External heat transfer systems act at the skin and change core temperature (TC) by creating a temperature gradient (ΔT) between the core and the skin that causes heat to flow between those sites against the body's internal thermal resistance. While thermal resistance is a complex function of thermoregulatory physiology, heat transfer at the skin is a simple function of physics and can be analysed by standard physical principles .
The efficiency of any heat transfer mechanism is defined by its heat transfer coefficient (h), which is the heat transfer rate (q, Watts) per unit heat transfer area (A, m2) per unit temperature gradient (ΔT, °C): h = q A−1 ΔT−1 = W m−2 °C−1. The heat transfer coefficient (h) is determined by changing ΔT and measuring the resulting heat flux (q″ = qA−1, W m−2) with heat flux transducers (HFT). The slope of the least squares linear regression analysis of q″ as a function of ΔT defines h.
There are three temperature-dependent heat transfer mechanisms: conduction, convection and radiation. All clinical heat transfer systems exploit, principally, one of these three mechanisms, although, incidentally, their overall effectiveness may be helped or hindered by the other two. Each mechanism has its own h and several of them have been measured in volunteers: e.g. h during exposure [1,2], with a water blanket  and with convective air warmers .
For the same temperature gradient, q from the body is higher in water than in air, because the mass heat capacity of water is ≈3500× that of air, and the thermal conductivity W m−1 °C−1 ≈ 25×. Although, historically, patients were immersed in iced-water to induce hypothermia, this method was replaced by the one that used water blankets. But water blankets are less efficient than water immersion because adequate skin contact, which is essential for any conductive heat transfer mechanism, is difficult to achieve. The problem of skin contact has been addressed in the Medivance Arctic Sun® Temperature Management System, the Energy Transfer Pad (Medivance, Inc., Louisville, CO, USA), which is composed of a highly conductive hydrogel layer, fixes intimately to the skin.
The primary aim of the volunteer study was to measure and compare h of the Arctic Sun pad (hPAD) with that of cold-water immersion (hWATER), the most effective, external method to change core temperature . The secondary aim was to compare hPAD measured in volunteers with that measured in a model, to determine the accuracy of this model for thermal analysis.
The Arctic Sun Temperature Management System comprises Arctic Sun Energy Transfer Pads and a control module. The control module pulls temperature-controlled water through the pads under negative pressure resulting in heat transfer between the water and the patient. The negative pressure flow minimizes the risk of leaks since a break in the circuit will cause air to enter the system instead of water leaking out. Patient temperature set points are programmed in the control module. Control module water temperature is automatically adjusted via a feedback algorithm to achieve the desired patient target temperature. Water temperature set points can also be programmed in the control module to provide water at a constant temperature and this method was used in this study.
The Arctic Sun Energy Transfer Pads have a tri-layer construction. The outermost layer is flexible closed-cell foam with moulded fluid channels and also acts to insulate the circulating water from ambient conditions. The middle layer is a polymeric film that is laminated to the outer layer to seal the thin fluid channels. The inner layer is a highly heat conductive biocompatible hydrogel that adheres to the patient's skin on application and provides intimate pad-to-skin contact for efficient heat transfer.
The model is a 0.9 m2, matt-black, semi-cylinder of 0.6 mm copper sheet, 0.61 × 1.473 m (24″ × 58″). A Cincinnati Sub-Zero (CSZ) Maxi-Therm® mattress (Cincinnati Sub-Zero Products, Inc., Cincinnati, OH, USA) is bonded to the inner surface of the model and by varying the water temperature of the CSZ Blanketrol® II water heater, the ‘skin' temperature (TSK) of the model can be controlled. This model was the prototype of the multi-cylinder manikin validated by Bräuer and colleagues , and has the same h (model, 11 W m−2 °C−1 (95% CI = 10.6–11.3), n = 95 vs. manikin, 11 W m−2 °C−1 (9.7–12.3), n = 30).
Heat flux was directly measured with calibrated HFTs (Heat Flow Sensor Model FR-025-T-12; Concept Engineering, Old Saybrook, CT, USA), which incorporated thermocouples to measure TSK. Each HFT was attached with a double-sided adhesive ring (‘Chest-piece tape'; Benson Medical, Markham, Ontario, Canada) enclosing a thin layer of thermal paste (‘Heat sink compound' Type 44; GC Electronics, Rockford, IL, USA) to ensure good thermal contact. Data were collected at 1-min intervals with three calibrated Columbus Instruments IsoThermex Model 256 interfaces and stored with IsoThermex V3.20 software (Columbus Instruments, Columbus, OH, USA). After equilibrium was reached, temperatures and q″ were averaged over the next 5 min.
Heat transfer coefficient of the Arctic Sun Energy Transfer Pads
The Arctic Sun Energy Transfer Pad (‘Universal Small' # 313-05) is a rectangular pad of 25 × 53 cm. Seven HFTs were fixed on the model to contact the applied pad along its right and left halves, and at its centre, opposite the perfusing water entry point. The contact surface temperature of the pad (TPAD) was measured with Mallinckrodt skin thermocouples (Mon-a-Therm ® catalog # 503-0102; Mallinckrodt Inc., St Louis, MO, USA) positioned immediately to the side of each HFT. The whole model and the pad under test were insulated with a sleeping bag of 2.2 clo insulation units. The model was perfused at a constant water temperature of 34°C and ΔT between pad and model was changed by randomly varying the set water temperature (TSET) of the Arctic Sun control module from 25°C to 42°C.
With ethical approval and written informed consent, nine volunteers (two females, seven males, average age 32 ± 8 yr; height 176.6 ± 7.2 cm; weight 75.1 ± 10.7 kg; BSA 1.91 ± 0.16 m2) were enrolled. Three HFTs were fixed to the skin at the midpoint of the volunteer's thigh, on the lateral, top and medial surfaces. Pad temperature was measured with a skin thermocouple at the side of each HFT. Average q″, mean skin temperature (TMSK), and TPAD were calculated from these three sites. A ‘Universal Small' Energy Transfer Pad was applied directly to the thigh, with the HFTs at the centre of the pad, and insulated with the sleeping bag. Set water temperature was randomly varied from 30°C to 42°C in 2°C intervals.
In both the model (Fig. 1) and the volunteers (Fig. 2), ΔT was designated as (TPAD – TMSK) and q″ from the pad to model or to the skin was considered as positive.
The water immersion study received ethical approval and the volunteers signed an informed consent. This was a collaborative study between Fisher & Paykel Healthcare Ltd and the Middlemore Hospital, Auckland, New Zealand, where the immersions were carried out under medical supervision.
Eleven volunteers (two females, nine males, average age 25 ± 6 yr; height 176.6 ± 9.2 cm; weight 71.7 ± 11.2 kg; BSA 1.88 ± 0.19 m2) were immersed to the neck in iced-water, stirred and maintained at ≈10°C (TWTR), in a climate-controlled room (TAIR 20.4 ± 0.9°C; RH 46 ± 4%). Each volunteer was immersed 3× at weekly intervals. Core temperature (TC) was measured in the oesophagus (Mon-a-Therm 12Fr; Mallinckrodt Inc.). Each volunteer was instrumented with 14 calibrated HFTs (Model FR-025-TH44033-F16; Concept Engineering) attached with double-sided adhesive rings and thermal paste, and incorporating thermistors to measure TSK. Eight HFTs on the anterior body surface (chest, abdomen, thigh, leg, foot, hand, upper arm and lower arm)  were used to calculate the heat transfer coefficient during immersion (hWATER). HFT output was increased by 6% to account for the insulating effect of the HFT on the skin in the highly conductive water medium . After instrumentation, the volunteers rested, covered with a blanket, for 20 min to establish control values before immersion. Immersion ended at TC ≈ 35°C or at ≈60 min immersion time or at the volunteer's request. Data were recorded every minute using a National Instruments data acquisition card (DAQ 700) and LabViewTM software (National Instruments Corporation, Austin, TX, USA). All eight HFTs were averaged to calculate an average value for q″ and TMSK. Water temperature (TWTR) was measured with a thermistor placed 10 cm above the abdomen and the water was stirred to disrupt any stagnant temperature areas.
Beginning at 3 min after immersion, hWATER was calculated as ΔT, designated as TMSK – TWTR, decreased to equilibrium. Data from all immersions were pooled and analysed as q″ replicates at 0.1°C intervals of ΔT. For consistent scaling with the preceding figures, q″ from the body to the water was considered as positive (Fig. 3).
The heat transfer coefficient was determined by least squares linear regression analysis and is presented in the text as the average slope with (95% confidence limit) and, in the figures, with both the 95% CI and prediction interval (GraphPad Software, Inc., San Diego, CA, USA). Volunteer data and environmental data are presented as the mean ± SD. The threshold P value for statistically significant difference was taken as 0.05.
The figures show the linear regression of q″ as a function of ΔT. The regression slope defines h, which is shown with (95% CI), coefficient of determination (R2) and data number (n) (Fig. 1: hPAD in the model, Fig. 2: hPAD in nine volunteers and Fig. 3: water immersion, hWATER). For each regression, the ANOVA P < 0.0001. The P values for comparison of the regression slopes were: hWATER vs. hPAD volunteers, P = 0.83; hPAD volunteers vs. model, P = 0.92; and hWATER vs. hPAD model, P = 0.51.
The equations for TSET vs. TMSK, TPAD and ΔT, for the seven settings of TSET, were
Water temperature was 9.8 ± 0.5°C and immersion time, 41.8 ± 12.6 min. Core temperature decreased from 36.8 ± 0.3°C to 35.4 ± 0.3°C and TMSK from 33.1 ± 0.3°C to 12.1 ± 1.3°C. In all, 1069 q″ results were assigned to 94 intervals of 0.1°C ΔT. From the third minute till the end of immersion, ΔT decayed exponentially with a half-life of 3.5 (3.2→3.8) min: ΔT = 9 exp (−0.2 × min) + 1.7°C; R2 = 0.65, n = 61. Averaged over the last 5 min of 33 immersions: ΔT = 1.5 ± 0.8°C; q″ = 266.2 ± 55.2 W m−2.
The purpose of h is to allow q to be calculated for any combination of ΔT and heat transfer area, without requiring sophisticated HFT technology . Previous heat transfer studies [7,8] have not measured ΔT and, therefore, their application is unique and limited. But h offers universal application.
Analysing the disparate heat transfer conditions presented here (water immersion vs. a warmer, small area, heat transfer pad) is what only h can do and explains why h is extensively used in engineering to study and model heat transfer processes. The heat transfer coefficient defines heat transfer per unit temperature gradient per unit area. Individual temperatures are irrelevant. Only the temperature gradient associated with those individual temperatures is relevant, and irrespective of heating or cooling, h is the same (Fig. 1). While a smaller contact area will reduce the heat transfer rate (q = h × ΔT × A), it will not affect the heat transfer coefficient (h), because h is the proportionality coefficient defining q in terms of ΔT and A.
The heat transfer coefficient of the pad, measured at the thigh of nine volunteers, was not statistically significantly different from hWATER measured at the anterior body surface of 11 other volunteers during 33 head-out immersions in 10°C water. The Energy Transfer Pad achieves this equivalence through its highly conductive, hydrogel layer, which creates intimate pad-to-skin contact for effective heat conduction. Because of its high thermal conductivity, the thermal resistance of the hydrogel is significantly less than that of a conventional water mattress, which is shown by the close coupling of TPAD to TSET: Arctic Sun, TPAD ∝ 0.91TSET (0.89–0.93) vs. conventional water mattress, TPAD ∝ 0.67TSET (0.57–0.78) .
Plattner and colleagues  wrote: ‘Water immersion was by far the most effective treatment we tested and cooled the core (temperature) about 6× as fast as forced air or circulating water.' The Arctic Sun hPAD is equivalent to hWATER and, at 109.8 W m−2 °C−1, is >2.5× larger than that of a conventional water blanket  (41 ± 5 W m−2 °C−1, n = 7 volunteers), and, from Perl's data, >4× larger than that of convective air warmers  (26.5 ± 7.6 W m−2 °C−1, n = 6 volunteers) (Fig. 4). While convective air warmers might be the most popular , they are not the most efficient.
The change in core temperature induced by an external system is a function of that system's heat transfer rate, q = h × ΔT × A (and q has unit W = W m−2 °C−1 × °C × m2). The heat transfer coefficient of the pad is equivalent to hWATER. Therefore, for the same ΔT and heat transfer area, the Arctic Sun's q would equal that of water immersion. The predicted ΔT for an Arctic Sun TSET of 10°C is 3.3°C: >2× that at the end of the water immersion study (1.5°C). But the limitation of the currently available Arctic Sun pads is that their maximum coverage area of 0.6 m2 is only one-third of the ≈1.7 m2 area exposed to heat transfer in head-out water immersion. This reduced area coverage will produce a lower q than water immersion and, therefore, the change in core temperature will not be as dramatic as Plattner demonstrated. The concept and, in particular, the implications of h that are discussed here are widely utilized in other areas of practical thermal analyses, from predicting exposure survival times  to measure and to compare clothing insulation . While irrefutable validation of the relative heat transfer capability of the Arctic Sun system vs. water immersion would require a cross-over study, the ethical justification for such a study would need convincing evidence of probable equivalence. These results provide that evidence.
Although hPAD was measured at the thigh of volunteers, it applies to any body site because hPAD defines the efficiency of this heat transfer mechanism at the skin. No thermoregulatory factors (e.g. core or skin temperatures, body heat, vasomotor status, etc.) affect hPAD: it is determined only by the external heat transfer mechanism. When measuring hPAD, the only relevant body factor is skin temperature and that, simply, as one component of the defining temperature gradient. The actual skin temperature is immaterial: in five volunteers exposed and cooled in a climate chamber, h for combined radiative and convective heat transfer was changed neither by skin temperature cooling nor by the onset of thermoregulatory vasoconstriction . The surface is immaterial: hPAD was the same in the copper model as in volunteers, despite the higher thermal conductivity of copper than skin. (Surface emissivity is important in radiant heat transfer and the model is painted matt-black to simulate the radiant emissivity of skin.) The pad's heat transfer coefficient (W m−2 °C−1) is not affected by the actual temperatures of the heat transferring surfaces, or by the temperature gradient between them: but q (W) and q″ (W m−2) are critically dependent on that temperature gradient.
Model vs. volunteers
Whether measured in the model or in volunteers, hPAD was not significantly different. However, the precision of measurement was greater in the model: R2 0.99 vs. 0.83. This was probably due to differences in skin contact caused by the different geometries and consistencies of the surfaces of the model and the thigh.
Others have also shown similar agreement in h measured in a manikin when compared with volunteers. In five volunteers cooled in a climate chamber, h averaged 10.8 W m−2 °C−1 (10.3–11.3) and in an exposed manikin, h averaged 11 W m−2 °C−1 (9.7–12.3) . In six volunteers heated with four different convective air warmer systems and upper body covers, h averaged 25.9 W m−2 °C−1 (15.4–36.3)  and in a manikin, warmed with the same four systems, h averaged 26.5 W m−2 °C−1 (14.4–38.7) . That h is similar between a model or manikin and volunteers is to be expected, for h is a function of the external heat transfer mechanism, not of thermoregulation.
The intercept for q″ (89.4 W m−2) as a function of (TMSK – TWTR) (Fig. 3) implies the impossible condition of heat flow without a driving temperature gradient. In fact, this intercept represents the convection-induced temperature error by which the true (TMSK – TWTR) gradient differed from the measured one. The size of the error was the ratio of the intercept to hWATER: 89.4 W m−2/107.1 W m−2 °C−1 = 0.8°C.
Published values for hWATER have ranged from ≈90 to 350 W m−2 °C−1 [9, 14-22]. Recently, Tikuisis  measured heat transfer with similar HFTs and, also, with a more accurate water calorimeter, in six volunteers during prolonged immersion in ≈19°C water. Based on the water calorimeter, Tikuisis found hWATER ≈ 105–112 ± 5 W m−2 °C−1. Tikuisis also found that HFTs underestimated heat transfer by ≈16%, which implies that this study's hWATER of 107.1 W m−2 °C−1 was ≈16% higher than that of Tikuisis. This difference in hWATER is probably due to shivering, which increased oxygen consumption to 3× control in this study, but to 2× control in Tikuisis' volunteers. Thermoregulation does not specifically affect h but the movement associated with shivering incidentally affects h by increasing its convective component.
In conclusion, the model accurately predicted the hPAD measured in volunteers, which further supports the valuable contribution models make to thermal analysis. The heat transfer coefficient for the Medivance Arctic Sun® Temperature Management System and Energy Transfer Pad was equivalent to hWATER for 10°C water immersion. Two key design features of the pad account for this: the intimate contact of the hydrogel pad with the skin and the high thermal conductivity of the hydrogel itself. At ≈110 W m−2 °C−1, hPAD was >2.5× larger than that for a conventional water blanket and >4× that for convective air warmers. Water immersion is the most effective external method in altering core temperature. Since hPAD and hWATER are equivalent, for the same ΔT and heat transfer area, the Arctic Sun Energy Transfer Pad would produce the same heat transfer rate as water immersion. While the predicted ΔT for the pad at a TSET of 10°C is 2× larger than that at the end of 10°C water immersion, the area coverage of the currently available pads is only one-third that of head-out water immersion. Because of this area limitation, the overall heat transfer rate with the Arctic Sun, and the resulting change in core temperature, will not be as large as in water immersion.
Financial support: Anesthesiology, McGill University; The Last Foundation, Montreal General Hospital; Cincinnati Sub-Zero Products, Inc., Cincinnati, OH, USA; University of Texas, Houston, TX, USA; Gaymar Industries, Inc., Orchard Park, NY, USA; Medivance, Inc., Louisville, CO, USA.
Neither author has acted or acts as a paid consultant to, or has a financial interest in, any of the named companies.
We thank Andrew Salmon DipID (Milan), Product Group Manager, Fisher & Paykel Healthcare Ltd, Auckland, New Zealand, for permission to analyse and publish the immersion data and Andrew Scott FRCA, Associate Professor, Anesthesiology, St Mary's Hospital, Montreal, Quebec, Canada, for intellectual support.
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