The induction of a mild reduction in body core temperature has been demonstrated to provide neuroprotection for patients who have suffered a medical event resulting in ischemia to the brain or vital organs. Temperatures in the range of 32–34 °C provide the required level of protection and can be produced and maintained by diverse means for periods of days. Rewarming from hypothermia must be conducted slowly to avoid serious adverse consequences and usually is performed under control of the thermal therapeutic device based on a closed-loop feedback strategy based on the patient's core temperature. Given the sensitivity and criticality of this process, it is important that the device control system be able to interact with the human thermoregulation system, which itself is highly nonlinear. The therapeutic hypothermia device must be calibrated periodically to ensure that its performance is accurate and safe for the patient. In general, calibration processes are conducted with the hypothermia device operating on a passive thermal mass that behaves much differently than a living human. This project has developed and demonstrated an active human thermoregulation simulator (HTRS) that embodies major governing thermal functions such as central metabolism, tissue conduction, and convective transport between the core and the skin surface via the flow of blood and that replicates primary dimensions of the torso. When operated at physiological values for metabolism and cardiac output, the temperature gradients created across the body layers and the heat exchange with both an air environment and a clinical water-circulating cooling pad system match that which would occur in a living body. Approximately two-thirds of the heat flow between the core and surface is via convection rather than conduction, highlighting the importance of including the contribution of blood circulation to human thermoregulation in a device designed to calibrate the functioning of a therapeutic hypothermia system. The thermoregulation simulator functions as anticipated for a typical living patient during both body cooling and warming processes. This human thermoregulatory surrogate can be used to calibrate the thermal function of water-perfused cooling pads for a hypothermic temperature management system during both static and transient operation.

## Introduction

Therapeutic hypothermia is induced by the intentional lowering of the core body temperature to the range of 32 °C to 34 °C. This therapy is applied to decrease ischemic tissue damage as may be precipitated by cardiac arrest, stroke, neurotrauma, or traumatic brain injury [13]. Ischemia leads to cell and neuronal destruction via temperature-dependent processes. By inducing hypothermia, these detrimental processes may be slowed and their effects minimized [4,5]. Similarly, induced hypothermia can be used to combat the deleterious processes resulting from elevated intracranial pressure, reduced cerebral blood flow, overall ischemia, and cerebral herniation [6]. Specifically, therapeutically cooling the core often has the following beneficial outcomes: reduction of cerebral metabolism, restoration of gene expression, inhibition of cytoskeletal breakdown, reduction of excitatory amino acids, and prevention of deleterious signals leading to unnecessary apoptosis and inflammation [4,7]. Because of these benefits, many methods have been developed to induce therapeutic hypothermia.

Both invasive and noninvasive techniques have been used to lower the body core temperature in the clinical setting. Endovascular cooling uses a closed-loop catheter filled with a circulating chilled liquid inserted into the vena cava to cool the blood as it flows around the catheter [8]. This invasive method allows for a relatively rapid induction of a hypothermic state once the catheter is inserted, followed by active control of the core temperature. Alternatively, intensive care units may apply cold packs for cooling with or without intravenous saline infusions [9]. Another noninvasive method to induce hypothermia is the use of external water-perfused cooling pads applied to the patient's skin (Fig. 1). Water at a conditioned temperature is pumped through the pads at a specific flow rate in order to cause heat transfer over large areas of the body surface. The surface pads function in conjunction with a feedback control system that regulates the temperature of the circulating water. This type of circulating water hypothermia induction system is the subject of the present study.

Fig. 1
Fig. 1
Close modal

Physicians often face difficulties during the rewarming of patients from a state of induced hypothermia, since the process must be conducted at a slow and well-controlled rate for the sake of safety. Because the physiological mechanisms of human thermoregulation are highly nonlinear, coupled, and dynamic, during clinical procedures it can be extremely challenging to use manipulation of the temperature of the water that is circulated through the heat transfer pads on the body's surface to produce targeted transients in a patient's core temperature. Asynchronous fluctuations between the temperatures of the device and that of the patient may occur, thereby leading to dangerous thermal instabilities during rewarming. The safe operation of a therapeutic hypothermia device demands that it be able to effectively interact thermally with patients in a manner that is compatible with their thermoregulatory function and response.

In order to ensure the safe and effective use of external cooling pad devices in the clinical setting, the control system must be calibrated to be able to adjust the patient core temperature according to a prescribed protocol. Currently, a control unit with the associated pad system is often calibrated according to its capability to regulate the temperature of a passive thermal mass with an internal heater to represent body metabolism. The sole mechanism of heat flow between the center and periphery of the passive system is via conduction. In contrast, the core temperature of humans is modulated by a complex and sophisticated thermoregulatory system that uses multiple parallel and often nonlinear mechanisms to control the flow of heat into and/or out of body, plus its rate of internal generation. For a living person, in general, the convective flow of blood between the core and the surface is the primary means by which heat is transported, occurring in parallel with, and often dominating, conduction of heat through the tissue mass. A passive thermal mass has no capacity for mimicking an internal convective heat flow and therefore lacks the capability to ascertain whether a specific therapeutic hypothermia device can safely and accurately manage a patient's core temperature under conditions for which the internal thermal state may be governed by blood flowing between the core and the skin. The rate at which the core temperature changes during transient procedures may be critical in determining patient outcome, particularly during rewarming from a therapeutic hypothermia state for which too great a heating rate may have dire consequences [8]. If the device control system is unable to accommodate for the effects of varying blood flow rates during this procedure, the warming process may become thermally unstable. Therefore, it is important to have a calibration system that can account for the influence of core to surface blood flow when evaluating the function of a therapeutic hypothermia device. Thus, a significant need exists for a human thermoregulatory simulation device that will generate more accurate representation of how heat moves between the body core and surface.

We have developed a human thermoregulation simulator (HTRS) that embodies the primary thermoregulatory functions of patients that are relevant during therapeutic hypothermia procedures. This simulator does not intend to replace the human body as the basis for design of the rewarming strategy of a therapeutic hypothermia device, but rather to provide a means of calibration that more accurately reflects how the body would react under both cooling and rewarming conditions compared to current calibration devices that simulate the body with a passive thermal mass. The HTRS can be used both for calibration of existing clinical devices and for evaluating the efficacy of new innovations to improve performance.

## HTRS Design

The HTRS is purposely designed to use mechanically simple components to physically replicate the highly sophisticated physiological system of thermoregulation. The objective is to create a simple physical surrogate with the ability to simulate the combination of conductive and convective heat flows between the body core and surface that govern thermoregulatory function and that has physical dimensions that are representative of an average human adult. The initial proof-of-concept implementation features three cylindrical containers concentrically stacked within one another, each representing a discrete layer of the body torso: a central core container with a metabolic equivalent heat generator and a pump, a middle tissue container, and an outer container for both the skin and the peripheral circulatory system, which is the primary site of heat exchange between blood and tissue (Fig. 2). These containers are not intended to match the exact size and shape of the human torso. Rather, their function is to present to an external therapeutic hypothermia induction and control device a thermal load that behaves in much the same manner as would an actively thermoregulating human body. The core consists of three key components: a water volume, a submersion pump, and an immersion heater. The water in the core container represents the blood therein. The total blood volume of the body is approximately 4–6 L. The HTRS contains roughly 4 L, representing the trunk and the head but excluding the extremity limbs [9]. Water comprises approximately 83% of blood [10], and although it has a lower viscosity than blood, the thermal and flow properties make it an appropriate simulant choice for the HTRS [9]. The submersion pump mimics the heart, and the immersion heater represents the body's basal metabolic rate—the amount of energy expended by the body while at rest to maintain homeostasis and vital functions such as breathing, nutritive circulation of blood, brain and nerve function, cell growth, and thermoregulation [11]. The operation of these components is coordinated in the following manner: the immersion heater warms the water in the core reservoir; the submersion pump causes water to flow from the core through a closed-loop network of small tubing in the skin with its cutaneous vasculature, returning back to the core reservoir. The pump also produces a mixing effect for the water in the core reservoir to maintain a homogeneous temperature.

Fig. 2
Fig. 2
Close modal

The middle container represents the tissues of the torso, and the outermost skin container represents the skin plus the peripheral network of vessels that function as a convective heat exchanger for circulating blood (water, in the HTRS) to the body surface. Both the tissue and skin containers are also filled with water to replicate the torso thermal properties and energy capacitance. The body is composed of roughly 60% water; more specifically, muscles are 76%, bones are 22%, and adipose (fat) tissues are 10% [10]. The central tissue container contains open-cell foam immersed into and saturated with the water. This water-soaked open-cell foam serves as a conduction conduit between the core and the skin, just as do the various tissues within the human body. The thermal conductivities of a composite consisting of foam (k = 0.030 W/m K) soaked with water (0.060 W/m K) are a reasonable approximation for a composite tissue consisting of muscle (k = 0.046 W/m K) and fat (k = 0.023 W/m K).

The heat conduction pathway between the inner and outer containers is through the water and foam matrix in the middle container, representing the aggregate thermal behavior of the muscles, bone, and fat. The core container with its heater (not shown immersed in the photo) and the tissue container with its open-cell foam are shown in Fig. 3. The outer skin container holds the tubing network on its inside surface representing the blood vessels of the peripheral circulation (Fig. 4). The design of the tubing pattern aims to emulate the body's branched vascular network and to maximize heat transfer between the circulating water and the outermost container through which it flows. Although the simulator's tubing network is not of the same dimensions as the body's peripheral vasculature, it serves the purpose of thermally equilibrating a flowing stream of water with a physical mass through which it passes as does blood with the tissue through which it is perfused. Thus, from the perspective of an external therapeutic hypothermia device, the exact internal mechanism of heat transfer between a fluid convecting from the core and the peripheral tissue mass has little consequence on the has very minimal effect on thermal interaction between the device and body.

Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal

The HTRS as a whole simulates major components of the thermoregulatory function of the human body by mimicking internal metabolism, convection of the blood between the core and the periphery, and conduction of heat through tissues. The conduction and convection are parallel processes, just as they occur in the body. The outer surface of the container represents the atmosphere–skin interface during normothermia testing (Fig. 5) and the cooling pad–skin interface during induced hypothermia testing (Fig. 6).

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

## HTRS Testing

A series of tests was conducted on the HTRS to evaluate three issues: to determine whether the HTRS is able to create an accurate thermal gradient from the core to the skin for conditions of normothermia with exposure to room air and of operation with a commercial whole body hypothermia system with cold-water circulation pads applied to the surface; to highlight the need for the HTRS to demonstrate the difference between using dynamic and static devices to represent the body during calibration of clinical hypothermia induction and control systems; and, to illustrate the efficacy of incorporating active internal thermal control into a device for calibrating the function of a therapeutic hypothermia system. Two types of performance tests were conducted. A baseline normothermia test consisted of the HTRS exposed to room air to evaluate its ability to maintain a core temperature of 37 °C while generating a basal level of internal metabolism in conjunction with normal blood circulation from the core to the skin and parallel heat conduction through overlying tissues, with natural convection between the skin surface and environment. The second set of tests consisted of replicating the thermal interaction between the body with an active thermoregulatory system and a cold-water circulation therapeutic hypothermia apparatus that is programmed to execute cooling and/or warming of the body core. The test periods and temperature ranges for these trials are shown in Table 1. A Philips InnerCool STx+ Core Surface Pad (Phillips Healthcare, Andover, MA) was used for the trials of therapeutic hypothermia (Fig. 7). For laboratory trials, the cooling pads were connected to a controlled-temperature water reservoir with an internal circulation pump, and the temperature was set to approximately 10 °C. Alternatively, a single clinical trial was conducted with a full Phillips InnerCool STx+ system to regulate the external pad water temperature and flow over time.

Fig. 7
Fig. 7
Close modal
Table 1

Ranges of thermal and temporal simulation conditions evaluated

Type of testTest duration (min)Core temperature maintenance target (°C)
Normothermia85–10337
Hypothermia151–23432–35
Type of testTest duration (min)Core temperature maintenance target (°C)
Normothermia85–10337
Hypothermia151–23432–35

The voltage and current applied to the heater to simulate metabolism were recorded using a LOGiT LCV Current and Voltage Data Logger (SUPCO, Inc., Monmouth, NJ) from which the internally generated (metabolic) power was calculated. Numerous type T thermocouples were applied at key locations throughout the HTRS (Fig. 8) to collect continuous temperature data that was input to a host computer via a NI 9213 analog to digital converter and labview signal express software (National Instruments, Austin, TX). Temperatures were also monitored for ambient air, heater water, and flows into and out of the peripheral circulatory tube network. Temperatures of flowing water were measured with inline thermocouples embedded in sealed “tee” connectors directly in the tubing network, as seen in Fig. 9.

Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal

Normothermia experiments were conducted under manual control of the thermoregulatory parameters. The heater was adjusted to bring the core temperature to 37 °C after which it was maintained constant throughout the experiment. The HTRS was allowed to come to an equilibrium state with the environment to establish a stable thermal gradient amongst its components based on parallel conduction and convection heat flow pathways between the core and the surface. The steady-state temperature distribution within the HTRS is shown in Fig. 10. This trial corresponds to a human resting in a thermoneutral environment.

Fig. 10
Fig. 10
Close modal

A second normothermia test was run to measure the contribution of blood circulation to the temperature distribution, i.e., to compare the system performance with both parallel conduction and convection versus conduction only. These two conditions can be characterized as active and passive heat flow regulation between the core and surface. The HTRS, when operated without water flow, mimics the behavior of passive thermal mass calibration devices. The primary difference between the HTRS without the pump operational and a typical solid thermal mass is that the HTRS will have a natural convection loop in the core due to the heating element. Figures 11(a) and 11(b) correspondingly present data for the HTRS operating with the water pump on (active) and off (passive).

Fig. 11
Fig. 11
Close modal

Tests were also conducted to replicate both the induction of therapeutic hypothermia as well as bringing a patient out of a hypothermic state. The protocol consisted of first establishing a normothermic state by appropriate manipulation of the metabolic heater to bring the core internal temperature to approximately 37 °C with the water circulation pump running, and then intentionally lowering the core to be between 32 °C and 35 °C through the use of the external water-perfused cooling pads. After a hypothermic equilibrium state was reached, the water temperature of the pads was increased progressively to return the HTRS core back to normothermia. After the core temperature reached 34.5 °C, the heater was set to maintain this state for long enough to establish a cooler thermal gradient across the HTRS. The transient temperature distribution during rewarming from hypothermia with and without water circulation is shown in Figs. 12(a) and 12(b), respectively. Data are plotted only for the time interval between 50 and 80 min to allow for easier visual interpretation.

Fig. 12
Fig. 12
Close modal

## Results

A simple heat transfer analysis was applied to help explain the experimental data. The convective delivery of heat between the core and the surface is described in terms of an enthalpy flow
$Q˙=m˙×Cp×ΔT$
(1)
where $Q˙$ is the rate heat is convected between the core and periphery (W), $m˙$ is the (mass) flow rate (kg/s), $Cp$ is the specific heat capacity of water (kJ/kg °C), and $ΔT$ is the difference in temperature between the inlet and outlet water flows for the peripheral circulation (°C). The average flow rate of the HTRS was 53.5 ml/s, and the average change in temperature across the peripheral circulation was 0.50 °C. The specific heat capacity for water at 37 °C is 4.178 kJ/kg K [12]. Thus, the convective heat flow between the core and periphery is calculated as
(2)
This rate of energy generation is reasonably close to the basal metabolic rate of an average adult human [13]. For comparison, the rate of electrical energy input to the core heater necessary to maintain the core temperature at 37 °C was measured to be 102 ± 9 W for the three trials conducted.

One additional test was performed with the HTRS attached to a clinical hypothermia machine, programmed to execute a cooling and warming protocol. Figure 13 presents a set of transient data plots for this trial. The HTRS was set to operate with water flow to the peripheral circulation network during the entire procedure, starting from equilibrium at a core temperature of 37 °C. After the equilibrium core temperature was achieved, the cold-water perfusion pads with water already flowing were wrapped around the outer surface of the HTRS. The application of the cold-water perfused pads immediately dropped the HTRS surface temperature dramatically, with the temperatures of the interior layers subsequently slowing following. The final temperature difference between the core and outer surface was slightly higher in the clinical trial compared to that of the laboratory testing. This difference is attributed to the fact that the clinical trial was 60 min shorter than the laboratory trial, allowing less time for heat loss. However, the overall trend of the data is the same in both testing environments as seen by comparing Figs. 11 and 13.

Fig. 13
Fig. 13
Close modal

## Discussion

The thermal performance of the HTRS may be compared with known features and operational properties of human thermoregulatory function to provide indicators of the veracity of simulation. For example, the temperature measured on the outside of the container represents the skin surface during thermoneutral trials in Fig. 10. With no circulation of water, Fig. 10(b), the HTRS is representative of a system in which passive conduction is the only means of heat transfer between the core and the skin. For these conditions, the temperature drop across the intermediate tissues of the body was 7 °C (33–26 °C), and the skin temperature was 25 °C, which does not match typical physiological status unless a person has a high degree of cutaneous vasoconstriction. In contrast, when water is circulated from the core to the peripheral shell in parallel with tissue conduction, Fig. 10(a), the skin temperature was 33.5 °C, which is much better aligned with values commonly reported in the literature [1416] and measured in our own lab under thermoneutral conditions. The conduction temperature drop across the intermediate tissues was reduced from 7 °C to 1.5 °C (36–34.5 °C). When there is a normal level of cutaneous blood flow, the major thermal resistance between the core and the environmental air is natural convection at the skin surface, as would be anticipated.

The water flow from the core to the inlet of the peripheral (cutaneous) flow network in the HTRS is largely insulated, with a drop of only 0.3 °C. Likewise, past studies have shown that only minimal heat is lost by blood flowing from the core until it reaches the larger elements of the microvasculature that are the primary site of tissue heat transfer [17]. Thus, a majority of heat is delivered directly from the core to the periphery where it is transferred by flow through the circulation. This effect is enhanced during the hypothermia experiments in which a low temperature is enforced onto the body surface.

Figure 11(b) shows that when the water-perfused cooling pads are applied to the exterior of the HTRS, but with no water flow in the peripheral circulation network, the internal temperature increments between each layer increase dramatically as a consequence of the lower outer boundary temperature. In this case, the difference between the core and innermost surface of the body tissue is 6.5 °C (36.3–29.8 °C) and across the tissue is 7.6 °C (29.8–21.2 °C). The temperature at the outer surface at the HTRS with the cooling pad is 18.4 °C. With water flowing through the peripheral circulation network, see Fig. 11(a), the temperature drop between the core and inner surface of the tissue is reduced to 1 °C (34.5–33.5 °C) and across the tissue is 1.2 °C (33.5–32.3 °C). The temperature drop across the skin is 5.4 °C (30.8–25.4 °C). The heat input to maintain the HTRS at steady state without peripheral circulation is 30.8 W, whereas with peripheral circulation, it is 88.4 W. This difference occurs because the convective water flow greatly augments the heat transfer pathway from the core to the environment.

The basal metabolic rate for the average human of 70 kg is approximately 80 W [13]. The heater energy input of the HTRS is somewhat higher than this at about 110 W (Table 2). Part of this discrepancy may be attributed to the loss of heat directly from the core container to the environment because it is not as well insulated in the HTRS as in the human body.

Table 2

Average power recorded during normothermia equilibrium

TrialDuration of equilibrium (min)Average current (A)Average voltage (V)Average power (W)
1302.4843.1107.1
2302.5042.9107.3
TrialDuration of equilibrium (min)Average current (A)Average voltage (V)Average power (W)
1302.4843.1107.1
2302.5042.9107.3

The large differential in conductive and convective heat flows is illustrated in Fig. 14 which shows that when the HTRS is operated with active convection, it is much more effective at transferring heat than when only conduction is allowed. Thus, a system with an active circulation is able to deliver more heat from the core to the outer layers of the HTRS compared to a system without circulation. This difference corresponds to states of extremes in cutaneous vasodilation and vasoconstriction associated with a primary function of the thermoregulation system. This difference also illustrates the inadequacy of a thermally passive system that does not embody the effect of convective heat transfer by vascular circulation in representing the human thermoregulation for calibration of therapeutic hypothermia device function.

Fig. 14
Fig. 14
Close modal

Evaluation of the rewarming trials in Fig. 12 with and without water circulated from the core to the periphery shows a very large difference in performance. Most simply stated, in the absence of convection (Fig. 12(b)), warming of the core occurs much more slowly. Since convection is more efficient than conduction in transmitting heat between the surface and core, it is anticipated that an active circulation will result in the core tissue temperatures rising faster (and under better control) than in its absence. For example, without internal circulation, after 80 min of surface warming, the temperatures at the center and the interior of the tissue compartment had risen to 28.0 °C and 31.7 °C, respectively. With an active water circulation, the corresponding temperatures were 34.8 °C and 35.6 °C. Thus, the HTRS with active circulation presents a much different thermal load to a therapeutic hypothermia device than does a passive, heated mass. This difference can be critical in assessing the efficacy of a hypothermia device in managing the core temperature of a patient safely.

Figure 13 displays the results for testing the HTRS when attached to a clinical therapeutic hypothermia device. The purpose of this experiment was to determine if the HTRS can effectively and accurately represent a human thermal interaction with a clinical hypothermia machine. Comparison with Fig. 11(a) shows that overall the data from this experiment closely resemble the results from the laboratory trials. In both cases, the temperature of the outer surface of the HTRS is dictated by the perfused cooling water; this temperature was 23 °C and 26 °C for the clinical and laboratory trials, respectively. Moving inwardly, by far the largest temperature drop within the HTRS occurs across the skin compartment that is governed thermally by the active circulation of water from the warm system core. This large temperature drop attests to the efficacy of convective heat transfer within the system and points to the importance that a human thermoregulation simulation system includes the influence of blood flow between the body core and the skin surface.

It should be noted that the temperatures of the skin compartment and the water leaving it (denoted by “flow out”) had nearly identical values of 33.5 °C for both trials. Thus, the convective heat transport between water flowing through the skin compartment and the compartment mass results in effective thermal equilibration. This is the same effect that occurs in the human peripheral circulation [17], pointing to the accuracy in simulation of the HTRS.

A relevant question to pose in considering whether the HTRS provides an advantage in calibrating a therapeutic hypothermia device is how much the process is improved. The answer depends on how the therapeutic hypothermia system is programmed and operated, which can cover a wide range of conditions. One method to compare the operation of the present system and a passive system is illustrated by the data in Fig. 14 in which the internal temperature gradient is plotted between the core and surface with and without circulation. When circulation is used, the internal temperature gradient is reduced approximately six fold, indicating a greatly heightened ability to respond to external stimuli. This difference represents an improved capability of the calibration device to respond to inputs from the therapeutic hypothermia system in a manner that mimics actual thermoregulatory behavior, which should result in a more relevant calibration outcome.

A key feature of the HTRS is its diverse spectrum of operating states. Both the blood flow rate and metabolism can be altered over wide ranges to simulate specific physiological states. Thus, it is possible to mimic thermoregulatory function during normothermia, hypothermia, and rewarming protocols. Removing the blood circulation component creates a passive system typifying many existing calibration systems for hypothermia devices. The ability to vary the flow rate may be of particular importance to study conditions in which a patient experiences transient vasoconstriction or vasodilation processes. Blood perfusion transients may be especially important during the rewarming phase of a hypothermia procedure during which the thermoregulatory system is susceptible to dynamic responses to input from the hypothermia device. Although manual control of the HTRS was used for the reported testing of the prototype device, a programmable control module may be easily added using well-established technology.

## Conclusions

The HTRS can improve the calibration process for therapeutic hypothermia systems by providing a load that replicates the internal parallel convection and conduction processes in the human body. The ability to modify the equivalent blood flow rate and metabolism contributes to this system's versatility to recreate and test a variety of relevant physiological states and processes. This feature may be of particular importance for evaluating the ability and safety of therapeutic hypothermia devices to lower or raise the core temperature at controlled rates. Since human thermoregulation processes operate independently, an external device controller must be able to accommodate a patient's physiological function in a manner that is compatible and safe. A passive lumped-mass calibration system is unable to satisfy this requirement, whereas the HTRS incorporates the primary features of active human thermoregulation to provide a physiologically meaningful load to test hypothermia device function.

The HTRS prototype is designed and built using simple and economical existing components. Thus, it should be straightforward to translate into an operational device for clinical application.

## Acknowledgment

This project was funded by an Undergraduate Research Fellowship from the Office of the Vice President for Research in the University of Texas at Austin to P.C., by the National Science Foundation Grant No. CBET 1250659 to K.R.D., and by the Robert and Prudie Leibrock Professorship in Engineering at the University of Texas at Austin.

## Funding Data

• National Science Foundation (Grant No. CBET 1250659)

## Nomenclature

• Cp =

specific heat capacity of water at 37 °C (kJ/kg °C)

•
• m =

mass flow rate (ml/s)

•
• Q =

rate of heat transfer (W)

•
• ΔT =

change in temperature (°C)

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