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Med Biol Eng ComputDOI 10.1007/s11517-014-1229-8

ORIGINAL ARTICLE

The effects of physiological thermoregulation on the efficacy of surface cooling for therapeutic hypothermia

Mayank Kalra · Majid Bahrami · Carolyn J. Sparrey

Received: 13 May 2014 / Accepted: 12 November 2014 © International Federation for Medical and Biological Engineering 2014

observations. Additionally, results indicate that thermal mass has a dominant effect on cooling rate; therefore, uni-form cooling over a large surface area will be more effec-tive than targeted cooling of areas with superficial blood vessels. This study is the first to analyze the effects of thermoregulation in hypothermic conditions and identify unique thermoregulatory effects that differentiate hypother-mic and normal conditions.

Keywords Induced hypothermia · Body temperature regulation · Computational modeling · Surface cooling · Vasoconstriction

1 Introduction

Systemic hypothermia has been shown to reduce neuro-logical damage in post-cardiac arrest patients [40], improve outcomes in spinal cord injury patients [1, 6], and reduce long-term functional losses in traumatic brain injury [25]. Recent studies have shown that faster or earlier cooling may further improve outcomes [2, 27], indicating that maximiz-ing the cooling rate is important. Invasive cooling methods such as endovascular heat-exchange catheters provide rapid cooling, but are difficult to implement. Surface cooling with cooling blankets or ice packs is the most prevalent method of cooling [28], but can be difficult to control and optimize. Physiological responses can affect the efficiency of surface cooling methods and affect the magnitude of the core tem-perature reduction. Although there have been laboratory and clinical studies of therapeutic hypothermia and models developed proposed therapeutic hypothermia methods, there has not been a validated computational model of therapeu-tic hypothermia in humans. A thermal model of the human body that accurately replicates hypothermic conditions is

Abstract Therapeutic hypothermia is rapidly becoming an integral part of post-resuscitative care for post-cardiac arrest and neurotrauma patients. Despite the significant impact of thermoregulation on core temperature drop dur-ing rapid cooling, current mathematical models for ther-moregulation have not been validated for hypothermic conditions. A geometrically accurate 3D model of an upper leg was developed by segmenting anatomical images from the visible human dataset into fat, muscle, bone, and blood vessels. Thermoregulation models from literature were implemented in the model. The numerical model results were compared with surface cooling experiments. There was a good agreement of simulation results with experi-mental data at 18 °C water immersion using existing mod-els. However, at lower temperatures, the model parameter values needed to be significantly altered to account for cold-induced vasodilation in the superficial blood vessels and variation in muscle perfusion to match experimental

M. Kalra · M. Bahrami Laboratory for Alternative Energy Conversion (LAEC), School of Mechatronic Systems Engineering, Simon Fraser University, 250-13450 102nd Avenue, Surrey, BC V3T 0A3, Canadae-mail: mkalra@sfu.ca

M. Bahrami e-mail: mbahrami@sfu.ca

M. Kalra · C. J. Sparrey (*) Neurospine Biomechanics Laboratory, School of Mechatronic Systems Engineering, Simon Fraser University, 250-13450 102nd Avenue, Surrey, BC V3T 0A3, Canadae-mail: csparrey@sfu.ca

C. J. Sparrey International Collaboration on Repair Discoveries (ICORD), Blusson Spinal Cord Centre, 818 West 10th Avenue, Vancouver, BC V5Z 1M9, Canada

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needed to improve our understanding of hypothermic treat-ments and optimize the technologies used to rapidly induce and maintain hypothermia in critical care patients.

Therapeutic hypothermia is primarily used to mitigate the effects of cellular inflammatory responses in the brain and spinal cord following acute injury or oxygen depriva-tion. It is critical to initiate cooling immediately after the injury or event to minimize secondary tissue damage. A decrease in core temperature of even 1–2 °C significantly reduced tissue damage in the spinal cord [21, 48]. Surface cooling has been proposed as a method to direct treatment only to the affected area, eliminating the complications of systemic hypothermia. However, to develop an effective cooling device and protocol, we require an understanding of the physiological responses such as shivering and vaso-constriction to surface cooling temperatures and the effect of these responses on heat transfer efficiency.

Animal models are frequently used to test hypotheses about optimization of cooling methods; however, physiological and anatomical differences between the human body and the ani-mal model can render the results unreliable [5, 19, 50]. Com-putational models of heat transfer in the human body provide important tools for systematically studying the effects of local-ized cooling temperatures and physiological responses on core temperature change. Several whole-body models [11, 13, 32, 39, 42, 49] and localized [7, 8, 12, 22, 23, 37, 43, 50] thermal models have been developed to study comfort and therapeu-tic cooling. The Fiala multi-node model incorporates math-ematical relations for shivering and vasoconstriction which are broadly used and have been validated for normothermic condi-tions, but not hypothermic conditions [3, 35, 44–46]. Whole-body finite element models are limited to concentric cylinders or ellipses for computational efficiency; however, localized models that focus on specific areas can accurately model the geometry [7, 43]. Geometric accuracy is required to account for the effects of variable tissue thickness and conductive heat transfer between blood vessels and the surrounding tissue. Pre-vious models of therapeutic hypothermia have not validated model predictions with in vivo results making it difficult to assess the accuracy or utility of the models [7, 8, 37]. Incor-porating the thermoregulatory effects of the Fiala multi-node model into a new geometrically accurate model of hypothermic cooling will provide important insights into the mechanisms of heat transfer resulting from localized cooling. Most impor-tantly, validating the model results with in vivo human experi-ments will identify physiological responses that affect heat transfer in hypothermic conditions and determine the suitability of the Fiala thermoregulation model for this application.

The overall goal of this study was to determine the effects of geometry and physiology on temperature distribution and surface heat flux in a computational model of hypothermia. The specific objectives of this study were (1) to test the validity of current thermoregulatory models in hypothermic

conditions, (2) to validate the computational model results against published experimental results, and (3) to identify physiological responses that affect heat transfer rates from surface cooling devices. This study is the first to evaluate the accuracy of standard thermoregulatory computational models to simulate hypothermic conditions.

2 Methods

2.1 Model development

A model of the upper human leg was developed because of its geometrical simplicity, significance as an area of cooling during therapy, and the availability of in vivo experimental results for validation [4, 31, 41]. The geometrically accu-rate 3D model of an upper leg was developed by manually segmenting seven transverse anatomical images from the visible human dataset into fat, muscle, bone, and blood ves-sels (Fig. 1). Skin tissue was not easily identified in the ana-tomical images; therefore, the outer 2 mm of tissue bound-ary is assumed to be skin, similar to previous models [13]. The femoral vein and artery, great saphenous vein, and anterior femoral vein were modeled assuming a circular cross section since the blood vessels in the visible human images were collapsed. The model was constructed using SolidWorks 2012 (Dassault Systèmes, Waltham) and then imported to COMSOL Multiphysics version 4.3a (COM-SOL Inc, Burlington) for meshing and bioheat simulation.

Penne’s bioheat transfer equation was used as the gov-erning equation:

where the subscripts t, b, met, and sh represent tissue, blood, metabolic, and shivering, respectively, ρ is the den-sity, C is the specific heat capacity, T is the local tempera-ture, k is the thermal conductivity, q is the local volumet-ric heat generation rate, and ω is the local blood perfusion rate. The subscript t represents a tissue, i.e., muscle, bone, fat, and skin. Due to thermoregulation, the parameters qmet, qsh, and ω can vary with local tissue temperature, core tem-perature, mean skin temperature, and time. Variation of qmet with local temperature is characterized by the Q10 model:

where qmet0 is the resting metabolic heat generation rate and ΔTt is the change in local tissue temperature from the resting (initial) value. The model is widely used in the lit-erature [13, 22, 43], is based on the reduction in biochemi-cal reactions with decreasing temperature, and has been experimentally validated [18].

(1)ρtCt∂Tt

∂t= k∇

2Tt + qmet + qsh + ωtρbCb(Tb − Tt)

(2)qmet = qmet0 2�Tt10

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Shivering and cutaneous vasoconstriction are charac-terized in the Fiala multi-node model by correlation with experimental data [13]:

Fig. 1 a Geometry and meshing of current model. b Schematic of the top cross section of the model, showing segmentation of the tissue and blood vessels

Table 1 Thermal properties of tissue used in the current model

C (J/Kg/°C) K (W/m/°C) ρ (kg/m3)qmet0 (W/m3)

ω0 (1/s)

Skin 3,680 0.47 1,085 368 1.05 × 10−3

Fat 2,300 0.16 850 58 0.0036 × 10−3

Muscle 3,768 0.42 1,085 684 0.538 × 10−3

Bone 1,700 0.75 1,357 0 0

Perfusion in fat and muscle is modeled by assum-ing that changes in blood flow in these regions are deter-mined by changes in metabolic activity of the tissue. A

proportionality constant µ defines the linear relationship between metabolic activity and blood flow [13, 38]:

where Δωt is the change in local tissue perfusion rate from the resting value and:

The formulation of this constant was assumed, and there is no clear physiological origin in the literature.

Tissue properties were assigned from the literature (Table 1) [13, 49]. The mesh was composed of 863,000 non-uniform tetrahedral elements. A mesh convergence study showed that increasing or decreasing the mesh size

(6)�ωt = µ�(qmet + qsh)

(7)µ =0.93

ρbcb

(3)qsh =ash

Vmuscle

(

10[

tanh(

0.48�Tskin,mean + 3.62)

− 1]

�Tskin,mean − 27.9�Thy + 1.7�Tskin,meandTskin,mean

dt− 28.6

)

where V is the central vasoconstrictor response that is regu-lated by the mean skin temperate across the entire body and is defined as:

ΔTskin, mean, and ΔThy are the change in mean skin tempera-ture of the whole body [13] and hypothalamus temperature from their resting values, and Vmuscle is the muscle volume. The terms ωskin and ωskin0

represent the skin perfusion and the resting skin perfusion, respectively. The terms av and ash are experimentally derived tissue constants that repre-sent the distribution of the thermoregulatory response rela-tive to the rest of the body [13, 16, 36, 38]. Values were previously reported to be 0.2 and 0.08, respectively, for both legs [13]; therefore, av and ash were assumed to be 0.1 and 0.04, respectively, for this single-leg model. Since shiv-ering is not dependent upon the local tissue temperature, it is only active when the core or hypothalamus temperature changes; the hypothalamus temperature was assumed to be equal to core temperature.

(4)ωskin =ωskin0

1 + avV2

�Tt10

(5)

V = 35[tanh(0.34(

�Tskin,mean + 1.07)

− 1]�Tskin,mean

+ 3.9�Tskin,mean

dTskin,mean

dt

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by a factor of 2 changed average surface heat flux by 0.05 %.

2.2 Simulation conditions

The numerical model results were compared with two cold-water immersion experiments [4, 41] and one involving selective cooling of a single leg with a neoprene leg wrap [31] (Table 2). These studies were selected as validation for the range of immersion temperatures and conditions. Vali-dating the simulation results at moderate water temperature (18 °C) allowed for isolation of model discrepancies due to variations in the thermoregulatory phenomena that only occur at lower temperatures. Likewise, validating the simu-lation results with localized cooling of the leg allows for the isolation of discrepancies caused by variations in central thermoregulation (qsh and V) in hypothermic conditions.

The simulation conditions were matched to each study. The walls of the blood vessels were assumed to be isother-mal at the core temperature in order to simplify computa-tion. The surface of the leg was convectively cooled with a heat transfer coefficient of 110 W/m2/°C, to simulate the water immersion study [10]. Mitchell et al. used a neoprene leg wrap with cold water flowing through the wrap and cal-culated a surface heat transfer coefficient of 140 W/m2/°C [29]. The initial condition (time = 0 min) for all simula-tions was determined by steady state simulation of ambient conditions (hsurface = 4 W/m2/°C, Tambient = 22 °C).

Localized cooling with the neoprene wrap did not affect the mean skin and core temperature and subjects did not shiver, so qsh and V were assumed to be 0 [31]. One cold-water immersion study recorded skin temperatures at vari-ous locations [41], allowing for calculation of mean skin temperature and its derivative with respect to time by using the DuBois equation [30]. These values were used to calculate the shivering and vasoconstriction terms accord-ing to Eqs. 3–5. The second cold-water immersion study did not provide the mean skin temperature [4], so vasocon-striction (V) was assumed to be 750, corresponding to a mean skin temperature of approximately 11 °C. The sen-sitivity of the model outcomes to the assumption was veri-fied by varying V between 400 and 1,000 and observing a

1 % change in cutaneous perfusion. Unlike other experi-ments, core temperature changed significantly during this experiment. To include this factor, the blood temperature, i.e., blood perfusion and blood vessel wall temperature, was modeled using a piecewise function to match the measured core temperature. Shivering was experimentally observed to linearly increase from the start of the experi-ment to 200 W at 20 min and was modeled as such in the simulations.

Both the localized cooling and immersion studies measured heat flux on the medial and lateral sides of the thigh. Under localized cooling, heat flux was measured on a 5 cm2 area of the medial and lateral sides of the thigh, about 10 cm from the top of the thigh [31]. In the immer-sion study, the exact location of heat flux measurement was not specified [41]. The simulation results for lateral and medial heat flux are calculated by averaging the results over 5 cm2 on equivalent locations on the model, with the center of the squares aligned with the cross-sectional cen-troid 10 cm from the top of the model.

To replicate experimental measures of muscle temper-ature profile in the leg [4], the temperature profile in the model was sampled along a line that crossed the center of mass 15 cm from the top of the model and rotated by 26° clockwise from the x axis. Comparing model predictions with experimental data provides good insight into the cool-ing penetration as a function of time.

The validated models were then used to develop para-metric studies to determine the sensitivity of the simulation results to physiological variables (variations in central and local vasoconstriction, shivering, and muscle blood flow). Additionally, the simulation results were used to determine the contribution of various heat sources to the total heat loss from the leg.

Developing a geometrically accurate model is time-consuming and computationally costly compared with 1D model of concentric cylinders. Results from the current model were compared to an established 1D model [12, 13]. The radii of tissue layers were selected to keep the skin sur-face area and volumetric tissue composition consistent with the 3D model. Radii were 1.59, 8.46, 9.79, and 9.99 cm for bone, muscle, fat, and skin, respectively.

Table 2 Specifications of experimental cooling studies which are used for validation of the current model

Validation study Number of subjects

Water temperature Areas cooled Shiv-ering

Core tempera-ture change

Data collected (upper leg)

Duration

Bristow et al. [4] 5 8 °C Full-body immersion Yes Yes Skin and muscle temperature

70 min

Tikuisis [41] 4 18 °C Full-body immersion Yes No Skin temperature, heat flux

400 min

Mitchell et al. [31] 1 −2, 4, 9 °C Localized leg cooling No No Heat flux 30 min

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3 Results

3.1 Moderate temperature cooling

Equations 3 and 5 were used to calculate the V and qsh val-ues for each of the four subjects in the cold-water immer-sion study by Tikuisis et al. [41] at each time interval. The values did not vary significantly with time, so the time-averaged values were used as constants during simulations for individual subjects. For the subjects 1,2,3, and 4, the V values were 229 ± 9, 249 ± 7, 339 ± 3, and 339 ± 11 and qsh values were 1.29 ± 0.28, 1.98 ± 0.28, 5.67 ± 0.11, 7.54 ± 0.31, respectively. A separate simulation was run for each subject using the unique V and qsh values.

There was a good agreement between the experimental transient heat flux and the present simulation results, espe-cially during the steady state period (10–50 min) (Fig. 2). The model also accurately predicted the difference in heat flux between the lateral and the medial side, which was about 50 W/m2 during the steady state period.

A parametric study was conducted to determine the exact effect of V and qsh on the medial heat flux for sub-ject 4, keeping all other conditions constant (Fig. 3). The study showed that the effect of eliminating qsh was negli-gible (4.3 % reduction in heat flux at 50 min), but elimi-nating central vasoconstriction increased heat flux by 35 % and eliminating both central and local vasoconstriction increased heat flux by 82 % at 50 min.

3.2 Low-temperature cooling

Simulation results for transient heat flux were compared with experimental results from the study by Mitchell et al. for localized cooling at coolant temperatures of −2, 4, and 9 °C (Fig. 4). Simulation results in all conditions showed significantly higher heat flux than experimental data in the transient period (0–10 min). There was also noticeable discrepancy in the steady state period (10–40 min) during cooling at −2 and 4 °C, but there was a good agreement at 9 °C. When the simulations were run assuming no vasocon-striction, the discrepancy was significantly smaller (time-averaged absolute error between simulation and experi-mental results was on average 30.2 % for all simulations with vasoconstriction, and 13 % without vasoconstriction). Irrespective of the state of vasoconstriction, the discrep-ancy was observed to decrease with increasing temperature (Fig. 4).

Analysis of the time-dependent magnitude of indi-vidual heat sources (including tissue metabolism, perfu-sion, and blood vessels) showed that a substantial amount of heat came from metabolic generation and blood per-fusion in the muscle, and heat loss from the blood ves-sels only accounted for 3.7 W (Fig. 5). As expected, the

magnitude of the heat source due to cutaneous perfusion changed drastically (factor of 4.8) when comparing the simulation results assuming local vasoconstriction and no vasoconstriction.

Comparison of experimental muscle temperature profile from the study by Bristow et al. with simulations of simi-lar conditions showed good agreement at a depth of 4.5 cm,

Fig. 2 Surface heat flux from the medial and lateral sides of the leg at water immersion temperatures of 18 °C and hsurface = 110 W/m2K. Experimental results obtained from Dr. Peter Tikuisis and were aver-aged between four subjects. The vertical error bars show the standard deviation between the different subjects. Standard deviation of heat flux between the different simulations is not shown because it was found to be insignificant (0.2 % for both medial and lateral heat flux)

Fig. 3 Surface heat flux from the medial side of the leg of subject 4 at water immersion temperature of 18 °C hsurface = 110 W/m2K. Experimental results were obtained from Dr. Peter Tikuisis. Simula-tion results are shown for model, model with no central vasoconstric-tion (no CV), model with no local and central vasoconstriction (no CV, no LV), and model with no shivering (no SH)

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but experimental temperatures were significantly lower at 1.5 and 3 cm at 20 and 60 min (Fig. 6). The tempera-ture profile was found to be very sensitive to variations in muscle perfusion, and decreasing the muscle perfusion to 50 % of the initial value significantly improved the agree-ment between the experimental data and simulation results (Fig. 6).

Even though the simplified 1D model did not include blood vessels, simulations showed that heat loss from this model was very similar to that of the 3D model. Results in the transient period (0–10 min) were practically identical, and a maximum difference of 9 % is observed in the steady period (10–40 min). However, due to the simplified geom-etry, the 1D model cannot accurately represent the spatial

Fig. 4 Comparison of medial and lateral heat flux between simulation results and experi-mental data (Mitchell et al. [31]) at hsurface = 140 W/m2K and a Tcoolant = 9 °C, b Tcoolant = 4 °C, c Tcoolant = −2 °C. Simulations were also run assuming no local vasoconstric-tion (no LV)

Fig. 5 Contribution of various heat sources to the cumulative heat generation with Tcoolant = 9 °C and hsurface = 140 W/m2K and a current model (including local vasoconstric-tion) and b no local vasocon-striction

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distribution of heat flux (e.g., the difference between the medial and lateral side).

4 Discussion

Therapeutic hypothermia is rapidly becoming an inte-gral part of post-resuscitative care for post-cardiac arrest patients [26] and a neuroprotective strategy for brain and spinal cord injuries [1, 6, 25]. The majority of physicians are choosing to induce hypothermia by surface cooling to avoid the complications associated with invasive cooling methods such as endovascular heat-exchange catheters [28]. The body’s thermoregulation during rapid surface cooling can significantly affect the effectiveness of cooling; however, current mathematical models for thermoregula-tion have not been validated for hypothermic conditions. This study is the first to quantify the sensitivity of surface heat loss to factors such as geometry, blood vessels, blood perfusion, and shivering during hypothermic conditions.

Comparison with the available experimental data allowed for validation of the present simulation results and identification of the limitations of current thermoregula-tion models. An important limitation of localized models of cooling is that we require a priori assumptions of the mean skin temperature and core temperature to simulate physio-logical responses of central vasoconstriction and shivering. Using mean skin and core temperatures from experiments that matched the simulated conditions provided a reason-able approximation for short duration studies. The results

of our simulations highlight the importance of central vaso-constriction in localized cooling models (Fig. 3).

There are a variety of factors that directly affect the heat loss from each individual, and not all of these factors could be analyzed in this study. For example, thermoregulatory response can be influenced by age [14], and thickness of the fat layer can significantly influence heat loss, since fat has a low thermal conductivity (Table 1). The thickness of fat can change with the weight of the individual, as well as the gender. In order to minimize this influence of this factor, all the experimental studies included here only had healthy male volunteers as the subjects. Additionally, the current study assumes that the thermoregulation distribu-tion coefficients (ash and av) used by Fiala et al. [12] are correct. Elimination of shivering had no significant effect on the heat flux (Fig. 3) because of the small value of ash, which allowed shivering to account for only approximately 3–14 % of heat generation (1.5–7 W) during the simulation at 18 °C. A comparison of all the av values available in the literature showed variation by up to a factor of 10, despite all the values being based on experimental results [36].

Vasoconstriction is a well-recognized physiological response to moderate cooling; however, the results of this study combined with previous studies demonstrates a lack of vasoconstriction, or perhaps even vasodilation at the low temperatures required rapid for hypothermic cool-ing. At moderate temperature (18 °C), inclusion of central and local vasoconstriction was necessary for the model to accurately predict heat flux for the immersion experiments (Fig. 3). This observation is corroborated by a study show-ing vasoconstriction that had a significant impact on heat loss in the finger [20]. However, our simulation results were improved by excluding vasoconstriction when coolant temperature was low (9, 4, or −2 °C), indicating that vaso-constriction may not occur at low temperatures. This lack of vasoconstriction has been experimentally observed and is known as cold-induced vasodilation [33]. Similarly, a leg immersion study by Gregson et al. [17] showed that cutane-ous perfusion in the leg was significantly reduced at immer-sion temperature of 22 °C, but remained at baseline levels at immersion temperature of 8 °C. This result has impor-tant implications for inducing therapeutic hypothermia with surface cooling. The presence of high skin blood flow (the absence of vasoconstriction) will result in more rapid core cooling because direct contact between a large volume of warm blood and the cold skin tissue allows for rapid cool-ing of the bloodstream (Fig. 5). Therefore, in addition to the large heat conduction expected at low surface tem-peratures, it is possible that the presence of cold-induced vasodilation will further increase the core cooling rate. Mapping the specific temperature range for cold-induced vasodilation combined with this new computational model

Fig. 6 Comparison of temperature profiles below surface of skin as measured experimentally (Bristow et al. [4]) and from simulation results at immersion temperature of 8 °C and hsurface = 110 W/m2K. All simulations were run assuming V = 748 and qsh ramped up from 0 to 200 W over the first 20 min. The last simulation was run assum-ing ωmuscle is held constant at half the initial value (ω = const)

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of hypothermia will assist in designing an optimally effi-cient surface cooling system.

The effects of hypothermia on blood flow in arteries and its effect on muscle perfusion were highlighted when validating the computation model predictions against experimental temperature profiles in the leg (Fig. 6). The model results showed that using the established lin-ear model to determine muscle perfusion parameters did not accurately capture the temperature profile in deep tissues. Reducing the muscle perfusion parameter to a constant value that was 50 % less than the base-line value provided better correlation with experimental results. This effect of hypothermia on muscle perfusion was observed in immersion experiments; femoral artery blood flow dropped to approximately 50 % of the base-line value at immersion temperatures of 8 °C and 22 °C over 30–40 min [17]. The decreased blood flow was attributed to a decrease muscle perfusion for immersion at 8 °C since the cutaneous blood flow remained con-stant; whereas, the decreased blood flow at 22 °C could be attributed primarily to a decrease in cutaneous blood flow. These results demonstrate the need to redefine the muscle perfusion parameter in current thermoregulatory models to accurately simulate hypothermia and the phys-iological changes in muscle perfusion that occur at low temperatures.

Targeted cooling of areas with superficial blood ves-sels is thought to improve heat transfer to the blood stream, as directly cooling the blood stream will result in the most rapid change in core temperature [34]. In prac-tice, ice packs are usually placed around the neck, groin, and axillae in order to target superficial blood vessels [15, 24]. However, the current simulations show that the maximum cooling power delivered to all the blood ves-sels is approximately 5 W, which is insignificant com-pared to the 150–300 W that is required for rapid cool-ing [9]. The small role of blood vessels observed in our study compares well with analytical studies of cooling of the carotid artery in a neck model that showed simi-lar insignificant heat transfer, even under the assumption that the neck surface was at 0 °C [23, 50]. These results suggest that even though the heat flux on the surface of areas such as axillae, groin, and neck may be higher than the rest of body surface, the small surface area in these regions limits the total cooling power, instead distrib-uting the surface cooling over a large surface area will maximize cooling rate. Similarly, a study involving sur-face cooling of pigs found that cooling the neck surface (7 % of total surface area) resulted in 15 % of the core cooling rate that was achieved by cooling 100 % of the surface, indicating that cooling the neck is twice as effec-tive as cooling other areas, but still results in a very low core cooling rate [47].

5 Conclusion

The simulation results showed that the current thermoregula-tory models do not accurately predict thermoregulation in hypothermic conditions because they do not include cold-induced vasodilation and reduction in leg muscle perfusion. Additionally, model simulations showed that an insignificant amount of cooling was directly delivered to the blood vessels, indicating that emphasis on uniform cooling over a large sur-face area will yield higher cooling rates than targeted cooling of areas with superficial blood vessels. This study establishes new parameters for vasodilation and muscle perfusion to accurately simulate and optimize surface cooling for therapeutic hypo-thermia, and suggests that hypothermia may be most rapidly induced when cold-induced vasodilation response is active.

Acknowledgments The authors acknowledge the National Library of Medicine (NLM) and the Visible Human Project as the source of the data used in this study. The authors also acknowledge Dr. Peter Tikuisis for providing unpublished experimental data for water immersion at 18 °C, and Dr. Michael English for providing unpub-lished experimental data for cooling blanket analysis. Financial sup-port for this research was provided by Natural Sciences and Engineer-ing Research Council (NSERC) and Simon Fraser University.

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