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.

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.

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.

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.

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.

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.

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.

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)

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).

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)

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.

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.

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.

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.

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.

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.

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.

Prediction of human thermoregulatory responses and endurance time in water at 20 and 24 degrees C.

A multi-compartmental mathematical model for predicting human thermoregulatory responses was applied to immersion in moderately cold water. Data were used from experiments where eight healthy male volunteers were immersed nude and up to the neck for 1 h in water at 20 and 24 degrees C under conditions of rest and exercise. Rectal temperature and metabolic rate were measured before and during immersion. Once agreement between the model prediction and experimental observation was obtained, the model was used for prediction beyond the duration of the experiment. Stabilization of core temperature was predicted after 4-5 h of immersion for rest and after 2-4 h for exercise. Stabilization for resting individuals has been observed in other experiments under similar conditions. These results suggest that linear extrapolations based on linear body cooling rates are inadequate for predicting endurance times in moderately cold water. In this study, predicted endurance times were based on the concept of relative exercise intensity and are in agreement with the limited data available.