kg, body fat = 14 +/- 5%, maximal O2 consumption = 51 +/- 4 ml. kg-1. min-1] participated in an experiment designed to test their thermoregulatory response to a challenging cold exposure after 5 h of demanding mixed exercise during which only water was consumed. Subjects expended 7,314 +/- 741 kJ on cycling, rowing, and treadmill-walking machines, performed 8,403 +/- 1,401 kg. m of mechanical work during resistance exercises, and completed 120 inclined sit-ups. Subjects then assumed a seated position in a 10 degrees C air environment while wearing shorts, T-shirt, rain hat, and neoprene gloves and boots. After 30 min the subjects were showered continuously with cold water ( approximately 920 ml/min at 10 degrees C) on their backs accompanied by a 6 km/h wind for up to 4 h. Blood samples were taken from the nondominant arm every 30 min during the exposure and assayed for energy metabolites, hormones, indexes of hydration, and neurotransmitters. Counterbalanced control trials without prior exercise were also conducted. Blood insulin was higher during the control trial, whereas values of glycerol, nonesterified fatty acids, beta-hydroxybutyrate, lactate, cortisol, free triiodothyronine, and thyroxine were lower. Three subjects lasted the maximum duration of 4.5 h for control and fatigue trials, with final rectal temperatures of 36.43 +/- 0.21 and 36.08 +/- 0.49 degrees C, respectively. Overall, the duration of 172 +/- 68 (SD) min for the fatigue trial was not significantly different from that of the control trial (197 +/- 72 min) and, therefore, was not affected by the preexposure exercise. Although duration was positively correlated to body fatness and shivering intensity, the latter was not correlated to any physical characteristic or the fitness level of the individual.

Prediction of shivering heat production from core and mean skin temperatures

Prediction formulae of shivering metabolism (Mshiv) are critical to the development of models of thermoregulation for cold exposure, especially when the extrapolation of survival times is required. Many such formulae, however, have been calibrated with data that are limited in their range of core temperatures (Tc), seldom involving values of less than 36 degrees C. Certain recent studies of cold-water immersion have reported Tc as low as 33.25 degrees C. These data comprise measurements of Tc (esophageal) and mean skin temperature (Ts), and metabolism from 14 males [mean (SD); age = 28 (5) years; height = 1.78 (0.06) m; body mass = 77.7 (6.9) kg; body fat (BF) = 18.4 (4.5)%] during immersion in water as cold as 8 degrees C for up to 1 h and subsequent self-rewarming via shivering under dry blanketed conditions. The data contain 3343 observations with mean (SD) Tc and Ts of 35.92 (0.93) degrees C and 23.4 (8.9) degrees C, respectively, and have been used to re-examine the prediction of Mshiv. Rates of changes of these temperatures were not used in the analysis. The best fit of the formulae, which are essentially algebraic constructs with and without setpoints, are those with a quadratic expression involving Ts. This is consistent with the findings of Benzinger (1969) who demonstrated that the thermosensitivity of skin is parabolic downwards with temperature peaking near a value of 20 degrees C. Formulae that included a multiplicative interaction term between Tc and Ts did not predict as well. The best prediction using 37 degrees C and 33 degrees C as the Tc and Ts setpoints, respectively, was found with BF as an attenuation factor: Mshiv (W x m(-2)) = [155.5 x (37- Tc) + 47.0 x (33 - Ts) - 1.57 x (33 - Ts)2]/(%BF)(0.5).

A mathematical model for human brain cooling during cold-water near-drowning

A two-dimensional mathematical model was developed to estimate the contributions of different mechanisms of brain cooling during cold-water near-drowning. Mechanisms include 1) conductive heat loss through tissue to the water at the head surface and in the upper airway and 2) circulatory cooling to aspirated water via the lung and via venous return from the scalp. The model accounts for changes in boundary conditions, blood circulation, respiratory ventilation of water, and head size. Results indicate that conductive heat loss through the skull surface or the upper airways is minimal, although a small child-sized head will conductively cool faster than a large adult-sized head. However, ventilation of cold water may provide substantial brain cooling through circulatory cooling. Although it seems that water breathing is required for rapid "whole" brain cooling, it is possible that conductive cooling may provide some advantage by cooling the brain cortex peripherally and the brain stem centrally via the upper airway.

Distribution of free and liposomal cefoxitin in plasma and peritoneal fluid in a porcine intra-abdominal sepsis model

The plasma and peritoneal fluid pharmacokinetic parameters obtained after the intravenous administration of free and liposomal cefoxitin were studied in a porcine model of intraabdominal sepsis. No prior assumptions were made to predict the number of compartments pertaining to drug clearance from the administration of either cefoxitin formulation. The experimental data obtained were applied to fit mathematical models of multiexponential drug clearance and the pharmacokinetic data were found to best fit a two-compartment open model. Liposomal encapsulation significantly altered the plasma drug distribution pattern resulting in changes in the magnitude of a number of pharmacokinetic parameters examined. The mean post-distributive half-life of liposomal cefoxitin was substantially longer than that of free cefoxitin by at least 3 times. The peritoneal cavity appeared to provide a reservoir for the initial distributive phase of rapid drug clearance from the plasma compartment followed by a less-rapid post-distributive phase. The cumulative drug level, as determined by the area under the concentration curve (AUC) as a function of time, in the plasma of animals treated with liposomal cefoxitin was about 3-4 fold as high as that of animals treated with free cefoxitin. The differences in pharmacokinetic parameters appeared to account for the improved therapeutic efficacy of liposomal cefoxitin in this animal model.

Exertional fatigue, sleep loss, and negative energy balance increase susceptibility to hypothermia

The purpose of this study was to determine how chronic exertional fatigue and sleep deprivation coupled with negative energy balance affect thermoregulation during cold exposure. Eight men wearing only shorts and socks sat quietly during 4-h cold air exposure (10 degreesC) immediately after (<2 h, A) they completed 61 days of strenuous military training (energy expenditure approximately 4,150 kcal/day, energy intake approximately 3,300 kcal/day, sleep approximately 4 h/day) and again after short (48 h, SR) and long (109 days, LR) recovery. Body weight decreased 7.4 kg from before training to A, then increased 6.4 kg by SR, with an additional 6.4 kg increase by LR. Body fat averaged 12% during A and SR and increased to 21% during LR. Rectal temperature (Tre) was lower before and during cold air exposure for A than for SR and LR. Tre declined during cold exposure in A and SR but not LR. Mean weighted skin temperature (Tsk) during cold exposure was higher in A and SR than in LR. Metabolic rate increased during all cold exposures, but it was lower during A and LR than SR. The mean body temperature (0.67 Tre + 0.33 Tsk) threshold for increasing metabolism was lower during A than SR and LR. Thus chronic exertional fatigue and sleep loss, combined with underfeeding, reduced tissue insulation and blunted metabolic heat production, which compromised maintenance of body temperature. A short period of rest, sleep, and refeeding restored the thermogenic response to cold, but thermal balance in the cold remained compromised until after several weeks of recovery when tissue insulation had been restored.

Prediction of survival time at sea based on observed body cooling rates

The prediction of survival time (ST) of individuals stranded at sea is particularly difficult since reliable controlled data are unavailable. An individual's rate of body cooling is governed by the difference between heat loss and heat production. It has been suggested that the rate of deep body cooling can be extrapolated to estimate ST. The observed linearity of this cooling rate against water temperature is consistent with the predictions of an independently-developed mathematical model of ST. This model has been extended to simulate conditions of partial immersion and wet clothing, and subsequently calibrated against observed human cooling rates. The resultant modification allows a much broader range of ST predictions involving calm and rough seas, and non-immersion wet conditions. Predictions are presented for lean vs. fat individuals, a "worst" case scenario where shivering is absent, and partial immersion. While these predictions must be considered speculative and subject to change as better information becomes available, the model can be useful as a decision aid. It would be prudent, however, to consider the predictions in a relative vs. absolute sense; i.e., for comparative purposes.

The effect of postural changes on body temperatures and heat balance

Early studies have demonstrated that rectal temperature (T(re)) decreases and mean skin temperature (Tsk) increases in subjects changing their posture from standing to supine, and vice versa. Such changes have important implications insofar as thermal stress experiments are conducted and interpreted. However, the extent of these changes between steady-state conditions is not known. In addition, it is not known whether thermal balance is also affected by postural changes. To examine these questions, 11 healthy males were exposed to a thermoneutral air environment (28.2-28.5 degrees C and 40% relative humidity) in various postures at rest. Body temperatures, heat losses, and metabolic rate were measured. Subjects wore shorts only and began in an upright posture (standing or sitting at an inclination of 7.5 degrees) on a customized tilt-table. They were tilted twice, once into a supine position and then back to the original upright position. Each tilt occurred after steady state was satisfied based on the subject's circadian variation of T(re) determined previously in a 4.25 h control supine trial. Times to supine steady state following the first tilt were [mean(SE)] 92.6 (6.4) and 116.6 (5.1) min for the standing and sitting trials, respectively. Times to upright steady state following the second tilt were 107.9 (11.4) and 124.1 (9.0) min. Mean steady-state T(re) and Tsk were 36.87 (0.07) and 34.04 (0.14), 37.47 (0.09) and 33.48 (0.14), and 37.26 (0.05) and 33.49 (0.10) degrees C for supine, standing, and sitting, respectively. Thermal balance was attained in all steady-state conditions, and allowing for a decrease in the weighting factor of T(re) for mean body temperature in the upright postures, it also appears that thermal balance was preserved between changes in posture. These results are consistent with no perceived changes by the subjects in their thermal comfort and skin wetness.

Predicting survival time for cold exposure

The prediction of survival time (ST) for cold exposure is speculative as reliable controlled data of deep hypothermia are unavailable. At best, guidance can be obtained from case histories of accidental exposure. This study describes the development of a mathematical model for the prediction of ST under sedentary conditions in the cold. The model is based on steady-state heat conduction in a single cylinder comprised of a core and two concentric annular shells representing the fat plus skin and the clothing plus still boundary layer, respectively. The ambient condition can be either air or water; the distinction is made by assigning different values of insulation to the still boundary layer. Metabolic heat production (M) is comprised of resting and shivering components with the latter predicted by temperature signals from the core and skin. Where the cold expousure is too severe for M to balance heat loss, ST is largely determined by the rate of heat loss from the body. Where a balance occurs, ST is govedrned by the endurance time for shivering. End of survival is marked by the deep core temperature reacing a value of 30 degrees C. Th emodel was calibrated against survival data of cold water (0 to 20 degrees C) immersion and then applied to cold air exposure. A sampling of ST predictions for the nude exposure of an average healthy male in relatively calm air (1 km/h wind speed) are the following: 1.8, 2.5, 4.1, 9.0, and > 24 h for -30, -20, -10, 0 and 10 degrees C, respectively. With two layers of loose clothing (average thickness of 1 mm each) in a 5 km/h wind, STs are 4.0, 5.6, 8.6, 15.4, and > 24 h for -50, -40, -30, -20, and -10 degrees C. The predicted STS must be weighted against the extrapolative nature of the model. At present, it would be prudent to use the predictions in a relative sense, that is, to compare or rank-order predicted STs for various combinations of ambient conditions and clothing protection.

Calibration of a bubble evolution model to observed bubble incidence in divers

The method of maximum likelihood was used to calibrate a probabilistic bubble evolution model against data of bubbles detected in divers. These data were obtained from a diverse set of 2,064 chamber man-dives involving air and heliox with and without oxygen decompression. Bubbles were measured with Doppler ultrasound and graded according to the Kisman-Masurel code from which a single maximum bubble grade (BG) per diver was compared to the maximum bubble radius (Rmax) predicted by the model. This comparison was accomplished using multinomial statistics by relating BG to Rmax through a series of probability functions. The model predicted the formation of the bubble according to the critical radius concept and its evolution was predicted by assuming a linear rate of inert gas exchange across the bubble boundary. Gas exchange between the model compartment and blood was assumed to be perfusion-limited. The most successful calibration of the model was found using a trinomial grouping of BG according to no bubbles, low, and high bubble activity, and by assuming a single tissue compartment. Parameter estimations converge to a tissue volume of 0.00036 cm3, a surface tension of 5.0 dyne.cm-1, respective time constants of 27.9 and 9.3 min for nitrogen and helium, and respective Ostwald tissue solubilities of 0.0438 and 0.0096. Although not part of the calibration algorithm, the predicted evolution of bubble size compares reasonably well with the temporal recordings of BGs.

Prediction of decompression illness using bubble models

The method of maximum likelihood was applied to models of bubble formation and evolution against data involving decompression illness (DCI). Equilibrium and non-equilibrium gas kinetic models were tested under the constraint of a finite tissue volume. The equilibrium model (leq), where the internal gas of a bubble is in partial pressure and mechanical equilibrium with the gas dissolved in tissue, assumed formation of a bubble upon any gas supersaturation. The non-equilibrium model (neq), where mechanical equilibrium is maintained but the exchange of gas between the bubble and the tissue is governed by a rate constant, assumed formation of a bubble at the metastable equilibrium state which requires a specific degree of gas supersaturation. In addition, another version of bubble evolution based on the diffusivity of gas in tissue (vl) was tested under similar finite volume constraints. Model parameters included liquid surface tension, the gas exchange rate constant, gas solubility, and the tissue time constant. The risk of DCI was based on the bubble radius (R) raised to powers ranging from 0 to 6. The data included 2,023 man-dives in 630 different dive profiles of air and nitrox gas mixtures with depth ranging from 1.75 to 7.09 bar and bottom time ranging from 2.8 to 300.2 min. There were 97 occurrences of DCI and 27 occurrences of marginal symptoms. Predictions of the neq and vl models were quite similar and suggested that the tissue primarily responsible for bubble formation leading to DCI in the present analysis has a perfusion rate of about 4.0 ml blood.100 ml-1.min-1. The best fit of the data for a single compartment of 10(-4) ml vol was obtained with the leq model and a risk based on R4, and an estimated time constant of 95.6 +/- 9.8 min.

Role of blood as heat source or sink in human limbs during local cooling and heating

The objective of the present study was to investigate the relative contribution of the convective heat transfer in the forearm and hand to 1) the total heat loss during partial immersion in cold water [water temperature (Tw) = 20 degrees C] and 2) the heat gained during partial immersion in warm water (Tw = 38 degrees C). The heat fluxes from the skin of the forearm and finger were continuously monitored during the 3.5-h immersion of the upper limb (forearm and hand) with 23 recalibrated heat flux transducers. The last 30 min of the partial immersion were conducted with an arterial occlusion of the forearm. The heat flux values decreased during the occlusion period at Tw = 20 degrees C and increased at Tw = 38 degrees C for all sites, plateauing only for the finger to the value of the tissue metabolic rate (124.8 +/- 29.0 W/m3 at Tw = 20 degrees C and 287.7 +/- 41.8 W/m3 at Tw = 38 degrees C). The present study shows that, at thermal steady state during partial immersion in water at 20 degrees C, the convective heat transfer between the blood and the forearm tissue is the major heat source of the tissue and accounts for 85% of the total heat loss to the environment. For the finger, however, the heat produced by the tissue metabolism and that liberated by the convective heat transfer are equivalent. At thermal steady state during partial immersion in water at 38 degrees C, the blood has the role of a heat sink, carrying away from the limb the heat gained from the environment and, to a lesser extent (25%), the metabolic and conductive heats. These results suggest that during local cold stress the convective heat transfer by the blood has a greater role than that suggested by previous studies for the forearm but a lesser role for the hand.

Is energy substrate mobilization a limiting factor for cold thermogenesis?

Energy substrate mobilization has been suggested as being a limiting factor for the rate of cold-induced thermogenesis (M), and consequently in delaying hypothermia. The evidence supporting this hypothesis in humans, however, is not convincing and the hypothesis has yet to be tested in a rigorous manner using a full heat balance analysis (partitional calorimetry). The goal of this study was therefore to re-investigate whether enhancing energy substrate mobilization by feeding cold-exposed subjects would improve M and affect heat debt (S; the minute-by-minute balance of M and heat losses) as well as rectal (Tre) and mean skin temperatures (Tsk). Nine healthy semi-nude fasted subjects were exposed to 5 degrees C (3 h at rest, 1 m.s-1 wind) on three occasions following the ingestion at min 0 and 90 of either: (1) a placebo, (2) 710 kJ of pure carbohydrates (100%-CHO), or (3) 710 kJ of a high-carbohydrate bar (High-CHO). As expected in the cold, Tre and Tsk decreased whereas M, S and heat losses increased (P < 0.01). However, there were no differences between treatments, including the final Tre [mean (SEM); 36.4 (0.2); 36.5 (0.3) and 36.5 (0.2) degrees C for the placebo, 100%-CHO and High-CHO tests, respectively]. During the 100%-CHO treatment, rates of carbohydrate oxidation were the highest and fat oxidation the lowest (P < 0.05), whereas the High-CHO treatment caused smaller changes.(ABSTRACT TRUNCATED AT 250 WORDS)

Relative intensity of muscular contraction during shivering

The intensity of cold-induced shivering, quantified by surface electromyography (EMG) and then expressed as a function of the maximal myoelectrical activity (integrated EMG) obtained during a maximum voluntary contraction (MVC), was examined in this study in individuals classified by body fat. In addition, the relationship between shivering and metabolic rate (MR) and the relative contribution of various muscle groups to total heat production were studied. Ten seminude male volunteers, 5 LEAN (less than 11% body fat) and 5 NORM (greater than 15% body fat) were exposed to 10 degrees C air for 2 h. EMG of six muscle groups (pectoralis major, rectus abdominis, rectus femoris, gastrocnemius, biceps brachii, and brachioradialis) was measured and compared with the EMG of each muscle's MVC. A whole body index of shivering, determined from the mass-weighted intensity of shivering of each muscle group, was correlated with MR. After the initial few minutes of exposure, only the pectoralis major, rectus femoris, and biceps brachii continued to increase their intensity of shivering. Shivering intensity was higher in the central muscles, ranging from 5 to 16% of MVC compared with that in the peripheral muscles, which ranged from 1 to 4% of MVC. Shivering intensities were similar in the peripheral muscles for the LEAN and NORM groups, whereas differences occurred in the trunk muscles for the pectoralis major and rectus abdominis. The whole body index of shivering correlated significantly with each individual's increase in MR (r = 0.63-0.97).(ABSTRACT TRUNCATED AT 250 WORDS)

Rate of formation of carboxyhemoglobin in exercising humans exposed to carbon monoxide

The purpose of this study was to test the CFK equation for its prediction of the rate of formation of carboxyhemoglobin (HbCO) in exercising humans by use of measured values of the respiratory variables and to characterize the rate of appearance of HbCO with frequent blood sampling. Ten nonsmoking male subjects were exposed to carbon monoxide (CO) on two separate occasions distinguished by the level of activity. Steady-state exercise was conducted on a cycle ergometer at either a low (approximately 45 W) or moderate (approximately 90 W) power output. Each experiment began with an exposure of 3,000 ppm CO for 3 min during a rest period followed by three intermittent exposures ranging from 3,000 ppm CO for 1 min at low exercise to 667 ppm CO for 3 min at moderate exercise. Increases in HbCO were normalized against predicted values to account for individual differences in the variables that govern CO uptake. No difference in the normalized uptake of CO was found between the low- and moderate-exercise trials. However, the CFK equation underpredicted the increase in HbCO for the exposures at rest and the first exposure at exercise, whereas it overpredicted for the latter two exposures at exercise. The net increase in HbCO after all exposures (approximately 10% HbCO) deviated by less than 1% HbCO between the measured and predicted values. The rate of appearance of HbCO fits a sigmoidal shape with considerable overshoot at the end of exposure. This can be explained by delays in the delivery of CO to the blood sampling point (dorsal hand vein) and by a relatively small blood circulation time compared with other regions of the body. A simple circulation model is used to demonstrate the overshoot phenomenon.

Forearm temperature profile during the transient phase of thermal stress

The transient temperature response of the resting human forearm immersed in water at temperatures (Tw) ranging from 15 to 36 degrees C was investigated. Tissue temperature (Tt) was continuously monitored by a calibrated multicouple probe during the 3-h immersions. Tt was measured every 5 mm, from the longitudinal axis of the forearm to the skin surface. Skin temperature, rectal temperature, and blood flow (Q) were also measured during the immersions. The maximum rate of change of the forearm mean tissue temperature (Tt, max) occurred during the first 5 min of the immersion. Tt, max was linearly dependent on Tw (P less than 0.001), with mean values (SEM) ranging from -0.8 (0.1) degrees C.min-1 at 15 degrees C to 0.2 (0.1) degrees C.min-1 at 36 degrees C. The maximum rate of change of compartment mean temperature was dependent (P less than 0.001) on the radial distance from the longitudinal axis of the forearm. The half-time for thermal steady state of the forearm mean tissue temperature was linearly dependent on Tw between 30 and 36 degrees C (P less than 0.01), with mean values (SEM) ranging from 15.6 (0.6) min at 30 degrees C to 9.7 (1.2) min at 36 degrees C and not different between 15 and 30 degrees C, averaging 16.2 (0.6) min. There was a significant linear relationship between the half-time for thermal steady-state of the compartment mean temperature and the radial distance from the longitudinal axis of the forearm for each value of Tw tested (P less than 0.001). The data of the present study suggest that the forearm Q is an important determinant of the transient thermal response of the forearm tissue during thermal stress.

Heat debt during cold air exposure before and after cold water immersions

Acclimation to cold can manifest itself in several different ways, insulative and metabolic being the most common. Bittel (J. Appl. Physiol. 62: 1627-1634, 1987) has demonstrated that heat debt, which encompasses both heat production and heat loss, can be used as a unitary index of acclimation. However, conflicting results are obtained if heat debt is calculated using a mean-weighted body temperature (Tb) vs. the change of body heat content through the integration of heat storage (S). The present study examines the determination of heat debt by three methods of calculation, the first based on Tb and the other two based on S where heat losses are measured in one and predicted in the other. Data were obtained from five healthy young males exposed to 10 degrees C air for 2 h on four different occasions. The first two exposures provided control data, while the last two were performed after 5 and 10 days, respectively, of daily immersions in 15 degrees C water to induce acclimation. The variability in response between the control exposures was as large as that among the other exposures. Although the method of calculation using Tb indicated that subjects were close to a thermal balance after 2 h of cold air exposure, this contrasted sharply with the result of the other two methods that indicated heat debt was still increasing steadily. The latter two methods are considered more accurate for transient heat debt calculation. Although cases of individual acclimation were found, these were different among the subjects, resulting in pooled responses that indicated no group acclimation by means of any of the three methods of calculation.(ABSTRACT TRUNCATED AT 250 WORDS)

Finite-element solution of thermal conductivity of muscle during cold water immersion

The in vivo or effective thermal conductivity (keff) of muscle tissue of the human forearm was determined through a finite-element (FE) model solution of the bioheat equation. Data were obtained from steady-state temperatures measured in the forearm after 3 h of immersion in water at temperatures (Tw) of 15 (n = 6), 20 (n = 5), and 30 degrees C (n = 5). Temperatures were measured every 0.5 cm from the longitudinal axis of the forearm to the skin approximately 9 cm distal from the elbow. Heat flux was measured at two sites on the skin adjacent to the temperature probe. The FE model is comprised of concentric annular compartments with boundaries defined by the location of temperature measurements. Through this approach, it was possible to include both the metabolic heat production and the convective heat transfer between blood and tissue at two levels of blood flow, one perfusing the compartment and the other passing through the compartment. Without heat exchange at the passing blood flow level, the arterial blood temperature would be assumed to have a constant value everywhere in the forearm muscles, leading to a solution of the bioheat equation that greatly underpredicts keff. The extent of convective heat exchange at the passing blood flow level is estimated to be approximately 60% of the total heat exchange between blood and tissue. Concurrent with this heat exchange is a decrease in the temperature of the arterial blood as it flows radially from the axis to the skin of the forearm, and this decrease is enhanced with a lowered Tw.(ABSTRACT TRUNCATED AT 250 WORDS)

In vivo thermal conductivity of the human forearm tissues

The effective thermal conductivities of the skin + subcutaneous (keff skin + fat) and muscle (keff muscle) tissues of the human forearm at thermal steady state during immersion in water at temperatures (Tw) ranging from 15 to 36 degrees C were determined. Tissue temperature (Tt) was continuously monitored by a calibrated multicouple probe during a 3-h immersion of the resting forearm. Tt was measured every 5 mm from the longitudinal axis of the forearm (determined from computed-tomography scanning) to the skin surface. Skin temperature (Tsk), heat loss (Hsk), and blood flow (Q) of the forearm, as well as rectal temperature (Tre) and arterial blood temperature at the brachial artery (Tbla), were measured during the experiments. When the keff values were calculated from the finite-element (FE) solution of the bioheat equation, keff skin + fat ranged from 0.28 +/- 0.03 to 0.73 +/- 0.14 W.degrees C-1.m-1 and keff muscle varied between 0.56 +/- 0.05 and 1.91 +/- 0.19 W.degrees C-1.m-1 from 15 to 36 degrees C. The values of keff skin + fat and keff muscle, calculated from the FE solution for Tw less than or equal to 30 degrees C, were not different from the average in vitro values obtained from the literature. The keff values of the forearm tissues were linearly related (r = 0.80, P less than 0.001) to Q for Tw greater than or equal to 30 degrees C. It was found that the muscle tissue could account for 92 +/- 1% of the total forearm insulation during immersion in water between 15 and 36 degrees C.

Shivering onset, metabolic response, and convective heat transfer during cold air exposure

The onset and intensity of shivering of various muscles during cold air exposure are quantified and related to increases in metabolic rate and convective heat loss. Thirteen male subjects resting in a supine position and wearing only shorts were exposed to 10 degrees C air (42% relative humidity and less than 0.4 m/s airflow) for 2 h. Measurements included surface electromyogram recordings at six muscle sites representing the trunk and limb regions of one side of the body, temperatures and heat fluxes at the same contralateral sites, and metabolic rate. The subjects were grouped according to lean (LEAN, n = 6) and average body fat (NORM, n = 7) content. While the rectal temperatures fluctuated slightly but not significantly during exposure, the skin temperature decreased greatly, more at the limb sites than at the trunk sites. Muscles of the trunk region began to shiver sooner and at a higher intensity than those of the limbs. The intensity of shivering and its increase over time of exposure were consistent with the increase in the convective heat transfer coefficient calculated from skin temperatures and heat fluxes. Both the onset of shivering and the magnitude of the increase in metabolic rate due to shivering were higher for the LEAN group than for the NORM group. A regression analysis indicates that, for a given decrease in mean skin temperature, the increase in metabolic rate due to shivering is attenuated by the square root of percent body fat. Thus the LEAN group shivered at higher intensity, resulting in higher increases in metabolic heat production and convective heat loss during cold air exposure than did the NORM group.

Maximum likelihood analysis of air and HeO2 dives

The method of maximum likelihood analysis was applied to data consisting of 1,949 man-dives, of which 1,041 were on air and 908 were on HeO2 mixtures. These dives represented a wide range of bottom time and depth combinations, and had an overall incidence of decompression sickness (DCS) of 4.64%. Several models, based on single exponential gas uptake in either one or two compartments, were tested for predicting the incidence of DCS. The criterion for defining the risk of DCS was based on the concept of potential gas volume (i.e., the volume of a bubble that could form and be in equilibrium with the remaining gas dissolved in solution). This criterion takes into account the solubilities of the gases in solution, but can be adjusted to account only for the partial pressures of the gases. The best model for the prediction of DCS was found for two compartments where the kinetics (time constants) and not the gas solubilities of nitrogen and helium were distinguished from each other. Results using the best prediction model with the present data suggests the following: 1) most of the risk of DCS occurs after surfacing; 2) most of the risk occurs in the "slow" compartment (approximately 420 min time constant); and 3) nitrogen contributes about twice as much as helium to the risk of DCS for HeO2 dives.

Errors in heat flux measurements due to the thermal resistance of heat flux disks

Questions have been raised regarding the effect of the thermal resistance of heat flux transducers (HFTs) on the thermal flux from the skin. A model capable of simulating a large range of "tissue" insulation (variable-R model) was used to study the effect of the underlying tissue insulation on the relative error in heat flux due to the thermal resistance of the HFTs. The data show that the deviation from the true value of heat flux increases as the insulation of the underlying tissue decreases (r = 0.99, P less than 0.001). The underestimation of the heat flux through the skin measured by an HFT is minimal when the device is used on vasoconstricted skin in cool subjects (3-13% error) but becomes important when used during vasodilation in warm subjects (29-35% error) and even more important on metallic-skin mannequins (greater than 60% error).

Prediction of the thermoregulatory response for clothed immersion in cold water

A multi-compartmental thermoregulatory model was applied to data of ten resting clothed males immersed for 3 h in water at 10 and 15 degrees C. Clothing consisted of a dry suit and either a light or heavy undergarment, representing a total insulation of 0.15 (0.95) or 0.20 m2 degrees CW-1 (1.28 clo), respectively. Data were grouped according to low (less than 14%) and high (14 to 24%) body fat individuals. Mean decreases in rectal temperature ranged from 0.79 to 1.38 degrees C, mean decreases in the mean weighted skin temperature ranged from 6.3 to 10.2 degrees C, and mean increases in the metabolic rate ranged from 33.9 to 80.8 W. The model consists of eight segments, each representing a specific region of the body. Each segment is comprised of compartments representing the core, muscle, fat, skin, and clothing. Each compartment is assigned thermophysical values of heat conduction and heat capacitance, and with the exception of clothing, physiological values of blood flow and metabolic heat production. During cold exposure, responses are directed towards increased heat production in the form of shivering and heat conservation in the form of vasoconstriction and convective heat exchange at the vascular level. Agreement between the model predictions and the experimental observations was obtained by adjusting the parameters governing these responses.(ABSTRACT TRUNCATED AT 250 WORDS)

Use of the maximum likelihood method in the analysis of chamber air dives

The method of maximum likelihood was used to evaluate the risk of decompression sickness (DCS) for selected chamber air dives. The parameters of two mathematical models for predicting DCS were optimized until the best agreement (as measured by maximum likelihood) corresponding to the observed DCS incidents from a series of dives was attained. The decompression data used consisted of 800 man-dives with 21 incidents of DCS and 6 occurrences of marginal symptoms. The first model investigated was based on a nonlinear gas exchange in a series arrangement of four compartments. The second model was based on a monoexponential gas exchange in a parallel arrangement of two compartments. The overall statistical success in describing the 800 man-dives was quite similar for the two models. Predictions of safety for dives not part of the original data differed for the models due to differences in gas kinetics. For short, no-decompression dives, the series arrangement of compartments predicted a lower incidence of DCS. These predictions were more consistent with the outcome of subsequent testing than were predictions of the parallel compartment model. Predictions of the series arrangement model were also similar to those of a single-compartment, two-exponential model that was evaluated with over 1700 man-dives by the U.S. Navy.

Role of body fat in the prediction of the metabolic response for immersion in cold water

Several empirical models for predicting the metabolic response to a lowered body temperature have been evaluated against available data of young healthy males immersed in cold water under resting conditions. Nude immersions took place in 20 and 24 degrees C water for 1 h, and clothed immersions took place in 10 and 15 degrees C for 3 h. The data were pooled according to low and high percent body fat (%BF). Decreases in the mean weighted skin temperature (Tsk) ranged from 5.3 to 11.9 degrees C and decreases in the core temperature (Tc) ranged from 0.56 to 1.54 degrees C, while increases in the metabolic rate over the immersion period ranged from 34 to 256 W. Through regression analysis, an inverse relationship between %BF and the metabolic response for a given lowered Tsk and lowered Tc was established. When this relationship was explicitly applied to the models, significant improvements in their predictive capability were found. Variables such as body weight, body surface area, and the rate of change of Tsk were not found to contribute to the predictive capability of the models.

Thermoregulatory model for immersion of humans in cold water

The mathematical models of thermoregulation of Stolwijk and Hardy, and Montgomery were used to develop a model suitable for the simulation of human physiological responses to cold-water immersion. Data were obtained from experiments where 13 healthy male volunteers were totally immersed under resting and nude conditions for 1 h in water temperatures of 20 and 28 degrees C. At these temperatures, the mean measured rectal temperature (Tre) fell by approximately 0.9 and 0.5 degrees C, respectively, yet mean measured metabolic rate (M) rose by approximately 275 and 90 W for the low body fat group (n = 7) and 195 and 45 W for the moderate body fat group (n = 6). To predict the observed Tre and M values, the present model 1) included thermal inputs for shivering from the skin independent of their inclusion with the central temperature to account for the observed initial rapid rise in M, 2) determined a thermally neutral body temperature profile such that the measured and predicted initial values of Tre and M were matched, 3) confined the initial shivering to the trunk region to avoid an overly large predicted initial rate of rectal cooling, and 4) calculated the steady-state convective heat loss by assuming a zero heat storage in the skin compartment to circumvent the acute sensitivity to the small skin-water temperature difference when using conventional methods. The last three modifications are unique to thermoregulatory modeling.

Percent carboxyhemoglobin in resting humans exposed repeatedly to 1,500 and 7,500 ppm CO

Eleven nonsmoking male resting subjects were exposed to two transient CO profiles to examine whether the resultant carboxyhemoglobin (HbCO) differs with CO concentration for a fixed total CO dose and to determine the predictive capability of the theoretical model of Coburn et al. (J. Clin. Invest. 44: 1899-1910, 1965) using measured alveolar ventilation. One profile consisted of five sequential exposures to 1,500 ppm CO for 5 min each and spaced 3 min apart. The other consisted of five sequential exposures to 7,500 ppm CO for 1 min each and spaced 7 min apart. The subjects, therefore, were exposed to the same overall nominal dose of 37,500 ppm.min. During the experiment, the subject's ventilatory functions and respiratory gases were recorded continuously, and the resultant HbCO% was measured in venous blood samples by gas chromatography. Mean increase (+/- SD) in HbCO% per exposure was 2.08 +/- 0.27% for the 1,500 ppm CO exposures and 2.05 +/- 0.29% for the 7,500 ppm CO exposures with no significant difference between the two. When the measured values of the subject's alveolar ventilation were applied to the theoretical model of Coburn et al., the predicted rate of HbCO% formation was found to agree with the experimental results.

A critical analysis of the use of the CFK equation in predicting COHb formation

Fifteen healthy young males, nine at rest and six at exercise, were exposed to high transient levels of carbon monoxide (CO) to simulate the breathing environment measured in an armored vehicle during weapons firing. Depending on the dosage, the CO exposures raised the subjects' carboxyhemoglobin saturation (%COHb) from 1.7% to 17.3%. The measured %COHb levels compared favorably (regression coefficient, b = 1.04) to those predicted by the theoretical model of Coburn et al. When the application of this same model by a method proposed by NIOSH was used, however, a significant overprediction was found (b = 1.28). It appears that this overprediction results primarily from the omission of water vapor in the lungs when the inspired pressure of CO is considered, and to the use of incorrect values for alveolar ventilation. These results demonstrate the errors that may arise from the incorrect utilization of the equation by Coburn et al. and the effect that this may have upon the calculation of the limits for safe occupational exposure to CO.

Modeling the observations of in vivo bubble formation with hydrophobic crevices

In vivo hydrophobic crevices from which bubbles emerge upon decompression are hypothesized to account for experimental observations of bubble formation in decompressed shrimp. The conical crevice model can be used to explain the sharp increase in the number of bubbles observed in shrimp for decompression ratios greater than 4:1. In accordance with the observed attenuating effects of pressure pretreatment on bubble formation in shrimp, the model can also be used to explain: the evolution of the gas nuclei to smaller stable sizes during compression; the return of the nuclei to their original stable configurations when the overpressure is removed; and the requirement for greater decompressions to cause emergence of bubbles from the nuclei as the magnitude and period of pressure pretreatment are increased. A new crevice geometry with elliptically shaped walls is introduced which reduces the height of the crevice needed for bubble emergence and relaxes the constraints for the stability of gas nuclei. This new geometry reduces the height of crevices required for the prediction of bubble emergence an order of magnitude when compared to the conical crevice, and satisfies the hydrophobic crevice condition as long as the crevice surface has a contact angle greater than 90 degrees.

Body cooling after death

In the analyses of cases of death in cold air environments, it is often of interest to determine the time required for the body of the individual to cool to ambient temperature. Usually such determinations have been based on Newton's law of cooling. This paper describes a case history in which this technique was experimentally tested and consequently abandoned in favour of a more complex biophysical model which more accurately described the thermo-physical events inherent in body cooling. This model is recommended for determination of the times required for various body parts to cool to ambient environmental temperatures.